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3 years ago

What is the equation of the line parellel to line L that passes through point (3, 3)?

1 answer:

5 0

The slope of line L is

$= \frac{ - 3 - 3}{2 - - 1} = \frac{ - 6}{3} = - 2$
Since the line is parallel to L , it also has the same gradient,

The equation is

$y = - 2(x - 3) + 3$
$y = - 2x + 6 + 3$
$y = - 2x + 9$

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What is the volume of a hemisphere with a radius of 2.1 m, rounded to the nearest tenth of a cubic meter?

Art [367]

Answer:

The volume of hemisphere is 19.4 cubic meter.

Step-by-step explanation:

Given:

A hemisphere is with a radius of 2.1 m.

Now, to find the hemisphere volume with radius 2.1 m.

$Radius\ (r) = 2.1 m.$

So, we put formula to get the volume of hemisphere:

$Volume=\frac{2}{3} \pi r^3\ \ \ \ \ (Taking\ the\ value\ of\ \pi =3.14)\\\\Volume=\frac{2}{3} \times 3.14\times 2.1^3\\\\Volume=\frac{2}{3} \times 3.14\times 9.26\\\\Volume=19.384\ cubic\ meter.$

Hence, the rounded to the nearest tenth of a cubic meter is 19.4 cubic meter.

Therefore, the volume of hemisphere is 19.4 cubic meter.

3 0

2 years ago

If D is midpoint of side BC of triangle ABC. P and Q are points lying respectively on side AB and AC such that DP is parallel to

LUCKY_DIMON [66]

See proof below

Step-by-step explanation:

Assume triangle ABC to have vertices at;

A(2,-1), B(2,-7) and C(6,-7)

D is midpoint of BC, thus D is at (4,-7)

The P and Q, are lying on side AB and AC, hence assume P is at (2,-4) and Q is at (4,-4) such at DP is parallel to QA

Plot the points on a graph tool and join the points to view the sketch.

To prove area of triangle CPQ is 1/4 area of ABC will be;

Find area ABC and CPQ then compare the areas.

Apply the distance formula to find the length of sides of the triangles then find the areas.

The distance formula is;

$d=\sqrt{x_2-x_1)^2+(y_2-y_1)^2}$

Length of side AB from the sketch is;

$AB=\sqrt{(2-2)^2+(-7--1)^2} =\sqrt{-6^2} =\sqrt{36} =6units$

Length of side BC will be;

$BC=\sqrt{(-7--7)^2+(6-2)^2} =\sqrt{4^2} =\sqrt{16} =4units$

Thus area of triangle ABC will be;

1/2 *base length*height ------because it is a right-triangle

1/2*4*6=12 square units

Find the lengths of all sides of triangle CPQ

Length of side PQ is half that of side BC thus PQ=2 units

Length of side PC is;

$PC=\sqrt{(6-2)^2+(-7--4)^2} =\sqrt{4^2+-3^2} =\sqrt{16+9} =\sqrt{25} =5units$

Length of side QC will be;

$QC=\sqrt{(6-4)^2+(-7--4)^2} =\sqrt{2^2+-3^3} =\sqrt{4+9} =\sqrt{13}$

QC= √13 = 3.6 units

Find area of triangle CPQ given all sides by applying the Heron's formula for area of triangle which is;

A=√s(s-a)(s-b)(s-c) where;

A=area of the triangle

s= half the perimeter of the triangle

a=side PQ = 2 units

b=side PC = 5 units

c= side QC = 3.6 units

Finding the perimeter of triangle CPQ will be;

P=sum of all sides

P=2+5+3.6 =10.6 units

s=10.6/2 = 5.3

Area of the triangle CPQ will be;

$A=\sqrt{5.3(5.3-2)(5.3-5)(5.3-3.6)} \\A=\sqrt{5.3(3.3)(0.3)(1.7)} \\A=\sqrt{8.9} =2.98$

A=3.0 (1 decimal place)

Compare the areas;

Area of triangle ABC=12 square units

Area of triangle CPQ = 3 square units

Area of triangle CPQ / Area of triangle ABC = 3/12 =1/4

Thus you have proved that area of triangle CPQ is 1/4 th area of triangle ABC because 1/4 *12 =3

Learn More

Area of a triangle ;brainly.com/question/14869984

The Heron's formula : brainly.com/question/10713495

Keywords: midpoint, triangle, sides, parallel, prove , area, equal

#LearnwithBrainly

6 0

3 years ago

Determine the domain of this relation

natulia [17]

Answer:0,1,2

Step-by-step explanation:every x

4 0

3 years ago

Please tell me how to do these questions, I'm confused.

Ahat [919]

Answer:

2. The office and the music room

6. 68 in. I think?

Step-by-step explanation:

7 0

2 years ago

Will mark brainliest to whoever can answer

tia_tia [17]

Answer:

A. 7

Step-by-step explanation:

h(x)=2x + 4

2(7)=14

14+4=18

3 0

2 years ago