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kompoz [17]
3 years ago
10

The side of the base of a square pyramid is increasing at a rate of 666 meters per minute and the height of the pyramid is decre

asing at a rate of 111 meter per minute. At a certain instant, the base's side is 333 meters and the height is 999 meters. What is the rate of change of the volume of the pyramid at that instant (in cubic meters per minute)
Mathematics
1 answer:
Otrada [13]3 years ago
8 0

Answer:

105m^3/min

Step-by-step explanation:

We are given that

Base side of square pyramid, a=3 m

Height of square pyramid, h=9m

\frac{da}{dt}=6m/min

\frac{dh}{dt}=-1/min

We have to find  the rate of change of the volume of the pyramid at that instant.

Volume of square pyramid, V=\frac{1}{3}a^2h

Differentiate w.r.t t

\frac{dV}{dt}=\frac{1}{3}(2ah\frac{da}{dt}+a^2\frac{dh}{dt})

Substitute the values

\frac{dV}{dt}=\frac{1}{3}(2(3)(9)(6)+(3^2)(-1)

\frac{dV}{dt}=105m^3/min

Hence, the rate of change of the volume of the pyramid at that instant=105m^3/min

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Answer:

3 inches to the right

Step-by-step explanation:

The first birdhouse is 27.7 inches to the right

The second birdhouse is 24.9 inches to the left  or -24.9  ( left is negative)

The distance between is  found by adding the distances

27.7 - (24.9)

27.7-24.9 =2.8

2.8

Rounding to the nearest integer

3 inches apart

Using integers

28 - (25)

3 inches

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2 years ago
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The locations, given in polar coordinates, for two ships are (8 mi, 63º) and (8 mi, 123º). Find the distance between the two shi
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The arrangement forms an isosceles triangle with equal legs of 8 mi. The angle between the legs is,

123-63 = 60°. Therefore, the other two angles ares:

Angles = (180-60)/2 = 120/2 = 60°

It can therefore be noted that all angles are equal and thus the resulting triangle is actual an equilateral triangle and thus all the sides are equal.

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3 years ago
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Find the least number which must be added to 6203 to obtain a perfect square.
andrey2020 [161]

Answer:

79

Step-by-step explanation:

       78

         ---------

7 |       62 03 

          49

         ----------

148 |   13 03

          11 84

         -----------

            19

         -----------

78^2 = 6084.

We observe that 78^2 < 6203.

79^2 = 6241.

We observe that 79^2 > 6203.

Hence the number to be added to 6203 is 6241 - 6203 = 38.

6203 + 38 = 3241

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Therefore 38 should be added to 6203 to obtain a perfect square.

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3 years ago
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Dimas [21]

Answer:

2y+1=0

Step-by-step explanation:

a number one greater than y is y+1

so sum of y and y+1= 2y+1

3 0
3 years ago
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Please help I really need help
katrin2010 [14]

Answer:

No

Step-by-step explanation:

Use the vertical line test, you can conclude that this is not a function.

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