Write a real-world problem that is solved by an equation and then solve (show work).
1 answer:
A company is selling books. It has to pay $500 to start printing the books, and once they have done that, the books sell at $14.99 each. How many books must they sell to make a profit?
First we would model an equation. X will be the amount of books sold, and Y will be profits (in dollars obv). They had to pay $500 before they could start selling, so we must account for that too.
This equation would be
because for every book sold, X increases by 1, increasing Y by 14.99
The answer would be 34 books sold in order to turn a profit. (500/14.99=
First we would model an equation. X will be the amount of books sold, and Y will be profits (in dollars obv). They had to pay $500 before they could start selling, so we must account for that too.
This equation would be
The answer would be 34 books sold in order to turn a profit. (500/14.99=
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Answer:
Step-by-step explanation:
a = 2, b = 1, c = -3
We need to factor this by finding the product of a and c, then from there find which factors of a * c will either add or subtract to give us b.
a * c = 6 and the factors of 6 and 1 and 6, 2 and 3. Well, 6 - 1 doesn't equal 1 and neither does 6 + 1. So our factors are 3 and 2. In order to combine those to get a 1 (our b), we will subtract 2 from 3 since 3 - 2 = 1. That means that 3 is positive and 2 is negative. Filling in the formula with 3 and 2 in place of 1 looks like this (always remember to put the absolute value of the largest number first):
Group the first 2 terms together and the second 2 term together in order to factor:
and factor out what's common in each set of parenthesis.
Notice that when we factor out a -1 from the second set of parenthesis, we can distribute it back in to get the equation we started with. We know that factoring by grouping "works" if what is inside both sets of parenthesis is exactly the same. Ours are identical: (2x + 3). That is common now, and can be factored out:
That matches your first choice
Answer:
a. see attached
b. H(t) = 12 -10cos(πt/10)
c. H(16) ≈ 8.91 m
Step-by-step explanation:
<h3>a.</h3>The cosine function has its extreme (positive) value when its argument is 0, so we like to use that function for circular motion problems that have an extreme value at t=0. The midline of the function needs to be adjusted upward from 0 to a value that is 2 m more than the 10 m radius. The amplitude of the function will be the 10 m radius. The period of the function is 20 seconds, so the cosine function will be scaled so that one full period is completed at t=20. That is, the argument of the cosine will be 2π(t/20) = πt/10.
The function describing the height will be ...
H(t) = 12 -10cos(πt/10)
The graph of it is attached.
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<h3>b. </h3>See part a.
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<h3>c.</h3>The wheel will reach the top of its travel after 1/2 of its period, or t=10. Then 6 seconds later is t=16.
H(16) = 12 -10cos(π(16/10) = 12 -10cos(1.6π) ≈ 12 -10(0.309017) ≈ 8.90983
The height of the rider 6 seconds after passing the top will be about 8.91 m.
