The water level in a tank can be modeled by the function h(t)=8cos(pi t /7)+11.5, where t is the number of

Mathematics

1 answer:

denis23 [38]3 years ago

4 0

Answer:

NO amount of hour passed between two consecutive times when the water in the tank is at its maximum height

Step-by-step explanation:

Given the water tank level modelled by the function h(t)=8cos(pi t /7)+11.5. At maximum height, the velocity of the water tank is zero

Velocity is the change in distance with respect to time.

V = {d(h(t)}/dt = -8π/7sin(πt/7)

At maximum height, -8π/7sin(πt/7) = 0

-Sin(πt/7) = 0

sin(πt/7) = 0

Taking the arcsin of both sides

arcsin(sin(πt/7)) = arcsin0

πt/7 = 0

t = 0

This shows that NO hour passed between two consecutive times when the water in the tank is at its maximum height

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Which of the following graphs represents the function f(x) = x4 - 2x3 - 3x2 + 4x + 1?

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Answer: Graph D will be correct graph for the given function.

Explanation:

Given function $f(x) = x^4-2x^3-3x^2+4x+1$

Since it is a bi-quadratic equation thus it must have 4 roots and (0,1) is one of its point.

Moreover, the degree of the function is even thus the end behavior of the function is $f(x)\to+\infty$ , as $x\to-\infty$ and $f(x)\to+\infty$ as $x\to+\infty$

In graph A, function has four root but it does not have the end behavior same as function f(x).( because in this graph $f(x)\to-\infty$ , as $x\to-\infty$ and $f(x)\to-\infty$ , as $x\to+\infty$ .) so, it can not be the graph of given function.

In graph B, neither it has four root nor it has the end behavior same as function f(x).(because in this graph $f(x)\to+\infty$ as $x\to-\infty$ and $f(x)\to-\infty$ as $x\to+\infty$ .) so, it can not be the graph of given function.

In graph C, neither it has four root nor it has the same end behavior as function f(x).(because in this graph $f(x)\to-\infty$ as $x\to-\infty$ and $f(x)\to+\infty$ as $x\to\infty$ .) so, it also can not be the graph of given function.