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3 years ago

What is the answer is this problem?

Mathematics

1 answer:

USPshnik [31]3 years ago

8 0

Answer:

First One = 0.000045 Second One = 0.024

Step-by-step explanation:

When 10 has a negative power, move the decimal to the right the number of times the power is. For example, 10^-5 is moved 5 places to the LEFT, so it is 0.000045.

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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

$0.028x=0.68$

$x=24.3$

Alternative method

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

2 years ago

the stemplot below represents the distribution of the test scores for the final exam in a high school algebra course. what was t

Deffense [45]

Answer:

Option A. 94

Explanation:

The column of digits to the left (before the vertical line) contains the largest place-value digits.

Here is how you read the values:

First row: 65

Second row: 73, 74, 78

Third row: 80, 80, 81, 82, 85, 88, 89

Fourth row: 92, 93, 94.

Thus, the highest score received is 94.

8 0

2 years ago

Hi best answer receives a brainlist :))

il63 [147K]

Answer:

its A increases as x goes to ∞

decreases as x goes to -∞

Step-by-step explanation:

6 0

2 years ago

Anyone??? Answer plz

zloy xaker [14]

Answer:

45 degrees

Step-by-step explanation:

8 0

2 years ago

Read 2 more answers

I'm not sure where to begin, can someone help me begin?

VLD [36.1K]

First, convert the mixed number into an improper fraction.
To convert a mixed number into an improper fraction, find the product of the whole number and the denominator and then add the numerator.
Then the denominator will be the original denominator from the mixed number.

$1 \frac{1}{3}$ = $\frac{4}{3}$

Now the fraction $\frac{4}{3}$ is being raised to the third power negative.
When an exponent is negative, it means to take the reciprocal of the number then raise it to the power of the absolute value of the exponent.

In a mathematical expression: $x^{-n} = \frac{1}{x^n}$

So, first take the reciprocal of $\frac{1}{3}$ which is 3.

Then raise 3 to the absolute value of the exponent. The exponent is -3.
The absolute value of -3 is 3.

3^3 = 3 * 3 * 3 = 27

So, the answer is 27.

7 0

3 years ago