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Leni [432]
2 years ago
10

Does anyone know how to do this???

Mathematics
1 answer:
Bond [772]2 years ago
6 0

Answer:

  x° ≈ 77.6°

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you of the relationships between trig functions and triangle sides. Side CD is common to the triangle on the left and the one on the right, so we can consider relationships that might help us use that to find the answer.

In the triangle on the right, we need a relationship between CD and BD. These sides are opposite and adjacent to the given angle, so we can use the relation ...

  Tan = Opposite/Adjacent

  tan(38°) = CD/3.5

Multiplying by 3.5, we can find CD:

  CD = 3.5·tan(38°)

__

In the triangle on the left, we know sides CD and CA, the side opposite x° and the hypotenuse of that right triangle. This lets us use the sine relationship:

  Sin = Opposite/Hypotenuse

  sin(x°) = CD/2.8

__

Using our value for CD, this becomes ...

  sin(x°) = (3.5·tan(38°)/2.8)

  sin(x°) = (5/4)tan(38°)

Using the inverse sine function, we can find x° to be ...

  x° = arcsin(5/4·tan(38°)) ≈ 77.6°

The size of the angle marked x° is about 77.6°.

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Jovita divides $12,000 into three investments: a savings account paying 4% annual interest, a bond paying 6%, and a money market
xenn [34]

Answer:

$2080 was invested in the savings account, $4241 was invested in the bond account, & $6539 was invested in the money fund.

Step-by-step explanation:

Let a, b, and c be the fractions of the $12,000 that is invested in the savings, bond, & money fund respectively.

Let S1, S2, S3 be the total monies from the savings, bond, & money fund after the year with interest respectively.

We know that a+b+c=1

and

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S1+S2+S3 = 12860

From, the question, we know that b = 2a, and c = 1 - 3a based on the condition of 2 times more in the bond account that the savings account.

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S2 = 2a(12000)(1.06) = 25,440a

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We already know that;

S1+S2+S3 = 12860

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220 = 1320a

a = 220/1320

a = 0.1667

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c = 1 - (3 x 0.1667)

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S3 = 13080 - 39240(0.1667) ≈ 6539

So, $2080 was invested in the savings account, $4241 was invested in the bond account, & $6539 was invested in the money fund.

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