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2 years ago

Write a compound interest function to model each situation. Then find the balance after the given number of years.

Mathematics

1 answer:

Reika [66]2 years ago

7 0

Answer:

Step-by-step explanation:

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Cos^2x+cos^2(120°+x)+cos^2(120°-x)<br>i need this asap. pls help me

o-na [289]

Answer:

$\frac{3}{2}$

Step-by-step explanation:

Using the addition formulae for cosine

cos(x ± y) = cosxcosy ∓ sinxsiny

---------------------------------------------------------------

cos(120 + x) = cos120cosx - sin120sinx

= - cos60cosx - sin60sinx

= - $\frac{1}{2}$ cosx - $\frac{\sqrt{3} }{2}$ sinx

squaring to obtain cos² (120 + x)

= $\frac{1}{4}$ cos²x + $\frac{\sqrt{3} }{2}$ sinxcosx + $\frac{3}{4}$ sin²x

--------------------------------------------------------------------

cos(120 - x) = cos120cosx + sin120sinx

= -cos60cosx + sin60sinx

= - $\frac{1}{2}$ cosx + $\frac{\sqrt{3} }{2}$ sinx

squaring to obtain cos²(120 - x)

= $\frac{1}{4}$ cos²x - $\frac{\sqrt{3} }{2}$ sinxcosx + $\frac{3}{4}$ sin²x

--------------------------------------------------------------------------

Putting it all together

cos²x + $\frac{1}{4}$ cos²x + $\frac{\sqrt{3} }{2}$ sinxcosx + $\frac{3}{4}$ sin²x + $\frac{1}{4}$ cos²x - $\frac{\sqrt{3} }{2}$ sinxcosx + $\frac{3}{4}$ sin²x

= cos²x + $\frac{1}{2}$ cos²x + $\frac{3}{2}$ sin²x

= $\frac{3}{2}$ cos²x + $\frac{3}{2}$ sin²x

= $\frac{3}{2}$ (cos²x + sin²x) = $\frac{3}{2}$

5 0

2 years ago

A side of the triangle below has been extended to form an exterior angle of 164º. Find the value of x.

OverLord2011 [107]

Answer:

x=111

Step-by-step explanation:

the supplementary angle is 16. triangles should add up to 180.

4 0

3 years ago

Amplitude of y=-3sin5x

GaryK [48]

Answer:

Amplitude is 3

Step-by-step explanation:

in y=-3sin5x

the number in front of sign is always the amplitude. Its not negative 3 because the negative simply means it reflects across the x-axis

4 0

3 years ago

Read 2 more answers

If the measure of angle 4 is (11 x) degrees and angle 3 is (4 x) degrees, what is the measure of angle 3 in degrees?

GarryVolchara [31]

Answer:

Step-by-step explanation:

Angle 4 × Angle 3 = 90

Complementary angles

11x + 4x = 90

15x = 90

x = 6

Angle 3 = 4x = 4(6) = 24°

5 0

2 years ago

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The selling price for a classic speedboat is $16,000, which is $500 more than two times its original price. What was the origina

lbvjy [14]

$7,750 is the answer :)

3 0

3 years ago