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Resources

Simplify radical expressions with variables

f(x)=b \sqrt{a-x}+7 \sqrt{a-x}

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For the function

f, a

b

are constants and

f(16)=0

f(9)>0

, which of the following could be the value of

a+b

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-3

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7

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9

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15

f(x)=b \sqrt{a-x}+7 \sqrt{a-x}

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For the function

f, a

b

are constants and

f(16)=0

f(9)>0

, which of the following could be the value of

a+b

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-3

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7

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9

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15

57

2

57

0

In the given solution, a and b are constants. The product of the solutions to the given equation is kab, where k is a constant. what is the value of k?

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1

57

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1

19

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1

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57

(1,3)

a solution of the system of equations below? Justify.

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y=4x-1

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2x+2y=8

The coordinates of the vertices of

\triangle D E F

D(2,3), E(4,0)

F(1,-2)

. The coordinates of the vertices of

\triangle T V W

T(0,3)

V(-2,0)

W(1,-2)

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Which series of transformations correctly shows that

\triangle D E F \cong \triangle T V W ?

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a reflection over the

y

-axis and a translation

2

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a reflection over the

x

-axis and a translation

2

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a reflection over the

x

-axis and a translation

2

Use the information given below to find

\cos(\alpha-\beta)

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\cos \alpha=\frac{3}{5}

\alpha

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\tan \beta=\frac{3}{4}

\beta

in quadrant III

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Give the exact answer, not a decimal approximation.

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\cos(\alpha-\beta)=

How many integers

n

are there, where

1 \leq n \leq 100

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\frac{206+9 n^{2}}{2+3 n}

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is a number that does not repeat decimals?

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(Repeating os do not count)

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f

has a Taylor series about

x=1

that converges to )

f(x)

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x

in the interval of convergence. It is known that

f(1)=1

f'(1)=-\frac{1}{2}

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n

th derivative of

f

x=1

f^{(n)}(1)=(-1)^{n}\frac{(n-1)!}{2^{n}}

x=1

0

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(a) Write the first four nonzero terms and the general term of the Taylor series for

f

x=1

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(b) The Taylor series for

f

x=1

has a radius of convergence of

x=2

. Find the interval of convergence. Show the work that leads to your answer.

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(c) The Taylor series for

f

x=1

can be used to represent

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f(1.2)

as an alternating series. Use the first three nonzero terms of the alternating series to approximate

f(1.2)

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(d) Show that the approximation found in part (c) is within

0.001

of the exact value of

f(1.2)

Find the minimum and maximum values of the function

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y=26t-t^{2}

[14,2]

by comparing values at the critical points and endpoints.

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(Use symbolic notation and fractions where needed. If the function does not have extreme values, enter DNE.)

(5+2i)(1+3i)

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5+6i

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-1

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-1+17 i

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11+17 i

Express the given expression without logs, in simplest form. Assume all variables represent positive values.

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\left(e^{\ln (4 w)+\ln \left(10 x^{3}\right)}\right)

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Express the given expression without logs, in simplest form. Assume all variables represent positive values.

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\left(e^{\ln (10 z)+\ln \left(6 y^{3}\right)}\right)

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Express the given expression without logs, in simplest form. Assume all variables represent positive values.

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\left(e^{\ln (8 \sqrt{w})}\right)

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Express the given expression without logs, in simplest form. Assume all variables represent positive values.

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\ln \left(e^{3 w^{2}}\right)

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f(x)=\left\{\begin{array}{lll} -(x+2)^{2}+5 & \text { for } & x \neq-1 \\ 3 & \text { for } & x=-1 \end{array}\right.

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f(-1)

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f(x)=\left\{\begin{array}{lll} (x+1)^{2}-3 & \text { for } & x \leq-1 \\ x-8 & \text { for } & x \geq 4 \end{array}\right.

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f(2)

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The quotient of

\frac{\sqrt[5]{m^{4}}}{\sqrt[4]{m^{3}}}

\frac{\sqrt{m}}{\sqrt[5]{m^{6}}}

m^{y}

. What is the value of

y

3 - m = 2(l-4) \newline m = l - 4

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Consider the given system of equations. If

(\ell,m)

is the solution to the system, then what is the value of

\ell\cdot m

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