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Andrej [43]
2 years ago
5

Find an equation of the line containing the given points.(3,-7) (0,2)

Mathematics
1 answer:
hammer [34]2 years ago
7 0

Answer:

y = -3x +2

Step-by-step explanation:

To find slope of the equation:

(y^2-y^1) / (x^2-x^1)

= (2-(-7)) / (0-3)

= 9 / -3

= -3

Use Point- Slope form to find equation

y - y1 = m (x - x1)

y - 2 = -3 (x - 0)

y - 2 = -3x + 0

y = -3x +2

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What’s this question
shusha [124]

Multiply the first equation by -1

-3x-y=-4

2x+y=5

Add them up

-x=1

So x=-1

And y=7

So the first option is correct

8 0
2 years ago
Find all points on the portion of the plane x+y+z=5 in the first octant at which f(x, y, z) = xy2z2 has a maximum value.
irina1246 [14]
Lagrange multipliers:

L(x,y,z,\lambda)=xy^2z^2+\lambda(x+y+z-5)

L_x=y^2z^2+\lambda=0
L_y=2xyz^2+\lambda=0
L_z=2xy^2z+\lambda=0
L_\lambda=x+y+z-5=0

\lambda=-y^2z^2=-2xyz^2=-2xy^2z

-y^2z^2=-2xyz^2\implies y=2x (if y,z\neq0)

-y^2z^2=-2xy^2z\implies z=2x (if y,z\neq0)

-2xyz^2=-2xy^2z\implies z=y (if x,y,z\neq0)

In the first octant, we assume x,y,z>0, so we can ignore the caveats above. Now,

x+y+z=5\iff x+2x+2x=5x=5\implies x=1\implies y=z=2

so that the only critical point in the region of interest is (1, 2, 2), for which we get a maximum value of f(1,2,2)=16.

We also need to check the boundary of the region, i.e. the intersection of x+y+z=5 with the three coordinate axes. But in each case, we would end up setting at least one of the variables to 0, which would force f(x,y,z)=0, so the point we found is the only extremum.
4 0
3 years ago
Find the range. 83, 71, 62, 86, 90, 95, 61, 60, 87, 72, 95, 74, 82, 54, 99, 62, 78, 76, 84, 92
galina1969 [7]

Answer: 45

Step-by-step explanation: The range is the difference between the greatest number in the data set and the least number in the data set which in this case is 99 - 54 or 45. So the range of this data set is 45.

6 0
2 years ago
Read 2 more answers
I have to find the area
Alina [70]
The formula for finding the area of a triangle is: base*height*1/2
So, if we use this information....
4.2*5.5*1/2=11.55
Area=11.55
4 0
3 years ago
Read 2 more answers
A parking garage charges a 3.50$ base fee plus an hourly rate of 7.00$. If you have at most 21.50$ to pay for parking, how long
pentagon [3]

Answer:

You get a total of two hours of parking.

Step-by-step explanation:

First, you subtract the base fee of $3.50, which gives you $18.00. Then you subtract as many sevens there are in 18, which is two. And then your answer is shown, as two. Hope this helps!

3 0
3 years ago
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