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3 years ago

A rectangular prism has a length of 4 1/4 in a width of 3 in, and a height of 1 1/4 in.

Mathematics

1 answer:

olchik [2.2K]3 years ago

4 0

Answer:

4 1/4 × 3 × 1 1/4

Step-by-step explanation:

To find volume you need to do length×width×height

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What is 77.2-43.778?<br>what is 2.072 divided by 5.6

Shkiper50 [21]

2.072/5.6= 0.37

77.2- 43.778= 33.422

Hope this helps!

~LENA~

8 0

2 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

HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

frutty [35]

Answer:

m∠7=34°

Step-by-step explanation:

m∠2=m∠8=146° because alternate interior angles are congruent.

m∠7=180-m∠8=34° because it is a linear pair.

3 0

2 years ago

Read 2 more answers

Factor strings for 36

Marina CMI [18]

Factor strings for 36:

6 x 6
2 x 18
3 x 12
4 x 9
2 x 2 x 3 x 3
2 x 2 x 9
4 x 3 x 3
6 x 2 x 3

Hope that helped :D

4 0

3 years ago

Read 2 more answers

If m < A = 4x + 12 and x = 15, is < A acute, obtuse, or right? Justify your answer.

BlackZzzverrR [31]

Step-by-step explanation:

Angle A = 4x + 12 = 4(15) + 12 = 72°.

Acute is for angles that are less than 90°.

Obtuse is for angles that are between 90° and 180°, not inclusive.

Right is for angles that are 90°

Hence the answer is acute.

3 0

2 years ago