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2 years ago

13

Which ordered pair is the solution to the system of equations?

1 answer:

kozerog [31]2 years ago

8 0

The answer and process is shown in the following picture

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The frog population at a lake doubles every three weeks. The population can be modeled by f(x)=15(2)^x and f(6)=960. What does t

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We have to answer what does the 15 represent in the function : f ( x ) = 15 * 2^x, which models the increasing of the frog population at a lake. We know that the frog population doubles every 3 weeks and that: f ( 6 ) = 960. It means that: 15 * 2^ 6 = 15 * 64 = 960. And also f ( 0 ) = 15 * 2^0 = 15 * 1 = 15. Therefore it is a starting population. Answer: The 15 represents <span>B - The starting population.</span>

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A vertical cylinder is leaking water at a rate of 4m3/sec. If the cylinder has a height of 10m and a radius of 2m, at what rate

Katyanochek1 [597]

Answer:

Therefore the rate change of height is $\frac{1}{\pi}$ m/s.

Step-by-step explanation:

Given that a vertical cylinder is leaking water at rate of 4 m³/s.

It means the rate change of volume is 4 m³/s.

$\frac{dV}{dt}=4 \ m^3/s$

The radius of the cylinder remains constant with respect to time, but the height of the water label changes with respect to time.

The height of the cylinder be h(say).

The volume of a cylinder is $V=\pi r^2 h$

$=( \pi \times 2^2\times h)\ m^3$

$\therefore V= 4\pi h$

Differentiating with respect to t.

$\frac{dV}{dt}=4\pi \frac{dh}{dt}$

Putting the value $\frac{dV}{dt}$

$\Rightarrow 4\pi \frac{dh}{dt}=4$

$\Rightarrow \frac{dh}{dt}=\frac{4}{4\pi}$

$\Rightarrow \frac{dh}{dt}=\frac{1}{\pi}$

The rate change of height does not depend on the height.

Therefore the rate change of height is $\frac{1}{\pi}$ m/s.

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