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devlian [24]
2 years ago
6

The class president is organizing a class trip to a nearby amusement park for 314 students. The regular price is $35 per ticket.

However, some students can receive a discount due to volunteer community service work that they took part in on Saturdays. The students who are eligible for the discount will pay $21.50. The total ticket cost for the class trip will be $10,072. How many students are eligible for the discount?
Mathematics
1 answer:
salantis [7]2 years ago
7 0

Answer:

287 students were eligible for the discount :)

Step-by-step explanation:

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How to use trig to find missing side or angle of right triangles.
andrew11 [14]
Explanation

Right triangles are triangles with one right angle i.e. one angle with a measure of 90° so when we deal with this type of figures we know at least one of its internal angles. The opposite side to the right angle is known as the hypotenuse whereas the other two sides are called legs.

Trigonometric functions in right triangles give us the following identities:

\begin{gathered} \tan x=\frac{\text{opposite side}}{\text{adjacent side}} \\ \cos x=\frac{\text{adjacent side}}{\text{hypotenuse}} \\ \sin x=\frac{\text{opposite side}}{\text{hypotenuse}} \end{gathered}

We also have the Pythagorean theorem that states that the square of the hypotenuse is the sum of the squares of the legs.

Let's imagine that we have a right triangle like the following:

If we want to find the missing angles A and/or B we need to know at least two sides of the triangle.

For example, if we want to find B and we have b and a we can use the tangent of B and its inverse the arctangent (tan^(-1)):

\tan B=\frac{b}{a}\rightarrow B=\tan^{-1}(\frac{b}{a})

If we know a and c we can find B using its cosine:

\cos B=\frac{a}{c}\rightarrow B=\cos^{-1}(\frac{a}{c})

If we know b and c then we can use the sine:

\sin B=\frac{b}{c}\rightarrow B=\sin^{-1}(\frac{b}{c})

We can also do the same for angle A, we just need to use its corresponding opposite side and adjacent side. And that's how you find a missing angle using trigonometry in a right triangle.

If we are looking for a missing side we can also use trigonometry. In order to find a missing side we need two other sides or another side and an angle. For example, let's assume that we want to find side a.

If we have b and c then we just need to use the Pythagorean theorem:

c^2=a^2+b^2\rightarrow a=\sqrt{c^2-b^2}

If we have b and A then we can use the tangent of A to built an equation for a:

\tan A=\frac{a}{b}\rightarrow a=b\cdot\tan A

If we have b and B we can use the tangent of B:

\tan B=\frac{b}{a}\rightarrow a=\frac{b}{\tan B}

If we have A and c we can use the sine of A:

\sin A=\frac{a}{c}\rightarrow a=c\cdot\sin A

If we have B and c we can use the cosine of B:

\cos B=\frac{a}{c}\rightarrow a=c\cdot\cos B

And that's how you find a missing side using trigonometry.

8 0
9 months ago
Which equation can be used to find one multiple of 16? 16 ÷ 8 = 2 16 ÷ 4 = 4 16 × 0 = 0 16 × 2 = 32
lawyer [7]

Answer:

  16 × 2 = 32

Step-by-step explanation:

Since you want a multiple, you can ignore anything with a "divided by" symbol in it.

0 is a multiple of anything, so is considered a "trivial" or "degenerate" case. Usually, that is not of interest.

Multiplying 16 by 2 will give a multiple of 16, as will multiplying 16 by any other non-zero integer.

7 0
3 years ago
Read 2 more answers
What is the surface area of this rectangular prism?
Lesechka [4]

Answer:

160cm^2

Step-by-step explanation:

So the surface area is basicly the sum of all the areas of the rectangles in this prism.

So the formula can be written as  2(wl + hl+hw).

The w stands for width, the h stands for height, and the l stands for length.

5cm is the width, 10 cm is the length, and 2 cm is the height.

So inserting all those values for the variabls the formula now looks like this.

2((5)(10)+(2)(10)+(2)(5)).

So 5*10 is <u><em>50</em></u>

2*10 is <u><em>20</em></u>

2*5 is <em><u>10</u></em>

So adding all that up we get 80.

Then multiplyong that by 2 we get 160cm^2.

4 0
3 years ago
What is the measure of angle A?
fgiga [73]

Answer:

∠A=65º

Step-by-step explanation:

  • A angle of a line is 180º, so we can say that angle ABC=(180-6x)º
  • The interior angkes of a triangle is 180º, so (x+40)º+(3x+10)º+(180-6x)º=180º
  • Remove parenthesis, x+40+3x+10+180-6x=180
  • Combine like terms, -2x+230=180
  • Subtract 180, -2x=-50
  • Divide by -2, so x=25

Now:

  • ∠CAB=(25+40)º=65º
  • ∠ABC=[180-6(25)]º=30º
  • ∠BCA=[3(25)+10]=85º
5 0
2 years ago
Jack has two jars of wax. One jar is 1/6 full. The other jar is 4/6 full. Write an equation to find the amount of wax Jack has.
Solnce55 [7]

Answer:

1/6 + 4/6 = 5/6

Step-by-step explanation:

I hope this helped

5 0
3 years ago
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