Mathematics: For number 7 i need an explanation with steps for why is true or false you

For number 7 i need an explanation with steps for

flamingtacos4026

13.01.2022

Part 1) The statement is false

Part 2) The statement is false

Part 3) The statement is true

Step-by-step explanation:

Let

h(t)-----> the height of an object launched to the air

t ----> the time in seconds after the object is launched

we have

$h(t)=-16t^{2} +72t$

Verify each statement

case 1) The factored form of the equation is h(t)=-16(t-4.5)

The statement is false

Because

The factored form is equal to

h(t)=-16t(t-4.5)

case 2) The object will hit the ground at t=72 seconds

The statement is false

Because

we know that

The object will hit the ground when h(t)=0

substitute in the equation and solve for t

0=-16t(t-4.5)

(t-4.5)=0

$t=4.5\ sec$

case 3) The t-value for the maximum of the function is 2.25

The statement is true

Because

Convert the quadratic equation in vertex form

$h(t)=-16t^{2} +72t$

$h(t)=-16(t^{2} -4.5t)$

$h(t)-81=-16(t^{2} -4.5t+2.25^{2})$

$h(t)-81=-16(t-2.25)^{2}$

$h(t)=-16(t-2.25)^{2}+81$ ---> quadratic equation in vertex form

The vertex is a maximum

The vertex is the point (2.25,81)

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