Elanor paints this figure on her wall. Find the area of the figure.

The students in Mr. Wilson's Physics class are making golf ball catapults. The

Mnenie [13.5K]

Answer:

Part a) About 48.6 feet

Part b) About 8.3 feet

Part c) The domain is $0 \leq x \leq 48.6\ ft$ and the range is $0 \leq y \leq 8.3\ ft$

Step-by-step explanation:

we have

$y=-0.014x^{2} +0.68x$

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

The vertex represent a maximum

where

x is the ball's distance from the catapult in feet

y is the flight of the balls in feet

Part a) How far did the ball fly?

Find the x-intercepts or the roots of the quadratic equation

Remember that

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

The formula to solve a quadratic equation of the form

$ax^{2} +bx+c=0$

is equal to

$x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}$

in this problem we have

$-0.014x^{2} +0.68x=0$

so

$a=-0.014\\b=0.68\\c=0$

substitute in the formula

$x=\frac{-0.68(+/-)\sqrt{0.68^{2}-4(-0.014)(0)}} {2(-0.014)}$

$x=\frac{-0.68(+/-)0.68} {(-0.028)}$

$x=\frac{-0.68(+)0.68} {(-0.028)}=0$

$x=\frac{-0.68(-)0.68} {(-0.028)}=48.6\ ft$

therefore

The ball flew about 48.6 feet

Part b) How high above the ground did the ball fly?

Find the maximum (vertex)

$y=-0.014x^{2} +0.68x$

Find out the derivative and equate to zero

$0=-0.028x +0.68$

Solve for x

$0.028x=0.68$

$x=24.3$

<em>Alternative method</em>

To determine the x-coordinate of the vertex, find out the midpoint between the x-intercepts

$x=(0+48.6)/2=24.3\ ft$

To determine the y-coordinate of the vertex substitute the value of x in the quadratic equation and solve for y

$y=-0.014(24.3)^{2} +0.68(24.3)$

$y=8.3\ ft$

the vertex is the point (24.3,8.3)

therefore

The ball flew above the ground about 8.3 feet

Part c) What is a reasonable domain and range for this function?

we know that

A reasonable domain is the distance between the two x-intercepts

so

$0 \leq x \leq 48.6\ ft$

All real numbers greater than or equal to 0 feet and less than or equal to 48.6 feet

A reasonable range is all real numbers greater than or equal to zero and less than or equal to the y-coordinate of the vertex

so

we have the interval -----> [0,8.3]

$0 \leq y \leq 8.3\ ft$

All real numbers greater than or equal to 0 feet and less than or equal to 8.3 feet

8 0

3 years ago

What is 14310.912 rounded two decimal places

Reil [10]

Answer:

14310.91

Step-by-step explanation:

look at the second decimal which is one. then look at the number to the right and see if its 0-4 or 5-9. in this case its a 2 so it is in the first category

so you will keep the number the same and get rid of the remaining numbers

hope i explain alright :)

7 0

3 years ago

Spaceship Earth, a spherical attraction at Walt Disney World’s Epcot Center, has a diameter of 50 meters. Find the surface area

Black_prince [1.1K]

The surface area of Spaceship Earth is: 7850 m^2

Step-by-step explanation:

Given

Diameter of spherical structure = d = 50 meters

As the attraction is in the form of a sphere, its radius will be used to find the surface area.

$Radius = r = \frac{d}{2} = \frac{50}{2} = 25\ m$

The formula for surface area of sphere is:

$SA = 4\pi r^2\\= 4 * 3.14 * (25)^2\\= 4*3.14*625\\=7850\ m^2$

The surface area of Spaceship Earth is: 7850 m^2

Keywords: surface area, sphere

Learn more about surface area about:

#LearnwithBrainly

6 0

3 years ago

Ian ran f fewer laps than matt. Who ran 17 laps.

balandron [24]

17 Matt's laps - f laps = Ian's laps

4 0

3 years ago

Read 2 more answers

The Japanese Yen corresponds to the American Dollar. If the exchange rate is 150 Yen for 1 Dollar, then a Japanese car sold in A

Papessa [141]

Answer:

125,000

Step-by-step explanation:

Take the Japanese yen and divide by 12

1,500,000 divided by 12 = 125,000

3 0

4 years ago