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4 years ago

Can u guys please help me?

Mathematics

1 answer:

Eduardwww [97]4 years ago

5 0

Answer:

Step-by-step explanation:

The surface area of a cube is given by

SA = 6s^2 where s is the side length

We know the surface area is 486 and the side length is z

486 = 6z^2

Divide each side by 6

486/6 = 6z^2/6

81 = z^2

Take the square root of each side

sqrt(81) = sqrt(z^2)

9 = z

Each side has a length of 9m

You might be interested in

A toy factory sold 120,587 toys in 25 days. If each toy was sold for $58, about how much money did the factory earn in 25 days?

Rina8888 [55]

<h3>Answer: $7,018,000</h3>

This value is a little over 7 million dollars

======================================================

Explanation:

120,587 rounds to 121,000 when rounding to the nearest thousand.

The instructions don't mention rounding 58, so we'll leave it as that

Multiply the values to get

58*121,000 = 7,018,000

which is the estimate of how much money was earned.

-----------

The actual amount of money earned is

58*120,587 = 6,994,046

which isn't too far off of our estimate.

-----------

Note: the value of 25 days is never used. You could have any other number of days you want, and the answer is still the same. This value is probably either filler or some kind of distraction.

6 0

3 years ago

<img src="https://tex.z-dn.net/?f=%24a%2Ba%20r%2Ba%20r%5E%7B2%7D%2B%5Cldots%20%5Cinfty%3D15%24%24a%5E%7B2%7D%2B%28a%20r%29%5E%7B

riadik2000 [5.3K]

Let

$S_n = \displaystyle \sum_{k=0}^n r^k = 1 + r + r^2 + \cdots + r^n$

where we assume |r| < 1. Multiplying on both sides by r gives

$r S_n = \displaystyle \sum_{k=0}^n r^{k+1} = r + r^2 + r^3 + \cdots + r^{n+1}$

and subtracting this from $S_n$ gives

$(1 - r) S_n = 1 - r^{n+1} \implies S_n = \dfrac{1 - r^{n+1}}{1 - r}$

As n → ∞, the exponential term will converge to 0, and the partial sums $S_n$ will converge to

$\displaystyle \lim_{n\to\infty} S_n = \dfrac1{1-r}$

Now, we're given

$a + ar + ar^2 + \cdots = 15 \implies 1 + r + r^2 + \cdots = \dfrac{15}a$

$a^2 + a^2r^2 + a^2r^4 + \cdots = 150 \implies 1 + r^2 + r^4 + \cdots = \dfrac{150}{a^2}$

We must have |r| < 1 since both sums converge, so

$\dfrac{15}a = \dfrac1{1-r}$

$\dfrac{150}{a^2} = \dfrac1{1-r^2}$

Solving for r by substitution, we have

$\dfrac{15}a = \dfrac1{1-r} \implies a = 15(1-r)$

$\dfrac{150}{225(1-r)^2} = \dfrac1{1-r^2}$

Recalling the difference of squares identity, we have

$\dfrac2{3(1-r)^2} = \dfrac1{(1-r)(1+r)}$

We've already confirmed r ≠ 1, so we can simplify this to

$\dfrac2{3(1-r)} = \dfrac1{1+r} \implies \dfrac{1-r}{1+r} = \dfrac23 \implies r = \dfrac15$

It follows that

$\dfrac a{1-r} = \dfrac a{1-\frac15} = 15 \implies a = 12$

and so the sum we want is

$ar^3 + ar^4 + ar^6 + \cdots = 15 - a - ar - ar^2 = \boxed{\dfrac3{25}}$

which doesn't appear to be either of the given answer choices. Are you sure there isn't a typo somewhere?

7 0

2 years ago

An apartment building contains 12 units consisting of 1-2 bedroom apartments that rent for $360 and $450 per month, respectively

qwelly [4]

The number of 2 bedroom apartments is 7.
($450*7)+($360*5)=$4950

4 0

4 years ago

Read 2 more answers

Please help and thank you

mamaluj [8]

Answer:

Step-by-step explanation:

a is defined first as 5. So a = 5.

b is defined after the circle b = -2

a^2 = 5^2 = 25

B^4 =(- 2)^4 = 16

Therefore sqrt(a^2 * b^4) = sqrt(25 * 16) = sqrt(400) = 20

The answer is C

5 0

3 years ago

Read 2 more answers

In ΔMNO, the measure of ∠O=90°, the measure of ∠M=74°, and OM = 5.4 feet. Find the length of NO to the nearest tenth of a foot.

torisob [31]

Answer:

140.6 feet

Step-by-step explanation:

gave up on deltamath

8 0

3 years ago