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Alex Ar [27]
3 years ago
7

-4x -8y = -24 y = -5x -6

Mathematics
1 answer:
Butoxors [25]3 years ago
8 0
I would say this 7 because when you subtract
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Given the function f(x) = log3 (x + 1), determine f^−1(2).
zavuch27 [327]
Given:  <span>f(x) = log3 (x + 1), look for f^-1 (2)

We are looking for the inverse of a function. The inverse of the function can be obtained by switching the variables and obtaining the values of the new function, before substituting f(2). Using a calculator:

</span><span>f^-1 (2) = 8</span>
6 0
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

8 0
3 years ago
Can I get help with finding the Fourier cosine series of F(x) = x - x^2
trapecia [35]
Assuming you want the cosine series expansion over an arbitrary symmetric interval [-L,L], L\neq0, the cosine series is given by

f_C(x)=\dfrac{a_0}2+\displaystyle\sum_{n\ge1}a_n\cos nx

You have

a_0=\displaystyle\frac1L\int_{-L}^Lf(x)\,\mathrm dx
a_0=\dfrac1L\left(\dfrac{x^2}2-\dfrac{x^3}3\right)\bigg|_{x=-L}^{x=L}
a_0=\dfrac1L\left(\left(\dfrac{L^2}2-\dfrac{L^3}3\right)-\left(\dfrac{(-L)^2}2-\dfrac{(-L)^3}3\right)\right)
a_0=-\dfrac{2L^2}3

a_n=\displaystyle\frac1L\int_{-L}^Lf(x)\cos nx\,\mathrm dx

Two successive rounds of integration by parts (I leave the details to you) gives an antiderivative of

\displaystyle\int(x-x^2)\cos nx\,\mathrm dx=\frac{(1-2x)\cos nx}{n^2}-\dfrac{(2+n^2x-n^2x^2)\sin nx}{n^3}

and so

a_n=-\dfrac{4L\cos nL}{n^2}+\dfrac{(4-2n^2L^2)\sin nL}{n^3}

So the cosine series for f(x) periodic over an interval [-L,L] is

f_C(x)=-\dfrac{L^2}3+\displaystyle\sum_{n\ge1}\left(-\dfrac{4L\cos nL}{n^2L}+\dfrac{(4-2n^2L^2)\sin nL}{n^3L}\right)\cos nx
4 0
3 years ago
Three-fifths of the spanish club is girls. there are a total of 30 girls in the spanish club
crimeas [40]

Answer: whats the question here if you wanna know how many boys there are there should be 12

Step-by-step explanation:

7 0
3 years ago
You are making fruit baskets using 54 apples, 36 oranges, and 73 bananas. a. Explain why you cannot make identical fruit baskets
Basile [38]
Question 1:
73 is a prime number. It can only be divided by 1 and by itself. 

The GCF of the three numbers:
 54                               36                            73
1×54                           1×36                          1×73
2×27                          2×18
3×18                           3×12
6×9                            4×9
                                   6×6

GCF of 54, 36 and 73  is 1

GCF of 54 and 36 is 18

If we divide 54 apples into 18 baskets, we have 3 apples in each basket
If we divide 36 oranges into 18 baskets, we have 2 oranges in each basket
If we divide 73 bananas into 18 baskets, we have 4 bananas in each basket + one banana left over.

So the greatest number of identical fruit baskets we can make with the least amount of fruit left over is 18 baskets
3 0
3 years ago
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