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quester [9]
3 years ago
8

What is the slope-intercept form of the line?

Mathematics
1 answer:
Anna11 [10]3 years ago
4 0

The slope-intercept of the line is

y= -2/3x + 2

Going up 2, left 3

Change in y

------------------

change in x

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Find the points on the ellipse 4x2 + y2 = 4 that are farthest away from the point (−1, 0).
Hitman42 [59]
<span>The two points that are most distant from (-1,0) are exactly (1/3, 4sqrt(2)/3) and (1/3, -4sqrt(2)/3) approximately (0.3333333, 1.885618) and (0.3333333, -1.885618) Rewriting to express Y as a function of X, we get 4x^2 + y^2 = 4 y^2 = 4 - 4x^2 y = +/- sqrt(4 - 4x^2) So that indicates that the range of values for X is -1 to 1. Also the range of values for Y is from -2 to 2. Additionally, the ellipse is centered upon the origin and is symmetrical to both the X and Y axis. So let's just look at the positive Y values and upon finding the maximum distance, simply reflect that point across the X axis. So y = sqrt(4-4x^2) distance is sqrt((x + 1)^2 + sqrt(4-4x^2)^2) =sqrt(x^2 + 2x + 1 + 4 - 4x^2) =sqrt(-3x^2 + 2x + 5) And to simplify things, the maximum distance will also have the maximum squared distance, so square the equation, giving -3x^2 + 2x + 5 Now the maximum will happen where the first derivative is equal to 0, so calculate the first derivative. d = -3x^2 + 2x + 5 d' = -6x + 2 And set d' to 0 and solve for x, so 0 = -6x + 2 -2 = -6x 1/3 = x So the furthest point will be where X = 1/3. Calculate those points using (1) above. y = +/- sqrt(4 - 4x^2) y = +/- sqrt(4 - 4(1/3)^2) y = +/- sqrt(4 - 4(1/9)) y = +/- sqrt(4 - 4/9) y = +/- sqrt(3 5/9) y = +/- sqrt(32)/sqrt(9) y = +/- 4sqrt(2)/3 y is approximately +/- 1.885618</span>
7 0
3 years ago
Find the arc length for a circle with diameter 10 inches and central angle 60 degrees. Round to the nearest tenth.
UkoKoshka [18]

Answer:

C. 5.2 cm

Step-by-step explanation:

Arc length formula:

s = \dfrac{n}{360^\circ} 2 \pi r

where s = arc length

n = central angle of arc

r = radius of circle

diamter = d = 10 cm

r = d/2 = 10 cm/2 = 5 cm

n = 60 deg

s = \dfrac{n}{360^\circ} 2 \pi r

s = \dfrac{60^\circ}{360^\circ} 2 \times 3.14159 \times 5 ~cm

s = 5.2~cm

Answer: 5.2 cm

6 0
3 years ago
Find the range of g(x)=x²+2 for the domain {0,2,5,9}
erastova [34]
For a function, domain means the x value & range is the y value. So, simply, substitute each value in the domain for the x in your function, and you'll find the range.
Here're the answers:
g(0)=(0)^2+2
g(0)=2
g(2)=(2)^2+2
g(2)=6
g(5)=(5)^2+2
g(5)=27
g(9)=(9)^2+2
g(9)=83
Hope this helps!
8 0
3 years ago
Break apart ones to make a ten<br><br> 62 + 9 =
dsp73

Answer:

71

Step-by-step explanation:

I know this because 62 and 9 equal 71

7 0
3 years ago
(x+5)(X + 11)<br> please help
dexar [7]

Answer:

\left(x+5\right)\left(x+11\right)\\\\=xx+x\cdot \:11+5x+5\cdot \:11\\\\=xx+11x+5x+5\cdot \:11\\\\=x^2+16x+55

hope this helps you

3 0
2 years ago
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