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Rom4ik [11]
3 years ago
14

Write the point-slope form of the given line that passes through the points (0, -3) and (4, 1). Identify (x1, y1) as (0, -3). In

clude your work in your final answer. Type your answer in the box provided or use the upload option to submit your solution.
Mathematics
1 answer:
ikadub [295]3 years ago
8 0
X1=0
Y1=-3
X2=4
Y2=1
Slop=(y2-y1)/(x2-x1)
Slop=(1-(-3))/(4-0)
Slop=4/4
Slop=1
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I already have the first question done! I just need help with the other two.
Rainbow [258]

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.

x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(40)\pm\sqrt{(40)^2-4(-5)(45)}}{2(-5)}\\\\x = \frac{-40\pm\sqrt{2500}}{-10}\\\\x = \frac{-40\pm50}{-10}\\\\x = \frac{-40+50}{-10} \ \text{ or } \ x = \frac{-40-50}{-10}\\\\x = \frac{10}{-10} \ \text{ or } \ x = \frac{-90}{-10}\\\\x = -1 \ \text{ or } \ x = 9\\\\

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>
3 0
3 years ago
Square root of 512m^3. show work
ElenaW [278]

The solution would be like this for this specific problem:

√512m³ = √256m² × √2m

= 16 × √2m

I am hoping that this answer has satisfied your query and it will be able to help you in your endeavor, and if you would like, feel free to ask another question.

6 0
3 years ago
Nine less than five times a number is equal to -30.
notka56 [123]

Answer: 5x-30-9

-159

Step-by-step explanation:

-159 is the answer

6 0
3 years ago
What is the answer to this inequality 84 is no less than 7 times a number k
lyudmila [28]
84 is no less than 7 times K, 84 divided by 7= 12,
  
 K=12
5 0
3 years ago
Read 2 more answers
Find the slope of the line that passes through (4,9) and (1,7)
denis-greek [22]

Answer:

2/3

Step-by-step explanation:

Use the formula for finding gradient.

7 0
3 years ago
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