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2 years ago

Find the sum of ∑4/k=1 (-4k)

Mathematics

1 answer:

Annette [7]2 years ago

4 0

Answer:

Hello,

Answer C: -40

Step-by-step explanation:

$\displaystyle \sum_{k=1}^4\ (-4k)\\\\=-4*\sum_{k=1}^4\ k\\\\=-4*4*\dfrac{1+4}{2} \\\\=-4*5*2\\\\=-40\\$

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If (cos)x= 1/2 what is sin(x) and tan(x)? Explain your steps in complete sentences.

Natasha_Volkova [10]

The correct answers are:
1) sin(x) = $\frac{ \sqrt{3} }{2}$
2) tan(x) = $\sqrt{3}$

Explanation:
Given:
$cos(x) = \frac{1}{2}$

Step 1:
Since, according to the Trigonometric identity:
$sin^2(x) + cos^2(x) = 1$ -- (1)

Step 2:
Plug in the value of cos(x) in equation (1):
$sin^2(x) + ( \frac{1}{2} )^2 = 1 \\ sin^2(x) + \frac{1}{4} = 1 \\ sin^2(x) = \frac{3}{4}$

Step 3:
Take square-root on both sides:
$\sqrt{sin^2(x)} = \sqrt{\frac{3}{4}}$

sin(x) = $\frac{ \sqrt{3} }{2}$

Now to find the tan(x), we would use the following formula:

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

Plug in the values of sin(x) and cos(x) in equation (2):
tan(x) = $\frac{ \frac{ \sqrt{3} }{2} }{ \frac{1}{2} }$

Hence tan(x) = $\sqrt{3}$

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3 years ago

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Hank put $10,000 in an account for 10 years. The account earned 2.5% interest. How much interest had been earned by the end of t

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Answer:

A = P ( 1+ i )^n

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Step-by-step explanation:

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2 years ago

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Answer:

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Step-by-step explanation:

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3 years ago

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Solve for x and explain

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Since the two lines are parallel, the angle labeled 130 is congruent to the angle labeled x+ 136 so you can set them equal to each other

130 = x + 136
subtract 136 from both sides

x = -6

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3 years ago

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Violet bought 2 yards of fabric. She will use it to make new pillow covers. How many inches of fabric did Violet get?

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Answer:

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Step-by-step explanation:

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