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Before performing any calculation it's good to recall a few properties of integrals:
So we apply the first property in the first expression given by the question:
![\small \sf{\longrightarrow\int ^3_{-2} [2f(x) +2]dx= 2 \int ^3 _{-2} f(x) dx+ \int f^3 _{2} 2dx=18}](https://tex.z-dn.net/?f=%5Csmall%20%5Csf%7B%5Clongrightarrow%5Cint%20%5E3_%7B-2%7D%20%5B2f%28x%29%20%2B2%5Ddx%3D%202%20%5Cint%20%5E3%20_%7B-2%7D%20f%28x%29%20dx%2B%20%5Cint%20f%5E3%20_%7B2%7D%202dx%3D18%7D)
And we solve the second integral:
Then we take the last equation and we subtract 10 from both sides:
And we divide both sides by 2:
Then we apply the second property to this integral:
Then we use the other equality in the question and we get:
We substract 8 from both sides:
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Answer:
a) C = 250 + 1.25n
b) 1800
c) 300
Step-by-step explanation:
a) To write the equation for these problems, let's establish the constant, $250, since we are given that $250 is a FIXED cost, meaning no matter how many brochures we print, we will have to pay $250. Then, we have to pay $1.25 for each brochure, so for n amount of brochures, so we have 1.25*n. Putting it together, we have the fixed cost + the cost of producing n brochures, C = 250 + 1.25C
b) The cost of printing 2500 brochures can be found by pluggin number into the equation above. C = 250 + 1.25*2500 = $1800
c) This is the opposite question, since 625 is the final cost, we plug it into the final cost, 625 = 250 + 1.25*n. Solving gives n = 300
Answer:
First blank- 32000 ounces
Second blank- 2000 pounds
Yes the bridge can hold 1 ton.
Step-by-step explanation:
The ratio of the scale of the model to the real bridge = 1:4
The test model shows the model can take 8000 ounces
The real bridge will therefore take 8000 x 4 = 32000 ounces
16 ounces = 1 pound
32000 ounces = x pounds
==> = 32000/16 = 2000 pounds
2000 pounds = 1 ton
therefore the bridge holds 1 ton
Answer:
-7.5x3+(20+2.5)=0
this one is equal to 0 ;)
