Identify which line from the graph the following right triangles could lie on

A circle with area \blue{9\pi}9πstart color #6495ed, 9, pi, end color #6495ed has a sector with a central angle of \purple{60^\c

Liono4ka [1.6K]

Answer:

The area of the sector is 3pi/2

Step-by-step explanation:

A sector is that part of a circle bounded by 2 radii and an arc

The circle has an area of 9 pi with a central angle of 60 degrees.

Now the area of the sector is pretty much straight forward to calculate. Since it is a circle, the total angle we have is 360.

Now the sector subtends an angle of 60 degrees at the centre. What this means is that the sector is exactly 1/6 of the circle. meaning that cutting the circle into 6 slices will give the sector.

Thus, the area of the sector is one-sixth the area of the circle.

The area of the sector is thus 1/6 * 9pi = 9pi/6 = 3pi/2 or 3/2 pi

6 0

3 years ago

What is 100,897,567×25

Afina-wow [57]

It equals to <span>2,522,439,175.</span>

3 0

4 years ago

Read 2 more answers

What is (4x - 3)^6 expanded

fenix001 [56]

Expad the expression:

4096x^(6)-18432x^(5)+34560x^(4)-34560x^(3)+19440x^(2)-5832x-729

4 0

3 years ago

If triangle STR ~ triangle PTQ, find QT

lana [24]

Answer:

QT = 45

Step-by-step explanation:

ST = 65

SP = 26

RQ = 30

QT = 4x - 3

Given that ∆STR is similar to ∆PTQ, therefore:

$\frac{ST}{PT} = \frac{RT}{QT}$

Plug in the values

$\frac{65}{65 - 26} = \frac{30 + (4x - 3)}{4x - 3}$

Solve for x

$\frac{65}{39} = \frac{30 + 4x - 3)}{4x - 3}$

$\frac{5}{3} = \frac{27 + 4x}{4x - 3}$

Cross multiply

$5(4x - 3) = 3(27 + 4x)$

$20x - 15 = 81 + 12x$

Collect like terms

$20x - 12x = 81 + 15$

$8x = 96$

Divide both sides by 8

$x = \frac{96}{8}$

$x = 12$

✅QT = 4x - 3

Plug in the value of x

QT = 4(12) - 3 = 48 - 3

QT = 45

3 0

3 years ago

Please help, I've been trying for an hour and I don't know how to set up this problem.

labwork [276]

Given ratio of the width of Francois's wife's vegetable garden to its length is 5:8.

Let l1,w1 be the length and width of Francois's wife's vegetable garden.

Then $\frac{w1}{l1} = \frac{5}{8}$

Given ratio of the width of the herb garden to its length is 3:5.

Let l2,w2 be the length and width of herb garden.

That is $\frac{w2}{l2} = \frac{3}{5}$

Given that length of the herb garden is same as the width of the vegetable garden.

That is l2=w1 let this common value be x.

So, first ratio is $\frac{x}{l1}=\frac{5}{8}$

l1 = $\frac{8x}{5}$

Second ratio is $\frac{w2}{x} = \frac{3}{5}$

w2 = $\frac{3x}{5}$

perimeter of vegetable garden = 2(l1+w1) = $2(\frac{8x}{5} +x) = 2*\frac{13x}{5} = \frac{26x}{5}$

Perimeter of herb garden = 2(l2+w2) = $2(x+\frac{3x}{5} ) = 2*\frac{8x}{5} =\frac{16x}{5}$

Given that francois has 252ft of fencing material.

That is perimeter of vegetable garden + perimeter of herb garden = 252

$\frac{26x}{5} +\frac{16x}{5} = 252$

$\frac{42x}{5} =252$

$x = \frac{252*5}{42} = 30 feet$

So, $l1 = \frac{8x}{5} = \frac{8*30}{5} = 48 feet$

And $w2 = \frac{3x}{5} = \frac{3*30}{5} = 18 feet$

So dimensions of vegetable garden are 48ft, 30ft.

And dimensions of herb garden are 30ft,18ft.

4 0

4 years ago