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3 years ago

What is the midpoint of CD?

Mathematics

1 answer:

Otrada [13]3 years ago

8 0

Answer:

The endpoints of the line segment CD are:

$$C=(x_1,y_1)= (-4, 8) \\ D= (x_2,y_2)= (8, -4) $$

We find the midpoint using th

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Find gradient xe^y + 4 ln y = x² at (1, 1)

cricket20 [7]

$xe^y+4\ln y=x^2$

Differentiate both sides with respect to x, assuming y = y(x).

$\dfrac{\mathrm d(xe^y+4\ln y)}{\mathrm dx}=\dfrac{\mathrm d(x^2)}{\mathrm dx}$

$\dfrac{\mathrm d(xe^y)}{\mathrm dx}+\dfrac{\mathrm d(4\ln y)}{\mathrm dx}=2x$

$\dfrac{\mathrm d(x)}{\mathrm dx}e^y+x\dfrac{\mathrm d(e^y)}{\mathrm dx}+\dfrac4y\dfrac{\mathrm dy}{\mathrm dx}=2x$

$e^y+xe^y\dfrac{\mathrm dy}{\mathrm dx}+\dfrac4y\dfrac{\mathrm dy}{\mathrm dx}=2x$

Solve for dy/dx :

$e^y+\left(xe^y+\dfrac4y\right)\dfrac{\mathrm dy}{\mathrm dx}=2x$

$\left(xe^y+\dfrac4y\right)\dfrac{\mathrm dy}{\mathrm dx}=2x-e^y$

$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{2x-e^y}{xe^y+\frac4y}$

If y ≠ 0, we can write

$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{2xy-ye^y}{xye^y+4}$

At the point (1, 1), the derivative is

$\dfrac{\mathrm dy}{\mathrm dx}\bigg|_{x=1,y=1}=\boxed{\dfrac{2-e}{e+4}}$

4 0

3 years ago

How do you calculate the midpoint of question e)? I am very desperate. please help

andrey2020 [161]

Answer:

(-1,-1)

Step-by-step explanation:

Midpoint equation: $(\frac{x_2+x_1}{2}, \frac{y_2+y_1}{2})$

= $(\frac{-5/2+1/2}{2},\frac{-1/2-3/2}{2} )$

= $(\frac{-2}{2},\frac{-2}{2})$

=(-1,-1)

Use the formula and plug it in :)

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2 years ago

What is the value of z in the equation 4 x 2- z=7?

saw5 [17]

Z=1

Hope this helped! :)

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3 years ago

Read 2 more answers

Find the slope of the line that passes through each pair of points

pantera1 [17]

Answer:

upper left: -7/3, lower: 3, upper right: -2/3

Step-by-step explanation:

upper left :

(1-8)/(7-4)=-7/3

lower:

(9-0)/(4-1)=9/3=3

upper right:

(-1-5)/(6-(-3))=-6/9=--2/3

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3 years ago

Expand & simplify: 3 (C-7)+2(3c+4)

cupoosta [38]

Answer: 3 (C-7)+2(3c+4)

Step-by-step explanation: Given

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= 3c - 21 + 6c + 8 ← collect like terms

= 9c - 13

4 0

3 years ago