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Romashka [77]
2 years ago
6

An inverted pyramid is being filled with water at a constant rate of 35 cubic centimeters per second. The pyramid, at the top, h

as the shape of a square with sides of length 6 cm, and the height is 8 cm. Find the rate at which the water level is rising when the water level is 3 cm.
Mathematics
1 answer:
Anna [14]2 years ago
8 0

Answer:

6.913 cubic-meters/second.

Step-by-step explanation:

Volume of pyramid is.

$v = \frac{s^2 h}{3} $$

and

\frac{dv}{dt}=35cubic meters/sec.

we essentially need to compute derivative at h = 3.

but firs we need to write s in terms of h only, to do that we use the fact that ration of side to height of a pyramid is always constant, which means.

$\frac{S}{h} = \frac{6}{8}= \frac{3}{4}   $

solving for s and substituting in Volume function gives.

$v =\frac{3h^{3} }{16} $

and taking derivative with respect to time gives.

$\frac{dv}{dt}=\frac{9h^2}{16}\frac{dh}{dt}

but we have been given that piece of information so.

$35 = \frac{9h^2}{16}\frac{dh}{dt}  $

at h = 3 in above we have finally.

\frac{dh}{dt} = 6.913.

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If ray JG is an angle bisector of ∠FJH, find m∠FJH.
miss Akunina [59]

Answer:

m∠FJH=60°

Step-by-step explanation:

The complete question is

JG bisects FJH, FJG= (2x + 4)° and GJH = (3x -9)°  

What is FJH

we know that

m∠FJH=m∠FJG+m∠GJH -----> equation A

If ray JG is an angle bisector of ∠FJH

then

m∠FJG=m∠GJH -----> equation B

substitute the given values in equation B and solve for x

(2x + 4)°=(3x -9)°

3x-2x=4+9

x=13

Find the measure of angle FJH

m∠FJH=(2x + 4)°+(3x -9)°

substitute the value of x

m∠FJH=(2(13) + 4)°+(3(13) -9)°

m∠FJH=(30)°+(30)°

m∠FJH=60°

3 0
2 years ago
108 divided by 9 times (-12) dived by 6 - (100 divided by 5)
Nataliya [291]

108 divided by 9 = 12 x -12 = -144 divided by 6 = -24 - (100 divided by 5) =

-24 - 20 = -44

answer= -44

3 0
2 years ago
Read 2 more answers
Katarina bought a package of 500 stickers. Each sheet in the package has 20 stickers.
Mashcka [7]
I think there are 125 heart stickers and 375 star stickers. 20/4 = 5, so there are 5 heart stickers per sheet. there are 25 sheets in the package, 5 x 25 = 125. if the remaining stickers on a sheet are stars then there are 15 star stickers per sheet. 15 x 25 = 375.
5 0
2 years ago
Jamie just bought two boxes.The first box is square with each side measuring 10 units and is 4 units high.The second box is rect
MakcuM [25]
Step 1
find the volume of the square box
volume=area of the base*height
area of the base=10²-----> 100 units²
height=4 units
volume square box=100*4----> 400 units³

step 2
volume rectangular box=2*volume square box
volume rectangular box=2*400------> 800 units³

volume rectangular box=L*W*H
H=5 units
W=10 units
Volume=800 units³
800=L*10*5------> solve for L
L=800/(10*5)------> L=16 units

the answer is
the length of the rectangular box is 16 units

7 0
3 years ago
The cup, on the 9th hole of a golf course, is located, dead center, in the middle of a circular green, which is 35 feet in radiu
ale4655 [162]

Answer:

± 27.33 ft

Step-by-step explanation:

For the given problem, we can estimate the initial and final coordinates of the line of the ball path as (-40,-50) and (0,0). Therefore, the slope is:

(-50-0)/(-40-0) = 50/40 = 1.25

Similarly, we can estimate the slope of a perpendicular line to the line of the ball path as: -1*(1/1.25) = -0.8.

Therefore, using (0,0) and the slope -0.8, the equation of the perpendicular line is: -0.8 = (y-0)/(x-0);

-0.8 = y/x

y = -0.8x

Furthermore, we are given the circle radius as 35 ft and we can use the distance formula to find the two points 35 ft far from the origin:

35^2 = x^2 + y^2

y = -0.8x

35^2 = x^2 + (-0.8x)^2

1225 = (x^2 + 0.64x^2)

1225 = 1.64x^2

x^2 = 1225/1.64 = 746.95

x = sqrt(746.95) = ± 27.33 ft

5 0
2 years ago
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