Yes, there is a way for this equation to be true in now, take the square root of both sides of the equation (c^2 = n^2) and write the resulting equation
To take the square root of both sides of the equation (c^2 = n^2), you would perform the following steps:
1. Take the square root of both sides:
√(c^2) = √(n^2)
2. Simplify the square roots:
c = n
The resulting equation is c = n.
This equation can be true if both c and n have the same value. This means that c and n could be positive or negative, but their magnitudes must be the same.
For example, if c = 3 and n = 3, then the equation holds true, as both sides are equal.
Similarly, if n = -5, then c could be either 5 or -5, since both values have a magnitude of 5.
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Hello! Help please thank you
Answer:
2(2(3) + 2(5) + 3(5)) = 2(6 + 10 + 15) = 2(31)
= 62
D is the correct answer.
PLS ANSWER QUICK
The table shows the length, in inches, of fish in a pond.
11 19 9 15
7 13 15 28
Determine if the data contains any outliers. If so, list the outliers.
There is an outlier at 28.
There is an outlier at 7.
There are outliers at 7 and 28.
There are no outliers.
Answer:
There is an outlier at 28.
On your own paper, make a frequency table for and find the mean to the nearest hundredth. 6. 7, 6, 6, 7, 6, 5, 8, 6, 5, 9, 8, 5, 6, 8 9, 5, 8, 8, 6, 8, 7, 5, 6,9,7,7,9,6 7. 501 501
After drawing our frequency table, we also find out that our mean is 6.73.
How to make a frequency table and find the mean?To make a frequency table, we have to count the number of times each value appears in the data set.
Frequency table:
Value Frequency
5 4
6 8
7 4
8 6
9 3
To find the mean, we will add all values and divide by total number of values. The mean is:
= EF / N
= (6 + 7 + 6 + 6 + 7 + 6 + 5 + 8 + 6 + 5 + 9 + 8 + 5 + 6 + 8 + 9 + 5 + 8 + 8 + 6 + 8 + 7 + 5 + 6 + 9 + 7 + 7 + 9 + 6 + 7) / 30
= 6.83333333333
= 6.83.
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what is 88 closer to 64 or 125
Answer:
64
Step-by-step explanation:
Answer:
64...i think
Step-by-step explanation:
125 - 88=37
88-64=24
PLS MARK BRAINLIEST
Which statement is true about the relationship between the diameter and circumference of a circle?
A. The diameter and circumference of a circle have a proportional relationship.
B. The diameter is a product of the circumference and pi.
C. The constant of proportionality between the diameter and circumference of a circle is a rational number.
D. The circumference of a circle is the quotient of the diameter and pi.
Option A The diameter and circumference of a circle have a proportional relationship is True .
What is diameter and circumference?Diameter
The diameter is the length acrοss the circle at its widest pοint, measured frοm center tο center . The radius, a related measurement, is a line that extends frοm the circle's centre tο its edge. The diameter is equivalent tο twice the radius. (A chοrd is a line that crοsses the circle but is nοt at the widest pοint.)
Circumference
The circle's perimeter, οr the distance arοund it, is knοwn as its circumference. Imagine encircling a circle with a string. Imagine taking the string οut and extending it in a straight line. This string's length, if measured, wοuld represent yοur circle's circumference.
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What is the quotient of 223 + 3x2 + 5x – 4 divided by 22 +2+1?
Pls I need help
The quotient is -58x2 + 131x - 234 with a remainder of -5898.To solve this problem, we need to use long division. The dividend is 223 + 3x2 + 5x - 4 and the divisor is 22 + 2 + 1, which simplifies to 25.
We start by dividing 2 into 22, which gives us 11. We then write 11 above the 2 and multiply it by 25, which gives us 275. We subtract 275 from 223, which gives us -52. We bring down the 3, which gives us -523. We then repeat the process by dividing 2 into 52, which gives us 26. We write 26 above the 5 and multiply it by 25, which gives us 650. We subtract 650 from -523, which gives us -1173. We bring down the 1, which gives us -11731. We divide 2 into 117, which gives us 58.
We write 58 above the x and multiply it by 25, which gives us 1450. We subtract 1450 from -1173, which gives us -2623. We bring down the -4, which gives us -26234. We divide 2 into 262, which gives us 131. We write 131 above the 5 and multiply it by 25, which gives us 3275. We subtract 3275 from -2623, which gives us -5898. Therefore, the quotient is -58x2 + 131x - 234 with a remainder of -5898.
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On the curve y = x3, point p has the coordinates (2, 8). what is the slope of the curve at point p?
The slope of the curve y = x^3 at point P(2, 8) is 12.
To find the slope of the curve y = x^3 at point P with coordinates (2, 8), we need to determine the derivative of the function and then evaluate it at x = 2.
Step 1: Find the derivative of the function y = x^3.
The derivative, dy/dx, represents the slope of the curve. To find the derivative of y = x^3, apply the power rule: d(x^n)/dx = n * x^(n-1).
So, dy/dx = 3 * x^(3-1) = 3x^2.
Step 2: Evaluate the derivative at the given point P (2, 8).
To find the slope at point P, substitute the x-coordinate (2) into the derivative: 3 * (2)^2 = 3 * 4 = 12.
Thus, the slope of the curve y = x^3 at point P(2, 8) is 12.
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plunk and ms. q run a $100$-meter race. plunk runs at $8$ meters per second, and ms. q runs at $5$ meters per second. because ms. q runs slower, she is given a $3$-second head start. plunk wins the race. how much time, in seconds, is it between the time plunk passes ms. q and the time that plunk finishes the race?
The seconds, is it between the time plunk passes Ms. q and the time that plunk finishes the race is 7.5 seconds..
Flow Distance In the Mathematics or Quants part of any competitive test, time is one of the most well-liked and significant topics. For inquiries about a variety of subjects, including motion in a straight line, circular motion, boats and streams, races, clocks, etc.
The notion of Speed, Time, and Distance is frequently employed. Candidates should make an effort to comprehend how the variables of speed, distance, and time interact.
Ms. q being slow will get a head start for the race so,
3 second head start = 3 x 5 = 15 meters
There difference in speed is 8- 5 = 3 m/s
Time required for the Plunk to catch up to Ms. q is:
15 / 3 = 5 seconds when P catches Q
(this is 8 seconds after Q starts the race)
In 5 seconds Plunk runs 5 x 8 = 40 meters this is when they are at the same point that is at time 8 seconds.
60 meters left in the race will take Plunk :
60 m / 8 m/s = 7.5 seconds to finish the race.
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Drag each number to the correct location. classify each number according to its value. 4. 2 × 10-6 2. 1 × 10-3 3. 1 × 10-2 3. 2 × 10-5 3. 5 × 10-4 5. 8 × 10-3 5. 2 × 10-4.
Each number is classified according to its value in the given image.
We are given some numbers and we have to drag each number to the correct location according to its value. The numbers given are 4.2×[tex]10^{-6}[/tex], 2.1×[tex]10^{-3}[/tex], 3.1×[tex]10^{-2}[/tex], 3.2×[tex]10^{-5}[/tex], 3.5×[tex]10^{-4}[/tex], 5.8×[tex]10^{-3}[/tex], 5.2×[tex]10^{-4}[/tex].
We will classify these numbers in the categories given in the table.
(a) Now the numbers which are greater than 3.1×[tex]10^{-3}[/tex] are:
3.1×[tex]10^{-2}[/tex] and 5.8×[tex]10^{-3}[/tex].
(b) Numbers falling between 3.1 × [tex]10^{-3}[/tex] and 4.3 × [tex]10^{-5}[/tex] are:
2.1×[tex]10^{-3}[/tex], 3.5×[tex]10^{-4}[/tex], and 5.2×[tex]10^{-4}[/tex]
(c) Numbers that are less than 4.3 × [tex]10^{-5}[/tex] are:
4.2×[tex]10^{-6}[/tex]and 3.2×[tex]10^{-5}[/tex]
So, the numbers are classified according to their values in the table given in the image.
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In △abc , m∠b=20° and m∠c=40°. the angle bisector at a intersects side bc at point d. find the difference between bc and ab if ad = 1
In the △ABC, the the difference between bc and ab if ad = 1 is found to be 0.709.
We can use the angle bisector theorem to solve this problem. Let's denote the length of segment BD as x and the length of segment CD as y. Then, we can write,
BD/DC = AB/AC
Using the angle bisector theorem, we know that AB/AC = BD/DC, so we can substitute to get,
x/y = AB/AC
We can solve for AB by multiplying both sides by AC,
AB = x/y * AC
Now, we can use the law of sines to find the length of AC. We have,
sin(20°)/AB = sin(140°)/AC
Solving for AC, we get,
AC = AB * sin(20°) / sin(140°)
Substituting the expression we found for AB, we get,
AC = x/yACsin(20°) / sin(140°)
Simplifying, we get,
y = xsin(140°) / (sin(20°) - sin(140°))
We know that AD = 1, so we can use the Pythagorean theorem to find BC:
BC² = BD² + CD²
Substituting the expressions we found for BD and CD, we get,
BC² = x² + y²
Substituting the expression we found for y, we get,
BC² = x² + (xsin(140°) / (sin(20°) - sin(140°)))²
Simplifying, we get,
BC² = x²(1+sin²(140°)/(sin²(20°)-2sin(20°)sin(140°)+sin²(140°)))
Using the identity sin(140°) = sin(180° - 40°) = sin(40°), we can simplify further.
Now, we can substitute x = AD = 1 and sing a calculator, we can evaluate this expression to get,
BC² ≈ 2.917
Taking the square root, we get,
BC ≈ 1.709
Therefore, the difference between BC and AB is 0.709.
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Construct a square, and a regular Pentagon with equal side equal to 0. 5 inch.
To construct a square and a regular pentagon with equal side lengths of 0.5 inch, we need to use basic geometric constructions.
How can I create a square and a regular pentagon with equal side lengths of 0.5 inch?To construct a square and a regular pentagon with equal side length of 0.5 inch, follow these steps:
(a) Construct a Square:
Draw a horizontal line segment of length 0.5 inch.From the endpoints of the line segment, draw two perpendicular lines of length 0.5 inch each, meeting at the endpoints of the original line segment.From the endpoints of these new line segments, draw two more perpendicular lines of length 0.5 inch each, meeting at the endpoints of the second line segment.Connect the endpoints of the four line segments to form a square.
(b) Construct a Regular Pentagon:
Draw a circle with a radius of 0.5 inch. This will be the circumcircle of the pentagon.Draw a horizontal line through the center of the circle.Mark the points where the line intersects the circle. These will be the vertices of the pentagon.Draw a line segment connecting two adjacent vertices of the circle.Using a compass, copy the length of this line segment to the next vertex, and connect the two vertices to form a line segment of the pentagon.Repeat this process for all five vertices of the circle to form the regular pentagon.
A geometric construction is a method of drawing a figure using only a straightedge (an unmarked ruler) and a compass.
For the square, we start by drawing a horizontal line segment of length 0.5 inch. We then draw two perpendicular lines of length 0.5 inch each, meeting at the endpoints of the original line segment.
These two new line segments represent the adjacent sides of the square. We then repeat this process to create the remaining two sides of the square, and connect all four endpoints to form the complete square.
For the regular pentagon, we need to construct a circle with a radius of 0.5 inch. This will be the circumcircle of the pentagon, meaning that all five vertices of the pentagon will lie on the circle.
We draw a horizontal line through the center of the circle, and mark the points where the line intersects the circle. These five points will be the vertices of the pentagon.
We then draw line segments connecting adjacent vertices, using a compass to copy the length of each line segment from the previous one.
This process will create all five sides of the pentagon, and the figure will be a regular pentagon with equal side lengths of 0.5 inch.
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I. Suppose you a business owner and sell clothing. The following represents the number of items sold and the cost for each item: Use matrix operations to determine the total revenue over the two days:
Monday: 3 T-shirts at GH¢10 each, 4 hats at GH¢15 each, and 1 pair of shorts at GH¢20.
Tuesday: 4 T-shirts at GH¢10 each, 2 hats at GH¢15 each, and 3 pairs of shorts at GH¢20.
The total revenue over the two days is GH¢305.
We can represent the number of items sold and the cost for each item in matrices as follows:
[tex]\begin{equation}A = \begin{bmatrix} 3 & 4 & 1 \ 4 & 2 & 3 \end{bmatrix}, \quad B = \begin{bmatrix} 10 \ 15 \ 20 \end{bmatrix}\end{equation}[/tex]
Here, matrix A represents the number of items sold on each day, and matrix B represents the cost per item. To find the total revenue, we need to multiply the two matrices and then take the sum of all the elements in the resulting matrix:
[tex]\begin{equation}A \cdot B = \begin{bmatrix} 3 & 4 & 1 \ 4 & 2 & 3 \end{bmatrix} \cdot \begin{bmatrix} 10 \ 15 \ 20 \end{bmatrix} = \begin{bmatrix} 95 \ 140 \end{bmatrix}\end{equation}[/tex]
Therefore, the total revenue over the two days is GH¢(95 + 140) = GH¢305.
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Find the cosine of K.
24
Save answer
26
blo
J
10
Simplify your answer and write it as a proper fraction, improper fraction, or whole number.
cos (K) =
K
Skip to
Step-by-step explanation:
remember the original trigonometric triangle inside the norm circle (radius = 1).
sine is the up/down distance from the triangle baseline or corresponding circle diameter.
cosine is the left/right distance from the center of the circle (and the point of the angle).
for larger triangles and circles all these function results need to be multiplied by the actual radius (which we skipped for the norm circle, as a multiplication by 1 is not changing anything).
when you look at the triangle with K representing the angle, we have 10 a the cosine value, 24 as the sine value and 26 as the radius.
so,
10 = cos(K) × 26
cos(K) = 10/26 = 5/13
Frank cuts a piece of cork to make trivet that has the shape and dimensions as shown.Find The Area Of The Trivet.Round Your Answer to the nearest tenth if needed
Answer:
52.5
Step-by-step explanation:
First, we can see that the base is 14m. The top is 7m, and the height is 5m. Since the formula for a trapezoid is
top + base / 2 ∙ h,
we plug in our numbers to get
7 + 14 / 2 ∙ 5.
We can solve to get
21 / 2 ∙ 5
10.5 ∙ 5
52.5
The outside temperature was 4°C for the next six hours the temperature changed at a mean rate of -0. 8°C per hour for the next two hours what was the final temperature
The final temperature after the next 8 hours (6 hours at -0.8°C per hour, followed by 2 hours at -0.8°C per hour) will be -2.4°C.
The final temperature can be calculated by subtracting the total temperature change from the initial temperature of 4°C.
The total temperature change during the next six hours can be calculated by multiplying the mean rate of -0.8°C per hour by the number of hours, which is 6.
-0.8°C/hour x 6 hours = -4.8°C
Therefore, the temperature after the next six hours will be:
4°C - 4.8°C = -0.8°C
For the next two hours, the temperature changed at a mean rate of -0.8°C per hour. This means the temperature decreased by:
-0.8°C/hour x 2 hours = -1.6°C
So the final temperature will be:
-0.8°C - 1.6°C = -2.4°C.
Therefore, the final temperature after the next 8 hours (6 hours at -0.8°C per hour, followed by 2 hours at -0.8°C per hour) will be -2.4°C.
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PLEASE HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
Answer:true
Step-by-step explanation:
Answer:
true
Step-by-step explanation
I need help ASAP PLEASE! Z-score question
The weights of logs in a wood pile are normally distributed with a mean of 17 pounds and a standard deviation of 3. 4 pounds
The majority of logs in the pile will have a weight close to the mean of 17 pounds, with a smaller number of logs having a weight that is farther away from the mean.
In statistics, the normal distribution is a commonly used continuous probability distribution.
It is also referred to as a Gaussian distribution, and it has a bell-shaped curve that is symmetrical around the mean.
The mean is the center of the distribution, and the standard deviation describes how spread out the data is around the mean.
In this case, the weights of logs in a wood pile are normally distributed with a mean of 17 pounds and a standard deviation of 3.4 pounds.
This means that the majority of logs in the pile will have a weight close to the mean of 17 pounds, with a smaller number of logs having a weight that is farther away from the mean.
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if f' * (x) = 2x - 1 and g(x) - x + 3 prove that f g(x) is a linear function
The composite function fg(x) is a linear function by the proof shown below
Proving that the function fg(x) is a linear functionFrom the question, we have the following parameters that can be used in our computation:
f(x) = 2x - 1
g(x) = -x + 3
The above functions are linear functions
This means that the function fg(x) will also be a linear function
To prove this, we have
f(g(x)) = 2(g(x)) - 1
substitute the known values in the above equation, so, we have the following representation
f(g(x)) = 2(-x + 3) - 1
So, we have
f(g(x)) = -2x - 7
Hence, the function is a linear function
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Christie builds a model airplane that has a wingspan of 11. 8 inches. The model airplane has a scale of 1 inch to 2. 5 feet. What is the wingspan, in feet, of actual airplane?
A. 4. 72
B. 9. 30
C. 14. 30
D. 29. 50
PLEASE HELP!!!!!!!!!!!!!!!!!!!!!!!!
The correct answer is D. 29.50.
To find the wingspan of the actual airplane, we will use the given scale factor and the wingspan of the model airplane.
Given information:
Model airplane wingspan = 11.8 inches
Scale factor = 1 inch to 2.5 feet
Step 1: Convert the model wingspan to feet using the scale factor.
1 inch on the model represents 2.5 feet on the actual airplane. To convert 11.8 inches to feet, multiply by the scale factor.
Step 2: Calculate the actual wingspan.
Actual wingspan = Model wingspan * Scale factor
Actual wingspan = 11.8 inches * 2.5 feet/inch
Step 3: Perform the multiplication.
Actual wingspan = 29.5 feet
So, the wingspan of the actual airplane is 29.5 feet.
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pls hurry
Write y = 2x²-12x+16 in vertex form.
Step-by-step explanation:
f(x) = 2x^2 -12x + 16 to get to vertex form you will need to complete the square for 'x'....to do THAT you will need the x^2 coefficient to be '1'
Start like this:
2 (x^2 - 6x) + 16 now complete the square
2 (x^2 - 6x +9) - 18 + 16
f(x) = 2 (x-3)^2 - 2 Done.
At a hot dog eating contest, Flora ate 3 hot dogs in one minute. At this rate, how many hot dogs will Flora eat in 12 minutes? Write a proportion and solve.
Answer:36
Step-by-step explanation:
3 a minute
18 in 6 minutes
36 in 12
3:1
Solve this quick please thank you.
Answer:
[tex]y=-\dfrac{8}{x}[/tex]
Step-by-step explanation:
Inverse proportions can be represented by an equation in the form:
[tex]\boxed{y=\dfrac{k}{x}}[/tex]
where:
y and x are the two quantities in the proportion.k is the constant of proportionality.To write an expression for the graphed function, first input the given point (-2, 4) into the inverse proportion equation and solve for k:
[tex]\implies y=\dfrac{k}{x}[/tex]
[tex]\implies 4=\dfrac{k}{-2}[/tex]
[tex]\implies 4 \cdot (-2)=\dfrac{k}{-2}\cdot (-2)[/tex]
[tex]\implies -8=k[/tex]
[tex]\implies k=-8[/tex]
Therefore, the expression for the graphed function is:
[tex]\boxed{y=-\dfrac{8}{x}}[/tex]
A traingle has side of 7cm and 18cm if the length of the third side is a whole number how many possible traingles are there explain your answer
Therefore, there are 13 possible triangles that can be formed with sides of 7cm, 18cm and a whole number as the third side.
How to get the number of trianglesUsing the triangle inequality law, Let's denote the sides of the triangle as a, b, and c. In this case, we have:
a = 7 cm
b = 18 cm
c = the third side, a whole number
Now, we apply the triangle inequality theorem to these sides:
a + b > c
=> 7 + 18 > c
=> 25 > c
a + c > b
=> 7 + c > 18
=> c > 11
b + c > a
=> 18 + c > 7
=> c > -11
Since c is a whole number, the third condition is always true, as there are no negative whole numbers. Therefore, we only need to consider the first two conditions:
11 < c < 25
Now, we list the whole numbers that fall within 11 and 25 within this range:
these are listed and counted
12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24
There are 13 whole numbers in this range. So, there are 13 possible triangles with sides of 7 cm and 18 cm, and a third side that is a whole number.
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PLEASE SHOW ALL YOUR WORK AS NEATLY AS POSSIBLE: 1) Given f(x) = 3sqrt(x + 2)^2 a) Find the derivative, f'(x). b) Solve f'(x) = 0
The only critical point of f(x) is x = -2.
a) To find the derivative of f(x), we can use the chain rule and the power rule of differentiation.
f(x) = 3sqrt(x + 2)^2
f'(x) = 3 * 2 * sqrt(x + 2) * (x + 2)^1/2-1 * (1)
Applying the power rule, we simplify the expression as:
f'(x) = 6(x + 2)^1/2
Therefore, the derivative of f(x) is f'(x) = 6(x + 2)^1/2.
b) To solve f'(x) = 0, we set f'(x) equal to zero and solve for x:
f'(x) = 6(x + 2)^1/2 = 0
Dividing both sides by 6, we get:
(x + 2)^1/2 = 0
Squaring both sides, we get:
x + 2 = 0
Subtracting 2 from both sides, we get:
x = -2
Therefore, the only critical point of f(x) is x = -2.
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Find the magnitude of v. v = 7i
|lv|| = _____
The magnitude of vector v is:
|v| = 7
The magnitude of v is simply the length of the vector v, which can be found using the Pythagorean theorem. The vector v is given as v = 7i.
To find the magnitude of v (|v|), use the formula:
|v| = √(x² + y²)
where x and y are the components of the vector v. In this case, x = 7 (from 7i) and y = 0 (since there is no j component).
Now, plug in the values of x and y into the formula:
|v| = √(7² + 0²)
|v| = √(49 + 0)
|v| = √(49)
|v| = 7
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Triangle ABC is similar to triangle DBE. Select the responses that make the statements true. Large triangle A B C with side length 7. 5. Smaller triangle D B C inside A B C, which shares vertex B. Side B E has length 5 and base D E has length 13
The correct responses are: "Triangle DBC is similar to triangle ABC" and "The length of side DE is 13."
Since triangle ABC is similar to triangle DBE, we know that the corresponding angles are congruent and the corresponding sides are proportional.
From the given information, we know that side BC of triangle ABC corresponds to side BE of triangle DBE, since they share vertex B. Therefore, we can use the proportion:
BC / BE = AC / DE
Substituting the given values, we have:
BC / 5 = 7.5 / 13
Solving for BC, we get:
BC = (5 x 7.5) / 13 = 2.88 (rounded to two decimal places)
Therefore, the length of side BC is 2.88.
Now we can check which of the given statements are true:
"The length of side AB is 3.75." We do not have enough information to determine the length of side AB, so this statement cannot be determined to be true or false based on the given information.
"Triangle DBC is similar to triangle ABC." This statement is true, since they share angle B and the sides BC and BE are proportional.
"Angle C in triangle ABC is congruent to angle D in triangle DBE." This statement cannot be determined to be true or false based on the given information, since we do not know which angle in triangle DBE corresponds to angle C in triangle ABC.
"The length of side AC is 4.29." This statement cannot be determined to be true or false based on the given information, since we only have information about side BC and side BE. We do not have enough information to determine the length of side AC.
"The length of side DE is 7.8." This statement is false, since the length of side DE is given as 13, not 7.8.
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Please help I need this done ASAP
Answer:
Domain is all x values
Range is all y values
Step-by-step explanation:
Your image is not clear enough for me to see the x or y coordinates so hope that helps you to figure it out on your own
A trip to white mountains of new hampshire from boston will take you 2 3/4 hours. assume you have traveled 1/11 of the way. how much longer will the trip take?
The trip will take another 1 hour to complete.
If a trip from Boston to the White Mountains of New Hampshire takes 2 3/4 hours, and you have already traveled 1/11 of the way, then the remaining distance is:
1 - 1/11 = 10/11 of the total distance.
To find how much longer the trip will take, we can use the proportion:
time taken for 10/11 of the trip = x (time taken for the whole trip)
distance traveled for 10/11 of the trip = 1 - 1/11 = 10/11 of the total distance
Since the time taken is proportional to the distance traveled, we can set up the following equation:
2 3/4 hours / (1 - 1/11) = x
where x is the time it will take for the whole trip.
Simplifying the left side of the equation, we get:
2 3/4 hours / (10/11) = x
Multiplying both sides by (11/10), we get:
x = (2 3/4 hours) × (11/10) = 3 1/4 hours
Therefore, the remaining time to complete the trip is:
3 1/4 hours - 2 3/4 hours = 1 hour
So the trip will take another 1 hour to complete.
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Find the length of side x.
Give answer to 1dp.
Answer:
Set your calculator to degree mode.
Use the Law of Cosines.
x^2 = 18^2 + 15^2 - 2(18)(15)(cos 105°)
x^2 = 688.7623
x = 26.2 cm
Find the domain and range of the function V(x, y) = 9√9y – 45x^2. Indicate the domain of V in equality or inequality notation. Use <= to denote ≤ and >= to denote ≥.
Domain of V = {(2,y) }
The minimum value of 9y – 45x^2 is 0, which occurs when y = 5x^2/3, so the range of V is all non-negative real numbers:
Range of V: [0, ∞)
To find the domain and range of the function V(x, y) = 9√(9y – 45x^2), we need to consider the values of x and y that make the expression under the square root non-negative, since we cannot take the square root of a negative number.
So, we have:
9y – 45x^2 >= 0
Dividing both sides by 9 and rearranging, we get:
y >= 5x^2/3
This means that the domain of V is all points (x, y) such that y is greater than or equal to 5x^2/3:
Domain of V: {(x, y) | y >= 5x^2/3}
To find the range of V, we note that the square root is always non-negative, so V(x, y) will be non-negative whenever 9y – 45x^2 is non-negative. The minimum value of 9y – 45x^2 is 0, which occurs when y = 5x^2/3, so the range of V is all non-negative real numbers:
Range of V: [0, ∞)
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