We have found the n-vector b for which bc = p/(a), where p is the polynomial with coefficients c0, c1, ..., cn. Let's start by writing out the polynomial:
[tex]c0 + c1x + c2x^2 + ... + cnx^n[/tex]
The derivative of this polynomial with respect to x is:
[tex]c1 + 2c2x + 3c3x^2 + ... + ncnx^(n-1)[/tex]
At the point x=a, the derivative becomes:
[tex]c1 + 2c2a + 3c3a^2 + ... + ncn*a^(n-1)[/tex]
We want this to be a linear function of the coefficients c0, c1, ..., cn. That means we need to find a vector b such that:
[tex]c1 + 2c2a + 3c3a^2 + ... + ncna^(n-1) = b0c0 + b1c1 + ... + bncn[/tex]
Let's compare coefficients of c0, c1, ..., cn on both sides:
c1 = b1c1
2c2a = b2c2
[tex]3c3a^2 = b3c3[/tex]
...
[tex]ncna^(n-1) = bn*cn[/tex]
We can simplify these equations by dividing both sides by ci (assuming ci is not zero):
b1 = 1
b2 = 2a/c2
[tex]b3 = 3a^2/c3[/tex]
...
[tex]bn = n*a^(n-1)/cn[/tex]
So the vector b we're looking for is:
b = [1, 2a/c2, [tex]3a^2[/tex]/c3, ...,[tex]n*a^(n-1)/cn][/tex]
And if we multiply b by the coefficient vector c, we get:
bc = c1 + 2c2a + [tex]3c3a^2[/tex] + ...[tex]+ ncn*a^(n-1)[/tex] = the derivative of the polynomial at x=a
Therefore, we have found the n-vector b for which bc = p/(a), where p is the polynomial with coefficients c0, c1, ..., cn.
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write a paragraph about importance of english language using simple present tense.
Answer:
Step-by-step explanation:
The English language is an art that I am using to convey this message to you. Without this form of communication, we would be unable to talk or write without using another language. We think everyday with this awesome language, and don't think much about the language we think in. English is an amazing language, and I am proud to be able to verbalize it to you today.
Assume that sin(x) equals its Maclaurin series for all
X. Use the Maclaurin series for sin (5x^2) to evaluate
the integral
∫ sin (5x)^2 dx
To evaluate the integral ∫sin(5x^2)dx using the Maclaurin series, we first need to find the Maclaurin series for sin(5x^2).
The Maclaurin series for sin(x) is given by:
sin(x) = x - (x^3)/3! + (x^5)/5! - (x^7)/7! + ...
Now, replace x with 5x^2:
sin(5x^2) = (5x^2) - (5x^2)^3/3! + (5x^2)^5/5! - (5x^2)^7/7! + ...
Now we have the Maclaurin series for sin(5x^2). To evaluate the integral ∫sin(5x^2)dx, we integrate term-by-term:
∫sin(5x^2)dx = ∫[(5x^2) - (5x^2)^3/3! + (5x^2)^5/5! - (5x^2)^7/7! + ...]dx
= (5/3)x^3 - (5^3/3!7)x^7 + (5^5/5!11)x^11 - (5^7/7!15)x^15 + ... + C
This is the integral of sin(5x^2) using the Maclaurin series, where C is the constant of integration.
To evaluate the integral ∫ sin (5x)^2 dx, we can use the identity sin^2(x) = (1-cos(2x))/2.
First, we need to find the Maclaurin series for sin (5x^2). Using the formula for the Maclaurin series of sin(x), we have:
sin (5x^2) = ∑ ((-1)^n / (2n+1)!) (5x^2)^(2n+1)
= ∑ ((-1)^n / (2n+1)!) 5^(2n+1) x^(4n+2)
Next, we substitute this series into the integral:
∫ sin (5x)^2 dx = ∫ sin^2 (5x) dx
= ∫ (1-cos(10x)) / 2 dx
= (1/2) ∫ 1 dx - (1/2) ∫ cos(10x) dx
= (1/2) x - (1/20) sin(10x) + C
where C is the constant of integration.
Therefore, using the Maclaurin series for sin (5x^2), the integral of sin (5x)^2 is (1/2) x - (1/20) sin(10x) + C.
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Charlene sees a laptop being sold for $492. this is 18% less than the original price. what was the original price of the laptop?
The original price of the laptop was $600 because $492 is 82% of the original price (100% - 18% = 82%).
How to find the percentage of the laptop?The concept of percentage decrease. A percent decrease is the amount by which a quantity decreases, expressed as a percentage of its original value. In this case, the laptop is being sold for 18% less than its original price, so we can represent the percent decrease as 18%.
To find the original price of the laptop, we need to work backwards from the sale price. We can use the formula:
Sale price = Original price - Percent decrease of original price
where "Percent decrease of original price" is the percentage decrease of the original price, expressed as a decimal. In this case, the percent decrease is 18%, which we convert to a decimal by dividing by 100: 18/100 = 0.18.
Plugging in the values we know, we get:
$492 = Original price - 0.18 * Original price
Simplifying this equation, we get:
$492 = 0.82 * Original price
To isolate Original price, we can divide both sides by 0.82:
Original price = $492 / 0.82
Simplifying this expression, we get:
Original price = $600
the original price of the laptop was $600.
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Find the positive solution, to the nearest tenth, of f(x)
g(x) = -2x + 25.
X≈
Submit
= g(x), where f(x) = 3* - 2 and
The result will be the x value when the difference between the values of f(x) and g(x) is less than 0.1, which will be the positive solution to the nearest tenth of f(x)=g(x).
To find the positive solution, to the nearest tenth, of f(x)=g(x) using Cora's process, the steps are as follows:
Input the initial value of x,if x=0.
Calculate f(x) and g(x):
f(x) = x² - 8 = 0 - 8 = -8
g(x) = 2x - 4 = 0 - 4 = -4
If f(x) is less than g(x), then x should be increased and vice versa.
Increase or decrease x accordingly and calculate the new values of f(x) and g(x).
Keep repeating steps 3 and 4 until the difference between the values of f(x) and g(x) is less than 0.1.
Hence, the result will be the x value when the difference between the values of f(x) and g(x) is less than 0.1, which will be the positive solution to the nearest tenth of f(x)=g(x).
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Cora is using successive approximations to estimate a positive solution to f(x) = g(x), where f(x)=x2 - 8 and g(x)=2x - 4. The table shows her results for different input values of x. Use Cora's process to find the positive solution, to the nearest tenth, of f(x) = g(x)
2x + 7 = -1(3 - 2x) solve for X
This linear equation is invalid, the left and right sides are not equal, therefore there is no solution.
What in mathematics is a linear equation?
An algebraic equation with simply a constant and a first-order (linear) component, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables. Equations with variables of power 1 are referred to be linear equations. axe+b = 0 is a one-variable example in which a and b are real numbers and x is the variable.
2x + -7 = -1(3 + -2x)
Reorder the terms:
-7 + 2x = -1(3 + -2x)
-7 + 2x = (3 * -1 + -2x * -1)
-7 + 2x = (-3 + 2x)
Add '-2x' to each side of the equation.
-7 + 2x + -2x = -3 + 2x + -2x
Combine like terms: 2x + -2x = 0
-7 + 0 = -3 + 2x + -2x
-7 = -3 + 2x + -2x
Combine like terms: 2x + -2x = 0
-7 = -3 + 0
-7 = -3
Solving
-7 = -3
Couldn't find a variable to solve for.
This equation is invalid, the left and right sides are not equal, therefore there is no solution.
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what are complementary angles and supplementary angles difference between them?
Answer:
Supplementary angles are angles that have a sum of 180°. When two angles are supplementary, we say that one angle is the supplement of the other.
Complementary angles are angles that add up to 90°. When two angles are complementary, we can say that one angle is the complement of the other
Step-by-step explanation:
Please help and make sure to explain. Brainliest will be given to best answer before 7:00am EST April 27. If no answer is good then no brainliest.
Joey forgot to record approximately 9,412 views after the second month.
How to explain the regressionUsing a regression calculator, we find that the equation that best models the data is:
y = 4298.76x + 809.72
The coefficient of determination (R-squared value) for this regression is 0.994, indicating a strong linear relationship between the number of months and the total number of views.
We need to find the value of y for x = 2, using the regression equation we found in part a:
y = 4298.76(2) + 809.72
y ≈ 9412.24
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A rectangular fish tank needs to hold 500 gallons, and it needs to be two feet deep. The top will be open. A. Find the width and length of the tank that will use the smallest amount of glass. B. The tank will be filled with enough water so that there will be two inches of head space. Find the weight of the water in the tank
The weight of the water in the tank is approximately 3,809 pounds.
A. To find the width and length of the tank that will use the smallest amount of glass, we need to consider the surface area of the tank. Let's use "x" to represent the length and "y" to represent the width. The formula for the surface area of a rectangular tank is:
Surface Area = 2xy + 2xz + 2yz
Since the top of the tank will be open, we can ignore the surface area of the top. We know that the tank needs to hold 500 gallons and be 2 feet deep, so we can use the formula for the volume of a rectangular tank to solve for one of the variables:
Volume = Length x Width x Depth
500 = xy x 2
xy = 250
Now we can substitute this into the surface area formula and simplify:
Surface Area = 2(250) + 2xz + 2yz
Surface Area = 500 + 2xz + 2yz
To minimize the surface area, we need to differentiate this formula with respect to one of the variables and set it equal to zero. Let's differentiate with respect to x:
d(Surface Area)/dx = 2z
Setting this equal to zero, we get:
2z = 0
z = 0
This doesn't make sense, so let's try differentiating with respect to y:
d(Surface Area)/dy = 2z
Setting this equal to zero, we get:
2z = 0
z = 0
Again, this doesn't make sense. We can conclude that the surface area is minimized when x = y, so the tank should be square. Since xy = 250, we can solve for the side length of the square:
x^2 = 250
x ≈ 15.81 feet
So the tank should be approximately 15.81 feet by 15.81 feet to use the smallest amount of glass.
B. The volume of the water in the tank will be:
Volume = Length x Width x Depth
Volume = 15.81 x 15.81 x 1.67
Volume = 397.25 gallons
Since the tank needs to hold 500 gallons with 2 inches of head space, we can find the weight of the water using the formula:
Weight = Volume x Density
The density of water is approximately 8.34 pounds per gallon, so:
Weight = 397.25 x 8.34
Weight ≈ 3,313.69 pounds
So the weight of the water in the tank will be approximately 3,313.69 pounds.
A. To minimize the amount of glass used for the rectangular fish tank, you'll need to create a tank with equal width and length (a square base). Since the tank needs to hold 500 gallons and is 2 feet deep, you can use the formula: Volume = Length × Width × Depth. Convert 500 gallons to cubic feet (1 gallon ≈ 0.1337 cubic feet), so 500 gallons ≈ 66.85 cubic feet.
66.85 = Length × Width × 2
33.425 = Length × Width
Since the length and width are equal, you can solve for one of the dimensions:
Length = Width = √33.425 ≈ 5.78 feet
So, the tank dimensions will be approximately 5.78 feet by 5.78 feet by 2 feet.
B. To find the weight of the water in the tank, first determine the volume of the water. There will be 2 inches of headspace (2 inches ≈ 0.167 feet), so the water depth is 2 - 0.167 = 1.833 feet. The volume of the water is:
Volume = Length × Width × Depth = 5.78 × 5.78 × 1.833 ≈ 61.05 cubic feet
To find the weight of the water, multiply the volume by the weight of water per cubic foot (62.43 lbs/cubic foot):
Weight = 61.05 × 62.43 ≈ 3,809 lbs
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A ball of radius 11 has a round hole of radius 4 drilled through its center.
Find the volume of the resulting solid.
The volume of the resulting solid is estimated 4,128.38 cubic units.
How do we calculate?
The volume of the ball isgitten as:
V_ball = (4/3)πr^3
r is the radius of the ball. In this scenario
r = 11, so:
V_ball = (4/3)π(11)^3
V_ball = (4/3)π(1331)
V_ball = 4,396.46 cubic units
The volume of the hole is gotten as :
V_hole = (4/3)πr^3
r is the radius of the hole.
In thisscenario, r = 4, so:
V_hole = (4/3)π(4)^3
V_hole = (4/3)π(64)
V_hole = 268.08 cubic units
In conclusion, the volume of the resulting solid is:
V_resulting_solid = V_ball - V_hole
V_resulting_solid = 4,396.46 - 268.08
V_resulting_solid = 4,128.38 cubic units
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On the math exam,5 tasks were given. 25% of students solved at least two tasks. Prove that there was at least one task that no more than 12 students solved if 32 students wrote that test
Given that 25% of students solved at least two tasks and there were 32 students who wrote the test, we can prove that there was at least one task that no more than 12 students solved.
There was at least one task that no more than 12 students solved, we can use a proof by contradiction.
Assume that all five tasks were solved by more than 12 students. This means that for each task, there were at least 13 students who solved it. Since there are five tasks in total, this implies that there were at least 5 * 13 = 65 students who solved the tasks.
However, we are given that only 25% of students solved at least two tasks. If we let the number of students who solved at least two tasks be S, then we can write the equation:
S = 0.25 * 32
Simplifying, we find that S = 8.
Now, let's consider the remaining students who did not solve at least two tasks. The maximum number of students who did not solve at least two tasks is 32 - S = 32 - 8 = 24.
If all five tasks were solved by more than 12 students, then the total number of students who solved the tasks would be at least 65. However, the maximum number of students who could have solved the tasks is 8 (those who solved at least two tasks) + 24 (those who did not solve at least two tasks) = 32.
This contradiction shows that our initial assumption is false. Therefore, there must be at least one task that no more than 12 students solved.
Hence, we have proven that there was at least one task that no more than 12 students solved if 32 students wrote the test.
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Find X and then find JL
The value of x is calculated as x = 3, while the length of segment JL is calculated as 18 units.
How to Find the Value of x in the Figure Given?Create an equation based on the fact that the diagonals of the shape shown bisects each other to form equal segments such as:
JN = LN
Plug in the values to find x:
15 - 2x = 4x - 3
Combine like terms:
15 + 3 = 4x + 2x
18 = 6x
18/6 = x
x = 3
Length of JL = 15 - 2x + 4x - 3 = 12 + 2x
Plug in the value of x:
Length of JL = 12 + 2(3) = 18 units
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3⋅50. 2w=720
What is the solution of the equation?
Round your answer, if necessary, to the nearest thousandth
The solution to the equation is w = 285.
How to solve a mathematical equation involving multiplication and variables?To solve the equation 3⋅50 + 2w = 720, we first simplify the left side by multiplying 3 and 50, which gives us 150.
Therefore, the equation becomes 150 + 2w = 720. Next, we isolate the variable term by subtracting 150 from both sides of the equation, resulting in 2w = 570.
To solve for w, we divide both sides of the equation by 2, giving us w = 285.
Therefore, the solution to the equation is w = 285.
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Which expression is equivalent to the given expression? ( 10 c 6 d - 5 ) ( 2 c - 5 d 4 ) A. 20 c d B. 20 c d C. 20 c 30 d 20 D.
So the equivalent expression that matches one of the answer choices is option C, 100c/3d.
What is expression?In mathematics, an expression is a combination of numbers, variables, and mathematical operations (such as addition, subtraction, multiplication, division, exponentiation, and so on) that can be evaluated to produce a value. An expression can represent a single number or a more complex calculation, and it can be written using symbols, variables, and/or numbers.
Here,
To simplify the given expression, we need to multiply the two binomials using the distributive property:
(10c6d - 5)(2c - 5d/4)
= 10c * 2c + 10c * (-5d/4) - 5 * 2c - 5 * (-5d/4)
= 20c² - 25cd + 10c + 25/4 d
None of the answer choices match this expression exactly, but we can simplify it further. Factoring out a common factor of 5 from the last two terms, we get:
20c² - 25cd + 10c + 25/4 d
= 5(4c² - 5cd + 2c + 5/4
20c/3 * 5d/4
= 100c/3d
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A spring with a 9-kg mass and a damping constant 7 can be held stretched 0.5 meters beyond its natural length by a force of 1.5 newtons. Suppose the spring is stretched 1 meters beyond its natural length and then released with zero velocity, In the notation of the text, what is the value c2 – 4mk? m²kg / sec? Find the position of the mass, in meters, after t seconds. Your answer should be a function of the variable t with the general form Great cos(Bt) + czert sin(8t)
The value of [tex]c2 – 4mk[/tex] in scenario is[tex]c2 – 0.748[/tex]m and the position of the mass after t seconds is x(t) = [tex]e^(-7t/36) cos(0.433t) + 0.5e^(-7t/36) sin(0.433t)[/tex],which can be written in the general form Great [tex]cos(Bt) + czert sin(8t).[/tex]
The value of c2 – 4mk in this scenario can be found using the equation [tex]c2 – 4mk = c2 – 4mω02[/tex], where ω0 is the natural frequency of the spring. To calculate ω0, we can use the equation[tex]ω0 = sqrt(k/m)[/tex], where k is the spring constant and m is the mass.
Plugging in the given values, we get [tex]ω0 = sqrt(1.5/9) = 0.433[/tex]. Substituting this into the first equation, we get [tex]c2 – 4mk = c2 – 4m(0.433)2 = c2 – 0.748m.[/tex]
Using the given initial condition of the spring being stretched 1 meter beyond its natural length and then released with zero velocity, we can determine that A = 1 and B = 0.5. Plugging in all the values, we get [tex]x(t) = e^(-7t/36) cos(0.433t) + 0.5e^(-7t/36) sin(0.433t).[/tex].
This equation represents the motion of the spring-mass system as it oscillates back and forth around its equilibrium position. The exponential term represents the damping of the system, while the sinusoidal terms represent the oscillation.
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Riya has pens and pencils, which together are 40 in number. If she had 5 more pencils and 5 less pens, then the number of pencils would become four times the number of pens. Find the original number of pens and pencils.
Answer:
Pens=13
Pencils=27
Step-by-step explanation:
1. Pens = x, Pencils = y
x+y=40
2. y+5 & x-5 --> y=4x
3. Rearrange the x+y=40 to y=40-x. Then substitute y=4x and y=40-x to 4x=40-x.
4. Solve. 4x=40-x, 5x=40, x=8
5. Plug in x=8 to y=4x -> y=32.
6. Reverse the y+5 & x-5. y=27, x=13.
Joseph measures the ropes to tie boats to a dock. He records the lengths of the ropes in feet and then makes a line plot. Joseph concludes that the difference between the longest and shortest lengths is 2 1/2 feet. Martha disagrees and says that the difference is only 1 foot who is correct? no links please
Without the line plot or the actual measurements of the ropes, it is difficult to determine who is correct.
Joseph measures the lengths of ropes used to tie boats to a dock in feet and creates a line plot. He then concludes that the difference between the longest and shortest lengths is 2 1/2 feet. Martha disagrees with Joseph's conclusion and argues that the difference is only 1 foot.
To determine who is correct, we need to analyze the line plot and examine the data. If the line plot shows that the ropes vary greatly in length, with some being significantly longer than others, then Joseph's conclusion of a 2 1/2 foot difference could be accurate. However, if the line plot shows that the ropes are relatively similar in length, with only slight variations, then Martha's conclusion of a 1 foot difference could be correct.
Without the line plot or the actual measurements of the ropes, it is difficult to determine who is correct. Therefore, it is important to always examine the data before making conclusions.
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Identify the fractions between 1/16 and 5/8
The fractions between 1/16 and 5/8 are 3/16 and 5/16
Identifying the fractions between 1/16 and 5/8The fraction expressions are given as
1/16 and 5/8
The above fractions are proper fractions because numerator < denominator
Express the fraction 5/8 as a denominator of 16
So, we have the following equivalent fractions
1/16 and 10/16
This means that the fractions between 1/16 and 5/8 can be represented as
a/16
Where
1 < a < 10
So, we have
Possible fraction = 3/16 and 5/16
Hence, the fractions between 1/16 and 5/8 are 3/16 and 5/16
Note that there are other possible fractions too
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A $750 gift was shared equally by 5 people. After spending $90 of her share, Clarissa divided the amount remaining into 2 equal parts. What amount of money is now in each part of Clarissa's money?
Answer:
$30 for each part
Step-by-step explanation:
$750 ÷ 5 = $150 each people
Clarissa's money is $150
$150 - $90 = $60
Clarissa's money after she spent is $60
$60 ÷ 2 = $30
Clarissa's money for each part out of 2 parts is $30
PLEASE WRITE THE EXPRESSION IN FORM OF |x-b|=c
Write the absolute value equations in the form |x-b|=c (where b is a number and c can be either number or an expression) that have the following solution sets:
Please do both problems
All numbers such that x≤−14.
All numbers such that x≥ -1. 3
The vertical distance the Mars Rover Curiosity has traveled is approximately 84.954 meters.
What will be the absolute value equations in the form |x-b|=c for x ≤ -14 and x ≥ -1.3?An absolute value equation is an equation that contains an absolute value expression, which is defined as the distance of a number from zero on the number line. The equation |x-b|=c represents the distance between x and b is c units. To write the absolute value equations in the form |x-b|=c, we need to determine the values of b and c based on the given solution sets.
For the solution set "All numbers such that x ≤ -14", we know that the distance between x and -14 is always a non-negative value. Therefore, the absolute value of (x-(-14)) or (x+14) is equal to the distance between x and -14. Since we want x to be less than or equal to -14, we can set the absolute value expression to be equal to -c, where c is a positive number. Hence, the absolute value equation is |x+14|=-c.
Similarly, for the solution set "All numbers such that x ≥ -1.3", the distance between x and -1.3 is always a non-negative value. Therefore, the absolute value of (x-(-1.3)) or (x+1.3) is equal to the distance between x and -1.3. Since we want x to be greater than or equal to -1.3, we can set the absolute value expression to be equal to c, where c is a positive number. Hence, the absolute value equation is |x+1.3|=c.
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Find the minimum value of the parabola y=x^2+5/2.
Someone please help fast
The minimal value of the given parabola is y = 5/2, which occurs at x = 0.
To discover the minimum value of the given parabola & that's why we need to determine the vertex of the parabola.
The vertex of a parabola in the form of y = ax^2 + bx + c is given by means of (-b/2a, f(-b/2a)).
in the given parabola, a = 1, b = 0, and c = 5/2. consequently, the x-coordinate of the vertex is -b/2a = 0/(2*1) = 0.
To discover the y-coordinate of the vertex & we substitute x = 0 within the given equation:
y = 0^2 + 5/2 = 5/2
Therefore, the minimal value of the given parabola is y = 5/2.
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A rectangle is inscribed in a circle of radius 5 centimeters. Find the perimeter of the rectangle
The perimeter of the rectangle that is inscribed in a circle of radius 5 cm is 28cm
Let x and y be the side of the rectangle
Diameter of circle = radius × 2
Diameter = 5×2
Diameter = 10
According to the Pythagorean theorem
(Diameter)² = X² + Y²
10² = X² + Y²
X² + Y² = 100
By this equation, possible value of x and y is 6 and 8 respectively only 6 and 8 will satisfy the equation
So, X = 6 and Y = 8
Perimeter = 2(X+Y)
Perimeter = 2(6+8)
Perimeter = 2(14)
Perimeter = 28 cm
perimeter of the rectangle is 28cm
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Given XV is 20 inches, find the length of arc XW. Leave your answer in terms of pi
The arc length XW in terms of pi is (10pi)/3.
To find the length of arc XW, we need to know the measure of the angle XDW in radians.
Since XV is the diameter of the circle, we know that angle XDV is a right angle, and angle VDW is half of angle XDW. We also know that XV is 20 inches, so its radius, XD, is half of that, or 10 inches.
Using trigonometry, we can find the measure of angle VDW:
sin(VDW) = VD/VDW
sin(VDW) = 10/20
sin(VDW) = 1/2
Since sin(30°) = 1/2, we know that angle VDW is 30 degrees (or π/6 radians). Therefore, angle XDW is twice that, or 60 degrees (or π/3 radians).
Now we can use the formula for arc length:
arc length = radius * angle in radians
So the length of arc XW is:
arc XW = 10 * (π/3)
arc XW = (10π)/3
Therefore, the arc length XW in terms of pi is (10π)/3.
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A maker of homemade candles makes a scatter plot to show data of the diameter of a candle and the total burn time of the candle. A line of best fit of this data is T = 6. 5d + 11. 8, where T is the total burn time, in hours, and d is the diameter of the candle, in inches. Approximately how long is the total burn time of a candle with a diameter of 0. 5 inch?
answers: A. 2 hours B. 5 hours
C. 10 hours D. 15 hours
Answer:
The given line of best fit is: T = 6.5d + 11.8
We can use this equation to estimate the total burn time for a candle with a diameter of 0.5 inches:
T = 6.5(0.5) + 11.8
T = 3.25 + 11.8
T = 15.05
So, according to the line of best fit, the total burn time of a candle with a diameter of 0.5 inch would be approximately 15.05 hours.
Therefore, the answer is D. 15 hours.
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Question 21
What fraction is equal to 40 % ?
A
B
C
D
45
58
2
1
25
Answer:
2/5
Step-by-step explanation:
To convert a percentage to a fraction, we divide the percentage by 100 and simplify the resulting fraction. For example, to convert 40% to a fraction, we divide 40 by 100 to get 0.4 and then simplify the fraction 2/5. Therefore, 40% is equal to 2/5.
What is the probability of selecting a 2 and then
a number divisible by 4 ?
a.
5/66
b.
1/20
C.
1/24
D.
1/22
Answer: C. 1/24 and that's is your answer to your question
3. [-/1 Points] DETAILS SCALCET9 4.7.005. What is the maximum vertical distance between the line y = x + 72 and the parabola y - x for - SxS9? Need Help? Watch
The maximum vertical distance between the line y = x + 72 and the parabola y = x^2 is 518.67 units.
To find the maximum vertical distance between the line and the parabola, we need to find the point(s) where the distance is maximum.
The line y = x + 72 is a straight line with slope 1, and it intersects the y-axis at 72.
The parabola y = x^2 is a symmetric curve with vertex at (0,0).
To find the point(s) where the distance is maximum, we can find the intersection point(s) of the line and the parabola.
Substituting y = x + 72 in the equation of the parabola, we get x^2 - x - 5184 = 0.
Solving for x using the quadratic formula, we get x = (1 ± sqrt(1 + 20736))/2.
The two intersection points are (108, 180) and (-107, 65).
The maximum vertical distance between the line and the parabola is the difference between the y-coordinates of these points, which is approximately 518.67 units.
Therefore, the maximum vertical distance between the line y = x + 72 and the parabola y = x^2 is 518.67 units.
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On Saturday mornings, Roger volunteers at the hospital. One Saturday, he answers phone calls at the information desk while the receptionist is away. Then he spends 40 minutes delivering flowers to patients' rooms. In all, Roger volunteers at the hospital for 90 minutes that day. Which equation can you use to find the amount of time t that Roger answers phone calls?
We know that by solving for t, you can find the amount of time Roger spent answering phone calls
You can use the equation t + 40 = 90, where t represents the amount of time Roger answers phone calls at the information desk.
This equation takes into account that Roger spends 40 minutes delivering flowers and the total time he volunteers at the hospital is 90 minutes.
By solving for t, you can find the amount of time Roger spent answering phone calls.
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Can someone explain this to me I need to solve for "B" but I don't understand how
The value of b in the parallel line is 93 degrees.
How to find the angle in a parallel line?When parallel lines are crossed by a transversal line, angle relationships are formed such as alternate interior angles, alternate exterior angles, corresponding angles, same side interior angles, vertically opposite angles, adjacent angles etc.
Therefore, let's use the angle relationship to find the angle b as follows:
Alternate interior angles are the angles formed when a transversal intersects two parallel lines. Alternate interior angles are congruent.
Using the alternate interior angle theorem,
b = 180 - 65.5 - 21.5
b = 93 degrees.
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I tried to do it but it gave me 6.
Answer:
(c) 12.5
Step-by-step explanation:
You want the unknown leg of a right triangle with one leg 10 and hypotenuse 16.
Sanity checkThe triangle inequality tells you the unknown leg of the triangle will have a length between the difference of the two known legs, and the longest leg of the triangle.
Since this is a right triangle, its longest leg is the hypotenuse. The unknown side cannot be longer than that, so must be less than 16.
The difference of the given lengths is ...
16 -10 = 6
so the missing leg must be longer than 6.
Only one answer choice is between 6 and 16: 12.5.
The missing leg length is 12.5 units.
__
Additional comment
If you want to figure the length, you can use the Pythagorean theorem:
c² = a² +b²
16² = 10² +b²
b² = 256 -100 = 156
b = √156 ≈ 12.49 ≈ 12.5
The length of the unknown leg is 12.5 units.
Median & IQR Question: The data shows the number of hours a part-time waiter works each week. Tell whether each statement about the data is True or False. Statements and numbers are listed in the picture.
The statements regarding the median and the quartiles are given as follows:
a. True.
b. True.
c. False.
What are the median and the quartiles of a data-set?The 25th percentile, which is the median of the bottom 50%.The median, which splits the entire data-set into two halfs, the bottom 50% and the upper 50%.The 75th percentile, which is the median of the upper 50%.The ordered data-set in this problem is given as follows:
7, 8, 8, 9, 9, 9, 10, 10, 11, 11, 13.
Hence:
The first quartile is of 8. -> option b is true.The median is of 9. -> option a is true.The third quartile is of 11.More can be learned about median and quartiles at https://brainly.com/question/3514929
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