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butalik [34]
3 years ago
10

As you are walking down a path, you see a sign telling the path has a 2% grade (ie., a rise of 2 metres for a horizontal change

of 100m). Which of the following expressions will calculate the angle between the path and horizontal?

Mathematics
1 answer:
Leni [432]3 years ago
5 0

Answer:

Option (A)

Step-by-step explanation:

It has been given in this question that sign telling path has a 2% grade.

2% grade means a rise of 2 meters for a horizontal change of 100 m (As given in the figure attached).

All the trigonometric ratios for the angle θ between the path and the horizontal are,

Sinθ = \frac{\text{Opposite side}}{\text{Hypotenuse}}

Cosθ = \frac{\text{Adjacent side}}{\text{Hypotenuse}}

tanθ = \frac{\text{Opposite side}}{\text{Adjacent side}}

Since measures of the opposite side and adjacent sides are given

Therefore, tangent ratio will be applied to get the measure of the angle,

tanθ = \frac{2}{100}

θ = \text{tan}^{-1}(\frac{2}{100})

Option (A) will be the answer.

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Help. Solving Multi Step Ratio Problems!
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Answer:

Part 1) 30\ coupons

Part 2) 12\ sandwiches

Part 3) 60\ push-ups

Part 4) 96\ minutes

Part 5) \$95

Part 6) 1\frac{7}{8}\ cups\ of\ pretzel

Step-by-step explanation:

Part 1) we know that

At the Green House of Salad , you get a $1 coupon for every 3 salads you buy

so

Using proportion

Find out the number of salads you could buy to get $10 in coupons

\frac{1}{3}=\frac{10}{x} \\\\x=3(10)\\\\x=30\ coupons

Part 2) we know that

Kim orders catering for $35

She spend $5 on a large order of potato salad and the rest on turkey sandwiches

Each sandwich is $2.50

How many sandwiches does Kim buy?

step 1

Find out how many Kim spent on turkey sandwiches

Subtract $5 from $35

35-5=$30

step 2

Using proportion, find out the number of sandwiches

so

\frac{1}{2.50}=\frac{x}{30}\\\\x=30/2.50\\\\x= 12\ sandwiches

Part 3) we know that

Molly does 10 push-ups at the same time as Liza does  15 push-ups

so

Using proportion

Find out how many push-ups Liza does when Molly does 40 push-ups

\frac{10}{15}=\frac{40}{x}\\\\x=15(40)/10\\\\x=60\ push-ups

Part 4) we know that

A shark swim at a speed of 25 miles per hour

The shark rest after 40 miles

How long in minutes, does the shark swim before resting?

Using proportion

Find out how long in minutes the shark swim 40 miles

Remember that

1\ h=60\ min

\frac{25}{60}\ \frac{miles}{minutes}=\frac{40}{x}\ \frac{miles}{minutes}\\\\x=60(40)/25\\\\x=96\ minutes

Part 5) we know that

For every bar of soap that Aly sells, she earns $5

For every mug that Janet sells, she earns twice as much as Aly

Aly sells 5 bars of soap and Janet sells 7 mugs

How much money did they make altogether?

step 1

Find out the amount earned by Aly

using proportion

\frac{1}{5}=\frac{5}{x}\\\\x=5(5)\\\\x=\$25

step 2

Find out the amount earned by Janet

Remember that

For every mug that Janet sells, she earns twice as much as Aly

so

For every mug that Janet sells, she earns 2($5)=$10

using proportion

\frac{1}{10}=\frac{7}{x}\\\\x=10(7)\\\\x=\$70

step 3

Adds the amount earned by Aly plus the amount earned by Janet

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Part 6) we know that

Ted is making trail mix for a party

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Adds the quantities

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Convert to mixed number

\frac{15}{8}=\frac{8}{8}+\frac{7}{8}=1\frac{7}{8}\ cups\ of\ pretzel

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