Solve -2a + 9 = -3. Show all work

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

Enter the next three numbers of the repeating decimal produced by the

Tanya [424]

Answer:

The next three numbers are; 2,8, and 5.

Step-by-step explanation:

7 0

3 years ago

Solve for x and y

bekas [8.4K]

Answer:

x = 2√2

y = 2√6

Step-by-step explanation:

Consider the ratio of the two legs of the two smaller interior right triangles. (refer to attached diagrams for the triangles - I have outlined one in blue and the other in red)

These will be equal since the triangles are similar

shorter leg : longer leg

(blue triangle = red triangle)

⇒ x : 4 = 2 : x

⇒ x/4 = 2/x

⇒ x² = 8

⇒ x = √8

⇒ x = 2√2

Now we have x, we have the two legs of the right triangle with hypotenuse labelled y.

Using Pythagoras' Theorem a² + b² = c² (where a and b are the legs and c is the hypotenuse)

⇒ 4² + (2√2)² = y²

⇒ y² = 24

⇒ y = √24

⇒ y = 2√6

7 0

2 years ago

Two positive integers have a sum of 23 and a product of 126. Find the two numbers.

meriva

Answer:

SUBTRACT

Step-by-step explanation:

6 0

3 years ago

leslie needs to roll an 8 with 2 dice to win a game. How many possible outcomes are these for her to win?

bekas [8.4K]

Answer:there are 36 outcomes with 2 dice, there are 6 outcomes that have the number 8

Step-by-step explanation:

6 0

3 years ago