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tigry1 [53]
3 years ago
8

An inverted pyramid is being filled with water at a constant rate of 50 cubic centimeters per second. The pyramid, at the top, h

as the shape of a square with sides of length 8 cm, and the height is 15 cm. Find the rate at which the water level is rising when the water level is 3 cm.

Mathematics
2 answers:
Ipatiy [6.2K]3 years ago
7 0

Answer:

19.53125 cm/s

Step-by-step explanation:

h : s

15 : 8

s/h = 8/15

s = 8h/15

V = ⅓×s²×h

V = ⅓(8h/15)²×h = 64h³/675

dV/dh = 64h²/225

At h=3,

dV/dh = 64(3²)/225 = 64/25

dh/dV = 25/64

dV/dt = 50

dh/dt = dh/dV × dV/dt

= 25/64 × 50

= 19.53125 cm/s

klio [65]3 years ago
3 0

Step-by-step explanation:

Below is an attachment containing the solution.

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The two triangles are similar.
Neko [114]

Given that the triangles are similar.

When triangles are similar, all three pairs of corresponding sides are in the same ratio.

Similarly in the given triangles, the ratio of the corresponding sides are equal.

\frac{8}{2x-2}= \frac{8+6}{3x}

\frac{8}{2x-2}= \frac{14}{3x}

Cross multiplying, we get

8 \times 3x = 14 \times (2x-2)

24x = 28x-28

-4x = -28

Dividing both sides of the equation by -4.

So, we get

x = 7.

7 0
3 years ago
Read 2 more answers
Which expressions are equivalent to (7^-2)*(7^6)
Ierofanga [76]

Answer:

D

Step-by-step explanation:

(7^-2)*(7^6)=7^-2+6

......since the base 7 is the same, when u multiply them, you should add the exponents and keep 7 as it is. That will be 7^4, which in equivalent to ans D(7^2)^2.

8 0
2 years ago
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May I please get help with other this problem for I am confused as I have tried multiple times to get the right answer
Aleks [24]

Using pythagoras

\begin{gathered} x^2=16^2+12^2 \\ x^2=256+144 \\ x^2=400 \\ \text{Take the square root} \\ x=20 \end{gathered}

The final answer

20

5 0
1 year ago
Consider the function f ( x ) = 1 − 4 x 2 on the interval [ − 1 , 3 ] . Find the average or mean slope of the function on this i
Blababa [14]

Answer:

The average slope is 8.

Step-by-step explanation:

Let <em>f</em> be defined on the closed interval [a, b]. The average slope of <em>f </em>between a and b is the quotient

                                       average slope = \frac{f(b)-f(a)}{b-a}

To find the average slope of the function f(x)=1-4x^2 on the interval [-1, 3] you have to evaluate your function in the interval and then divide by the interval.

So,

f(-1)=1-4(-1)^2=-3\\\\f(3)=1-4(3)^2=-35

The average slope is  \frac{f(3)-f(-1)}{3+1}= \frac{-3+35}{3+1}=\frac{32}{4}=8

4 0
3 years ago
a carpenter cut four lengths of wood. the lengths were 36 3/4 in., 36 3/8 in., 37 1/2., and z in. if the mean of lengths is 36 5
lisov135 [29]
36 3/4 = 36.75
36 3/8 = 36.375
37 1/2 = 37.5
36 5/8 = 36.625

(36.75 + 36.375 + 37.5 + z) / 4 = 36.625
(110.625 + z) / 4 = 36.625
110.625 + z = 36.625 * 4
110.625 + z = 146.5
z = 146.5 - 110.625
z = 35.875 or 35 7/8 <===
6 0
3 years ago
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