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4 years ago

(22) Geometry

1 answer:

8 0

Answer: y = (-1/2)x+1

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Explanation:

D = Midpoint of A and B
D = (x,y)
x = [(xCoord of A)+(xCoord of B)]/2
x = [(-4)+(4)]/2
x = 0/2
x = 0
y = [(yCoord of A)+(yCoord of B)]/2
y = [(-2)+(4)]/2
y = 2/2
y = 1
So the midpoint of AB is D = (x,y) = (0,1)

The median for point C will go through the points D = (0,1) and C = (18,-8)

Let's find the slope of line DC
m = (y2-y1)/(x2-x1)
m = (-8-1)/(18-0)
m = -9/18
m = -1/2

Then use the slope m and one of the points D or C to find the y intercept b
I'm going to use the coordinates of point D
y = m*x+b
1 = (-1/2)*(0)+b
1 = 0+b
b = 1

So the equation of line DC is y = (-1/2)x+1, which contains the median that goes through point C

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3 years ago

Find the linear approximation of the function g(x) = 3 1 + x at a = 0. g(x) ≈ Correct: Your answer is correct. Use it to approxi

EleoNora [17]

Answer:

$3.296x+3$

2.835

3.330

Step-by-step explanation:

$g(x) = 3^{1+x}$

Let the linear approximation be L(x) at a = 0. This is given by

$L(x) = g(a) + g'(a)(x-a)$

$g'(x)$ is the derivative of $g(x)$ . To find this, we use the form

If $f(x) = a^x$ , then $f'(x) =a^x\ln a$

By doing this and applying chain rule for the power (which is a function of x), we have

$g'(x) = 3^{1+x}\ln 3$

Then

$g'(0) = 3^{1+0}\ln 3 = 3.296$

Also $g(0) = 3^{1+0} = 3$

Hence $L(x) = 3+(x-0)\times3.296 = 3.296x + 3$

For $3^{0.95}$ , $1+x = 0.95$ and $x=-0.05$

Using this in $L(x)$ ,

$3^{0.95} = 3.296(-0.05) + 3 = 2.835$

For $3^{1.1}$ , $1+x = 1.1$ and $x=0.1$

Using this in $L(x)$ ,

$3^{1.1} = 3.296(0.1) + 3 = 3.330$

7 0

4 years ago

The equation Y equals 4/10 X describes the number of kilometers y that a van travels in x minutes. What is the constant speed of

Mekhanik [1.2K]

Answer:

$\frac{4}{10}=0.4$ kilometers per hour.

Step-by-step explanation:

We have been given an $y=\frac{4}{10}x$ , which describes the number of kilometers y that a van travels in x minutes. We are asked to to find the constant speed of the van in terms of hours.

We can see that van travel $\frac{4}{10}x$ kilometers in x hours. To find the constant speed of van, we will substitute $x=1$ in our given equation as:

$y=\frac{4}{10}(1)$

$y=\frac{4}{10}$

Since van travels $\frac{4}{10}$ kilometers in one hour, therefore, constant speed of van is $\frac{4}{10}$ kilometer per hour or $0.4$ kilometers per hour.