A rectangular prism and a cylinder both have a height of 8m, and their cross-sectional areas are equal at every level parallel to their respective bases.
Complete the steps to find the prism.
Answers
1) [tex]V=lwh=5(x)(8)=\boxed{40x}[/tex]
2) [tex]V=\pi r^{2}h=(\pi)(3^{2})(8)=\boxed{72}\pi[/tex]
3) [tex]40x=72\pi\\\\x=\frac{72\pi}{40} \approx \boxed{5.7}[/tex]
Related Questions
Given positive integers $x$ and $y$ such that $2x^2y^3 + 4y^3 = 149 + 3x^2$, what is the value of $x + y$?
Answers
Answer:
5
Step-by-step explanation:
2x²y³ + 4y³ = 149 + 3x²
[tex] 2x^2y^3 - 3x^2 = 149 - 4y^3 [/tex]
[tex] x^2(2y^3 - 3) = 149 - 4y^3 [/tex]
[tex] x^2 = \dfrac{149 - 4y^3}{2y^3 - 3} [/tex]
[tex] x = \pm \sqrt{\dfrac{149 - 4y^3}{2y^3 - 3}} [/tex]
Try y = 1
[tex]x = \pm \sqrt{\dfrac{149 - 4(1)}{2(1)^3 - 3}} = \pm \sqrt{-145} = i\sqrt{145}[/tex]
For y = 1, x is imaginary.
Try y = 2
[tex] x = \pm \sqrt{\dfrac{149 - 4(2)^3}{2(2)^3 - 3}} = \pm \sqrt{9} = \pm 3[/tex]
Since x and y are positive integers, ignore x = -3.
When x = 3, y = 2.
x + y = 3 + 2 = 5
The value of x + y is 5.
What is Polynomial?Polynomials are expressions which consist of variables, constants, coefficients and exponents.
We have the equation,
2x²y³ + 4y³ = 149 + 3x²
2x²y³ - 3x² = 149 - 4y³
x² (2y³ - 3) = 149 - 4y³
x² = (149 - 4y³) / (2y³ - 3)
x = √[(149 - 4y³) / (2y³ - 3)]
Now, we have to find two positive integers.
We can use trial and error method here.
Trial putting y = 1.
x = √[(149 - 4 × 1³) / (2 × 1³ - 3)]
= √[145 / (-1)]
= √(-145)
There is no real root for √(-145). So y = 1 is not applicable.
Trial putting y = 2.
x = √[(149 - 4 × 2³) / (2 × 2³ - 3)]
= √[117 / 13]
= √(9)
= ± 3
But we need positive integers. So we ignore -3.
So x = 3 and y = 2 ⇒ x + y = 5
Hence x + y = 5.
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Lashawn makes scrambled eggs with 3 spoonfuls of salsa for every 2 eggs. Gilberta adds 7 spoonfuls of salsa for every 5 eggs.
Whose scrambled eggs have a stronger salsa taste?
A. Lashawn's eggs
B. Gilberta's eggs
C. The dishes of scrambled eggs have equal salsa tastes
Answers
Lashawn's scrambled eggs have a stronger salsa taste than Gilberta's scrambled eggs. Then the correct option is A.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
Lashawn makes scrambled eggs with 3 spoonfuls of salsa for every 2 eggs.
Gilberta adds 7 spoonfuls of salsa for every 5 eggs.
Then the scrambled eggs have a stronger salsa taste will be
Lashawn's eggs = 3/2 = 1.5
Gilberta's eggs = 7/5 = 1.4
Lashawn's scrambled eggs have a stronger salsa taste than Gilberta's scrambled eggs.
Then the correct option is A.
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Find the equation of the line that
is perpendicular to y = -8x + 2
and contains the point (-4,1).
Answers
Answer:
Step-by-step explanation:
slope of line ⊥ to y=-8x+2
is -1/-8=1/8
eq. of line with slope 1/8 thro' (-4,1) is
y-1=1/8 (x+4)
8y-8=x+4
8y=x+4+8
8y=x+12
y=1/8 x+12/8
or
y=1/8 x+3/2
also can someone check this too? just want to make sure i got the the first part right before proceed further
Answers
Answer:
the answers are all right
If each pound of beef costs $3.69, how much does 2 pounds cost? Round to the nearest cent.
Answers
Answer: Two pounds of beef costs $7.38.
Step-by-step explanation:
Multiply the cost for one pound by the amount of pounds you need.
$3.69×2=$7.38
I hope this helps!!
A cliff on the seashore is eroding at the rate of 17 cm per year. Write and solve an equation to find the number of years in which the cliff will erode 85cm.
Answers
Answer: 0.2 years
Step-by-step explanation:
The set of all numbers greater than or equal to −5 and less than 5.
Answers
Answer:
No. greater than of equal to (-5) = -4,-3,-2,-1,0,1,2,3,4,5,6...........
No. less than 5 = 4,3,2,1 ,0,-1......
{ -4,-3,-2,-1,0,1,2,3,4}
what is (x^2y^3)^1/3 / 3 sqrt x^2
Answers
Answer: y/(3x^1/3)
Step-by-step explanation:
Challenge time! Isn't time to give your brains a break? Its a fun challenge! EARN 20 POINTS NOW
Answers
Answer:
The answer is 64
Step-by-step explanation:
If you find this answer helpful pls mark it the brainliest answer
it's easy 64 the key is in the pic.
Reuben rented a truck for one day. There was a base fee of $14.95, and there was an additional charge of 80 cents for each mile driven. Reuben had to pay
$135.75 when he returned the truck. For how many miles did he drive the truck?
Answers
Answer:
hczgdjatulsfulsitsfisfula7tl7roa7pts
Identify each pair of angles as corresponding, alternate interior, alternate exterior, same-side interior, vertical, or adjacent
Answers
1) Alternate exterior
2) Corresponding
3) Alternate exterior
4) Alternate exterior
5) Vertical
6) Corresponding
7) Adjacent
8) Corresponding
9) Corresponding
10) Alternate interior
my sis needs help asap SHOW WORK! :)
Answers
Step-by-step explanation:
el resultado le puedo ayudar si sabe Spanish
Answer:
see below
Step-by-step explanation:
White = 1 1/3 = 4/3 = 16/12
Color = 3/4 = 9/12
white - color == 16/12 - 9/12 = (16-9) / 12 = 7/12 of a scoop more for the white load
find the slope of the line that passes through (3,10) and (1,17)
Answers
Answer:
[tex]m=- \frac{7}{2}[/tex]
Step-by-step explanation:
The slope of a line passing through the two points [tex]\displaystyle{\large{{P}={\left({x}_{{1}},{y}_{{1}}\right)}}}[/tex] and[tex]\displaystyle{\large{{Q}={\left({x}_{{2}},{y}_{{2}}\right)}}}[/tex] is given by [tex]\displaystyle{\large{{m}=\frac{{{y}_{{2}}-{y}_{{1}}}}{{{x}_{{2}}-{x}_{{1}}}}}}[/tex].
We have that [tex]x_1=3[/tex], [tex]y_1=10[/tex], [tex]x_2=1[/tex], [tex]y_2=17[/tex].
Plug the given values into the formula for slope: [tex]m=\frac{\left(17\right)-\left(10\right)}{\left(1\right)-\left(3\right)}=\frac{7}{-2}=- \frac{7}{2}[/tex]
Answer: the slope of the line is [tex]m=- \frac{7}{2}[/tex].
Answer:
slope = - [tex]\frac{7}{2}[/tex]
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{x_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (3, 10 ) and (x₂, y₂ ) = (1, 17 )
m = [tex]\frac{17-10}{1-3}[/tex] = [tex]\frac{7}{-2}[/tex] = - [tex]\frac{7}{2}[/tex]
Instructions: Write the equation of the line in Point-Slope Form
given the information below. Use Point One.
Point One (-3, 3)
=
Point Two (-2,-1)
Point-Slope
=
Point-Slope Form:
Answers
Answer: [tex]y-3=-4(x+3)[/tex]
Step-by-step explanation:
The slope is
[tex]\frac{-1-3}{-2-(-3)}=\frac{-4}{1}=-4[/tex]
So, using the point (-3, 3) to substitute into point-slope form, the equation is [tex]\boxed{y-3=-4(x+3)}[/tex]
URGENT + 20 Points! The regression equation for water being poured into a large, cone-shaped cistern is In(volume) = -1.327 +2.993 In(Time). What is the predicted volume for a time of 12 seconds?
- There is a line above "(volume)"
1.810 cm3
6.110 cm3
34.589 cm3
450.485 cm3
Answers
The predicted volume for a time of 12 seconds of the large, cone-shaped cistern is; V = 450.485 cm³
How to Solve Regression Equations?We are given the regression equation;
In V = -1.327 + 2.993 In T
Where;
V is volume
T is time
At T = 12, we have;
In V = -1.327 + 2.993 In 12
In V = -1.327 + 7.4373
In V = 6.1103
V = e^(6.1103)
V = 450.485 cm³
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Find the area.
help pls
Answers
Answer:
30 square feet
Step-by-step explanation:
The area of a trapezoid is equal to (a+b)/2 * h
In this case, the value of a is 5, b is 10, and h is 4. You can substitute those numbers into the formula and get the answer of 30.
Find the ratio of 18 inches to 2 yards B
A. 3/4 B. 1/4
C. 1/5 D. 2/5
Answers
Answer:
B. 1 / 4
Step-by-step explanation:
Step 1: We can turn 2 yards into 6 feet.
Step 2: Then we can turn 6 feet into 72 inches.
Step 3: We plug it into the ratio, getting 18 / 72.
Step 4: Simplify. We get 1 / 4 as the answer. Therefore, we choose B.
Need help with algebra homework
Answers
Answer:
the answer for this problem is A, big
how many ways are there to make $3 with pennies, nickels, and dimes
Answers
Answer:
10
Step-by-step explanation:
if the third place value of a number is 64 , What base is the number in ?
A) 2
B) 4
C) 8
D) 16
Answers
Answer:
B
Step-by-step explanation:
4, 16, 64 should be the correct order
Simplify this problem!!!
Answers
Answer:
C
Step-by-step explanation:
HOPE THAT HELPSBDNQBDB
PLEASE HELP ME WITH MY MATH
Answers
The definition for the graphed function is the one shown in option d:
y = -x + 2 if x < 1
y = -2x + 1 if x ≥ 1.
Which piecewise function coincides with the graph?Here we have a piecewise function, where for the first part we have a linear equation with a negative slope (for x < 1, we know that the symbol "<" must be used because of the open dot at the end of the line).
Then, we have another linear equation with a negative (and steeper) slope. This time there is a closed dot, so the domain for this second part is x ≥ 1.
With that we can conclude that the correct option is:
d:
y = -x + 2 if x < 1
y = -2x + 1 if x ≥ 1.
Where you can see that the second part has a larger (in module) slope, and the domains are defined as we saw above.
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You are given that cos(A)=−5/13, with A in Quadrant II, and sin(B)=7/25, with B in Quadrant II. Find cos(A+B). Give your answer as a fraction.
Answers
The value of cos(A+B) is 36/325.
What is Trigonometry?The branch of mathematics concerned with specific functions of angles and their application to calculations.
Given:
cos(A)=−5/13
sin(B)=7/25
Now Using identity,
sin²A + cos² A= 1
sin A= √1 - cos² A
sin A = √1- 25/169
sin A= √144/169
sin A= 12/13
Again,
sin²B + cos² B= 1
cos B= √1 - sin² B
cos B = √1- 49/625
cos B= √576/625
cos B= -24/25
Now,
cos (A +B) = cos A cos B - sin A sin B.
= -5/13* (-24/25) - 12/13* 7/25
= 120/325 - 84/325
= 36/325
Hence, the value of cos (A + B) is 36/325.
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Problem
Suppose that J is between H and K. If HJ=2x+4, JK=3x+3, and KH=22, find the lengths of HJ and JK. Remember to always draw an image first and to pay attention to what the question is asking for!
Solution
Find the Segment Addition Postulate
Use the Segment Addition Postulate and then substitute what we know. Do not use any spaces in your answers.
HJ+JK= Answer
( Answer
)+( Answer
)= Answer
Find x
Once we combine our like terms we get:
Answer
x+ Answer
= Answer
x= Answer
Find HJ and JK
Our questions asked us for the lengths of HJ and JK so we must plug in the value of x to solve for those values. We were given HJ=2x+4 and JK=3x+3.
HJ=2x+4
HJ=2( Answer
)+4
HJ= Answer
And
JK=3x+3
JK=3( Answer
)+3
JK= Answer
3x-4
Check Work
View checked work
Answers
Answer:
The lengths of HJ and JK are 50 and 72 respectively.
Given:
J is between H and K.
HJ=2x+4
JK=3x+3
HK=22
Step-by-step explanation:
The total length is given as:
HJ+JK=HK
⇒ (2x+4)+(3x+3)=22
⇒ 5x+7=22
⇒ 5x=22-7
⇒ 5x=15
⇒ x=3
Thus, the length of HJ is (2x+4)=(2*3+4)=10
And the length of JK is (3x+3)=(3*3+3)=12
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The lengths of HJ and JK are 50 and 72 respectively.
Given: J is between H and K. the length of HJ=2x+4, JK=3x+3, and HK=22.
The line HJ and JK are collinear then the total length is given as: HJ+JK=HK
substitute values
⇒ (2x+4)+(3x+3)=22
⇒ 5x+7=22
⇒ 5x=22-7
⇒ 5x=15
⇒ x=3
Thus, the length of HJ is (2x+4)=(2*3+4)=10
And the length of JK is (3x+3)=(3*3+3)=12
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find the area dimensions are in centimeters.
Answers
Answer:
[tex]9600cm^{2}[/tex]
Step-by-step explanation:
Get the area of the triangle and the rectangle, then subtract the triangle's area for the rectangle's
Suppose we have already saved $55 towards the cost of a new television set.
We plan to save $6 more each week for the next several weeks.
i) Write an equation for the total amount T we will have after w weeks from now.
ii) Find the total amount that would be saved after 8 weeks.
Answers
Step-by-step explanation:
T = 55 + 6w
after 8 week $103
George buys a computer. He pays a deposit of £200 and six monthly instalments of £55_
How much does George pay for his computer in total?
Answers
Want to earn 20 points for correct answer CLICK ME
Answers
Answer:
64 is the answer
Step-by-step explanation:
Mark me brainliest answer pls
Is 3.5 greater than 3.39
Answers
Answer:
yes
Step-by-step explanation:
Calculate the length of the diagonal of the state of Wyoming.
Answers
The length of the diagonal of the state of Wyoming is 457 miles.
What is the length of the diagonal?The length of the diagonal of the diagonal can be determined using Pythagoras theorem.
The Pythagoras theorem: a² + b² = c²
where:
a = lengthb = basec = hypotenuse√365² + 275² = 457 miles
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