To solve this problem, we can use the formula for inverse variation, which is:
time = k/ rate
where k is a constant of proportionality.
We can start by finding the value of k using the given information. We know that when the pumping rate is 400 gallons per hour, it takes 12 hours to drain the pool. Therefore:
12 = k/400
Multiplying both sides by 400 gives us:
k = 4800
Now we can use this value of k to answer the second part of the question. We want to know how many hours faster the pool can be drained if the pumping rate is increased to 500 gallons per hour. Let's call this new time t:
t = 4800/500
t = 9.6 hours
So the pool can be drained 12 - 9.6 = 2.4 hours faster if the pumping rate is increased to 500 gallons per hour.
I need help please
here is the picture is about Row Ops
The given operation of the matrix is expressed as: -9y + 2z = 12
How to use Matrix to solve simultaneous Equations?Matrices can be used to solve simultaneous linear equations, by first writing them in matrix form and then pre-multiplying by the inverse. Note firstly that these simultaneous equations can be written as the following matrix equation. If you need convincing, multiply out the matrices.
The simultaneous equations formed by the matrix are:
x + 2y + z = -5
4y - 2 = 3
4x - y + 6 = -8
We are told to Multiply row 1 by -4 and this gives us:
-4x - 8y - 4z = 20
Adding it to row 3 gives us:
-9y + 2z = 12
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Below is a model of the athletic field at IDEA Brentwood what is the area in square yards
The area in square yards of the athletic field at IDEA Brentwood would be 170. 24 yards ²
How to find the area ?The shape of the athletic field at IDEA Brentwood is shown to be a rectangle with two semi - circles attached.
The area of the athletic field at IDEA Brentwood is the sum of the areas of these shapes.
Area of rectangle :
= 15 x 8
= 120 yards ²
The area of the two semi - circles would be:
= π x radius x radius
= π x ( 8 / 2 ) x ( 8 / 2 )
= 50. 24 yards ²
The area of the athletic field at IDEA Brentwood is :
= 50. 24 + 120
= 170. 24 yards ²
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which value of x is in the solution set of -4/3x+5<17
A. -8
B. -9
C. -12
D. -16
Please help!
Answer:
-9
Step-by-step explanation: Definitely correct
Review the proof.
Step
1
2
3
5
6
7
8
Statement
cos(2x)= 1-2sin²(x)
Let 2x = 0.
Then x =
cos() = 1-2sin²()
-1 + cos() = -2sin²)
1 + cos(e) = 2sin²)
1-cos(0) = sin²)
sin() = ±
1-cos(0)
2
Which step contains an error?
O step 2
O step 4
step 6
O step 8
The error is in step 2 based on the given statement.
How to solveThe given statement is[tex]cos(2x) = 1-2sin^2(x),[/tex] and it is not appropriate to simply let 2x = 0.
By doing this, you are only considering a specific case where x = 0, rather than proving the statement for all values of x.
To properly prove the given statement, you should consider using trigonometric identities or double-angle formulas to establish the equivalence between cos(2x) and 1-2sin²(x) for all x.
Thus, the error is in Step 2
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A store manager kept track of the number of newspaper sold each week over a seven week period.the result were as fellows 71,81,202,113,269,248,242
The median number of newspapers sold is 202 newspaper. So, correct option is C.
To find the median, we need to arrange the given data in ascending or descending order.
The given data in ascending order: 71, 81, 113, 202, 242, 248, 269
Since there are 7 data points, the median will be the fourth value in the sorted list. Therefore, the median number of newspapers sold is 202.
Hence, the correct answer is option C, which states that the median number of newspapers sold is 202.
The median is the middle value of a dataset when arranged in order, and it's a measure of central tendency that is less affected by outliers than the mean. In this case, the median value represents the value at which half the data points are below it and half are above it.
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Complete question is:
A store manager kept track of the number of newspaper sold each week over a seven week period. the result were as fellows 71,81,202,113,269,248,242
Find the median number of newspapers sold.
A. 175 newspapers
B. 113 newspapers
C. 202 newspapers
D. 242 newspapers
Solution to augmented matrix? Never seen a problem like this one. How do I solve it?
The row of zeros at the bottom immediately lets us conclude "infinitely many solutions". This system is consistent and dependent. This is because we have 0x+0y+0z = 0 aka 0 = 0 which is always true for any choice of x, y, and z.
The second row of values lead to the equation 0x+0y+1z = 6, aka z = 6
The first row says: 1x+6y+0z = 1 which is the same as x+6y = 1
Let's say we isolate x
x+6y = 1
x+6y-6y = 1-6y
x = 1-6y
Then we have these three values or expressions
x = 1-6yy = any real numberz = 6All of the infinitely many solutions are of the form (x,y,z) = (1-6y, y, 6)
A lot of textbooks will use a parameter such as t, so we could write it as (1-6t, t, 6).
The choice of the letter for the parameter does not matter. I think t is most popular because it represents time. Each (x,y,z) point could represent a particle's location at any given time.
If t = 0, then we have (1, 0, 6)If t = 1, then we have (-5, 1, 6)If t = 2, then we have (-11, 2, 6)If t = 3, then we have (-17, 3, 6)and so on.
=============================
Conclusion:
There are infinitely many solutions of the form (x,y,z) = (1-6t, t, 6) where t is any real number.
This system is consistent and dependent.
The number of meters a student swam this week are listed.
200, 450, 600, 650, 700, 800
What is the appropriate measure of variability for the data shown, and what is its value?
The range is the best measure of variability and equals 600.
The IQR is the best measure of variability and equals 250.
The mean is the best measure of variability and equals about 567.
The median is the best measure of variability and equals 625.
The appropriate measure of variability for the data shown and its value is A. The range is the best measure of variability and equals 600.
What is the range?The range is one of the three measures of variability.
The range shows the difference between the highest value and the lowest value in a data set.
The other measures of variability are the IQR (Interquartile Range) and the the Standard Deviation.
Range:Highest value = 800 m
Lowest value = 200 m
The range = 600 m (800 - 200)
IQR = 400 (600 - 200)
Mean = 567 (3,400 ÷ 6)
Median = 625 [(650 + 600) ÷ 2]
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Solve 4x-8 + 4 = 16.
The solutions are x =
and x =
BEYHODNA
MIGRANTA
www
www
wer
Answer:
x = 5
Step-by-step explanation:
To solve the equation 4x-8 + 4 = 16, we first combine the constants on the left-hand side:
4x-8+4 = 16
4x-4 = 16
Next, we add 4 to both sides to isolate the variable on one side:
4x-4+4 = 16+4
4x = 20
Finally, we divide both sides by 4 to solve for x:
4x/4 = 20/4
x = 5
Therefore, the solution to the equation 4x-8 + 4 = 16 is x = 5.
Solve the following logarthlic equations : 3ln(2x) =12
Step-by-step explanation:
[tex]3 ln(2x) = 12[/tex]
[tex] ln(2x) = 4[/tex]
Let both sides be a power of a base e.
[tex]e {}^{ln(2x)} = e {}^{4} [/tex]
The e and ln would just cancel out so
[tex]2x = e {}^{4} [/tex]
[tex]x = \frac{ {e}^{4} }{2} [/tex]
<
1
0.964
8.92
-0.982 increasing decreasing strong
z, hours
y.gallons
Generate a linear regression equation and a correlation coefficient for these data.
1
9.2
2
The linear regression equation is y =
This means there is a ¦
8.4
The correlation coefficient is
O
The number of of gallons is
3
7.7
4
6.1
weak -1.17 10.69
O+O
5
4.5
correlation between the gallons and hours.
as the hours are increasing.
-0.82
Please help bro. Im struggling.
1. The linear regression equation is y = -1.17x+ 10.69
2. The correlation coefficient is -0.982.
3. This means there is a strong negative correlation between the gallons and hours.
4. The number of gallons is decreasing as the hours are increasing.
How do we calculate for the linear regression equation and correlation coefficient?Step 1: find slope.
Formula for slope m = (n × Σ(xy) - Σx × Σy) / (n × Σ(x²) - (Σx)²)
Σx = 1 + 2 + 3 + 4 + 5 = 15
Σy = 9.2 + 8.4 + 7.7 + 6.1 + 4.5 = 35.9
Σ(xy) = (1 × 9.2) + (2 × 8.4) + (3 × 7.7) + (4 × 6.1) + (5 × 4.5) = 96
Σ(x²) = 1 + 4 + 9 + 16 + 25 = 55
n = 5
Therefore ∴
m = (5 × 96 - 15 × 35.9) / (5 × 55 - 15²) = -1.17
y-intercept b = (Σy - m × Σx) / n
b = (35.9 - (-1.17) × 15) / 5 = (53.15) / 5 = 10.63
Therefore the linear regression equation is y = -1.17x + 10.63
correlation coefficient (r): (n × Σ(xy) - Σx × Σy) / sqrt((n × Σ(x²) - (Σx)²) × (n × Σ(y²) - (Σy)²))
r = (5 × 96 - 15 × 35.9) / sqrt((5 × 55 - 15²) × (5 × 271.95 - 35.9²)) = -0.982
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The circle below is centered at the point (-3, 4) and has a radius of length 3.
What is its equation?
-10
-5
5
Answer:
C. (x + 3)² + (y - 4)² = 9
Step-by-step explanation:
The equation for a circle is r² = (x - a)² + (y - b)² where "r" is the radius and (a, b) is the center.
We are given that (-3, 4) is the center and the radius is 3, so that means a = -3, b = 4, and r = 3. Insert the values to their respective places in the equation:
3² = (x - (-3))² + (y - 4)²
9 = (x + 3)² + (y - 4)²
Answer:
equation of a circle: (x-a)²+(y-b)²=r²
(x-(-3))²+(y-4)²=3²
(x+3)²+(y-4)²= 9
(x+6x+9)+(y-8y+16) =9
x+6x+9+y-8y+16=9
x+y+6x-8y+9+16-9=0
x+y+6x-8y+16 =0
A landscaper worded 8-1/2 hours on Monday, 3-1/3 hours on Tuesday and 6-1/4 hours on Wednesday. How many total hours did she work?
If landscaper worked 8-1/2 hours on Monday, 3-1/3 hours on Tuesday and 6-1/4 hours on Wednesday then total of 18.08 hours worked.
To find the total number of hours worked, we need to add up the hours worked on each day.
On Monday, the landscaper worked for 8-1/2 hours, which is the same as 8.5 hours.
On Tuesday, the landscaper worked for 3-1/3 hours, which is the same as 3.33 hours
On Wednesday, the landscaper worked for 6-1/4 hours, which is the same as 6.25 hours.
To find the total hours worked, we add the hours worked on each day:
Total hours worked = 8.5 + 3.33 + 6.25
Total hours worked = 18.08
Therefore, the landscaper worked a total of 18.08 hours.
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Help please!!!!
Whoever answers right gets brainliest!
The equation of the axis of symmetry of the given quadratic function is x = -2. So, correct option is C.
The axis of symmetry of a parabola is a vertical line that passes through the vertex of the parabola. For a quadratic function in the form y = ax² + bx + c, the equation of the axis of symmetry is given by x = -b/(2a).
In the given equation, y = 2x² + 8x - 3, the coefficients of x² and x are a = 2 and b = 8, respectively. Substituting these values in the equation of the axis of symmetry, we get:
x = -b/(2a)
x = -8/(2*2)
x = -8/4
x = -2
This means that the parabola is symmetric about the vertical line x = -2. So the correct answer is x=-2.
So, correct option is C.
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Use synthetic division to rewrite the following fraction in the form q(x)+r(x)d(x)
, where d(x) is the denominator of the original fraction, q(x)is the quotient, and r(x) is the remainder.
The result of the synthetic division is:4x⁵+17x⁴+14x³-3x²+2 = (4x⁴ + 5x³ - x²) (x + 3) + 56
what is synthetic division ?
Synthetic division is a simplified method of dividing a polynomial by a linear factor. It is commonly used in algebra to find the quotient and remainder when dividing a polynomial by a linear factor of the form (x-a).
In the given question,
To use synthetic division to rewrite the fraction, we first set up the problem like this:
-3 | 4 17 14 -3 0 2
| -12 -15 3 0
+----------------------------------
4 5 -1 0 0 2
The coefficients of the polynomial are written in descending order of powers of x, with any missing terms replaced by zeros. The divisor, x + 3, is written on the left, and the first coefficient of the polynomial is written on the top of the vertical line.
We then proceed to perform synthetic division as follows:
Bring down the first coefficient, which is 4, and write it under the horizontal line.
Multiply the divisor, -3, by the number we just brought down, which gives -12. Write this number under the next coefficient, 17.
Add the two numbers, 17 and -12, to get 5. Write this number under the next coefficient, 14.
Multiply the divisor, -3, by 5, which gives -15. Write this number under the next coefficient, -3.
Add the two numbers, -3 and -15, to get -18. Write this number under the next coefficient, 0.
Multiply the divisor, -3, by -18, which gives 54. Write this number under the next coefficient, 2.
Add the two numbers, 2 and 54, to get 56. This is the remainder, which we write above the divisor.
The result of the synthetic division is:
4x⁵+17x⁴+14x³-3x²+2 = (4x^4 + 5x³ - x²) (x + 3) + 56
Therefore, we have rewritten the fraction in the desired form:
4x⁵+17x⁴+14x³-3x²+2
---------------------- = 4x⁴ + 5x³ - x² + 56/(x+3)
x+3
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Find f(-1).
Provide your answer below:
f(t)=-3t²-2t+1
Answer:
f(-1)=0
Step-by-step explanation:
To evaluate the function f(t) = -3t² - 2t + 1, we will start by plugging in -1 everywhere t occurs in the function :
[tex]\star \phantom{t-u} f(-1)=-3(-1)^2-2(-1)+1\\\\\\\star\phantom{t-u} f(-1)=-3*1+2+1\\\\\star\phantom{t-u} f(-1)=-3+3\\\\\underline{\star\phantom{t-u}f(-1)=0}[/tex]
[tex]\bigstar[/tex] Therefore the answer is f(-1) = 0
Element X is a radi
an experiment starts out with 490 grams of Element X, write a function to represent
the mass of the sample after t years, where the monthly rate of change can be found
from a constant in the function. Round all coefficients in the function to four decimal
places. Also, determine the percentage rate of change per month, to the nearest
hundredth of a percent.
If it takes 15 minutes for water in a pot to boil, the expression 20x+ 15 can be used to find the total time needed to cook x batches of boiled cornbread. Which expression can also be used to determine the total time needed to cook x batches of boiled cornbread? PLS ANSWER ASAPP I REALLY NEED TO ANSWER THIS QUESTION
A 18x + 4x + 6 + 7
B 10x + 10x + 20 - 5
C 6(5x + 5) - 10x + 15
D 3(x + x + x + 3)+ 2x + 15
the correct expression which can also be used to determine the total time needed to cook x batches of boiled cornbread is,
B) 10x + 10x + 20 - 5.
Given that;
The expression 20x + 15 represents the total time needed to cook x batches of boiled cornbread.
We can simplify this expression by factoring out the common factor of 5: = 20x + 15
= 5(4x + 3)
Therefore, the expression that can also be used to determine the total time needed to cook x batches of boiled cornbread must have a factor of 5 in it.
Option A:
18x + 4x + 6 + 7 does not have a factor of 5,
so it cannot be the correct answer.
Option B:
10x + 10x + 20 - 5
= 20x + 15,
which is the same as the original expression.
Therefore, Option B is equivalent to the original expression and can also be used to determine the total time needed to cook x batches of boiled cornbread.
Option C:
6(5x + 5) - 10x + 15 = 30x + 15 - 10x + 15 = 20x + 30,
which does not have a factor of 5.
Therefore, Option C is not correct.
Option D:
3(x + x + x + 3) + 2x + 15 = 9x + 6 + 2x + 15 = 11x + 21,
which does not have a factor of 5.
Therefore, Option D is not correct.
Therefore, the correct answer is,
B) 10x + 10x + 20 - 5.
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Denise is designing the seating arrangement for a concert at an outdoor theater. To give everyone a good view, each row must have 6 more seats than the row before it, and the 1st row can only have 11 seats. Explain to Denise how to create an equation to predict the number of seats in any row. Then using your equation. show your work to determine the number of seats in row 18.
Answer:113
Step-by-step Explanation:
To create an equation to predict the number of seats in any row, we need to start by defining a few variables:
Let's call the number of seats in the first row "a".
Let's call the number of additional seats in each row after the first row "d".
Since we know that each row has 6 more seats than the previous row, we can set d equal to 6:
d = 6
We also know that the first row has 11 seats, so we can set a equal to 11:
a = 11
To find the number of seats in any row, we can use the following formula:
number of seats in a given row = a + (n - 1) * d
Where "n" is the number of the row we are interested in.
Using this formula, we can find the number of seats in row 18:
number of seats in row 18 = 11 + (18 - 1) * 6
= 11 + 102
= 113
Therefore, there are 113 seats in row 18.
Question 6(Multiple Choice Worth 1 points)
(06.01 MC)
P
The cross-sectional areas of a triangular prism and a right cylinder are congruent. The triangular prism has a height of 5 units, and the right cylinder has a height of 5 units. Which
conclusion can be made from the given information?
O The volume of the prism is half the volume of the cylinder.
O The volume of the prism is twice the volume of the cylinder.
The volume of the prism is equal to the volume of the cylinder.
O The volume of the prism is not equal to the volume of the cylinder.
N
we cannot conclude that the volume of the prism is half the volume of the cylinder, twice the volume of the cylinder, or not equal to the volume of the cylinder.
How to solve the problem ?
The given information states that the cross-sectional areas of a triangular prism and a right cylinder are congruent, and both have a height of 5 units. Based on this information, we can conclude that the volumes of the two shapes may be equal, but we cannot conclude that the volume of the prism is half or twice the volume of the cylinder.
To determine the volumes of the two shapes, we need to know their respective formulas. The volume of a triangular prism is given by V = (1/2)bh, where b is the length of the base of the triangular cross-section and h is the height of the prism. The volume of a right cylinder is given by V = πr²h, where r is the radius of the circular cross-section and h is the height of the cylinder.
Since the cross-sectional areas of the two shapes are congruent, we can assume that their bases are similar. Therefore, the base of the triangular prism must be a triangle with the same area as the circular base of the cylinder. However, without further information about the shape and size of the cross-section, we cannot determine the values of b and r.
Therefore, we cannot conclude that the volume of the prism is half the volume of the cylinder, twice the volume of the cylinder, or not equal to the volume of the cylinder. The only conclusion that can be made is that the volume of the prism is equal to the volume of the cylinder, assuming that the cross-sectional areas are congruent.
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Question 10 of 10
A minor arc will have a measure that is
O A. less than 180°
B. equal to 180°
OC. more than 180°
Answer:
Less than 180
Step-by-step explanation:
Minor: Less than 180
Major: More than 180
What is the length of the side labeled x cm?
10.8
13.7
9.9
20.8
Answer:
B
Step-by-step explanation:
the answer is B because I know it
y + 6 < 10 or 2y - 3> 9
Answer:
2y - 3> 9 it is not y + 6< 10
Please help me with this math problem
1. Josiah is making a candle by pouring melted wax into a mold in the shape of a square pyramid. Each side of the base of the pyramid is 12 in and the height of the pyramid is 14in. To get the wax for the candle, Josiah melts cubes of wax that are each 6 in by 6 in by 6 in. How many of the wax cubes will Josiah need in order to make the candle? Show your work.
Answer:
10 wax cubes
Step-by-step explanation:
the volume of the square pyramid can be found by using the following formula:
[tex]V = \frac{1}{3} * B * h[/tex]
where b is the base of the pyramid and h is the height of the pyramid
The area of the base of the pyramid is given as 12 in * 12 in = 144 in^2
So, the volume of the pyramid is:
V = (1/3) * 144 in^2 * 14 in = 2,016 in^3
Each wax cube has a volume of 6 in * 6 in * 6 in = 216 in^3.
To find the number of wax cubes needed, we can divide the volume of the pyramid by the volume of each wax cube:
Number of wax cubes = Volume of pyramid / Volume of each wax cube
Number of wax cubes = 2,016 in^3 / 216 in^3
Number of wax cubes = 9.33 (rounded to two decimal places)
Since we can't have a fraction of a wax cube, Josiah will need to use 10 wax cubes to make the candle.
cost function definition
I-Ready
What is the distance between point P and point Q?
You deposit $3000 each year into an account earning 7% interest compounded annually. How much will you have in the account in 30 years?
The amount you will have in the account in 30 years is $22836.77
How much will you have in the account in 30 years?From the question, we have the following parameters that can be used in our computation:
You deposit $3000 each year 7% interest compounded annually.Using the above as a guide, we have the following:
Amount = P * (1 + r)^t
Where
P = Principal = 3000
r = Rate = 7%
t = time = 30
Substitute the known values in the above equation, so, we have the following representation
Amount = 3000 * (1 + 7%)^30
Evaluate
Amount = 22836.77
Hence, the amount is 22836.77
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A worker completes a job in a certain number of hours. The standard time allowed for the job is 10 hours, and the hourly rate of wages is Re. 1. The worker earns at the 50% rate a bonus of Rs. 2 under Halsey Plan. Ascertain his total wages under the Rowan Premium Plan.
HELPPPPPPPPP GNG IM STURGGLING 100 POINTS
Guadalupe's credit card has an APR of 23%, calculated on the previous monthly balance, and a minimum payment of 2%, starting the month after the first purchase. Her credit card record for the last 7 months is shown in the table below. End of month 2 3 5 6 7 Previous balance $0.00 $900.00 $899.25 $898.50 $897.75 $897.00 $896 26 New charges $900.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 Payment Finance Principal received charges paid $0.00 $0.00 $0.00 $18.00 $17.99 $17.97 $17.96 $17.94 $17.93 How is the new balance calculated? $17.25 $17.24 $17.22 $17.21 $17.19 $17.18 $0.75 $0.75 $0.75 $0.75 $0.75 $0.75 New balance $900.00 $899.25 $898.50 $897.75 $897.00 $896.26 $895.51
Answer:$909.03
Step-by-step explanation:he new balance on Guadalupe's credit card is calculated as follows:
First, we calculate the interest charged on the previous balance. Since the APR is 23%, the monthly interest rate is 23%/12 = 1.92%. So the interest charged on the previous balance for the month is:
Interest = Previous balance x Monthly interest rate
= $900.00 x 1.92%
= $17.28
Next, we add the finance charge, which is calculated as 1% of the previous balance plus any new charges. So the finance charge for the month is:
Finance charge = 1% x (Previous balance + New charges)
= 1% x ($900.00 + $0.00)
= $9.00
The total amount due is the sum of the previous balance, the interest charged, and the finance charge:
Total amount due = Previous balance + Interest + Finance charge
= $900.00 + $17.28 + $9.00
= $926.28
The minimum payment due is 2% of the total amount due, which is:
Minimum payment = 2% x Total amount due
= 2% x $926.28
= $18.53
If the minimum payment is less than $25, the minimum payment due is $25. So in this case, the minimum payment due is $25.
Guadalupe made a payment of $18.00, which is less than the minimum payment due, so she will be charged a late fee in addition to the interest on the unpaid balance.
The principal paid is the difference between the payment made and the interest charged, which is:
Principal paid = Payment - Interest
= $18.00 - $17.28
= $0.72
The new balance is the sum of the previous balance, any new charges, and the interest charged, minus the payment made, plus any finance charge and late fee:
New balance = Previous balance + New charges + Interest - Payment + Finance charge + Late fee
= $900.00 + $0.00 + $17.28 - $18.00 + $9.00 + $0.75
A cylinder with a radius of 8 inches is cut from the prisim. What is the volume of the new object
The volume of the new object is approximately 439.3 cubic inches
What is the volume of the new object?To find the volume of the new object, we need to first know the volume of the prism before the cylinder is removed hence we do this:
The volume of a cylinder: = πr²h
where:
r = radius
h = height
Note that the volume of a rectangular prism is : = lwh
l = length
w = width
h = height
Assumption: In the above case, we will assume that the dimensions of the rectangular prism because the cylinder can be cut out from the center of one of the faces.
Hence the length and width of the prism will be taken to be twice the radius of the cylinder, that is 16 inches, and the height will be taken to be same as the radius of the cylinder, that ia 8 inches.
So V_prism = lwh
= 16 × 16 × 8
= 2048 cubic inches
V_cylinder = πr²h
= π × 8² × 8
= 512 π cubic inches
Hence To get the volume of the new object, we need to subtract the volume of the cylinder from the volume of the prism:
V_new = V_prism - V_cylinder
= 2048 - 512π
= 2048 - 1608.70
= 439.3 cubic inches
Hence, the volume of the new object is about 439.3 cubic inches
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