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Anon25 [30]
1 year ago
7

Find the length of the semi-major axis of the ellipse x^2/49+y^2/36=1

Mathematics
1 answer:
Slav-nsk [51]1 year ago
4 0

The length of the semi-major axis of the ellipse is 7.

What is the semi-major axis of an ellipse?

The semi-major axis of an ellipse is the half of the longest diameter passing through its vertex and focus.

The general equation of an ellipse is :

⇒ x²/a²+y²/b²=1, where a is the semi-major axis and b, is the semi-minor axis

x²/49+y²/36=1

x²/(7²)+y²/(6²)=1

x²/a²+y²/b²=1

a=7

Learn more about the semi-major axis here:

brainly.com/question/14180045

#SPJ1

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Find the equation of the line that contains the given point and the given slope. Write the equation in slope-intercept form.
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The slope-point form of a line:

y-y_0=m(x-x_0)

The slope-intercept form of a line:

y=mx+b

1.

m=6,\ (4,\ 1)\to x_0=4,\ y_0=1

Substitute

y-1=6(x-4)\qquad|\text{use distributive property}\\\\y-1=6x-24\qquad|\text{add 1 to both sides}\\\\\boxed{y=6x-23}

2.

m=-5,\ (6,\ -3)

Substitute

y-(-3)=-5(x-6)\qquad|\text{use distributive property}\\\\y+3=-5x+30\qquad|\text{subtract 5 from both sides}\\\\\boxed{y=-5x+24}

3.

m=-\dfrac{1}{2},\ (-8,\ 2)\\\\y-2=-\dfrac{1}{2}(x-(-8))\\\\y-2=-\dfrac{1}{2}(x+8)\\\\y-2=-\dfrac{1}{2}x-4\qquad|\text{add 2 to both sides}\\\\\boxed{y=-\dfrac{1}{2}x-2}

4.

m=0,\ (-7,\ -1)\\\\y-(-1)=0(x-(-7))\\\\y+1=0\qquad|\text{subtract 1 from both sides}\\\\\boxed{y=-1}

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3 years ago
The plate is rotated 90° about the origin in the counterclockwise direction. In the image trapezoid, what are the coordinates of
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Answer:

The coordinates of the endpoints of the side congruent to side EF is:

E'(-8,-4) and F'(-5,-7).

Step-by-step explanation:

<em>" when point M (h, k) is rotated about the origin O through 90° in anticlockwise direction or we can say counter clockwise. The new position of point </em><em>M (h, k) will become M' (-k, h) "</em>

We are given a trapezoid such that the vertices of trapezoid are:

E(-4,8) , F(-7,5) , G(-4,3) , H(-2,5)

Then the new coordinates after the given transformation is:

E(-4,8) → E'(-8,-4)

F(-7,5) → F'(-5,-7)

G(-4,3) → G'(-3,-4)

H(-2,5) → H'(-5,-2)

Hence the coordinates of the endpoints of the side congruent to side EF is:

E'(-8,-4) and F'(-5,-7).


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Question 9 (1 point)
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Answer:

7

Step-by-step explanation:

16x-80+18=4x+22

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