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Art [367]
3 years ago
12

Which of the following expressions is equivalent to (–7)5?

Mathematics
1 answer:
Vinvika [58]3 years ago
5 0

Answer:

A

Step-by-step explanation:

(-7)5 is the same as saying you're multiplying -7 5 times by its self.

Hope this helps!!

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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 100/ 5 i need help asap
zepelin [54]

Answer:

20

Step-by-step explanation:

You can take a 0 off of 100.

10/5=2

Add the 0 back to the end

20 is your answer.

3 0
3 years ago
If X²+1=2x then what the value of x²?
natka813 [3]

Answer:

x² = 2x - 1

Step-by-step explanation:

x² + 1 = 2x

→ Minus 1 from both sides

x² = 2x - 1

7 0
3 years ago
Read 2 more answers
Is adding polynomials will always yield a polynomial answer true or false ?
zhuklara [117]
True: adding two polynomials will always result in another polynomial
3 0
3 years ago
Linda planned to spend 9 hours practicing the piano this week. by tus​
Misha Larkins [42]

Answer:

So, this week Linda will to practice 63 hours.

Best regards

Step-by-step explanation:

9 hours * 7 day/week

7 0
3 years ago
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