For questions 1 - 2, complete the given table of values. Then sketch a graph that shows two complete cycles. 1. Y=- cosx 2. Y =
sin x+1
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Problem 2
Part 1
I'll replace h with y and replace t with x.
The equation turns into y = -5x^2 + 40x + 45
It's of the form y = ax^2+bx+c where
- a = -5
- b = 40
- c = 45
Use the 'a' and b values to find the value of h, which is the x coordinate of the vertex
h = -b/(2a)
h = -40/(2(-5))
h = -40/(-10)
h = 4
At the four second mark is when the rocket will reach its peak height.
Plug this into the original equation to find its paired y value
y = -5x^2 + 40x + 45
y = -5(4)^2 + 40(4) + 45
y = 125
The vertex is at (h,k) = (4, 125).
<h3>The highest the rocket goes is 125 feet.</h3>---------------
Part 2
Plug in y = 0 and solve for x to find when the rocket hits the ground. I'll use the quadratic formula.
Ignore the negative x value. We cannot have negative time values.
The only practical root is that x = 9, meaning the rocket hits the ground at the 9 second mark.
<h3>The rocket is in the air for 9 seconds.</h3>=====================================================
Problem 3
You have a product that sells for $10 and 1000 people buy per month.
The revenue you pull in based on those figures is 10*1000 = 10,000 dollars per month.
If you raised the price by $1, then the $10 jumps to $11. The downside is that the 1000 people drops to 900 people (you lose 100 customers). The revenue would be 11*900 = 9900. So far, it seems like a bad idea to raise prices. But we'll increase the price once more to see what happens.
If the price goes to $12, then you lose another 100 customers and you now have 800 customers. So that's 12*800 = 9600 dollars in revenue per month. It seems the trend is getting worse.
---------------
Let's generalize what's going on.
x = number of times you raise the price by $1
The old price is $10 per item. It jumps up to 10+x per item. At the same time, the customer count goes from 1000 to 1000-100x. Each time x goes up by 1, the expression 1000-100x goes down by 100.
Multiply the price and customer count to get the amount earned.
revenue = (price)*(number of customers)
revenue = (10+x)*(1000-100x)
revenue = 10(1000 - 100x) + x(1000-100x)
revenue = 10,000 - 1000x + 1000x - 100x^2
revenue = 10,000 - 100x^2
revenue = -100x^2 + 10,000
If you were to use the methods done in the previous problem, you should find the vertex is at (0,10000). This means that the max revenue was already reached when x = 0 price increases were done. This reinforces the previous results we got earlier before we started generalizing in terms of x.
You should <u>not</u> raise the price, or else you'll just continue to lose customers until you go to 0. No amount of price raising will get your revenue up, which in turn means the profits will suffer as well. With the product at $10, you are already at the max revenue point.
<h3>Conclusion: Keep the price at $10</h3>Hi there! :)
So, to find the surface area, all you need to do is find the area of each surface on the shape.
Theres 5 different shapes in the model, so you're going to need to find the area of each one.
There is:
1. left side triangle
2.right side triangle
3.slanted rectangle
4.bottom rectangle
5. back rectangle
all the rectangles are simple, so let's start with them.
the dimensions of the slanted rectangle are 7m and 8m, so 8•7 is 56.
the dimensions of the bottom rectangle are 5m and 7m, so its 35.
the back rectangle has 5m and 7m so it is 35.
Halfway done!!
Now, onto the triangles. they're the same thing as the rectangles, but you half to 'cut it in half' or just divide by two. both of the triangles will be the same.
the triangles measurements are 5m and 8m, so 5•8 is 40, 40÷2 is 20. both of the triangles being 20, now all we have to do is add it up.
20+20+35+35+56=166
and that's about it!
I hope this helps, sorry it took so long to answer, but I hope you have a good day!
-Scarlet
(see photo for my paper work)
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