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4 years ago

What is the some need help????

Mathematics

1 answer:

snow_tiger [21]4 years ago

5 0

The sum formula for a geometric sequaence is:

sum(n) = a1(1-r^n)/1-r

Where n is the number of terms, a1 is the first term and r is the common ratio:

s(8) = 3(1-1/2^8) / (1-1/2)

s(8) = 3(1-1/256) / 1/2

s(8) = 2 253/256 / 1/2

s(8) = 765/128

The answer is C.

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Find tan2θ if θ terminates in Quadrant IV and cosθ = 3/5.

natali 33 [55]

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$\cos( \alpha ) = \frac{3}{5} \\$

${sin}^{2}( \alpha ) = 1 - {cos}^{2} ( \alpha )$

${sin}^{2}( \alpha ) = 1 - ({ \frac{3}{5} })^{2} \\$

${sin}^{2}( \alpha ) = 1 - \frac{9}{25} \\$

${sin}^{2}( \alpha ) = \frac{25}{25} - \frac{9}{25} \\$

${sin}^{2}( \alpha ) = \frac{16}{25} \\$

$sin( \alpha )= ± \sqrt{ \frac{16}{25} } \\$

In Quadrant IV , sin is negative .

Thus ;

$sin( \alpha ) = - \sqrt{ \frac{16}{25} } \\$

$\sin( \alpha ) = - \frac{4}{5} \\$

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$\tan(2 \alpha ) = \frac{ \sin(2 \alpha ) }{ \cos(2 \alpha ) } \\$

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$\sin(2 \alpha ) = 2. \sin( \alpha ). \cos( \alpha )$

$\sin(2 \alpha ) = 2 \times ( - \frac{4}{5} ) \times ( \frac{3}{5} ) \\$

$\sin(2 \alpha ) = - \frac{24}{25} \\$

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$\cos(2 \alpha ) = {cos}^{2}( \alpha ) - {sin}^{2}( \alpha )$

$\cos(2 \alpha ) = ({ \frac{3}{5} })^{2} - ({ - \frac{4}{5} })^{2} \\$

$\cos(2 \alpha ) = \frac{9}{25} - \frac{16}{25} \\$

$\cos(2 \alpha ) = - \frac{7}{25} \\$

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$\tan(2 \alpha ) = \frac{ \sin(2 \alpha ) }{ \cos(2 \alpha ) } \\$

$\tan(2 \alpha ) = \frac{ - \frac{24}{25} }{ - \frac{7}{25} } \\$

$\tan(2 \alpha ) = - \frac{24}{25} \div - \frac{7}{25} \\$

$\tan(2 \alpha ) = - \frac{24}{25} \times - \frac{25}{7} \\$

$\tan(2 \alpha ) = \frac{24}{7} \\$

Thus the correct answer is (( C )) .

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4 0

3 years ago

Read 2 more answers

John goes from a sauna at 115 Fahrenheit to an outside temperature of -30 Fahrenheit. What is the change in temperature?

IRINA_888 [86]

Answer: 115 - (-30) = 115 + 30 = 145 degrees change

Step-by-step explanation:

7 0

3 years ago

What is the circumference of the circle? Use 3.14 for .

Cerrena [4.2K]

Answer:

40.192 centimeters

Step-by-step explanation:

The circumference of a circle can be found using:

c= pi* diameter

First, we must find the diameter. The diameter of a circle is twice it’s radius.

d=2*radius

The radius of the circle is 6.4 centimeters. Substitute 6.4 for the radius.

d=2*6.4

d=12.8

Now we know the diameter. We can substitute 12.8 for diameter in the circumference equation.

c=pi*diameter

c=pi*12.8

We also know we are using 3.14 for pi, so we can substitute 3.14 for pi.

c=3.14*12.8

c=40.192

Use appropriate units: centimeters

c=40.192 centimeters

The circumference is 40.192 centimeters.

6 0

4 years ago

Read 2 more answers

NEED ALGEBRA HELP, WILL MARK AS BRAINLIEST

Nadusha1986 [10]

Answer:

The answer to your question is:

Step-by-step explanation:

Data

C (0, 0)

D (7, 12)

m = (12 - 0) / (7 - 0)

m = 12/7

Slope = 12/7

(y - y1) = m(x - x1)

(y - 12) = 12/7 (x - 7)

y - 12 = 12/7 x - 1

y = 12/7 x - 1 + 12

y = 12/7 x + 11

Domain [0, 7]

Range [0, 12]

6 0

3 years ago

Help with this question picture below

mezya [45]

Answer:

I think it is B,D, and E. Hope that helps.

8 0

3 years ago

What is the some need help????​

What is the some need help????