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2 years ago

Find m∠MON I have a hard time with theses

Mathematics

1 answer:

fredd [130]2 years ago

3 0

Answer:

m∠MON = 15°

Step-by-step explanation:

The given parameters are;

m∠LON = 77°

m∠LOM = 9·x + 44°

m∠MON = 6·x + 3°

By angle addition postulate, we have;

m∠LON = m∠LOM + m∠MON

Therefore, by substituting the known values, we have;

∴ 77° = 9·x + 44° + 6·x + 3°

77° = 9·x + 44° + 6·x + 3° = 15·x + 47°

77° = 15·x + 47°

77° - 47° = 15·x

15·x = 77° - 47° = 30°

15·x = 30°

x = 30°/15 = 2°

x = 2°

Given that m∠MON = 6·x + 3° and x = 2°, we have;

m∠MON = 6 × 2° + 3° = 12° + 3° = 15°

m∠MON = 15°.

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Answer:

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Step-by-step explanation:

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2 years ago

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Estimate the sum of 1.8+4.008+0.44 Round each number to the nearest tenth a.5 b.5.2 c.6 d.6.2

Oduvanchick [21]

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3 years ago

Is 10/18 in decimal form a terminates or repeating decimal

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3 years ago

The radius of a cone is decreasing at a constant rate of 7 inches per second, and the volume is decreasing at a rate of 948 cubi

inessss [21]

Answer:

The height of cone is decreasing at a rate of 0.085131 inch per second.

Step-by-step explanation:

We are given the following information in the question:

The radius of a cone is decreasing at a constant rate.

$\displaystyle\frac{dr}{dt} = -7\text{ inch per second}$

The volume is decreasing at a constant rate.

$\displaystyle\frac{dV}{dt} = -948\text{ cubic inch per second}$

Instant radius = 99 inch

Instant Volume = 525 cubic inches

We have to find the rate of change of height with respect to time.

Volume of cone =

$V = \displaystyle\frac{1}{3}\pi r^2 h$

Instant volume =

$525 = \displaystyle\frac{1}{3}\pi r^2h = \frac{1}{3}\pi (99)^2h\\\\\text{Instant heigth} = h = \frac{525\times 3}{\pi(99)^2}$

Differentiating with respect to t,

$\displaystyle\frac{dV}{dt} = \frac{1}{3}\pi \bigg(2r\frac{dr}{dt}h + r^2\frac{dh}{dt}\bigg)$

Putting all the values, we get,

$\displaystyle\frac{dV}{dt} = \frac{1}{3}\pi \bigg(2r\frac{dr}{dt}h + r^2\frac{dh}{dt}\bigg)\\\\-948 = \frac{1}{3}\pi\bigg(2(99)(-7)(\frac{525\times 3}{\pi(99)^2}) + (99)(99)\frac{dh}{dt}\bigg)\\\\\frac{-948\times 3}{\pi} + \frac{2\times 7\times 525\times 3}{99\times \pi} = (99)^2\frac{dh}{dt}\\\\\frac{1}{(99)^2}\bigg(\frac{-948\times 3}{\pi} + \frac{2\times 7\times 525\times 3}{99\times \pi}\bigg) = \frac{dh}{dt}\\\\\frac{dh}{dt} = -0.085131$

Thus, the height of cone is decreasing at a rate of 0.085131 inch per second.

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2 years ago

Sweets are sold loose, or pre-packed in 120g bags. The 120g bags are ?1.49 each. The loose sweets are ?0.89 for 100g. By calcula

tester [92]

Answer:

The loose sweets at ?0.89 for 100 g.

Step-by-step explanation:

First, calculate the price per gram. You do this by dividing the price by the grams.

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Because the answer was very long, I have rounded it to 4 decimal places (4 dp).

?0.89 / 100 g = 0.89 / 100 = 0.0089

Next, you must calculate both pre-packed and loose sweets to the same weight. I am calculating them both to 100 g.

0.0124 x 100 = 1.24

0.0089 x 100 = 0.89

Finally, the cheapest product for 100 g will be the better value. In this case, it is the loose sweets.

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3 years ago