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Karolina [17]
4 years ago
7

The height that a properly inflated basketball bounces decreases exponentially by 27.8% with each subsequent bounce after the in

itial drop. A local basketball league tests the inflation of their basketballs by dropping them from a height of 6 feet. Which equation can be used to model the height of the basketball, H, after b bounces?
Mathematics
1 answer:
n200080 [17]4 years ago
3 0

Answer:

H (b) = 0.722^b(6)

Step-by-step explanation:

The first time the basketball bounces it reaches a height of (1-0.278)(6) = (0.722) (6).

The second time the basketball bounces it reaches a height of (0.722) (0.722) (6) = [(0.722) ^ 2] (6). Therefore, after b rebounds the height that the basketball will reach is given by:

H (b) = 0.722^b(6)

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Suppose you are climbing a hill whose shape is given by the equation z = 1400 − 0.005x2 − 0.01y2, where x, y, and z are measured
Anarel [89]
Answer: You start to ascend

Explanation:

Since you are walking due south and the positive y-axis points north, the y-coordinate decreases.

Let 

y' = y-coordinate after walking due south
z' = z-coordinate (or the height) after walking due south

So, the point where you stand after walking due south has a coordinate of (100, y', z'). Moreover,

z' = 1,400 - 0.05(100)^2 - 0.01(y')^2
\\ \boxed{z' = 1350 - 0.01(y')^2}

Since the y-coordinate decreases after walking due south and z' = 1350 - 0.01(y')^2,

y'  \leq 120\\ \Rightarrow (y')^2 \leq 120^2 = 14,400\\ \Rightarrow -0.01(y')^2 \geq -0.01(14,400) = -144\\ \Rightarrow z' = 1,350 - 0.01(y')^2 \geq 1,350 - 0.01(14,400) = 1,206\\ \Rightarrow \boxed{z' \geq 1,206}

So, the height after walking due south exceeds 1,206 meters, which is the previous height before walking due south. Therefore, if you walk due south from point with coordinates (100, 120, 1206), you are ascending.
5 0
3 years ago
Homework (5)
adelina 88 [10]

Answer:

28

Step-by-step explanation:

Let's set the ratio as

7x : 9x

If you add all the states that border an ocean and do not, you will get 48 states (because Alaska and Hawaii are not part of the continental US, as they do not touch the "main" part of the country)

So, we can write this equation.

7x + 9x = 48

Simplify.

16x = 48

Divide both sides by 16.

x = 4

Now, find how many states border an ocean. In our ratio, the number of states that border an ocean was 7x. Substitute x = 4 into 7x

7 * x = 7 * 4 = 28

The number of states that border an ocean is 28.

I hope this helps! Feel free to ask any questions!

7 0
3 years ago
James is playing his favorite game at the arcade. After playing the game 3 times, he has 8 tokens remaining. He initially had 20
lapo4ka [179]
Sjehxhsbajwidjsbajjsjdbsjkwkkw
6 0
3 years ago
Can someone help me in this plssss I really need it
kompoz [17]

Answer:

\boxed{-3xy^{2}\sqrt [3] {2x^{2}}}

Step-by-step explanation:

Your expression is

\sqrt [3] {-54x^{5}y^{6}}

Here's how I would simplify it.

\begin{array}{rcll}\sqrt [3] {-54x^{5}y^{6}} & = & \sqrt [3] {(-1)^{3}\times 2 \times 27 \times x^{2} \times x^{3} \times y^{6}} & \text{Factored the cubes}\\& = & \sqrt [3] {(-1)^{3} \times 3^{3}\times x^{3} \times y^{6}\times 2 \times x^{2}} & \text{Grouped the cubes}\\\end{array}

\begin{array}{rcll}& = & \sqrt [3] {(-1)^{3} \times {3^{3}\times x^{3} \times y^{6}}} \times\sqrt [3] { 2 \times x^{2}} & \text{Separated the cubes}\\&=& \mathbf{-3xy^{2}\sqrt [3] {2x^{2}}} & \text{Took cube roots}\\\end{array}

\text{The simplified expression is $\boxed{\mathbf{-3xy^{2}\sqrt [3] {2x^{2}}}}$}

6 0
4 years ago
Nattalie picked 135 berries in 15 minutes at this rate how long will it take her to pick 486 berries
forsale [732]
Well, If she takes 15 minutes to pick 135 berries, 30 minutes total would be 270 berries, so if you take another 15 minutes picking berries it would be a total of 405 berries but you still need 81 more. so if she can pick 405 in 45 minutes, it would be around a hour and something. 

Hope I helped or at least made you think about it

3 0
3 years ago
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