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monitta
3 years ago
7

A force of F pounds is required to pull an object weighing W pounds up a ramp inclined at θ degrees from the horizontal. Find θ

if F = 5500 pounds and W = 16,000 pounds. (Round your answer to one decimal place.)
Mathematics
1 answer:
Pie3 years ago
5 0

Answer:

The value of θ is 20.105°

Step-by-step explanation:

Consider the provided information.

A force of F pounds is required to pull an object weighing W pounds up a ramp inclined at θ degrees from the horizontal.

Sine of angle is force over weight.

\sin\theta=\frac{F}{W}

Substitute F = 5500 pounds and W = 16,000 pounds in above formula.

\sin\theta=\frac{5500}{16000}

\sin\theta=\frac{11}{32}

\theta\approx20.105

Hence, the value of θ is 20.105°

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Answer:

2^{1.5} = 2.8284. This means that Larissa is not correct.

Step-by-step explanation:

To solve logarithms, we have to consider the following:

\log_{a}(b) = c means that a^{c} = b.

So, for example:

log_{2}(2) = 1 because 2^{1} = 2.

log_{2}(4) = 2 because 2^{2} = 4.

If 2^{1.5} = 3, then Larissa is correct. However, 2^{1.5} = 2.8284. This means that Larissa is not correct.

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3 years ago
686.924 to the nearest ten
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3 years ago
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Answer:

2a - 3b + 4c = 1

Step-by-step explanation:

Given

a^2 + b^2 + c^2 = 2(a - b - c) - 3

Required

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a^2 + b^2 + c^2 = 2(a - b - c) - 3

Open bracket

a^2 + b^2 + c^2 = 2a - 2b - 2c - 3

Equate the equation to 0

a^2 + b^2 + c^2 - 2a + 2b + 2c + 3 = 0

Express 3 as 1 + 1 + 1

a^2 + b^2 + c^2 - 2a + 2b + 2c + 1 + 1 + 1 = 0

Collect like terms

a^2 - 2a + 1 + b^2 + 2b + 1 + c^2  + 2c + 1 = 0

Group each terms

(a^2 - 2a + 1) + (b^2 + 2b + 1) + (c^2  + 2c + 1) = 0

Factorize (starting with the first bracket)

(a^2 - a -a + 1) + (b^2 + 2b + 1) + (c^2  + 2c + 1) = 0

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((a - 1) (a - 1)) + (b^2 + 2b + 1) + (c^2  + 2c + 1) = 0

((a - 1)^2) + (b^2 + 2b + 1) + (c^2  + 2c + 1) = 0

((a - 1)^2) + (b^2 + b+b + 1) + (c^2  + 2c + 1) = 0

((a - 1)^2) + (b(b + 1)+1(b + 1)) + (c^2  + 2c + 1) = 0

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((a - 1)^2) + ((b + 1)^2) + (c^2  + 2c + 1) = 0

((a - 1)^2) + ((b + 1)^2) + (c^2  + c+c + 1) = 0

((a - 1)^2) + ((b + 1)^2) + (c(c  + 1)+1(c + 1)) = 0

((a - 1)^2) + ((b + 1)^2) + ((c  + 1)(c + 1)) = 0

((a - 1)^2) + ((b + 1)^2) + ((c  + 1)^2) = 0

Express 0 as 0 + 0 + 0

(a - 1)^2 + (b + 1)^2 + (c  + 1)^2 = 0 + 0+ 0

By comparison

(a - 1)^2 = 0

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a - 1 + 1 = 0 + 1

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b + 1 = 0

Subtract 1 from both sides

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