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4 years ago

What is the simplified form of (2 X 102)2 in standard notation? Do not use commas in your answer. (HAS TO BE A NUMBER)

Mathematics

1 answer:

Oxana [17]4 years ago

7 0

Answer:

40000

Step-by-step explanation:

$(2 \times {10}^{2} )^{2} \\ = {2}^{2} \times {10}^{2 \times 2} \\ = 4 \times {10}^{4} \\ = 40000$

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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

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

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

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

$0 \leq x \leq 48.6\ ft$

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

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

The square pyramid represented below has a base edge of 6 inches and a height of 5 inches. What is the volume in cubic inches of

lawyer [7]

6*6*5*(1/3)=60in cubed

8 0

3 years ago

Read 2 more answers

Find the missing side and angles.

sweet [91]

Answer:

Step-by-step explanation:

This is an equilateral triangle.

The altitude bisects the 60 degree angle, so a=30

b=60 since its an interior angle of the isosceles triangle.

e = 4 since the two triangles formed by the altitude are congruent.

c = 8 since the side length is 4 + 4 = .

f = 4sqrt3 by the properties of 30 60 90 triangles.

5 0

2 years ago

Solve this inequality: 3b – 7 < 32

butalik [34]

It's a lot like solving equations.

3b-7 < 32
Add 7 to each side.
3b < 39
Divide by 3 on each side.
b < 13

Hope this helps :)

6 0

3 years ago

Read 2 more answers

g The probability that a university graduate will be offered no jobs within a month of graduation is estimated to be 5%. The pro

dexar [7]

Answer:

49% probability that a graduate is offered fewer than two jobs

Step-by-step explanation:

We have these following probabilities:

5% probabilities of not being offered a job

44% probability of receiving one job offer

28% probability of received two job offers.

23% probability of receiving three job offers.

Determine the following probabilities: A. P(A graduate is offered fewer than two jobs)

Zero or one

5 + 44 = 49%

49% probability that a graduate is offered fewer than two jobs

8 0

3 years ago