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coldgirl [10]
3 years ago
9

an auditorium holds 72 people for a school assembly. only staff and students will attend. if the number of students is 8 times t

he staff, then how many students are there?
Mathematics
2 answers:
lina2011 [118]3 years ago
7 0

Answer:

I would say there should be about 63 students

Solnce55 [7]3 years ago
5 0

Answer:

There would be around 64 students

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I need help proving this ASAP
Ket [755]

Answer:

See explanation

Step-by-step explanation:

We want to show that:

\tan(x +  \frac{3\pi}{2} )  =  -   \cot \: x

One way is to use the basic double angle formula:

\frac{ \sin(x +  \frac{3\pi}{2} ) }{\cos(x +  \frac{3\pi}{2} )}  =  \frac{ \sin(x)  \cos( \frac{3\pi}{2} )  +   \cos(x)  \sin( \frac{3\pi}{2}) }{\cos(x)  \cos( \frac{3\pi}{2} )   -    \sin(x)  \sin( \frac{3\pi}{2}) }

\frac{ \sin(x +  \frac{3\pi}{2} ) }{\cos(x +  \frac{3\pi}{2} )}  =  \frac{ \sin(x) ( 0)  +   \cos(x) (  - 1) }{\cos(x) (0)   -    \sin(x) (  - 1) }

We simplify further to get:

\frac{ \sin(x +  \frac{3\pi}{2} ) }{\cos(x +  \frac{3\pi}{2} )}  =  \frac{ 0  -   \cos(x) }{0 +    \sin(x) }

We simplify again to get;

\frac{ \sin(x +  \frac{3\pi}{2} ) }{\cos(x +  \frac{3\pi}{2} )}  =  \frac{- \cos(x) }{ \sin(x) }

This finally gives:

\frac{ \sin(x +  \frac{3\pi}{2} ) }{\cos(x +  \frac{3\pi}{2} )}  =  -  \cot(x)

6 0
4 years ago
School starts in 45 minutes and you live 17 miles from school. What average speed (in miles per hour) do you need to travel in o
Arada [10]
It would be 22.67mph
3 0
4 years ago
The perimeter of a rectangular goat pen is 28 meters. The pen is 5 meters wide. How long is it?
polet [3.4K]

Answer:

I think it would be 9 meters.

Step-by-step explanation:

5x2=10

28-10=18

18(divided by)2=9 meters

3 0
2 years ago
Read 2 more answers
3. Jim bought a new pair of glasses. The lenses had six sides. The lenses were in the shape of a A. hexagon. B. heptagon. C. qua
Vladimir [108]
Best Answer:<span>  </span><span>6 sides is a hexagon. 

the spoke of a wheel is like a radius. Circumference is equal to 2πr so r = 42/2π ≈ 6.69 inches, ans. D. 

that's it! ;)</span>
5 0
3 years ago
BAC ~ DEC what is the value of x?
Anna007 [38]

Answer: x = 37.8

Step-by-step explanation: We start with triangle ABC with two sides given as 15 and 18. We shall make angle C the reference angle and thereby calculate the third side, line BC.

Since we have the opposite side as 15, and the adjacent side (which lies between the reference angle and the right angle) as 18, we can use the tangent of the angle C

Tan C = Opp/Adj

Tan C = 15/18

Tan C = 0.8333

From our table of values/use of the calculator

Tan C = 39.8

Angle C in triangle ACB = Angle C in triangle ECD (Opposite angles are equal).

That takes us to triangle ECD, since the reference angle is known (39.8) and the opposite side is also given (31.5), we can now calculate the adjacent which is side x.

Tan C = Opp/Adj

Tan 39.8 = 31.5/x

when you cross multiply, x moves to the left hand side, while Tan 39.8 moves to the right hand side

x = 31.5/Tan 39.8

x = 31.5/0.8333

<u>x = 37.8</u>

5 0
3 years ago
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