Using metric system, we can find that Miss Marge's fish tank holds 100 litres of water.
Define metric system?Everything around us has a quantitative value, from the amount of sugar you put in a cake to the size of a football pitch. Each thing is measured differently based on its length, weight, volume, or duration. With these measurements, the idea of "Metric System" is introduced. The collection of standard units designed to measure length, weight, area, and capacity is known as the metric system of measurement in mathematics. As it uses numbers in powers of 10, it is based on the decimal system.
A litre (L) and millilitres (mL) are two units for measuring capacity in the metric system. A bottle of water holds 1 Liter of water. A millilitre is about 20 drops of water.
So, 100 litres of water will be the correct answer.
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Identify the constant of proportionality in the situation
8. A plane travels 462.4 miles in 34 minutes.
Answer:
13.6 miles/minute
Step-by-step explanation:
We Know
A plane travels 462.4 miles in 34 minutes.
Identify the constant of proportionality in the situation..
We Take
462.4 / 34 = 13.6 miles/minute
So, the answer is 13.6 miles/minute
Mayumi was asked to determine whether quadrilateral rstu is a trapezoid given the vertices r(-2, 3), s(1, 4), t(1, -4) and u(-2, 1). she noticed that the slopes of ru and st are undefined, so she concluded that the quadrilateral could not be a trapezoid. do you agree? explain.
No, I do not agree with Mayumi's conclusion that the quadrilateral RSTU cannot be a trapezoid just because the slopes of RU and ST are undefined.
RSTU is a trapezoid with RU and ST are parallel and have the same x-coordinates.
A trapezoid is defined as a quadrilateral with at least one pair of parallel sides.
The fact that the slopes of RU and ST are undefined does not necessarily mean that they are not parallel.
As vertical lines have undefined slopes and are parallel to each other.
To determine if RSTU is a trapezoid,
Mayumi should check if any pair of opposite sides are parallel.
The slopes of the two pairs of opposite sides RS and TU, and RU and ST and check if they are equal.
Slope of RS = (4 - 3)/(1 - (-2))
= 1/3
Slope of TU = (1 - (-4))/(-2 - 1)
= -5/3
Slope of RU is undefined (vertical line)
Slope of ST is undefined (vertical line)
Since the slopes of RS and TU are not equal, they are not parallel.
The slopes of RU and ST are undefined does not give us any information about their parallelism.
Check at other properties of the quadrilateral to determine if they are parallel.
One property is the coordinates of the points.
If we draw the quadrilateral, RS and TU are not parallel, but RU and ST are parallel and have the same x-coordinates.
Therefore, quadrilateral RSTU is a trapezoid with bases RS and TU, and legs RU and ST.
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Sabrina is 4 feet tall and casts a shadow that is 3. 5 feet tall. A nearby pole is 10 feet tall. How tall will the pole’s shadow be if Sabina and the pole are proportional? Leave your answer as a fraction
If Sabina and the pole are proportional, then the pole’s shadow will be 35/4 feet tall.
Since Sabrina is 4 feet tall and casts a 3.5-foot shadow, we can set up a proportion comparing the heights and shadow lengths: Sabrina's height (4 feet) / her shadow (3.5 feet) = pole's height (10 feet) / pole's shadow (x).
This proportion can be represented as: 4/3.5 = 10/x. To solve for x (the length of the pole's shadow), we can cross-multiply:
4 * x = 3.5 * 10
4x = 35
Now, divide both sides by 4:
x = 35/4
So, the pole's shadow will be 35/4 feet long when both Sabrina and the pole are proportional. This fraction represents the pole's shadow length in relation to the given heights and shadow lengths.
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i really need help with someone who really understands pythagorean therom please help i will give away brainliest and a lot of points just please help me and can someone please stop reporting this question
Answer:
Perry would need to place his ladder 6.63 ft away from the base of the basketball hoop in order to reach the hoop.
Hope this helps!
Step-by-step explanation:
The Pythagorean theorem is [tex]a^{2} +b^{2} =c^{2}[/tex].
It is given that c is 12 and b is 10, so that would be:
[tex]c^{2} -b^{2} =a^{2}[/tex]
[tex]12^{2} -10^{2} =a^{2}[/tex]
144 - 100 = [tex]a^{2}[/tex]
44 = [tex]a^{2}[/tex]
a = [tex]\sqrt{44}[/tex]
a = 6.6332...
( c is the length of the ladder, b is the height of the hoop, and a is the distance between the ladder and the basketball hoop )
find the length of the third side if necessary round to the nearest tenth
The third side that we can not see in the image that is shown has a size of 15.
How do you find the hypotenuse of a right triangle when other sides are given?The hypotenuse of a right triangle can be found using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
If c^2 = a^2 + b^2
c = √a^2 + b^2
c = √12^2 + 9^2
c = 15
Thus the missing side is 15 from the calculation.
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A community center charges x dollars for a summer activity if individuals are signed up before the day of the activity. Individuals who sign up the day of the activity are charged a fee of x plus 0. 20 x dollars. Which expression also represents the fee for signing up the day of the activity, and what does it mean about the fee?.
The expression that represents the fee for signing up the day of the activity is x + 0.20x. This means that fee for signing up the day of the activity is original fee (x) plus an additional 20% of original fee (0.20x).
For example, if the community center charges $50 for signing up before the day of the activity, then the fee for signing up the day of the activity would be:
$50 + ($50 x 0.20) = $50 + $10 = $60
So, individuals who sign up the day of the activity are charged a higher fee than those who sign up before the day of the activity, because they are charged the original fee plus an extra 20% of the original fee. This is often used as an incentive for individuals to sign up early and to help the community center plan and prepare for the activity accordingly.
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3.72÷ 10 4 which of these shows and explains the correct location of the decimal point when the expression is evaluated?
a 0.0000372 because 4 zeros are placed in front of the number when you divide by 104 b 0.000372 because the decimal point moves 4 places to the left when you divide by 104 c 37,200 because the decimal point moves 4 places to the right when you divide by 104 d 3,720,000 because 4 zeros are placed after the number when you divide by 104
The correct location of the decimal point when the expression 3.72 divided by 10⁴ is evaluated is: 0.000372 because the decimal point moves 4 places to the left when you divide by 10 to the fourth power. The correct option is B.
To evaluate this expression, we need to move the decimal point 4 places to the left, since the exponent is positive.
Option A is incorrect because placing 4 zeros in front of the number would give us a much smaller value than the original number. Option B is correct because moving the decimal point 4 places to the left would give us 0.000372, which is equivalent to 3.72 divided by 10⁴.
Option C is incorrect because moving the decimal point 4 places to the right would give us a much larger value than the original number. Option D is also incorrect because placing 4 zeros after the number would give us a value that is 10,000 times larger than the original number.
Therefore, the correct answer is B, which shows and explains the correct location of the decimal point when the expression 3.72 divided by 10⁴ is evaluated. The correct option is B.
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Complete question:
3.72 divided by 10⁴ which of these shows and explains the correct location of the decimal point when the expression is evaluated?
A 0.0000372 because 4 zeros are placed in font of the number when you divide by 10 to the fourth power
B 0.000372 because the decimal point moves 4 places to the left when you divide by 10 to the fourth power
C 37,200 because the decimal point moves for places to the right when you divide by 10 to the fourth power
D 3,720,00 because 4 zeros are placed after the number when you divide by 10 to the fourth power
Let C = {factors of 12}
Work out n(C)
The value or n(C) based on the information will be 6.
How to explain the FactorIn mathematics, a factor is a number or algebraic expression that divides another number or expression without leaving a remainder. More formally, if a is a factor of b, then b can be expressed as a product of a and some other number or expression.
For example, in the expression 12 = 2 x 2 x 3, the numbers 2 and 3 are factors of 12. Similarly, in the expression x² - 4, (x - 2) and (x + 2) are factors because if we multiply them together we get x² - 4.
The factors of 12 are 1, 2, 3, 4, 6, and 12. Therefore, the set C contains six elements. Hence, n(C) = 6.
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You ride 6 miles due west to the town of Happyville, where you turn south and ride 8 miles to the town of Crimson. When the sun begins to go down, you decide that it is time to start for home. There is a road that goes directly from Crimson back to Sunshine. If you want to take the shortest route home, do you take this new road, or do you go back the way you came? Justify your decision. How much further would the longer route be than the shorter route? Assume all roads are straight.
It would be more efficient to take the new road from Crimson to Sunshine to get home.
To determine the shortest route home, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In this case, the two sides are the distances you traveled west (6 miles) and south (8 miles).
Using the Pythagorean theorem, we have:
Hypotenuse² = 6² + 8²
Hypotenuse² = 36 + 64
Hypotenuse² = 100
Hypotenuse = √100 = 10 miles
So, the shortest route home (the new road) is 10 miles. If you go back the way you came, you would travel 6 miles west and then 8 miles north, for a total of 14 miles. The longer route (14 miles) is 4 miles longer than the shorter route (10 miles). Therefore, you should take the new road to get home more quickly.
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Choose the definition for the function acellus
Acellus is a powerful tool for students looking to achieve academic success and gain the skills they need to succeed in today's competitive world.
Acellus is an online learning management system designed to provide students with personalized, self-paced education. The system offers a wide range of courses in subjects such as mathematics, science, language arts, and social studies. The courses are designed to be interactive, engaging, and challenging, providing students with a comprehensive education in each subject area.
Acellus utilizes advanced technology to provide students with an adaptive learning experience. The system uses data analytics to track student progress and adapt the coursework to meet the needs of each individual student. This allows students to learn at their own pace, and to receive personalized instruction that is tailored to their specific needs.
In addition to providing high-quality educational content, Acellus also offers a number of other features and tools to support student learning. These include assessments, quizzes, and interactive games, as well as a student dashboard that allows students to track their progress and stay on top of their coursework.
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The Average Rate Of Change In The Interval (0, 2) Of The Function F F(X) = X^2 – 3x Is
To find the average rate of change of a function in a given interval, we need to calculate the difference in the function values at the endpoints of the interval and divide it by the length of the interval.
In this case, the interval is (0,2) and the function is f(x) = x^2 - 3x.
At the left endpoint, x=0, we have f(0) = 0^2 - 3(0) = 0.
At the right endpoint, x=2, we have f(2) = 2^2 - 3(2) = -2.
Therefore, the difference in the function values is f(2) - f(0) = -2 - 0 = -2.
The length of the interval is 2 - 0 = 2.
So the average rate of change of f(x) over the interval (0,2) is:
(-2)/2 = -1
Therefore, the average rate of change of f(x) over the interval (0,2) is -1.
Hi! To find the average rate of change in the interval (0, 2) for the function f(x) = x^2 - 3x, you can use the following formula:
Average Rate of Change = (f(b) - f(a)) / (b - a)
In this case, a = 0 and b = 2. First, calculate the function values at these points:
f(0) = (0)^2 - 3(0) = 0
f(2) = (2)^2 - 3(2) = 4 - 6 = -2
Now, apply the formula:
Average Rate of Change = (f(2) - f(0)) / (2 - 0) = (-2 - 0) / (2) = -2 / 2 = -1
So, the average rate of change in the interval (0, 2) for the function f(x) = x^2 - 3x is -1.
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Are the events "having a dog" and "having a cat" independent from each other?
a) Cannot tell with the given information
b) Yes, because P(cat) = P(cat | dog) and P(dog) = P(dog | cat)
c) The events are disjoint
d) No, because P(cat) is not equal to P(cat | dog) and P(dog) is not equal to P(dog | cat)
Option A) Cannot tell with the given information as the question doesn't provide any information about the relationship between having a dog and having a cat.
Without additional information, we cannot determine if these events are independent, dependent, disjoint, or have any other relationship. Independent events are events in which the occurrence or non-occurrence of one event does not affect the occurrence or non-occurrence of the other event.
In other words, the probability of one event happening does not depend on whether or not the other event happens.
Formally, events A and B are independent if and only if:
P(A ∩ B) = P(A) * P(B)
Where P(A) is the probability of event A occurring, P(B) is the probability of event B occurring, and P(A ∩ B) is the probability of both events A and B occurring simultaneously.
If the above equation holds true, then we can say that events A and B are independent. If not, then events A and B are dependent.
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4. Question: How can an antiderivative of a velocity function be used to find displacement of the body? Question: If velocity is negative, how does this impact the problem of finding displacement? 5.
If velocity is negative,The body is moving backwards instead of forwards, so the displacement will be measured as a negative value.
An antiderivative of a velocity function can be used to find displacement of the body by integrating the velocity function over a given time interval. The result of this integration will give the total displacement of the body over that time interval.
If the velocity is negative, it means that the body is moving in the opposite direction to the positive direction of the coordinate system. This has an impact on the problem of finding displacement because the displacement will also be negative. In other words, the body is moving backwards instead of forwards, so the displacement will be measured as a negative value.
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Here is an inequality: -2x > 10.
1. List some values for x that would make this inequality true.
2. How are the solutions to the inequality -2x [tex]\geq[/tex] 10 different fomt the solutions to -2x > 10? Explain your reasoning.
Therefore , the solution of the given problem of inequality comes out to be the solutions x = -6 or x = -10 would be acceptable.
What exactly is an inequality?Algebra, which lacking a symbol for this difference, can represent it using a pair or group of numbers. Equity usually comes after equilibrium. Inequality is bred by the persistent gap of standards. Equality and disparity are not the same thing. As was my least preferred symbol, notwithstanding knowing that the pieces are often not connected or close to one another. (). No matter how small the variations, they all affect value.
Here,
Finding values of x that cause the left side of the inequality to be bigger than the right side is necessary to make the inequality -2x > 10 true. Divide both sides by -2 and invert the inequality sign to achieve this:
=> -2x > 10
=> x < -5
The inequality is therefore true for any value of x that is less than -5. For instance, the solutions x = -6 or x = -10 would be acceptable.
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If you multiply each value in the data set below by 3, what are the mean, median, mode, and range of the resulting data set?
2 3 9 0 5 8 3
Answer: range=9 mode=3 mean=9
Step-by-step explanation:
The change in water level of a lake is shown in the table. How much did the water level change between Weeks 2 and 3?
The rate of change for the water level between Weeks 2 and 3 is: D. 3 7/8.
How to calculate or determine the rate of change or slope of a line?In Mathematics and Geometry, the gradient, rate of change, or slope of any straight line can be determined by using the following mathematical equation;
Rate of change (slope) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Rate of change (slope) = rise/run
Rate of change (slope) = (y₂ - y₁)/(x₂ - x₁)
By substituting the given data points into the formula for the slope of a line, we have the following;
Rate of change (slope) = (y₂ - y₁)/(x₂ - x₁)
Rate of change (slope) = (1 5/8 + 2 1/4)/(3 - 2)
Rate of change (slope) = (13/8 + 9/4)/(1)
Rate of change (slope) = 3 7/8
Based on the table, the rate of change is the change in y-axis with respect to the x-axis and it is equal to 3 7/8.
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The general form of the primitive of the function f (x) = 6 sin (2) / cos (2) is F (x) = ______ + C
The integral of f(x) can be found by using the substitution u = cos(x), du = -sin(x) dx. Thus, we have:
∫ (6 sin(2x) / cos(2x)) dx = -3 ∫ (2 sin(2x) / cos²(2x)) (-2cos(x)) dx
= 6 ∫ (sin(u) / u²) du
This integral can be evaluated using integration by parts, with u = sin(u) and dv = u⁻² du, giving:
6 ∫ (sin(u) / u²) du = -6 sin(u) / u + 6 ∫ (cos(u) / u) du
Substituting back u = cos(x), we have:
6 ∫ (sin(x) / cos²(x)) dx = -6 tan(x) + 6 ln |cos(x)| + C
Since tan(x) = sin(x) / cos(x) and cos²(x) = 1 - sin²(x), we have:
f(x) = 6 sin(x) / cos²(x) = 6 sin(x) / (1 - sin²(x)) = -6/(sin(x) - 1/sin(x))
Therefore, the general form of the primitive of f(x) is:
F(x) = -6 ln |sin(x) - 1/sin(x)| + C
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Does anyone know the answer?
Answer:
B. ∠FBG
Step-by-step explanation:
When an angle is in the three letter form, the first letter is the first line that forms the angle, the second letter is where the angle is located, and third letter is the line that forms the angle with the first line.
Thus, we can see that line E combines with line F, and the actual angle is located at point B.
The two angles adjacent to ∠EBF are ∠DBE and ∠FBG. Only ∠FBG is one of the answer choices so this is our final answer.
The trip to california from missouri was 2,800 miles one way. how many miles would a round trip take?
The total distance that a round trip will cover is 5,600 miles, under the condition that The trip to California from Missouri was 2,800 miles one way.
After considering all the given data induced by the question we come to the state that here we have to apply the principles of multiplication, to evaluate the distance cover when a round trip is taken from California to Missouri.
Then the calculation is
Round trip distance = 2 × one way distance
Round trip distance = 2 × 2,800 miles
Round trip distance = 5,600 miles
Then the distance covered in the couse of making a round trip from California to Missouri is 5,600 miles.
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Heather says that the ratio of bass and violins to cellos is 10 to 5. Allen says the ratio of cellos to bass and violins is 1 to 2. Who is correct?explain your answer
Both ratios provided by Heather and Allen are correct, they are just inverse.
Heather says that the ratio of bass and violins to cellos is 10 to 5. Allen says the ratio of cellos to bass and violins is 1 to 2. To determine who is correct, let's compare the ratios.
1: Simplify Heather's ratio.
Heather's ratio is 10:5, which can be simplified by dividing both sides by 5. This gives a simplified ratio of 2:1 (bass and violins to cellos).
2: Compare the simplified ratios.
Heather's simplified ratio is 2:1, which represents the ratio of bass and violins to cellos. Allen's ratio is 1:2, which represents the ratio of cellos to bass and violins.
3: Analyze the results.
Heather's ratio (2:1) and Allen's ratio (1:2) are inverses of each other. Both ratios are correct, but they represent different perspectives: Heather is expressing the ratio of bass and violins to cellos, while Allen is expressing the ratio of cellos to bass and violins.
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1. An oil spill is spreading such that its area is given by the exponential function A(t) = 250(1. 15)', where A is
the area in square feet and t is the time that has elapsed in days.
(b) By what percent is the oil spill increasing each
t=0?
hour?
The oil spill is increasing by approximately 0.58% per hour.
An oil spill is spreading such that its area is given by the exponential function A(t) = 250(1.15)^t, where A is the area in square feet and t is the time that has elapsed in days. To find the percent increase per hour, first convert the time from days to hours by replacing t with (t/24), since there are 24 hours in a day.
A(t) = 250(1.15)^(t/24)
To determine the hourly percent increase, find the growth factor for one hour (t=1) and subtract 1 to get the percentage:
A(1) = 250(1.15)^(1/24) ≈ 250(1.0058)
The growth factor for one hour is approximately 1.0058. To find the percent increase, subtract 1 and multiply by 100:
(1.0058 - 1) × 100 ≈ 0.58%
The oil spill is increasing by approximately 0.58% per hour.
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how long does it take light to travel to earth from sun ? the sun is 9.3 x 10 ^7mi from earth , and the light travels 1.86 x 10^5mi/s
.
It takes approximately 500 seconds for light to travel from the Sun to Earth.
To calculate the time it takes for light to travel from the Sun to Earth, we can use the formula:
time = distance / speed
Given:
Distance from the Sun to Earth = 9.3 x 10^7 miles
Speed of light = 1.86 x 10^5 miles per second
Plugging in the values into the formula, we have:
time = (9.3 x 10^7 miles) / (1.86 x 10^5 miles per second)
To simplify, we can divide the numerator and denominator by 10^5 to cancel out the units:
time = (9.3 x 10^7) / (1.86 x 10^5) seconds
Next, we can divide the numbers in scientific notation:
time = (9.3 / 1.86) x (10^7 / 10^5) seconds
Simplifying further:
time = 5 x 10^2 seconds
Therefore, light takes approximately 500 seconds to travel from the Sun to Earth.
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Question 9 Previous Consider the indefinite integral 63% (6x3 + 10x2 + 64x + 96 dx 24 + 16.02 Then the integrand has partial fractions decomposition b CC +d + + 22 + 16 where a - 2 a = b = C = du Integrating term by term, we obtain that 16x3 + 10x2 + 64x + 96 dc 24 + 16x2 +C
To do this, we first need to factor the denominator of the integrand into linear factors. In this case, the denominator is given as 24 + 16.02 = 40, which is already a factorization. Therefore, we can write:
∫ (6x3 + 10x2 + 64x + 96)/(24 + 16.02) dx = ∫ [(a/(24 + 16.02)) + (b/(22 + 16))] dx
where a, b are constants that we need to find. To do this, we can use the method of partial fractions, which involves equating the coefficients of like terms on both sides of the equation. Specifically, we can write:
6x3 + 10x2 + 64x + 96 = (a/(24 + 16.02))(22 + 16) + (b/(22 + 16))(24 + 16.02)
Multiplying both sides by the common denominator (24 + 16.02)(22 + 16), we get:
(6x3 + 10x2 + 64x + 96)(24 + 16.02)(22 + 16) = a(22 + 16) + b(24 + 16.02)(24 + 16)
Expanding both sides and collecting like terms, we get a system of two linear equations in two unknowns:
(24 + 16.02)(22 + 16)a + (24 + 16.02)(24 + 16)b = 6(24 + 16.02)(22 + 16) + 10(22 + 16)(24 + 16.02) + 64(24 + 16.02) + 96(22 + 16)
(22 + 16)a + (24 + 16.02)b = 6(22 + 16) + 10(24 + 16.02) + 64 + 96
Solving this system (which involves some algebraic manipulation) gives:
a = -6/5
b = 18/5
Therefore, we can write:
∫ (6x3 + 10x2 + 64x + 96)/(24 + 16.02) dx = (-6/5) ∫ (22 + 16)/(24 + 16.02) dx + (18/5) ∫ (24 + 16.02)/(22 + 16) dx
To evaluate these integrals, we can use the substitution u = 24 + 16.02 in the first integral and u = 22 + 16 in the second integral. This gives:
∫ (6x3 + 10x2 + 64x + 96)/(24 + 16.02) dx = (-6/5) ln|24 + 16.02| + (18/5) ln|22 + 16| + C
where C is the constant of integration. Finally, using the given expression for the integral, we can equate coefficients of like terms to obtain:
16x3 + 10x2 + 64x + 96 = (6/5)(24 + 16.02) ln|24 + 16.02| - (18/5)(22 + 16) ln|22 + 16| + C
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We want to find the mass of a solid 8 enclosed within a sphere of radius 1 centred at 2 the origin whose density is given by 8(x, y, z) 1 + (x2 + y2 + 22)3/2 Recall that the mass of B is given by the triple integral [S]_568, , z) AV. Since the region of integration is spherical, we will use spherical coordinates to carry out our work. (a) What is the density 8 as a function of spherical coordinates, that is, as a function of p. 0, and ? (Use the Vars tab that appears when you click in the answerbox, or you may type in rho, theta, or phi, respectively.) Answer: 8(0,0,0) (b) In spherical coordinates the bounds of integration for p. 0, and 6 are given by SP SOS sºs (C) What is the mass of the solid ? (If you enter your answer using a decimal approximation, then round your answer to three decimal places.)
A. 8(p, phi, theta) = 8p sin(phi) cos(theta) / (1 + p^2 + 2p cos(phi))^(3/2)
B. ∫0^(2π) ∫0^π ∫0^1 8p sin(phi) cos(theta) / (1 + p^2 + 2p cos(phi))^(3/2) p^2 sin(phi) dp d(phi) d(theta)
C. the mass of the solid 8 enclosed within the sphere is approximately 8.378.
(a) Using the conversion formulas for spherical coordinates, we have:
x = p sin(phi) cos(theta)
y = p sin(phi) sin(theta)
z = p cos(phi)
Substituting these expressions into the given density function, we get:
8(x, y, z) = 8(p sin(phi) cos(theta), p sin(phi) sin(theta), p cos(phi))
= 8p sin(phi) cos(theta) / (1 + p^2 + 2p cos(phi))^(3/2)
Therefore, the density 8 as a function of spherical coordinates is:
8(p, phi, theta) = 8p sin(phi) cos(theta) / (1 + p^2 + 2p cos(phi))^(3/2)
(b) Since the solid 8 is enclosed within a sphere of radius 1 centred at 2 the origin, we have:
0 ≤ p ≤ 1
0 ≤ theta ≤ 2π
0 ≤ phi ≤ π
Therefore, the bounds of integration in spherical coordinates are:
∫0^(2π) ∫0^π ∫0^1 8p sin(phi) cos(theta) / (1 + p^2 + 2p cos(phi))^(3/2) p^2 sin(phi) dp d(phi) d(theta)
(c) Evaluating the triple integral using a computer algebra system or numerical integration, we get:
M = 8π/3
Therefore, the mass of the solid 8 enclosed within the sphere is approximately 8.378.
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You purchased a home this year for $315,000. You applied for homestead exemption and were able to take off $50,000 of the appraised value for taxes. The taxes in your county are 1.22%. How much do you have to pay in property taxes?
You need to pay $3,243.50 in property taxes.
The appraised value of the house after setting out the homestead exemption is $315,000 - $50,000 = $265,000.
To calculate the assets taxes, we need to multiply the appraised cost by means of the tax rate, which is 1.22% or 0.0122 as a decimal:
property taxes = $265,000 x zero.0122 = $3,243.50
Therefore, you have to pay $3,243.50 in property taxes.
It's far essential to factor in property taxes whilst thinking about the general price of purchasing a home and to recognize the method for applying for exemptions or appealing the appraised cost if necessary.
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Clare made $160 babysitting last summer. She put the money in a saving account that pays 3% interest per year. If Clare doesn't touch the money in her account, she can find the amount she'll have the next year by multiplying her current amount by 1.03.
Write an expression for the amount of money Clare would have after 30 years if she never withdraws money from the account.
Evaluating an exponential function A(x) = 160*(1.03)ˣ we can see that in 30 years she will have:
$388.36
How much money will eh have in 30 years?We know that the initial investment is 160, and the rate per year is 3%.
Then after x years, the value is given by the exponential function.
A(x) = 160*(1.03)ˣ
The amount of money in the account after 30 years is what we get if we evaluate the equation in x = 30, then we will get:
A(30) = 160*(1.03)³⁰
A(30) = 388.36
In 30 years she will have a total amount of 388.36 dollars.
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what is the exact volume of a sphere with the radius of 17
Answer: 6,550.6666666666666666666666666667π
Step-by-step explanation:
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Gas prices are on the rise this summer as more Americans travel, Prices have increased by 40% from last summer's price, which averaged $2. 26 per gallon. Jonah's mom's car takes 14 1/2 gallons of gas to fill up. Find the cost that Jonah's mom would have to spend after the 40% increase in gas prices if she fills up her tank the entire 14 1/2 gallons.
Jonah's mom's would have to spend $45.878 to fill up her tank after the 40% increase in gas prices if her car takes 14 1/2 gallons of gas to fill up.
To find the cost that Jonah's mom would have to spend after the 40% increase in gas prices to fill up her 14 1/2 gallon tank, we need to follow these steps:
1. Find the increased price per gallon by multiplying last summer's price ($2.26) by 1.40 (since there's a 40% increase): $2.26 x 1.40 = $3.164 per gallon.
2. Convert 14 1/2 gallons to a decimal: 14.5 gallons.
3. Multiply the increased price per gallon ($3.164) by the number of gallons needed to fill up the tank (14.5 gallons): $3.164 x 14.5 = $45.878.
So, after the 40% increase in gas prices, Jonah's mom would have to spend $45.878 to fill up her 14 1/2 gallon tank.
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Enter the value of c when the expression 21. 2x + c is equivalent of to 5. 3(4x - 2. 6).
The value of c is 21.8.
We can solve for c by simplifying the expression on the right side of the equation and equating it to the expression on the left side.
Starting with the right side, we distribute the 3 across the parentheses:
5 * 3 * (4x - 2.6) = 60x - 13
Now, we can set this equal to the expression on the left and solve for c:
21.2x + c = 60x - 13
c = 60x - 13 - 21.2x
c = 38.8x - 13
However, we are asked to find the value of c, not in terms of x. Since we were not given a specific value for x, we cannot solve for c exactly. Therefore, we can only express the value of c in terms of x, which is c = 38.8x - 13.
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A pitcher contains 13 cups of iced tea. You drink 1. 75 cups of the tea each morning
and 1. 5 cups of the tea each evening. When will you run out of iced tea?
You will run out of iced tea in 5.33 days.
To calculate this, we need to first determine how much tea you drink each day:
1.75 cups in the morning + 1.5 cups in the evening = 3.25 cups per day.
Then, we can divide the total amount of tea by the amount you drink per day to find out how many days the tea will last:
13 cups ÷ 3.25 cups per day ≈ 4 days.
However, we need to account for the fact that you won't run out of tea at the end of the day, so we need to round up to the nearest day:
ceil(4 days) = 5 days.
Finally, we need to account for the partial day on the fifth day, which we can calculate by finding how much tea you drink in the morning before running out:
1.75 cups in the morning - (5 days x 3.25 cups per day) = 0.5 cups.
So, you will run out of iced tea on the fifth day in the evening, after drinking 1.5 cups. Therefore, you will run out of iced tea in 5.33 days.
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