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3 years ago

Richard and Teo have a combined age of 31. Richard is 10 years older than twice Teo's age. How old are Richard and Teo?

Mathematics

1 answer:

amm18123 years ago

8 0

Richard and Teo are 7 and 24.
7 times two is 14
24 is ten more than 14
31-7 is 24

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* ANSWER PLS * Convert 55° to radians.

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Answer:

11*pi/36

Step-by-step explanation:

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3 years ago

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Use the matrix tool to solve the system of equations 5x+2y=1 and -x-y=-2

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Answer:

Step-by-step explanation:

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At the first meeting of the Tennis Club, the 7 members decided to have a tournament in which every player will play a match agai

mariarad [96]

Answer:

21 matches

Step-by-step explanation:

This is a combination problem where we have to select two member out of 7 members

So we want calculation of 7C2

7C2 = 7!/[(2!)(7-2)!]

(7*6*5*4*3*2*1)/[(2*1) *(5*4*3*2*1]

(7*6)/2 ~ Note everything that easily cancels here!

42/2

21 matches

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3 years ago

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:

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

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

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

$S_{n}=910.22\ ft$

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3 years ago

Graph the inequality on the number line. x≥−3 1/2

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Answer:

I've done this before my friend...

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3 years ago