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3 years ago

What is the sum of the measures of 1 and 2?

Mathematics

1 answer:

Papessa [141]3 years ago

7 0

Answer:

56 degrees.

Step-by-step explanation:

angles 1 and 2 are the same as well as 62 and the angle across from it. With this knowledge, subtract 62 from 180 twice to get 56. Angle one plus angle two equals 56.

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4. a) A ping pong ball has a 75% rebound ratio. When you drop it from a height of k feet, it bounces and bounces endlessly. If t

Klio2033 [76]

First part of question:

Find the general term that represents the situation in terms of k.

The general term for geometric series is:

$a_{n}=a_{1}r^{n-1}$

$a_{1}$ = the first term of the series

$r$ = the geometric ratio

$a_{1}$ would represent the height at which the ball is first dropped. Therefore:

$a_{1} = k$

We also know that the ball has a rebound ratio of 75%, meaning that the ball only bounces 75% of its original height every time it bounces. This appears to be our geometric ratio. Therefore:

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

Our general term would be:

$a_{n}=a_{1}r^{n-1}$

$a_{n}=k(\frac{3}{4}) ^{n-1}$

Second part of question:

If the ball dropped from a height of 235ft, determine the highest height achieved by the ball after six bounces.

$k$ represents the initial height:

$k = 235\ ft$

$n$ represents the number of times the ball bounces:

$n = 6$

Plugging this back into our general term of the geometric series:

$a_{n}=k(\frac{3}{4}) ^{n-1}$

$a_{n}=235(\frac{3}{4}) ^{6-1}$

$a_{n}=235(\frac{3}{4}) ^{5}$

$a_{n}=55.8\ ft$

$a_{n}$ represents the highest height of the ball after 6 bounces.

Third part of question:

If the ball dropped from a height of 235ft, find the total distance traveled by the ball when it strikes the ground for the 12th time. 

This would be easier to solve if we have a general term for the <em>sum </em>of a geometric series, which is:

$S_{n}=\frac{a_{1}(1-r^{n})}{1-r}$

We already know these variables:

$a_{1}= k = 235\ ft$

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

$n = 12$

Therefore:

$S_{n}=\frac{(235)(1-\frac{3}{4} ^{12})}{1-\frac{3}{4} }$

$S_{n}=\frac{(235)(1-\frac{3}{4} ^{12})}{\frac{1}{4} }$

$S_{n}=(4)(235)(1-\frac{3}{4} ^{12})$

$S_{n}=910.22\ ft$

8 0

3 years ago

Is 216 more than 30% of 720

Natali [406]

Answer:

No, it is equal

Step-by-step explanation:

30% of 720 is 216.

5 0

3 years ago

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Use an induction proof to prove this statement:<br> For n≥1, 4^n+5 is divisible by 3.

Tpy6a [65]

Answer:

See below

Step-by-step explanation:

We shall prove that for all $n\in\mathbb{N},3|(4^n+5)$ . This tells us that 3 divides 4^n+5 with a remainder of zero.

If we let $n=1$ , then we have $4^{1}+5=9$ , and evidently, $9|3$ .

Assume that $4^n+5$ is divisible by $3$ for $n=k, k\in\mathbb{N}$ . Then, by this assumption, $3|(4^n+5)\Rightarrow4^k+5=3m,\: m\in\mathbb{Z}$ .

Now, let $n=k+1$ . Then:

$4^{k+1}+5=4^k\cdot4+5\\=4^k(3+1)+5\\=3\cdot4^k+4^k+5\\=3\cdot4^k+3m\\=3(4^k+m)$

Since $3|(4^k+m)$ , we may conclude, by the axiom of induction, that the property holds for all $n\in\mathbb{N}$ .

3 0

2 years ago

A car starts 40 meters away from home and every minute the car travels an additional 1000 meters. What

barxatty [35]

The equation would be y=1000x+40

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3 years ago

Which of the following is the largestest set? Becareful of spelling. Real numbers, Rational Numbers, Irrational numbers or Natur

vichka [17]

Real numbers. Others contain fractions and decimals which are breaking down a whole. Real numbers are 1 whole. Hope this helps (Hope i get brainliest to!)

8 0

3 years ago

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