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3 years ago

How many tiles would it take to cover the Washington monument?

Mathematics

1 answer:

aalyn [17]3 years ago

4 0

Ummm what mush is it is a good thing you can get it to get it and you can see it and then get it done

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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

2 years ago

Please answer this !!!

denis-greek [22]

Answer:

to do this we have to divide 43 by 83

0.51807228915

so the frequency is about 51.8%

8 0

3 years ago

For the equation |ax+b|=c (where a,b, and c are real numbers and a≠0), what value of c results in exactly one solution?

Degger [83]

Step-by-step explanation:

Correct option is



=0,b



The condition for ax+by+c=0 to be a linear eqaution in two variables is



=0,b



7 0

2 years ago

6x^2-2x+1=0 solve for x

Paraphin [41]

Solve by using the quadratic formula.

x=1+-i√5 / 6

6 0

3 years ago

Mike can be paid in one of two ways based on the amount of merchandise he sells: Plan A: A salary of $1,000.00 per month, plus a

Serggg [28]

Answer:

X > 21000

Step-by-step explanation:

Given the following :

Payment plans :

PLAN A:

salary = $1000 per month

Commision = 10% of sales

PLAN B:

salary = $1300 per month

Commision = 15% of sales in excess of $9,000

Hence, for plan B; 15% is paid after deducting $9000 from total sales

For what amount of monthly sales is plan B better than plan A if we can assume that Mike's sales are always more than $9,000.00?

That is ;

Plan B > plan A

Let total sales = x

Plan A:

$1,000 + 0.1x

Plan B:

$1,300 + 0.15(x - 9000)

1300 + 0.15(x - 9000) > 1000 + 0.1x

1300 + 0.15x - 1350 > 1000 + 0.1x

0.15x - 50 > 1000 + 0.1x

0.15x - 0.1x > 1000 + 50

0.05x > 1050

x > 1050/0.05

x > 21000

6 0

3 years ago