1.4.3 Quiz: Linear Equations And Inequalities

SOLVE THE QUESTION BELOW ASAP

qwelly [4]

Answer:

Part A) The graph in the attached figure (see the explanation)

Part B) 16 feet

Part C) see the explanation

Step-by-step explanation:

Part A) Graph the function

Let

h(t) ----> the height in feet of the ball above the ground

t -----> the time in seconds

we have

$h(t)=-16t^{2}+98$

This is a vertical parabola open downward (the leading coefficient is negative)

The vertex is a maximum

To graph the parabola, find the vertex, the intercepts, and the axis of symmetry

Find the vertex

The function is written in vertex form

so

The vertex is the point (0,98)

Find the y-intercept

The y-intercept is the value of the function when the value of t is equal to zero

For t=0

$h(t)=-16(0)^{2}+98$

$h(0)=98$

The y-intercept is the point (0,98)

Find the t-intercepts

The t-intercepts are the values of t when the value of the function is equal to zero

For h(t)=0

$-16t^{2}+98=0$

$t^{2}=\frac{98}{16}$

square root both sides

$t=\pm\frac{\sqrt{98}}{4}$

$t=\pm7\frac{\sqrt{2}}{4}$

therefore

The t-intercepts are

$(-7\frac{\sqrt{2}}{4},0), (7\frac{\sqrt{2}}{4},0)$

$(-2.475,0), (2.475,0)$

Find the axis of symmetry

The equation of the axis of symmetry in a vertical parabola is equal to the x-coordinate of the vertex

so

$x=0$ ----> the y-axis

To graph the parabola, plot the given points and connect them

we have

The vertex is the point $(0,98)$

The y-intercept is the point $(0,98)$

The t-intercepts are $(-2.475,0), (2.475,0)$

The axis of symmetry is the y-axis

The graph in the attached figure

Part B) How far is the artifact fallen from the time t=0 to time t=1

we know that

For t=0

$h(t)=-16(0)^{2}+98$

$h(0)=98\ ft$

For t=1

$h(t)=-16(1)^{2}+98$

$h(1)=82\ ft$

Find the difference

$98\ ft-82\ ft=16\ ft$

Part C) Does the artifact fall the same distance from time t=1 to time t=2 as it does from the time t=0 to time t=1?

we know that

For t=1

$h(t)=-16(1)^{2}+98$

$h(1)=82\ ft$

For t=2

$h(t)=-16(2)^{2}+98$

$h(2)=34\ ft$

Find the difference

$82\ ft-34\ ft=48\ ft$

so

The artifact fall 48 feet from time t=1 to time t=2 and fall 16 feet from time t=0 to time t=1

therefore

The distance traveled from t=1 to t=2 is greater than the distance traveled from t=0 to t=1

8 0

2 years ago

How do you get the answer for 10 millimeters increased by 30%

tiny-mole [99]

First you have to find what 30% of ten is, and then add it to the 10. So how do you find 30 % of 10? In math...

"of" means ×
"is" means =

30% of 10 is
30 % × 10 =

change 30% to a decimal by dividing by 100 ( move the decimal to the left 2 places)

.30 × 10 = 3

So 30% of ten is 3. Now since we are increasing by 30%, we have to add it to the original value, 10.

3 + 10 = 13

So 10 millimeters increased by 30% is

13 millimeters

8 0

3 years ago

Which rule describes the transformation?

ziro4ka [17]

The correct answer is the third one (x,y) - (-x, -y)

8 0

2 years ago

Can you help me out

Advocard [28]

The answer is 20

Your welcome

8 0

2 years ago

A local tree farm is donating 50 trees. The students will plant some of the trees at the school and the rest at the library.

Alex17521 [72]

Answer:

6

Step-by-step explanation:

First you know they have 50 trees. Then, you know 3 of 25 will die.

25*2=50. 3*2=6.

8 0

2 years ago