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3 years ago

Please help is and example of ?

Mathematics

2 answers:

stich3 [128]3 years ago

7 0

B. Foil. 100% sure.

Helen [10]3 years ago

5 0

I believe that it is B. Hope this helps!

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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 slope of the line that passes through (2, 3) and has a y-intercept of -1?

sashaice [31]

I believe that the slope would be 4/2 or 2, but i wouldn’t take my word for it

7 0

2 years ago

What is a budget?<br> only a savings plan<br> savings and spending plan<br> only a spending plan

son4ous [18]

Answer:

Step-by-step explanation:

A plan to only spend x amount of money while shopping

7 0

3 years ago

Read 2 more answers

An equation is shown below:

tatyana61 [14]

The beginning steps to solve the equation 6(3x - 7) = 2 is
Step 1: 18x - 42 = 2
Step 2: 18x = 44

4 0

3 years ago

Read 2 more answers

A shirt cost $46 and you have a 15 percent off coupon. What is the new price

Kryger [21]

If you have 15% off that means you should only pay 100 - 15 = 85% of the price so the answer is:
?/46 = 85/100
so ? is the price that you should pay:
85*46 /100 = $39.1 :)))
i hope this is helpful
have a nice day

3 0

3 years ago