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MA_775_DIABLO [31]
2 years ago
14

Two sides of a triangle have lengths 12 m and 14 m. The angle between them is increasing at a rate of 2°/min. How fast is the le

ngth of the third side increasing when the angle between the sides of fixed length is 60°? (Round your answer to three decimal places.) webassig n
Mathematics
1 answer:
Dvinal [7]2 years ago
4 0

Answer:

1.692 m/min

Step-by-step explanation:

Let \theta be the angle between the two sides and x be the length of the third side. By cosine rule,

x^2 = 12^2+14^2-2\times12\times14\cos\theta = 340 - 336\cos\theta

x= \sqrt{340 - 336\cos\theta}

We differentiate x with respect to \theta by applying chain rule.

\dfrac{dx}{d\theta} = \dfrac{336\sin\theta}{2\sqrt{340 - 336\cos\theta}} = \dfrac{168\sin\theta}{\sqrt{340 - 336\cos\theta}}

Rate of change of \theta is 2

\dfrac{\theta}{dt} = 2

Rate of change of x is

\dfrac{dx}{dt} = \dfrac{dx}{d\theta}\times\dfrac{d\theta}{dt}

\dfrac{dx}{dt} = \dfrac{168\sin\theta}{\sqrt{340 - 336\cos\theta}} \times2=\dfrac{336\sin\theta}{\sqrt{340 - 336\cos\theta}}

At 60°,

\dfrac{dx}{dt} = \dfrac{336\sin60}{\sqrt{340 - 336\cos60}} = 1.692 \text{ m/min}

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natima [27]

Answer:

The amount to be pay for coat is <u>$128.70</u>.

Step-by-step explanation:

Given:

The sales tax rate is 7.25% in California.

The cost for a coat in Los angeles is $120.00.

Now, to find amount to be paid.

Sales tax = 7.25%.

Cost = $120.00.

So, amount to be paid = $120 + 7.25% of $120.00.

=120+\frac{7.25}{100} \times 120.

=120+\frac{870}{100}.

=120+8.70

=\$128.70

Therefore, the amount to be pay for coat is $128.70.

7 0
2 years ago
Alex and 4 friends are playing baseball on the same team. Each time they play a game, they switch the batting order to a sequenc
mina [271]

Answer:

120.

Step-by-step explanation:

Since Alex and 4 friends are playing baseball on the same team, and each time they play a game, they switch the batting order to a sequence that has not yet been used, to determine what is the maximum number of games they can play before they have to repeat a batting order they have already used, the following calculation must be performed:

1 x 2 x 3 x 4 x 5 = X

2 x 3 x 4 x 5 = X

6 x 4 x 5 = X

24 x 5 = X

120 = X

Thus, the maximum number of games they can play before they have to repeat a batting order they have already used is 120.

7 0
2 years ago
Yuson used her calculator to solve the equation 4/5x - 8 = 3. She entered the following on her screen and got an incorrect answe
Firlakuza [10]

Answer:

55/4

Explanation:

Let's solve your equation step-by-step.

4 /5x−8=3

Step 1: Add 8 to both sides.

4 /5x−8+8=3+8

4 /5 x = 11

Step 2: Multiply both sides by 5/4.

( 5 /4 )*( 4 /5 x)=( 5 /4 )*(11)

x=  55/4

Answer:

x=

55 /4

Hope that helps :)

 

4 0
2 years ago
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2. José is using 12 brown tiles and
Karolina [17]

Answer:

12:20

Step-by-step explanation:

your trying to find the ratio to brown tiles to one section and theirs 12 brown tiles per section so you would start off with 12. and to find how many tiles would be in each section you would have to add 8 and 12 and you would end up with 20 which the number of tiles in each section

3 0
2 years ago
Hallie can use the equation p = 4l + 4w + 4h to determine the sum of the lengths of the edges of a rectangular prism. She begins
AfilCa [17]

Answer:

h = p - l - w

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p = l + w + h              Set the equation equal to h

h = p - l - w

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