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3 years ago

Two people can swing on a trapeze at the same time as long as

Mathematics

2 answers:

PtichkaEL [24]3 years ago

5 0

Yes there weight add up to 490

pychu [463]3 years ago

4 0

Answer:

Yes!

Step-by-step explanation:

Joe’s weight with Jake’s weight is 490, which is less than 500, so yes!

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A wealthy man just died and left his pet dogs the following estate: $20,000 per year for the next 11 years with the first cash f

Airida [17]

Answer is 400 please give me 5 stars

6 0

3 years ago

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the dance club is selling tickets to the next showcase adult tickets cost $5 and children's tickets cost $2 they sell twice as m

Marta_Voda [28]

Hey there! I'm happy to help!

Let's have the adult tickets be a and the children tickets be c.

a=2c (twice as many adult tickets as child tickets)

5a+2c=700 (dollar value of each ticket)

Have a wonderful day! I hope that the helps! :D

5 0

3 years ago

If the pattern continues how many cups of milk does George need to make 6 batches of muffins

alexdok [17]

Answer:

see explanation

Step-by-step explanation:

If we consider the differences between consecutive terms, that is

$\frac{3}{4}$ - $\frac{3}{8}$ = $\frac{3}{8}$

1 $\frac{1}{8}$ - $\frac{3}{4}$ = $\frac{3}{8}$

1 $\frac{1}{2}$ - 1 $\frac{1}{8}$ = $\frac{3}{8}$

To obtain the next term in the pattern add $\frac{3}{8}$ to the previous term.

batches = 5 ⇒ milk = 1 $\frac{1}{2}$ + $\frac{3}{8}$ = 1 $\frac{7}{8}$

batches = 6 ⇒ milk = 1 $\frac{7}{8}$ + $\frac{3}{8}$ = 2 $\frac{1}{4}$

6 0

2 years ago

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

94 times 39 = what?????

never [62]

Answer:

The answer is 3,666

3 0

3 years ago

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