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3 years ago

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in the coordinate plane, line m had a slope of 1/4 and a y-intercept of (0,-3). line n is the result of dialating line m by a sc

ale factor of 2 with a center of (0,0). what are the slope and y-intercept of line n?

1 answer:

Verizon [17]3 years ago

4 0

Answer:N/A

Step-by-step explanation:N/A

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Find the sum of the convergent series 7 0.7 0.007

mafiozo [28]

$7+0.7+0.007+\cdots=7\left(1+\dfrac1{10}+\dfrac1{100}+\cdots\right)$

Let $S_n$ denote the $n$ th partial sum of the series, i.e.

$S_n=1+\dfrac1{10}+\dfrac1{100}+\cdots+\dfrac1{100^n}$

Then

$\dfrac1{10}S_n=\dfrac1{10}+\dfrac1{100}+\dfrac1{1000}+\dfrac1{10^{n+1}}$

and subtracting from $S_n$ we get

$S_n-\dfrac1{10}S_n=\dfrac9{10}S_n=1-\dfrac1{10^{n+1}}$
$\implies S_n=\dfrac{10}9\left(1-\dfrac1{10^{n+1}}\right)$

As $n\to\infty$ , the exponential term vanishes, leaving us with

$\displaystyle\lim_{n\to\infty}S_n=\dfrac{10}9$

and so

$7+0.7+0.007+\cdots=7.777\ldots=\dfrac{70}9$

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3 years ago

The additive inverse of 10 is -17. If 10 + (-17) = 0, then the numbers are additive inverses. True or False?

Vesnalui [34]

Answer:

False

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2 years ago

A decorative window is made up of a rectangle with semicircles at either end. The ratio of AD to AB is 3:2 and AB is 30 inches.

scZoUnD [109]

Answer: The required ratio will be

$84:1034$

Step-by-step explanation:

Since we have given that

Ratio of AD to AB is 3:2

Length of AB = 30 inches

So, it becomes

$2x=30\\\\x=\frac{30}{2}=15\ inches$

So, Length of AD becomes

$3x=3\times 15=45\ inches$

Now, at either end , there is a semicircle.

Radius of semicircle along AB is given by

$\frac{30}{2}=15\ inches$

So, Area of semicircle along AB and CD is given by

$2\times \frac{\pi r^2}{2}\\\\=\frac{22}{7}\times 15\times 15\\\\=\frac{4950}{7}\ in^2$

Radius of semicircle along AD is given by

$\frac{45}{2}=22.5\ inches$

Area of semicircle along AD and BC is given by

$2\times \frac{1}{2}\pi r^2\\\\=\frac{22}{7}\times \frac{45}{2}\times \frac{45}{2}\\\\=\frac{445500}{28}\ in^2$

And the combined area of the semicircles is given by

$\frac{4950}{7}+\frac{445500}{28}\\\\=\frac{465300}{28}\ in^2$

Area of rectangle is given by

$Length\times width\\\\=AD\times AB\\\\=45\times 30\\\\=1350\ in^2$

Hence, Ratio of the area of the rectangle to the combined area of the semicircles is given by

$1350:\frac{465300}{28}\\\\=1350\times 28:465300\\\\=37800:465300\\\\=84:1034$

Hence, the required ratio will be

$84:1034$

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