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3 years ago

I WILL GIVE GOLD MEDALS PLEASE HELP ??? Can somebody help with these 2 math questions?

Mathematics

1 answer:

taurus [48]3 years ago

6 0

4)

$\bf \textit{area of a sector of a circle}\\\\
A=\cfrac{\theta\pi r^2}{360}\qquad 
\begin{cases}
\theta=\textit{angle in degrees}\\
r=radius\\
----------\\
r=CE=9\\
\theta=120
\end{cases}$

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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

2 years ago

What is the solution to the equation x - 5 = 15?

Nonamiya [84]

Answer:

x=20

Step-by-step explanation:

x - 5 = 15

x +5 = +5

x = 20

4 0

2 years ago

Read 2 more answers

Instructions: The polygons in each pair are similar. Find the missing side length.

adoni [48]

Answer:

Step-by-step explanation:

20 16

(25*16)/20 = 20

4 0

2 years ago

There are 2 grams of fat in 1 pound of chicken. there are 9 grams of fat in 4.5 pounds of chicken. How many grams of fat would b

kramer

Answer:

There will be 20 grams of fat in 10 pounds of chicken.

Step-by-step explanation:

Based of the pattern you can tell that the Grams of fat will always be double the amount of pounds.

2 grams of fat in 1 pound

9 grams in 4.5 pounds

So:

10 * 2 = Grams of fat

10 * 2 = 20 Grams of fat.

So there will be 20 grams of fat in 10 pounds of chicken.

5 0

3 years ago

Theo is a cleaner,

GaryK [48]

Step-by-step explanation:

1 hour 50 minutes = 110 mins

1 1/2 hours = 90 mins

add all these:

110

when you add all these you get 375

every hour has 60 minutes

375 ÷ 60 = 6.15

if he starts at 9 am and he cleans for 6.15 hours he will be finished by 3:15pm.

4 0

1 year ago