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sashaice [31]
2 years ago
10

1. find the exact value of cos2θ if sin 2θ=3/4 and θ is between 0° and 90°

Mathematics
1 answer:
musickatia [10]2 years ago
5 0

Answer:

<u>Identities used:</u>

  • sin²θ + cos²θ = 1
  • cos2θ = cos²θ - sin²θ

#1

  • sin2θ = 3/4, and θ in the first quadrant
  • cos²2θ = 1 - sin²2θ
  • cos2θ = √(1 - sin²2θ) = √(1 - 9/16) = √(7/16) = √7 / 4

#2

  • sinθ(cos²θ - cos2θ) =
  • sinθ(cos²θ - (cos²θ - sin²θ) =
  • sinθ(sin²θ) =
  • sin³θ

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Kristen has 64 coins in her bank. She has $9.25 in dimes and quarters. How many dimes and quarters does she have?
Stella [2.4K]
D= # of dimes
q= # of quarters

QUANTITY EQUATION:
d + q= 64

COST EQUATION:
0.10d + 0.25q= $9.25


STEP 1:
multiply quantity equation by -0.10 to be able to eliminate the d term in step 2

(-0.10)(d + q)= (-0.10)(64)
-0.10d - 0.10q= -6.40


STEP 2:
add equation from step 1 to cost equation to eliminate the d term and solve for q

Add
0.10d + 0.25q= $9.25
-0.10d - 0.10q= -6.40

0.15q= 2.85
divide both sides by 0.15

q= 19 quarters


STEP 3:
substitute q value in step 2 into either original equation to find d value

d + q= 64

d + 19= 64
subtract 19 from both sides

d= 45 dimes


CHECK:
0.10d + 0.25q= $9.25
0.10(45) + 0.25(19)= 9.25
4.50 + 4.75= 9.25
9.25= 9.25


ANSWER: There are 45 dimes and 19 quarters.

Hope this helps! :)
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Answer:

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And 4 pieces will be cut along the width.

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All together when the entire cake is cut, there will be 4*6 = 24 squares 2.5 inch long pieces.

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