All categories

3 years ago

A circle with radius 5 has a sector with a central angle of 9/10 pi

Mathematics

2 answers:

Solnce55 [7]3 years ago

5 0

Answer:

35.33

Step-by-step explanation:

The circle with radius 5 has a sector with a central angle of 9/10 pi.

The area of a sector is given as:

$A_s = \frac{\alpha }{2\pi} * \pi r^2$

where α = central angle of the sector in radians

r = radius of the circle

The area of the sector is therefore:

$A_s = \frac{\frac{9 \pi}{10} }{2 \pi} * (3.14 * 5^2)\\ \\A_s = \frac{9}{20} * 78.5\\\\A_s = 35.33$

The area of the sector is 35.33.

andriy [413]3 years ago

3 0

Answer:

<h2>The area of the sector to nearest hundredth is 35.33</h2>

Step-by-step explanation:

Formula for calculating the area of a sector is given as $\frac{\theta}{360} *\pi r^{2}$ where;

r is the radius of the circle

theta is the angle substended by the sector.

Given r = 5 and central angle theta = $\frac{9 \pi}{10}$

Area of the sector is expressed as shown;

$= \frac{9\pi/10}{2\pi}*\pi (5)^{2} \\= \frac{9\pi}{20\pi}*25\pi\\ = \frac{225\pi}{20} \\= 225*3.14/20\\= 35.33$

The area of the sector to nearest hundredth is 35.33

You might be interested in

A value pack of candy bars cost 7.50. If there 25 candy bars in the package,what is the cost per candy bar?

Advocard [28]

Answer:

i think 50 25 or 75 cents

Step-by-step explanation:

4 0

3 years ago

Two quadratic functions are shown.

slava [35]

Answer:

Option (1) is the correct option.

Step-by-step explanation:

Function 1,

f(x) = 4x² + 8x + 1

= 4(x² + 2x) + 1

= 4(x² + 2x + 1 - 1) + 1

= 4(x² + 2x + 1) - 4 + 1

f(x) = 4(x + 1)² - 3

This graph opens up with the vertex or minimum point at (-1, -3)

So, the minimum value of the function is (-3) at x = -1.

Function (2)

From the given table minimum value of the function is 0 at x = -1 or minimum point as (-1, 0)

Therefore, Function 1 has the least minimum value and its coordinates are (-1, -3)

Option (1) is the correct option.

7 0

3 years ago

Three boxes are stacked one on top of each other one box is 2 feet 11 inches tall one is 3 feet 5 inches tall and one is 4 feet

Natasha_Volkova [10]

Answer:

<u>11 feet 2 inches</u>

Step-by-step explanation:

ill add the inches first

11+5+10= 26

26inches= 2ft 2inches

now I add the feet

2+3+4+2=11 feet

<u>11 feet 2 inches</u>

7 0

2 years ago

A pyramid has a square base of length 8cm and a total surface area of 144cm². Find the volume of the pyramid. (Please use Pythag

Sveta_85 [38]

Answer:

$\displaystyle V_{ \text{pyramid}}= 64 \: {cm}^{3}$

Step-by-step explanation:

we are given surface area and the length of the square base

we want to figure out the Volume

to do so

we need to figure out slant length first

recall the formula of surface area

$\displaystyle A_{\text{surface}}=B+\dfrac{1}{2}\times P \times s$

where B stands for Base area

and P for Base Parimeter

$\sf\displaystyle \: 144=(8 \times 8)+\dfrac{1}{2}\times (8 \times 4) \times s$

now we need our algebraic skills to figure out s

simplify parentheses:

$\sf\displaystyle \: 64+\dfrac{1}{2}\times32\times s = 144$

reduce fraction:

$\sf\displaystyle \: 64+\dfrac{1}{ \cancel{ \: 2}}\times \cancel{32} \: ^{16} \times s = 144 \\ 64 + 16 \times s = 144$

simplify multiplication:

$\displaystyle \: 16s + 64 = 144$

cancel 64 from both sides;

$\displaystyle \: 16s = 80$

divide both sides by 16:

$\displaystyle \: \therefore \: s = 5$

now we'll use Pythagoras theorem to figure out height

according to the theorem

$\displaystyle \: {h}^{2} + (\frac{l}{2} {)}^{2} = {s}^{2}$

substitute the value of l and s:

$\displaystyle \: {h}^{2} + (\frac{8}{2} {)}^{2} = {5}^{2}$

simplify parentheses:

$\displaystyle \: {h}^{2} + (4 {)}^{2} = {5}^{2}$

simplify squares:

$\displaystyle \: {h}^{2} + 16 = 25$

cancel 16 from both sides:

$\displaystyle \: {h}^{2} = 9$

square root both sides:

$\displaystyle \: \therefore \: {h}^{} = 3$

recall the formula of a square pyramid

$\displaystyle V_{pyramid}=\dfrac{1}{3}\times A\times h$

where A stands for Base area (l²)

substitute the value of h and l:

$\sf\displaystyle V_{ \text{pyramid}}=\dfrac{1}{3}\times \{8 \times 8 \}\times 3$

simplify multiplication:

$\sf\displaystyle V_{ \text{pyramid}}=\dfrac{1}{3}\times 64\times 3$

reduce fraction:

$\sf\displaystyle V_{ \text{pyramid}}=\dfrac{1}{ \cancel{ 3 \: }}\times 64\times \cancel{ \: 3}$

hence,

$\sf\displaystyle V_{ \text{pyramid}}= 64 \: {cm}^{3}$

8 0

3 years ago

Please help thanks ❗

mojhsa [17]

Answer:

The Two Column Proof is given below.

Step-by-step explanation:

Given:

$\overline{MP} \cong \overline{MN}$

$\overline{PO} \cong \overline{NO}$

To Prove:

∠ P ≅ ∠ N

Proof:

In Δ MPO and Δ MNO

STATEMENT REASONS

1. MP ≅ MN 1. Given

2. PO ≅ NO 2. Given

3. MO ≅ MO 3. Reflexive property

4. ΔMPO ≅ ΔMNO 4. Side-Side-Side congruence test}

5. ∠MPO ≅∠MNO 5. Corresponding parts of congruent Triangles

i.e ∠ P ≅ ∠ N ..................Proved

3 0

3 years ago