2 years ago

What is an equation of the line that is parallel to y=3x-8 and passes through the point, (4,-5)

Mathematics

1 answer:

VladimirAG [237]2 years ago

5 0

Answer:

y= 3x-17

Step-by-step explanation:

When finding a parallel equation to y=mx+b, mx will always stay the same. So we have to find b.

In order to do this you plug the parallel lines passing point into the equation.

-5(y) goes into the y's spot. 4(x) goes into the x's spot.

-5 = 3 x 4 + b

-5 = 12 + b

-5 - 12 = 12 - 12 + b

-17 = b

y=3x-17

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2 years ago

Consider f(x)=3ax−x2. write down a formula in terms of a for the maximum of f(x).

lidiya [134]

For this case we have the following function:
$f (x) = 3ax-x ^ 2
$
To find the maximum of the function, what we should do is to derive the equation.
We have then:
$f '(x) = 3a-2x
$
We match zero:
$3a-2x = 0
$
We clear the value of x:
$2x = 3a

x = (2/3) a$
We substitute the value of x in the function to find the maximum:
$f ((2/3) a) = 3a ((2/3) a) - ((2/3) a) ^ 2
$
Rewriting:
$f ((2/3) a) = 2a ^ 2 - (4/9) a ^ 2

f ((2/3) a) = (18/9) a ^ 2 - (4/9) a ^ 2

f ((2/3) a) = (14/9) a ^ 2$
Answer:
a formula in terms of a for the maximum of f (x) is:
$f ((2/3) a) = (14/9) a ^ 2$