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4 years ago

Need help understanding this problem! If someone would explain how to do it that would be great!

Mathematics

1 answer:

Elodia [21]4 years ago

7 0

Answer:

m∠G = 31.83°

Step-by-step explanation:

From the triangle FGH,

FH = 6 ft

FG = 11 ft

And measure of the included angle ∠F = 73°

We have to find the measure of ∠G.

By applying law of cosine in the triangle to get the measure of third side GH first,

GH² = FH² + FG² - 2(FH)(FG)cos(∠F)

GH² = 6² + 11² - 2(6)(11)cos(73°)

GH² = 36 + 121 - 38.593

GH = √118.407

GH = 10.88 ft

Now apply sine rule in the given triangle to get the measure of ∠G.

$\frac{\text{sinG}}{FH}=\frac{\text{sinF}}{GH}$

$\frac{\text{sinG}}{6}= \frac{\text{sin(73)}}{10.88}$

sin(G) = 0.527374

G = $\text{sin}^{-1}(0.527374)$

m∠G = 31.83°

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One pipe can empty a tank 5 times faster than another pipe can fill the tank. Starting with a full tank, if both pipes are turne

xxTIMURxx [149]

Answer:

40 hours

Step-by-step explanation:

Let's say that the slower pipe can fill x amount of the tank in one hour. It adds x amount to the tank every hour. Therefore, we can say, for the slower pipe,

1 hour = x amount

Then, the faster pipe empties the tank 5 times faster than the slower pipe fills it, so it removes 5 times the amount that the smaller pipe puts in, so for the faster pipe,

1 hour = -5x amount (negative to symbolize removing).

For the problem at hand, the tank starts at full, or 100%=1. It ends empty, or at 0% = 0. After 10 hours, if we only account for the slower pipe, we add x amount to the tank every hour, so we add 10 times that total, resulting in

1 + 10 * x as the ending result if we don't include the faster pipe. Then, the faster pipe removes 5x every hour, so in 10 hours, it removes 50x, so we have

1+10 * x - 50 * x as the final amount of stuff in the tank, which is equal to 0. Therefore, we have

1 + 10 * x - 50 * x = 0

1 - 40 * x = 0

add 40*x to both sides to isolate the x and its coefficient

1 = 40 * x

divide both sides by 40 to isolate x

x= 0.025

Therefore, the slower pipe adds 0.025, or 1/40 = 2.5% to the tank every hour. We want to figure out how long it would take for the slower pipe to fill up an empty tank, or turn it from 0% to 100% full.

Because the slower pipe adds 2.5% of the tank every hour, we can say that over y hours, it fills up

2.5% * y amount of the tank. We want to figure out how many hours it would take to make it 100% (we need to add 100% of the tank in the problem), so we can say

2.5% * y = 100%

divide both sides by 2.5% to isolate y

100%/2.5% = y = 40

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3 years ago

Help help please i will mark u brill

Roman55 [17]

Answer:

Step-by-step explanation:

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Putting value of u = 24 in the equation

24/4 + 9.9 = 16.9

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