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katrin [286]
3 years ago
6

A segment with endpoint M Left parenthesis 5 comma 9 right parenthesis and N Left parenthesis 4 comma 3 right parenthesis is rot

ated 270°. What are the coordinates of M prime and N prime?
The correct answer is : M prime (9,-5) and N prime (3,-4)

Mathematics
1 answer:
mario62 [17]3 years ago
3 0
Refer to the diagram below

If we draw a line that connects the center of rotation to one of the points, say point N, and take this line as the 0° position, then we need three 'turn' of 90° to get to 270°.

Coordinate of N' (-3, 4)
Coordinate of M' (-9, 5)

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Need help with AP CAL
anzhelika [568]

Answer: Choice C

\displaystyle \frac{1}{2}\left(1 - \frac{1}{e^2}\right)

============================================================

Explanation:

The graph is shown below. The base of the 3D solid is the blue region. It spans from x = 0 to x = 1. It's also above the x axis, and below the curve y = e^{-x}

Think of the blue region as the floor of this weirdly shaped 3D room.

We're told that the cross sections are perpendicular to the x axis and each cross section is a square. The side length of each square is e^{-x} where 0 < x < 1

Let's compute the area of each general cross section.

\text{area} = (\text{side})^2\\\\\text{area} = (e^{-x})^2\\\\\text{area} = e^{-2x}\\\\

We'll be integrating infinitely many of these infinitely thin square slabs to find the volume of the 3D shape. Think of it like stacking concrete blocks together, except the blocks are side by side (instead of on top of each other). Or you can think of it like a row of square books of varying sizes. The books are very very thin.

This is what we want to compute

\displaystyle \int_{0}^{1}e^{-2x}dx\\\\

Apply a u-substitution

u = -2x

du/dx = -2

du = -2dx

dx = du/(-2)

dx = -0.5du

Also, don't forget to change the limits of integration

  • If x = 0, then u = -2x = -2(0) = 0
  • If x = 1, then u = -2x = -2(1) = -2

This means,

\displaystyle \int_{0}^{1}e^{-2x}dx = \int_{0}^{-2}e^{u}(-0.5du) = 0.5\int_{-2}^{0}e^{u}du\\\\\\

I used the rule that \displaystyle \int_{a}^{b}f(x)dx = -\int_{b}^{a}f(x)dx which says swapping the limits of integration will have us swap the sign out front.

--------

Furthermore,

\displaystyle 0.5\int_{-2}^{0}e^{u}du = \frac{1}{2}\left[e^u+C\right]_{-2}^{0}\\\\\\= \frac{1}{2}\left[(e^0+C)-(e^{-2}+C)\right]\\\\\\= \frac{1}{2}\left[1 - \frac{1}{e^2}\right]

In short,

\displaystyle \int_{0}^{1}e^{-2x}dx = \frac{1}{2}\left[1 - \frac{1}{e^2}\right]

This points us to choice C as the final answer.

5 0
2 years ago
The product of a number X and six is for more than the product of the number and 3/8. Which answer represents this situation?
stiks02 [169]

Answer:3/8y+(6x+4)

Step-by-step explanation:

I’m 99% sure to is is right

6 0
3 years ago
Determine whether each relationship is a function
Mademuasel [1]
It’s a function
hope you have a good day
8 0
2 years ago
Nikolai has a jar filled with 120 marbles. he has 72 red marbles, 17 blue marbles, 13 green marbles, and 18 purple marbles. what
asambeis [7]
To find the probability of both of these occurring, you will multiply the probability of choosing a blue marble by the probability of choosing a purple marble (with no replacement after the first one).

Probability of choosing a blue marble:  17/120
Probability of choosing a purple marble: 18/119

17/120 x 18/119 = 3/140

You will have a 3/140 chance of both of these occurring.
4 0
3 years ago
Goods are purchased for ₹1500. If one fifth of the goods sold at a profit of 5% and the remaining four-fifth of the goods at a p
Tpy6a [65]

Answer:

9%

Step-by-step explanation:

Cost of 1/5 good = 1500*1/5= 300

Profit= 5%

SP = (profit+100)/100*CP

SP= (5+100)/100*300

SP = 105/100*300

SP= 1.05*300= 315

Cost of 4/5 good = 1500*4/5= 1200

Profit= 10%

SP= (profit+100)/100*CP

SP= (10+100)/100*1200

SP = 110/100*1200

SP= 1.10*1200= 1320

Total SP = 315+1320= 1635

Net profit= 1635-1500= 135

Profit% = 135/1500*100%

Profit% = 0.09*100%

Profit% = 9%

6 0
3 years ago
Read 2 more answers
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