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4 years ago

Write as a mixed number 61/7

Mathematics

2 answers:

alekssr [168]4 years ago

6 0

61/7 is 8 and 5/7 as a mixed number.

lara [203]4 years ago

3 0

The answer is 8.7142, or as a mixed number, 8 and 3571/5000. I would really appreciate it if I could get brainliest! Thanks! =D

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slavikrds [6]

What exactly are you asking?

5 0

3 years ago

A lighthouse is located on an island 33 miles from the closest point on a straight shoreline. If the lighthouse light rotates cl

Zinaida [17]

Question:

A lighthouse is located on an island 3 miles from the closest point on a straight shoreline. If the lighthouse light rotates clockwise at a constant rate of 9 revolutions per minute, how fast does the beam of light move towards the point on the shore closest to the island when it is 52 miles from that point

Answer:

The beam of light moves at $16278\pi$ miles/min

Step-by-step explanation:

This question is illustrated with the attached image

Taking the instructions in the question, one at a time.

A revolution of 9 per minute implies that:

$\frac{d\theta}{dt} = \frac{9 * 2\pi\ rad}{1\ min}$

$\frac{d\theta}{dt} = 18\pi \frac{rad}{min}$

Take tan of the angle in the attachment:

$tan(\theta) =\frac{52}{3}$

Differentiate both sides with respect to time

$\frac{d\ tan(\theta)}{dt} =\frac{52}{3} * \frac{dx}{dt}$

Rewrite as:

$\frac{d\ tan(\theta)}{d\theta} * \frac{d\theta}{dt} =\frac{52}{3} * \frac{dx}{dt}$

In calculus:

$sec^2(\theta) =\frac{d\ tan(\theta)}{d\theta}$ -- Chain rule

So:

$sec^2(\theta) *\frac{d\theta}{dt} =\frac{52}{3} * \frac{dx}{dt}$

In trigonometry:

$sec^2(\theta) = tan^2(\theta) + 1$

So:

$(tan^2(\theta) + 1)\frac{d\theta}{dt} =\frac{52}{3} * \frac{dx}{dt}$

Recall that:

$tan(\theta) =\frac{x}{3}$

$((\frac{52}{3})^2 + 1)\frac{d\theta}{dt} =\frac{1}{3} * \frac{dx}{dt}$

$(\frac{52^2}{9} + 1)\frac{d\theta}{dt} =\frac{1}{3} * \frac{dx}{dt}$

$(\frac{2704}{9} + 1)\frac{d\theta}{dt} =\frac{1}{3} * \frac{dx}{dt}$

$(\frac{2704+9}{9})\frac{d\theta}{dt} =\frac{1}{3} * \frac{dx}{dt}$

$(\frac{2713}{9})\frac{d\theta}{dt} =\frac{1}{3} * \frac{dx}{dt}$

Recall that: $\frac{d\theta}{dt} = 18\pi \frac{rad}{min}$

$(\frac{2713}{9}) * 18\pi =\frac{1}{3} * \frac{dx}{dt}$

$2713 * 2\pi =\frac{1}{3} * \frac{dx}{dt}$

Multiply both sides by 3

$3 * 2713 * 2\pi =\frac{1}{3} * \frac{dx}{dt} * 3$

$3 * 2713 * 2\pi =\frac{dx}{dt}$

$16278\pi =\frac{dx}{dt}$

$\frac{dx}{dt} = 16278\pi$ miles/min

Hence:

The beam of light moves at $16278\pi$ miles/min

6 0

3 years ago

Which area of the rectangle is correct?

Goshia [24]

Answer:

55/96

Step-by-step explanation:

To find the area, we need to multiply l x w

Take the length 11/12 and the width 5/8 and multiply -

11 times 5 = 55

12 times 8 = 96

Answer: 55/96

3 0

3 years ago

State weather your function is bounded above, bounded below or bounded.

ivolga24 [154]

Answer:

C is the answer

Step-by-step explanation:

6 0

3 years ago

Solve the inequality : x-7 ≤ 3x + 1

Nina [5.8K]

Answer:

See below.

Step-by-step explanation:

x-7≤3x+1

+7 +7

x≤3x+8

-3x -3x

-2x≤8

/-2 /-2

x≥-4

The inequality symbol reverses when divided/multiplied by a negative term.

-hope it helps

6 0

3 years ago

Read 2 more answers