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grigory [225]
3 years ago
5

If the equation y = 1 3 x + 2 is changed to y = 3x + 2, what will be true about the graph of the equation? A) The graph will shi

ft up 3 units. B) The graph will shift down 3 units. C) The graph will shift left 3 units. D) The slope of the graph will be changed.
Mathematics
1 answer:
MrRa [10]3 years ago
4 0

Answer:

D.

Step-by-step explanation:

The number which multiplies x  is the slope of the graph so 13x becoming  3x means the slope of the graph will change.

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Juan was given a gift card for a coffee shop. Each morning, Juan uses the card to buy one cup of coffee. Each cup of coffee cost
Black_prince [1.1K]

Answer:

A=30-2x

Step-by-step explanation:

Cost of one cup of coffee=$2

The original amount of money on the gift card= $30

Juan's expenses in buying coffee, after x morning are \$2\times x.

The amount of money left, A, on the card = (Original amount) - (Total expenses)

A=30-2x

Hence, the equation for, A, the amount of money remaining on the card is

A=30-2x.

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3 years ago
Use the power series for 1 1−x to find a power series representation of f(x) = ln(1−x). What is the radius of convergence? (Note
Viktor [21]

a. Recall that

\displaystyle\int\frac{\mathrm dx}{1-x}=-\ln|1-x|+C

For |x|, we have

\displaystyle\frac1{1-x}=\sum_{n=0}^\infty x^n

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\displaystyle-\ln(1-x)=C+\sum_{n=0}^\infty\frac{x^{n+1}}{n+1}

If x=0, then

\displaystyle-\ln1=C+\sum_{n=0}^\infty\frac{0^{n+1}}{n+1}\implies 0=C+0\implies C=0

so that

\displaystyle\ln(1-x)=-\sum_{n=0}^\infty\frac{x^{n+1}}{n+1}

We can shift the index to simplify the sum slightly.

\displaystyle\ln(1-x)=-\sum_{n=1}^\infty\frac{x^n}n

b. The power series for x\ln(1-x) can be obtained simply by multiplying both sides of the series above by x.

\displaystyle x\ln(1-x)=-\sum_{n=1}^\infty\frac{x^{n+1}}n

c. We have

\ln2=-\dfrac\ln12=-\ln\left(1-\dfrac12\right)

\displaystyle\implies\ln2=\sum_{n=1}^\infty\frac1{n2^n}

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Answer:

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2 years ago
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8 4/9 hope this helps!!!
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With the process used in part A in mind, create a formula that you can use to convert radians into degrees. Let r represent a ra
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