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2 years ago

PLEASE HELP ASAP!!! CORRECT ANSWERS ONLY PLEASE!!!

Mathematics

1 answer:

dmitriy555 [2]2 years ago

3 0

Answer: 12

Step-by-step explanation:

Average rate of change is the slope (m) between the two coordinates (-1, 3) and (1, 27).

$m=\dfrac{y_2-y_1}{x_2-x_1}$

$m = \dfrac{27-3}{1+1}$

$=-\dfrac{24}{2}$

$= 12$

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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

Ms. Lorahs smartphone has 3.5 GB of free storage space, which is 27.5% of the total storage space on her smartphone. What is the

statuscvo [17]

12.73 GB total when rounded to the nearest 100th.

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2 years ago

(7p+8)-(5p-2) combine like terms

kotegsom [21]

The answer is:

= 2p+10

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2 years ago

Write the equation of the ellipse graphed below.

Lana71 [14]

Answer:

Step-by-step explanation:

This is a horizontally stretched ellipse. That means that the horizontal line which is represented by the x-axis is the longer one. The equation for this type of ellipse is

$\frac{(x-h)^2}{a^2} +\frac{(y-k)^2}{b^2} =1$

In an ellipse, the a value is ALWAYS bigger than the b value, and since the x-axis represents the longer axis, the a goes under the x-squared term.

To solve for the h, the k, the a, and the b, we simply have to do some counting. The center of the ellipse, the (h, k) our of equation, is sitting at (4, 6). Put them where they belong in the equation. The a axis (the horizontal one) is 8 units long, and the b axis (the vertical one) is 4 units long. Square both of them and put them where they belong in the equation:

$\frac{(x-4)^2}{64}+\frac{(y-6)^2}{16} =1$