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UNO [17]
3 years ago
5

At what point on the graph of y=2e^X -1 is the tangent line parallel to the line y= 5x -1

Mathematics
1 answer:
IgorLugansk [536]3 years ago
5 0
Paralell has same slope
y=mx+b
m=slope
y=5x-1
when is the slope 5?

take the derivitive of 2e^x
f'(2e^x)=2f'(e^x)=2e^x

that is the slope
5=2e^x
divide both sides by 2
2.5=e^x
take the ln of both sides
ln2.5=x

when x=ln2.5 they are paralell
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What are the foci of the hyperbola with equation 5y^2-4x^2=20?
shusha [124]
The foci of the hyperbola with equation 5y^2-4x^2=20 will be given as follows:
divide each term by 20
(5y^2)/20-(4x^2)/20=20/20
simplifying gives us:
y^2/4-x^2/5=1
This follows the standard form of the hyperbola
(y-k)²/a²-(x-h)²/b²=1
thus
a=2, b=√5 , k=0, h=0
Next we find c, the distance from the center to a focus.
√(a²+b²)
=√(2²+(√5)²)
=√(4+5)
=√9
=3
the focus of the hyperbola is found using formula:
(h.h+k)
substituting our values we get:
(0,3)
The second focus of the hyperbola can be found by subtracting c from k
(h,k-c)
substituting our values we obtain:
(0,-3)

Thus we have two foci
(0,3) and (0,-3)
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I need help figuring out the coordinate planes of these points ASAP.
d1i1m1o1n [39]

<u>Given</u>:

The vertices of the quadrilateral WXYZ are W(2,4), X(4,2), Y(2,1) and Z(0,2)

The graph is rotated 90° about the origin.

We need to determine the coordinates of the quadrilateral W'X'Y'Z'

<u>Coordinates of the quadrilateral W'X'Y'Z':</u>

The rule to transform the coordinates 90° counter clockwise about the origin is given by

(x, y) \implies(-y, x)

Let us substitute the coordinates.

The coordinates of W' is given by

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The coordinates of X' is given by

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The coordinates of Y' is given by

Y(2,1) \implies Y'(-1,2)

The coordinates of Z' is given by

Z(0,2) \implies Z'(-2,0)

Therefore, the coordinates of the vertices W', X', Y' and Z' are (-4,2), (-2,4), (-1,2) and (-2,0) respectively.

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3 years ago
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Answer:

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6
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