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3 years ago

Find the coordinates of the foot of the perpendicular from (6,8) the line through(1,5) and (9,3)

Mathematics

1 answer:

Murrr4er [49]3 years ago

4 0

Answer:

plz follow and thanks me

Step-by-step explanation:

Let (a,b) be the coordinates of the foot of the perpendicular from the point (−1,3) to the line 3x−4y−16=0

Slope of the line joining (−1,3) and (a,b), is m

a+1

b−3

Slope of the line 3x−4y−16=0 or y=

x−4,m

Since these two lines are perpendicular,m

=−1

∴{

a+1

b−3

}⋅{

}=−1

⇒

4a+4

3b−9

=−1

⇒3b−9=4a−4

⇒4a+3b=5...(1)

Point(a,b) lies on line 3x−4y=16

∴3a−4b=16....(2)

On solving equation (1) and (2) we obtain

and b=−

Thus, the required coordinates of the foot of the perpendicular are {

}

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Find the circumference given the area = 113.1 ft². Use 3.14 for π as necessary.

olga_2 [115]

The circumference of the circle is 37.68 ft

Step-by-step explanation:

Given,

The area of the circle is 113.1 sq ft

To find the circumference of the circle we need to find the radius of the circle first

Formula

The area of circle with radius r is = π $r^{2}$ sq unit

The circumference of circle with radius r is = 2πr unit

Let us take the radius of the circle is r ft

According to the problem,

π $r^{2} =113.1$

or, $r^{2} = \frac{113.1}{3.14}$

or, $r^{2} = 36.01 = 36 (approx)$

or, r = $\sqrt{36}$

or, r = 6

Now,

The circumference of the circle is 2×3.14×6 ft = 37.68 ft

5 0

2 years ago

Read 2 more answers

(3x3 + 11x2 + 4x + 1)/ (x2 + x)

lions [1.4K]

If those are exponents, then...

3x^3 + 11x^2 + 4x + 1
----------------------------- Cancel out the 11x^2 with the x^2
x^2 + x

3x^3 + 10x^2 + 4x +1
----------------------------- Cancel out the x with the 4x
x

3x^3 + 10x^2 + 3x +1

6 0

3 years ago

Part A

masya89 [10]

Answer:

Part A) The area of triangle i is $3\ cm^{2}$

Part B) The total area of triangles i and ii is $6\ cm^{2}$

Part C) The area of rectangle i is $20\ cm^{2}$

Part D) The area of rectangle ii is $32\ cm^{2}$

Part E) The total area of rectangles i and iii is $40\ cm^{2}$

Part F) The total area of all the rectangles is $72\ cm^{2}$

Part G) To find the surface area of the prism, we need to know only the area of triangle i and the area of rectangle i and the area of rectangle ii, because the area of triangle ii is equal to the area of triangle i and the area of rectangle iii is equal to the area of rectangle i

Part H) The surface area of the prism is $78\ cm^{2}$

Part I) The statement is false

Part J) The statement is true

Step-by-step explanation:

Part A) What is the area of triangle i?

we know that

The area of a triangle is equal to

$A=\frac{1}{2} (b)(h)$

we have

$b=4\ cm$

$h=1.5\ cm$

substitute

$A=\frac{1}{2} (4)(1.5)$

$Ai=3\ cm^{2}$

Part B) Triangles i and ii are congruent (of the same size and shape). What is the total area of triangles i and ii?

we know that

If Triangles i and ii are congruent

then

Their areas are equal

$Aii=Ai$

The area of triangle ii is equal to

$Aii=3\ cm^{2}$

The total area of triangles i and ii is equal to

$A=Ai+Aii$

substitute the values

$A=3+3=6\ cm^{2}$

Part C) What is the area of rectangle i?

we know that

The area of a rectangle is equal to

$A=(b)(h)$

we have

$b=2.5\ cm$

$h=8\ cm$

substitute

$Ai=(2.5)(8)$

$Ai=20\ cm^{2}$

Part D) What is the area of rectangle ii?

we know that

The area of a rectangle is equal to

$A=(b)(h)$

we have

$b=4\ cm$

$h=8\ cm$

substitute

$Aii=(4)(8)$

$Aii=32\ cm^{2}$

Part E) Rectangles i and iii have the same size and shape. What is the total area of rectangles i and iii?

we know that

Rectangles i and iii are congruent (have the same size and shape)

If rectangles i and iii are congruent

then

Their areas are equal

$Aiii=Ai$

The area of rectangle iii is equal to

$Aiii=20\ cm^{2}$

The total area of rectangles i and iii is equal to

$A=Ai+Aiii$

substitute the values

$A=20+20=40\ cm^{2}$

Part F) What is the total area of all the rectangles?

we know that

The total area of all the rectangles is

$At=Ai+Aii+Aiii$

substitute the values

$At=20+32+20=72\ cm^{2}$

Part G) What areas do you need to know to find the surface area of the prism?

To find the surface area of the prism, we need to know only the area of triangle i and the area of rectangle i and the area of rectangle ii, because the area of triangle ii is equal to the area of triangle i and the area of rectangle iii is equal to the area of rectangle i

Part H) What is the surface area of the prism? Show your calculation

we know that

The surface area of the prism is equal to the area of all the faces of the prism

The surface area of the prism is two times the area of triangle i plus two times the area of rectangle i plus the area of rectangle ii

$SA=2(3)+2(20)+32=78\ cm^{2}$

Part I) Read this statement: “If you multiply the area of one rectangle in the figure by 3, you’ll get the total area of the rectangles.” Is this statement true or false? Why?

The statement is false

Because, the three rectangles are not congruent

The total area of the rectangles is $72\ cm^{2}$ and if you multiply the area of one rectangle by 3 you will get $20*3=60\ cm^{2}$

$72\ cm^{2}\neq 60\ cm^{2}$

Part J) Read this statement: “If you multiply the area of one triangle in the figure by 2, you’ll get the total area of the triangles.” Is this statement true or false? Why?

The statement is true

Because, the triangles are congruent

8 0

3 years ago

Eva has borrowed 200 songs from her friend. She plans to download an equal number of songs on her music player each week for 5 w

Alenkasestr [34]

PART A)

The rate of change is -40 songs each week, because the amount of songs left to be downloaded decrease by 40 every week.

the initial value is 200 at 0 weeks, which means that there are 200 songs to be downloaded at the beginning

PART B)

calculate the slope:
 m = (y2- y1)/(x2 - x1) = (160 - 200)/(1 - 0)
m = -40
now use the line equation in form of point-slope
y - y1 = m(x - x1)
y - 200 = -40(x - 0)
y = -40x + 200

5 0

3 years ago

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DerKrebs [107]

The answer is 211.26087

3 0

3 years ago

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Find the coordinates of the foot of the perpendicular from (6,8) the line through(1,5) and (9,3)​

Find the coordinates of the foot of the perpendicular from (6,8) the line through(1,5) and (9,3)