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3 years ago

2x + 8y = 4 x = -3y + 5

Mathematics

1 answer:

Marianna [84]3 years ago

8 0

Answer:

(

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−

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Step-by-step explanation:

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p is the point on the line 2x+y-10=0 such that the length of OP, the line segment from the origin o to p is a minimum. find the

REY [17]

Coolio

alright, so the disatnce formula is
$D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

solve for y in the equation given on top
2x+y-10=0
y=10-2x
ok
so (x1,y1)=(0,0), the first point
(x2,y2)=(x,10-2x)
so subsitute to get

$D=\sqrt{(x-0)^2+(10-2x-0)^2}$
$D=\sqrt{(x)^2+(10-2x)^2}$
$D=\sqrt{x^2+4x^2-40x+100}$
$D=\sqrt{5x^2-40x+100}$
find the miniumum
we only need to minimize what is under the square root so
take the derivitive of 5x²-40x+100
that is 10x-40
it is 0 at x=4
when x<4, the derivitive is negative
when x>4, the derivitive is positve
goes from negative to positive
so it is a minimum

at x=4
find y
y=10-2x
y=10-2(4)
y=10-8
y=2

(4,2)
find min distance

$D=\sqrt{(x-0)^2+(y-0)^2}$
$D=\sqrt{(4-0)^2+(2-0)^2}$
$D=\sqrt{(4)^2+(2)^2}$
$D=\sqrt{16+4}$
$D=\sqrt{20}$
$D=2\sqrt{5}$

the point, P, is (4,2) and the minimum distance is 2√5

5 0

3 years ago

I NEED HELP PLZ I WILL GIVE THANKS AND BRAINLIST

GuDViN [60]

Answer:

yes

Step-by-step explanation:

you would multiply 2 and 3 then you would add whatever you got from that to 3 which would be 6+3

hope this helps!

4 0

3 years ago

The function f(x) = x2 is translated 7 units to the left and 3 units down to form the function g(x). Which represents g(x)? g(x)

Verdich [7]

Answer:

g(x)=(x+7)^2-3

Step-by-step explanation:

Given:

f(x)= x^2

Now we have to translate f(x) 7 units to the left and 3 units down to form the function g(x).

As per the rules of translation

when any parent function, in given case f(x)=x^2, is translated to 'a' units to the left then 'a' is added to the value of x. thus making f(x+a)

Also when the parent function is translated any 'a' units down then 'a' is subtracted from the value of function. thus making f(x)-a

Translating f(x), 7 units to the left

f(x+7)= (x+7)^2

Translating f(x+7), 3 units down

f(x+7)-3 = (x+7)^2-3

Hence new function g(x)=(x+7)^2-3!

7 0

3 years ago

I'm having a math test tomorrow, what the best way to study?

aliya0001 [1]

Answer:

You can try using flash cards or use quizlet

4 0

3 years ago

Read 2 more answers

Write an equation of the line with the given slope and y intercept: m = 2, b = - 3/4

Alex

Answer:

y = 2x - 3/4

Step-by-step explanation:

Adapt the slope-intercept form: y = mx + b.

Making the indicated substitutions, we get

y = 2x - 3/4

4 0

3 years ago