Mathematics, 17.07.2019 01:30 unkn03n78

An inverted pyramid is being filled with water at a constant rate of 50 cubic centimeters per second. the pyramid, at the top, has the shape of a square with sides of length 6 cm, and the height is 14 cm. find the rate at which the water level is rising when the water level is 6 cm.

Answers: 3

Show answers

Answers

Answer from: kordejah348

dh=30.25 cm/sec

Step-by-step explanation:

1. the first recommend step is to make a sketch of the situation. We draw the triangle representing the pyramid and we label the sides. (as the picture attached)

2. What we need to find is the change of the height of the water with respect the time (dh/dt), so we need to find an equation that allow us to find that. We start with the equation of the volume of the pyramid which is $V=\frac{b^2h}{3}$ . To find (dh/dt) it is necessary to take the derivative of this equation, however, the equation involves two variables (b and h). We only can derive if the equation is in terms of only one variable. therefore, we need to find another equation to do this.

3. Applying ratios of triangle, we can find and expression that relates b with h. To apply this ratio, it is necessary to split the triangle drawn in step 1, so we will form a right triangle. To apply the ratio of triangle we follow the next formula: $\frac{height1 }{base1} =\frac{height2}{base2}$

Where the subscript 1 is referring to the triangle 1 and the 2 to the triangle 2.

Replacing the values and isolating "b" we get...

$\frac{14}{3} =\frac{h}{b} \\\\b= \frac{3h}{14}$

4. Now we can replace the equation 2 into 1 and we get the volume of the pyramid in terms of only one variable (h)

5. Take the derivative of the last equation

6. isolate dh (dh is what we need to find, dh means how the height changes with respect the time)

An inverted pyramid is being filled with water at a constant rate of 50 cubic centimeters per second

Answer from: Quest

answer: about 22.67

step-by-step explanation:

Answer from: Quest

option: d is the correct answer.

d) none of the above.

step-by-step explanation:

clearly from the figure attached to the question we could see that there is no shape given. hence without any shape given in the figure and after rotation we can't obtained a square pyramid.

since, to obtain a image we need a proper figure of the pre-image so that it can be transformed.

hence, the correct answer is:

d) none of the above.

step-by-step explanation:

Another question on Mathematics

Mathematics, 21.06.2019 19:50

A3-dimensional figure has a square base and 4 lateral faces that meet at a point. explain the difference between the cross sections when a slice is made perpendicular to the base through the vertex, and when a slice is made perpendicular to the base and not through the vertex

Answers: 2

Answer

Mathematics, 21.06.2019 19:50

Table which ratio is equivalent to 3: 7? 6: 7 3: 21 24: 56 15: 30

Answers: 1

Answer

Mathematics, 21.06.2019 23:00

Square a has a side length of (2x-7) and square b has a side length of (-4x+18). how much bigger is the perimeter of square b than square a?and show all work! you so

Answers: 2

Answer

Mathematics, 21.06.2019 23:00

Aremote-controlled boat can travel at 4 feet per second in calm water. the boat traveled 48 feet with the current, and then it traveled 16 feet against the current in the same amount of time. how fast is the current?

Answers: 1

Answer

You know the right answer?

An inverted pyramid is being filled with water at a constant rate of 50 cubic centimeters per second...

Questions