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Write a formula for an arithmetic sequence

d. Grandma gave Kendra recipes for cranberry cookies and cranberry bread. One recipe calls for

\frac{2}{3}

cup cranberries, and the other recipe calls for

1 \frac{3}{4}

cup. How many cups of cranberries will Kendra need to make both recipes?

y=\frac{1}{x} \sin (x)

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\frac{d y}{d x}=

f(x)=x^{2} e^{x}

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f^{\prime}(x)=

\frac{1}{7}=0 . \overline{142857}

. Can you predict what the decimal expansions of

\frac{2}{7}, \frac{3}{7}

\frac{4}{7}, \frac{5}{7}, \frac{6}{7}

are, without actually doing the long division? If so, how?

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[Hint: Study the remainders while finding the value of

\frac{1}{7}

k^{\prime}(x)

k(x)=-3 x \cdot e^{-4 x^{3}+3 x^{2}}

Find an explicit formula for the arithmetic sequence

-11,-3,5,13, \ldots

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Note: the first term should be

b(1)

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b(n) = \square

Which of the following is equivalent to

\sec \frac{\pi}{5}

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\sec \frac{14 \pi}{5}

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\sec \left(-\frac{\pi}{5}\right)

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\sec \frac{6 \pi}{5}

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\sec \frac{4 \pi}{5}

Which of the following is equivalent to

\sec \frac{2 \pi}{7}

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\sec \frac{9 \pi}{7}

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\sec \frac{19 \pi}{7}

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\sec \frac{12 \pi}{7}

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\sec \frac{5 \pi}{7}

sider the following functions.

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f(x)=-4 x \text { and } g(x)=\sqrt[3]{x}

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1

2

: Find the formula for

(f+g)(x)

and simplify your answer. Then find the domain for

(f+g)(x)

. Round your answer to two decimal places, if necessa

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(f+g)(x)=

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\text { Domain }=

For the function

f(x)=\frac{3 x-5}{2 x}

f^{-1}(x)

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f^{-1}(x)=

For the function

f(x)=\frac{7}{2 x+7}

f^{-1}(x)

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f^{-1}(x)=

For the function

f(x)=\frac{10+3 x}{1-4 x}

f^{-1}(x)

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f^{-1}(x)=

y

-coordinate of the

y

-intercept of the polynomial function defined below.

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f(x)=-2 x(x+2)

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Write an explicit formula for

a_{n}

n^{\text {th }}

term of the sequence

144,24,4, \ldots

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a_{n}=

Write an explicit formula for

a_{n}

n^{\text {th }}

term of the sequence

5,-10,20, \ldots

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a_{n}=

Write an explicit formula for

a_{n}

n^{\text {th }}

term of the sequence

5,7,9, \ldots

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a_{n}=

Write an explicit formula for

a_{n}

n^{\text {th }}

term of the sequence

7,15,23, \ldots

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a_{n}=

Write an explicit formula for

a_{n}

n^{\text {th }}

term of the sequence

2,10,50, \ldots

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a_{n}=

Write an explicit formula for

a_{n}

n^{\text {th }}

term of the sequence

24,-12,6, \ldots

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a_{n}=

x

and write your answer in simplest form.

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\frac{1}{2}\left(\frac{3}{2} x+1\right)=-(-x-1)-3 x

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x=

\mathrm{x}

in simplest form.

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10=\frac{5}{6}(4 x+18)

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\mathrm{x}

in simplest form.

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2=\frac{3}{4}(3 x+16)

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Rewrite in simplest terms:

10 q-9(-8 q-6)

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For the following equation, evaluate

\frac{d y}{d x}

x=2

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y=x^{4}+5 x

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For the following equation, find

\frac{d y}{d x}

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y=x^{4}+x^{2}

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\frac{d y}{d x}=

y=3 \cot ^{3}(x)

\frac{d y}{d x}

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\frac{d y}{d x}=

y=-\csc (3 x)

\frac{d y}{d x}

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\frac{d y}{d x}=

y=3 \cot (2 x)

\frac{d y}{d x}

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\frac{d y}{d x}=

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y=2 \cot ^{3}(x)

\frac{d y}{d x}

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\frac{d y}{d x}=

y=3 \sec (2 x)

\frac{d y}{d x}

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\frac{d y}{d x}=

y=\tan ^{2}(x)

\frac{d y}{d x}

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\frac{d y}{d x}=

Given the function

y=-2\left(8 x^{2}-9 x-3\right)^{4}

\frac{d y}{d x}

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\frac{d y}{d x}=

u=3 w^{4}-5

\frac{d}{d w}\left(4 w^{2}-\sin u\right)

in terms of only

w

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v=4 y^{4}-5

\frac{d}{d y}\left(3 y^{3}-5 \sin v\right)

in terms of only

y

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x=4 w^{2}+4

\frac{d}{d w}\left(x^{4}-5 \sin w\right)

in terms of only

w

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y=u^{3}+3

\frac{d}{d u}\left(3 y^{2}+4 \sin u\right)

in terms of only

u

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y=3 u^{2}+4

\frac{d}{d u}\left(2 u^{5}-4 \sin y\right)

in terms of only

u

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x=w^{5}+5

\frac{d}{d w}\left(3 x^{2}+3 \cos w\right)

in terms of only

w

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Given the function

y=\frac{2 x^{2}}{6-5 x^{2}}

\frac{d y}{d x}

in simplified form.

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\frac{d y}{d x}=

Given the function

y=\frac{2 x^{3}}{2+x^{3}}

\frac{d y}{d x}

in simplified form.

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\frac{d y}{d x}=

Given the function

f(x)=\frac{x}{3-4 x^{3}}

f^{\prime}(x)

in simplified form.

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f^{\prime}(x)=

Priyanka and Ethan were asked to find an explicit formula for the sequence

-3,-14,-25,-36, \ldots

, where the first term should be

g(1)

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Priyanka said the formula is

g(n)=-3-11 n

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Ethan said the formula is

g(n)=-3+11 n

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Which one of them is right?

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1

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(A) Only Priyanka

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(C) Both Priyanka and Ethan

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(D) Neither Priyanka nor Ethan

g(n)=25-49(n-1)

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Complete the recursive formula of

g(n)

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g(1) = \(\square\)

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g(n) = g(n-1)+\(\square\)

Find an explicit formula for the arithmetic sequence

-31,-27,-23,-19, \ldots

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Note: the first term should be

b(1)

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b(n) = \(\square\)

Carlos and Ana were asked to find an explicit formula for the sequence

-10,-4,2,8, \ldots

, where the first term should be

f(1)

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Carlos said the formula is

f(n)=-10+6 n

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Ana said the formula is

f(n)=-10+6(n-1)

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Which one of them is right?

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1

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(A) Only Carlos

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(C) Both Carlos and Ana

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(D) Neither Carlos nor Ana

Imran and Aubrey were asked to find an explicit formula for the sequence

14,5,-4,-13, \ldots

, where the first term should be

g(1)

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Imran said the formula is

g(n)=14-9(n-1)

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Aubrey said the formula is

g(n)=14-9 n

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Which one of them is right?

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1

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(B) Only Aubrey

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(C) Both Imran and Aubrey

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(D) Neither Imran nor Aubrey

Find an explicit formula for the arithmetic sequence

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37,74,111,148, \ldots

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Note: the first term should be

a(1)

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a(n) = \(\square\)

Find an explicit formula for the arithmetic sequence

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-2,-14,-26,-38, \ldots \text {.. }

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Note: the first term should be

d(1)

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d(n) = \(\square\)

Find an explicit formula for the arithmetic sequence

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81,54,27,0, \ldots \text {.. }

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Note: the first term should be

a

1

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a(n) = \(\square\)

g(n)=-50-15 n

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Complete the recursive formula of

g(n)

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g(1) = \(\square\)

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g(n) = g(n-1)+\(\square\)