Mathematics, 16.07.2019 01:00 lbabineaux9887

When a baseball is hit by a batter, the height of the ball, h(t), at time t, t=0, is determined by the equation h(t)=-16t^2+64t+4. if t is in seconds, for which interval of time is the height of the ball greater than or equal to 52 feet?

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Answer from: rayray2083

The time interval is $1\leq t\leq 3$ in which the height of the ball greater than or equal to 52 feet.

Step-by-step explanation:

We have given,When a baseball is hit by a batter, the height of the ball, h(t), at time t, t=0, is determined by the equation h(t)=-16t^2+64t+4 where t is time in seconds.

We have to find, If t is in seconds, for which interval of time is the height of the ball greater than or equal to 52 feet?

Solution :

The equation represented as h(t)=-16t^2+64t+4

Where, t is time in seconds and h is the height.

We can solve the equation by putting h(t)=52

$-16t^2+64t+4\geq 52$

$-16t^2+64t+4-52\geq 0$

$-16t^2+64t-48\geq 0$

$-t^2+4t-3\geq 0$

$-t^2+3t+t-3\geq 0$

$t(-t+3)-1(-t+3)\geq 0$

$(t-1)(-t+3)\geq 0$

t=1,3

Therefore, The time interval is $1\leq t\leq 3$ in which the height of the ball greater than or equal to 52 feet.

Now, We plot the graph of the given equation.

Refer the attached graph below.

When a baseball is hit by a batter, the height of the ball, h(t), at time t, t=0, is determined by t

Answer from: kaitlynmoore42

For anyone who is lazy to read question above, it's D

Explanation:

Edg2020

Answer from: Quest

5/6

step-by-step explanation:

if i remember correctly with perpendicular stuff you just take away the negative

Answer from: Quest

the system of inequity is

$y\leq -x+4$

$3y> x$

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

the solid line passing through the points (0,4) and (4,0).

$y-4=\frac{0-4}{4-0}(x-0)$

$y=-x+4$

the related equation of solid line is $y=-x+4$ .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

$y-0=\frac{0-1}{3-0}(x-0)$

$3y=x$

the related equation of dashed line is $3y=x$

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

$1=-0+4$

$1=4$

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be $\leq$ . the required inequality is

$y\leq -x+4$

similarly, check the second related equation.

$3(1)=0$

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is

$3y> x$

15 points write a system of inequalities to represent the shaded portion of the graph

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