SOLUTION: 1. One number is 9 more than 2 times another. Their product is 5 more than 3 times their sum. Find the numbers. Answer in the form of paired points with the lowest of the two integ

Question 1055264: 1. One number is 9 more than 2 times another. Their product is 5 more than 3 times their sum. Find the numbers. Answer in the form of paired points with the lowest of the two integers first.
2. A company can manufacture x hundred items for a total cost of C=400+1100 x-100x^2. Find x if the total cost is $3,200.
3. A company that manufactures hair ribbons knows that the number of ribbons it can sell each week, x, is related to the price p per ribbon by the equation x=900-100p. At what price should the company sell the ribbons if it wants the weekly revenue to be $1,400? (Remember: The equation for revenue is R=xp).
4. A gun fires a bullet almost straight up from the edge of a 160-foot cliff. If the bullet leaves the gun with a speed of 636 feet per second, its height at time t is given by h(t)=-16t2+636t+160, measured from the ground below the cliff. When will the bullet land on the ground below the cliff? (Hint: What is its height when it lands? Remember that we are measuring from the ground below, not from the cliff.)
The bullet will land after __ seconds.
5. If a rocket is fired vertically into the air with a speed of 240 feet per second, its height at time t seconds is given by h=-16t2+240t.
At what time(s) will the rocket be the following number of feet above the ground?
a. The rocket will 864 feet high after __ seconds.
b. The rocket will 896 feet high after __ seconds.
c. How long will the rocket be in the air? (Hint: How high is it when it hits the ground?)
The rocket will be in the air for __ seconds.
Answer by ikleyn(52776)   (Show Source): You can put this solution on YOUR website!
.
One problem/question per post.

It is the RULE of this site.
By violating this rule, you work against yourself.

Regarding ##2 and 3, see the lessons
    - HOW TO complete the square to find the minimum/maximum of a quadratic function
    - Briefly on finding the minimum/maximum of a quadratic function
    - HOW TO complete the square to find the vertex of a parabola
    - Briefly on finding the vertex of a parabola
in this site.

Regarding ## 4 and 5, see the lessons
    - Problem on an arrow shot vertically upward
    - Problem on a ball thrown vertically up from the top of a tower

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