What is the surface area of the right prism below?

6. Write the explicit formula for the geometric sequence of the height of the ball on the 10th bounce.First bounce: 54 inchescom

Nat2105 [25]

The height of the ball initially is 54 inches. The common ratio has been provided which is 0.750.

The explicit formular for the geometric sequence is shown as;

$\begin{gathered} ar^{n-1} \\ \text{Where a is the first term in the sequence,} \\ r\text{ is the common ratio betw}een\text{ every successive term} \\ \text{And n is the nth term} \\ \text{The explicit formular for the height of the ball on the 10th bounce is;} \\ ar^{n-1} \\ 54\times(0.750)^{10-1} \\ 54\times(0.750)^9 \\ 54\times0.07508468\ldots \\ 4.0545 \end{gathered}$

The explicit formula is shown as;

54 x (0.750)^9

The rest is simply to solve for the height on the 10th bounce

5 0

1 year ago

Ms. Salta buys buffalo wings for a party. If there are 3 servings per buffalo pound, exactly how many servings does she have for

gtnhenbr [62]

Answer:

Not sure how many chicken wings to make or buy as appetizers for your ... 6 whole wings (or 1.125 lbs) in order to reach a 6 oz serving of actual chicken. ... That would mean there are approximately 4 to 5 chicken wings in a pound. ... You will need approximately 3 ounces of chicken meat per person as a ...

Missing

Step-by-step explanation:

i think

3 0

3 years ago

What is the solution to the system of equations? O (-6,-) O (-2, 6) O (6,2) O (-2,-6)

damaskus [11]

Answer:

Option (1)

Step-by-step explanation:

System of equations is represented by two straight lines on a graph.

And solution of the system of equations is the point of intersection of these lines.

From the graph attached, two straight lines represent the system of equations.

And the point of intersection of these lines is the solution.

Therefore, solution of the system of equations will be (-6, -2).

Option (1) will be the correct option.

4 0

3 years ago

Read 2 more answers

Of the following equations below, which equation represents a direct variation between x and y?

spin [16.1K]

Answer:

C. y +3 = x +3

Step-by-step explanation:

We need to find in below option x has direct variation with y.

We solve for each;

A. $2y = 3x-7$

From above equation we can state that 2 times y is equal to 7 less than 3 times of x.

Hence it doesn't represent direct variation.

B. $y-4 = x+6$

Solving above expression we get;

$y-4 = x+6\\y = x+6+4\\y=x+10$

From above equation we can state that y is equal to 10 more than x.

Hence it doesn't represent direct variation.

C. $y+3 = x+3$

Solving above expression we get;

$y+3 = x+3\\y = x+3-3\\y=x$

From above equation we can state that y is equal to x.

Hence it represent direct variation.

D. $4y+1 = 4x-1$

Solving above expression we get;

$4y+1 = 4x-1\\4y = 4x-1-1\\4y=4x-2$

From above equation we can state that 4 times y is equal to 2 less than 4 times of x.

Hence it doesn't represent direct variation.

Hence the Answer which represent direct variation of x and y is,

C. $y+3 = x+3$

7 0

3 years ago

In the △ABC, the height AN = 24 in, BN = 18 in, AC = 40 in. Find AB and BC. Consider all possible cases. Case 1 : N∈BC, AB = __,

aivan3 [116]

Answer:

Case 1:

$AB = 30$

$BC = 50$

Case 2:

$AB = 15.9$

$BC = 36.7$

Case 3: Not possible

Step-by-step explanation:

Given

See attachment for illustration of each case

Required

Find AB and BC

Case 1:

Using Pythagoras theorem in ANB, we have:

$AB^2 = AN^2 + BN^2$

This gives:

$AB^2 = 24^2 + 18^2$

$AB^2 = 576 + 324$

$AB^2 = 900$

Take square roots of both sides

$AB = \sqrt{900$

$AB = 30$

To calculate BC, we consider ANC, where:

$AC^2 = AN^2 + NC^2$

$40^2 = 24^2 + NC^2$

$1600 = 576 + NC^2$

Collect like terms

$NC^2 = 1600 - 576$

$NC^2 = 1024$

Take square roots

$NC = \sqrt{1024$

$NC = 32$

So:

$BC = NC + BN$

$BC = 32 + 18$

$BC = 50$

Case 2:

Using Pythagoras theorem in ANB, we have:

$AN^2 = AB^2 + BN^2$

This gives:

$24^2 = AB^2 + 18^2$

$576 = AB^2 + 324$

Collect like terms

$AB^2 = 576 - 324$

$AB^2 = 252$

Take square roots of both sides

$AB = \sqrt{252$

$AB = 15.9$

To calculate BC, we consider ABC, where:

$AC^2 = AB^2 + BC^2$

$40^2 = 252 + BC^2$

$1600 = 252 + BC^2$

Collect like terms

$BC^2 = 1600 - 252$

$BC^2 = 1348$

Take square roots

$BC = \sqrt{1348$

$BC = 36.7$

Case 3:

This is not possible because in ANC

The hypotenuse AN (24) is less than AC (40)

3 0

3 years ago