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3 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)

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It takes 58 pounds of seed to completely plant a 9-acre field. How many acres can be planted per pound of seed?

ozzi

Answer:

6 4/9

Step-by-step explanation:

You divide 58 and 8 and your answer would be 6.444444 repeating.

6 0

2 years ago

Pretty sure this work is wrong , need it corrected

Makovka662 [10]

C/30 = 8/12
c/30 = 2/3
3c = 60
c = 60/3
c = 20

8 0

3 years ago

Write the equation of a parabola having the vertex (1, −2) and containing the point (3, 6) in vertex form. Then, rewrite the equ

In-s [12.5K]

PART A

The equation of the parabola in vertex form is given by the formula,

$y - k = a {(x - h)}^{2}$

where

$(h,k)=(1,-2)$

is the vertex of the parabola.

We substitute these values to obtain,

$y + 2 = a {(x - 1)}^{2}$

The point, (3,6) lies on the parabola.

It must therefore satisfy its equation.

$6 + 2 = a {(3 - 1)}^{2}$

$8= a {(2)}^{2}$

$8=4a$

$a = 2$
Hence the equation of the parabola in vertex form is

$y + 2 = 2 {(x - 1)}^{2}$

PART B

To obtain the equation of the parabola in standard form, we expand the vertex form of the equation.

$y + 2 = 2{(x - 1)}^{2}$

This implies that

$y + 2 = 2(x - 1)(x - 1)$

We expand to obtain,

$y + 2 = 2( {x}^{2} - 2x + 1)$

This will give us,

$y + 2 = 2 {x}^{2} - 4x + 2$

$y = {x}^{2} - 4x$

This equation is now in the form,

$y = a {x}^{2} + bx + c$
where

$a=1,b=-4,c=0$

This is the standard form

7 0

3 years ago

Pleaseeeeeeee help .......ASAP

fenix001 [56]

Answer:

Option A

Step-by-step explanation:

Given:

Center of circle = (h,k)= (3,8)

Radius = r = 5

The standard form of equation of circle with center and radius is:

$(x-h)^2+(y-k)^2=r^2\\Putting\ the\ values\\(x-3)^2+(y-8)^2=(5)^2\\Simplifying\\x^2+9-6x+y^2+64-16y=25\\x^2+y^2-6x-16y+9+64=25\\x^2+y^2-6x-16y+73=25\\x^2+y^2-6x-16y+73-25=0\\x^2+y^2-6x-16y+48=0$

Therefore, the general form of the equation of circle given is:

$x^2+y^2-6x-16y+48=0$

Hence, option A is correct ..

5 0

3 years ago

The ratio of students wearing sneakers to those wearing boots is 4 to 5. If there are 36 students in the class, and all of them

yaroslaw [1]

Answer:

Step-by-step explanation:

Let's denote:

a: number of students wearing sneakers

b: number of students wearing boots

We have:

a + b = 36

a/b = 4/5 (multiply both sides by b => a = 4b/5)

Substitute a = 4b/5 into a + b = 36

=> 4b/5 + b = 36

=> 4b/5 + 5b/5 = 36

=> 9b/5 = 36

=> b/5 = 4

=> b = 20

=> a = 4b/5 = 4(20)/5 = 16

7 0

2 years ago