All categories

2 years ago

Find the point on the line 2x+4y−3=0 which is closest to the point (2,0)

1 answer:

7 0

L1: 2x+4y-3=0 ..........(1)
P: (2,0)
The point on the line L1 closest to the given point P is at the intersection of L1 with L2, which is the perpendicular passing through P.

Slope of L1=-2/4=-1/2
Slope of L2=-1/(-1/2)=2
Since it passes throug P(2,0), we can use the point-slope formula:
(y-0)=2(x-2) =>
L2: 2x-y-4=0.............(2)

Solve for x & y using (1) and (2) to get intersection point required:
(1)-(2)
2x-2x + 4y-(-y) -3 -(-4) =0
5y=-1, y=-1/5
Substitute y=1/5 in equation (1)
2x+4(-1/5)-3=0 =>
2x-19/5=0
x=19/10

=> the point on L1 closest to (2,0) is (19/10, -1/5)

You might be interested in

Now, determine a general rule for what happens when we have two exponential

fomenos

Y=mx+b so this means you’ll get the correct answer

3 0

2 years ago

I need hard and easy math questions with the answer, i need 10 questions<br><br>thnx

nydimaria [60]

Answer:

https://www.khanacademy.org/

Step-by-step explanation:

I am not entirely sure what you mean however if you sign up for this website and go to whichever grade level you need you can practice all you want

8 0

1 year ago

Lisa family drove 830.76 miles to visit her grandpaerents.Lisa calculated that they used 30.1 gallons og gas .how many miles per

Irina-Kira [14]

830.76/30.1=27.6 miles

7 0

2 years ago

A savings bank invests $58,800 in municipal bonds and earns 12% per year on the investment. How much money is earned per year?

seraphim [82]

To find the answer we simply have to find 12% of 58,800. So to do that, we can multiply it by .12

58,800 • .12 = 7,056

So $7,056 is earned per year

5 0

3 years ago

Read 2 more answers

A rectangular prism had a volume of 252 cubic centimeters. The length of the prism is 14 centimeters and the width of the prism

mojhsa [17]

<h2>Answer:</h2>

A prism is a solid object having two identical bases, hence the same cross section along the length. Prism are called after the name of their base. A rectangular prism is a solid whose base is a rectangle. Multiplying the three dimensions of a rectangular prism: length, width and height, gives us the volume of a prism:

$V=L\times W\times H$

FOR THE ORIGINAL PRISM WE HAVE THE FOLLOWING DIMENSIONS:

$L=14cm \\ \\ W=6cm \\ \\ H=3cm$

In fact, the volume is $252cm^3$ because:

$V=14\times 6\times 3 \therefore V=252cm^3$

Now the height of the prism was changed from 3 centimeters to 6 centimeters to create a new rectangular prism, therefore:

FOR THE NEW PRISM WE HAVE THE FOLLOWING DIMENSIONS:

$L=14cm \\ \\ W=6cm \\ \\ H=6cm$

So the new volume is:

$V=14\times 6\times 6 \therefore V=504cm^3$

<h3><em>What do we know about the volume of the new prism?</em></h3>

<em>Well, the volume has increased from </em> $252cm^3 \ to \ 504cm^3$ <em>and since</em> $504=2\times 252$ <em>we can say that the new volume is two times the original volume.</em>

8 0

2 years ago