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torisob [31]
3 years ago
5

It costs the theater $750 to put on each performance. If tickets are $8 each, how many tickets must they sell for their next per

formance to profit at least $1,200?
Mathematics
1 answer:
Colt1911 [192]3 years ago
8 0

Answer:

975 tickets

Step-by-step explanation:

1200 + 750 =1950/8 = 975

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1. Consider an athlete running a 40-m dash. The position of the athlete is given by , where d is the position in meters and t is
sasho [114]

There is some information missing in the question, since we need to know what the position function is. The whole problem should look like this:

Consider an athlete running a 40-m dash. The position of the athlete is given by d(t)=\frac{t^{2}}{6}+4t where d is the position in meters and t is the time elapsed, measured in seconds.

Compute the average velocity of the runner over the intervals:

(a) [1.95, 2.05]

(b) [1.995, 2.005]

(c) [1.9995, 2.0005]

(d) [2, 2.00001]

Answer

(a) 6.00041667m/s

(b) 6.00000417 m/s

(c) 6.00000004 m/s

(d) 6.00001 m/s

The instantaneous velocity of the athlete at t=2s is 6m/s

Step by step Explanation:

In order to find the average velocity on the given intervals, we will need to use the averate velocity formula:

V_{average}=\frac{d(t_{2})-d(t_{1})}{t_{2}-t_{1}}

so let's take the first interval:

(a) [1.95, 2.05]

V_{average}=\frac{d(2.05)-d(1.95)}{2.05-1.95}

we get that:

d(1.95)=\frac{(1.95)^{3}}{6}+4(1.95)=9.0358125

d(2.05)=\frac{(2.05)^{3}}{6}+4(2.05)=9.635854167

so:

V_{average}=\frac{9.6358854167-9.0358125}{2.05-1.95}=6.00041667m/s

(b) [1.995, 2.005]

V_{average}=\frac{d(2.005)-d(1.995)}{2.005-1.995}

we get that:

d(1.995)=\frac{(1.995)^{3}}{6}+4(1.995)=9.30335831

d(2.005)=\frac{(2.005)^{3}}{6}+4(2.005)=9.363335835

so:

V_{average}=\frac{9.363335835-9.30335831}{2.005-1.995}=6.00000417m/s

(c) [1.9995, 2.0005]

V_{average}=\frac{d(2.0005)-d(1.9995)}{2.0005-1.9995}

we get that:

d(1.9995)=\frac{(1.9995)^{3}}{6}+4(1.9995)=9.33033358

d(2.0005)=\frac{(2.0005)^{3}}{6}+4(2.0005)=9.33633358

so:

V_{average}=\frac{9.33633358-9.33033358}{2.0005-1.9995}=6.00000004m/s

(d) [2, 2.00001]

V_{average}=\frac{d(2.00001)-d(2)}{2.00001-2}

we get that:

d(2)=\frac{(2)^{3}}{6}+4(2)=9.33333333

d(2.00001)=\frac{(2.00001)^{3}}{6}+4(2.00001)=9.33339333

so:

V_{average}=\frac{9.33339333-9.33333333}{2.00001-2}=6.00001m/s

Since the closer the interval is to 2 the more it approaches to 6m/s, then the instantaneous velocity of the athlete at t=2s is 6m/s

8 0
3 years ago
What is the sum of the interior angles of a polygon shown below?
GREYUIT [131]

Answer: The sum of the interior angles of a polygon shown  in the picture is 540^{\circ}.

Step-by-step explanation:

The given polygon is a regular pentagon having 5 sides.

The sum of the interior angles of a regular polygon is given by :-

(n-2)\times180^{\circ}, wherer n= number of sides of the regular polygon.

Since it has 5 sides, then the sum of the interior angles of a polygon would be

(5-2)\times180^{\circ}\\\\=3\times180^{\circ}\\\\=540^{\circ}

Hence, the sum of the interior angles of a polygon shown  in the picture is 540^{\circ}.

7 0
3 years ago
Which graph shows a negative rate of change for the interval 0 to 2 on the x-axis?
PolarNik [594]

Answer:

Step-by-step explanation:

help

4 0
3 years ago
Please help! <br> i have no clue what to do!!
Oksi-84 [34.3K]

If you look up “Four 4s Challenge” on yt you should find a couple videos explaining it! i just watched a little bit of one so i’ll try and help now though.

I’ll do 1-5 for you and try my best to explain :)) and if you need more answers or more help just let me know

So first, we need to find out how to get 1 using four 4s

1. (4/4)/(4/4)

this would read “four divided by four divided by four divided by four” which equals 1

2. 4/4+4/4

3. (4+4+4)/4

4. 4*(4-4)+4

5. (4*4+4)/4

Remember that you’ve gotta use an equation with just four 4s to get to every number

8 0
3 years ago
What's 7xb +2ya +7xb
Kay [80]
14xb + 2ya is your answer don't report this but if you use math you can get the answer like i did
3 0
4 years ago
Read 2 more answers
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