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pentagon [3]
3 years ago
7

Please Help!! 10 Points! Brainliest Answer

Mathematics
1 answer:
Ivenika [448]3 years ago
6 0
The correct answer is D because you already have one side and one angle that are equal so you need one more side
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Find the point on the parabola y^2 = 4x that is closest to the point (2, 8).
guapka [62]

Answer:

(4, 4)

Step-by-step explanation:

There are a couple of ways to go at this:

  1. Write an expression for the distance from a point on the parabola to the given point, then differentiate that and set the derivative to zero.
  2. Find the equation of a normal line to the parabola that goes through the given point.

1. The distance formula tells us for some point (x, y) on the parabola, the distance d satisfies ...

... d² = (x -2)² +(y -8)² . . . . . . . the y in this equation is a function of x

Differentiating with respect to x and setting dd/dx=0, we have ...

... 2d(dd/dx) = 0 = 2(x -2) +2(y -8)(dy/dx)

We can factor 2 from this to get

... 0 = x -2 +(y -8)(dy/dx)

Differentiating the parabola's equation, we find ...

... 2y(dy/dx) = 4

... dy/dx = 2/y

Substituting for x (=y²/4) and dy/dx into our derivative equation above, we get

... 0 = y²/4 -2 +(y -8)(2/y) = y²/4 -16/y

... 64 = y³ . . . . . . multiply by 4y, add 64

... 4 = y . . . . . . . . cube root

... y²/4 = 16/4 = x = 4

_____

2. The derivative above tells us the slope at point (x, y) on the parabola is ...

... dy/dx = 2/y

Then the slope of the normal line at that point is ...

... -1/(dy/dx) = -y/2

The normal line through the point (2, 8) will have equation (in point-slope form) ...

... y - 8 = (-y/2)(x -2)

Substituting for x using the equation of the parabola, we get

... y - 8 = (-y/2)(y²/4 -2)

Multiplying by 8 gives ...

... 8y -64 = -y³ +8y

... y³ = 64 . . . . subtract 8y, multiply by -1

... y = 4 . . . . . . cube root

... x = y²/4 = 4

The point on the parabola that is closest to the point (2, 8) is (4, 4).

4 0
2 years ago
Doug read 231 pages in 7 hours.he read the same number of pages each hour.how many pages did he read in 1 hour
tino4ka555 [31]

If we let p be the number of pages read in 1 hour, then in 7 hours Doug reads 7p pages. We know that this number of pages is 231, so we have

7p=231 \iff p = \dfrac{231}{7} = 33

8 0
3 years ago
A line passes through the point (-2,2) and is parallel to the line of y=1/2(x-5/2) l. What is the equation of the line passing t
grin007 [14]
C is your answer. 

It contains the proper points and form. A is not in point-slope form and B has the incorrect slope. 
3 0
3 years ago
Seriously someone help me i answered it but i don’t know if it is right so please tell me if it is and how i got the answer or p
alex41 [277]

Answer:

<h2>C</h2>

Step-by-step explanation:

To determine a function rule, look at the table. Input the x and y value from one column into the function to see if it is correct.

<h3>Function a: y = 10 - 2x</h3>

Input values

22 = 10 - 2(6)

22 = 10 - 12

22 ≠ -2 ❌

As we can see, function a gives us a false statement, so a is incorrect.

<h3>Function b: y = 2 - 10x</h3>

Input values

22 = 2 - 10(6)

22 = 2 - 60

22 ≠ -58 ❌

We once again get a false answer, so b is also not correct.

<h3>Function c: y = 10 + 2x</h3>

Input values

22 = 10 + 2(6)

22 = 22 ✔

Finally, we get a true statement, so option c is correct.

<h3>Function d: y = 2 + 10x</h3>

Just to check that option c is correct, we need to prove that d is incorrect.

Input values

22 = 2 + 60

22 ≠ 62 ❌

This is also wrong, so that proves that c is correct.

I'm always happy to help :)

6 0
3 years ago
A bed is 0.63 m wide, and a door frame is 0.70 m wide.
NemiM [27]

Answer:

0.07

Step-by-step explanation:

0.70-0.63

5 0
2 years ago
Read 2 more answers
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