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3 years ago

What is the volume of a cube with length 7 cm? V = lwh cm3

Mathematics

2 answers:

bonufazy [111]3 years ago

5 0

343 Due to the fact that it is all the same length it will just multiply to 343 7*7*7=343

Zanzabum3 years ago

4 0

A cube has all lengths the same so 7 *7*7 = 343

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Triangle GHJ is rotated 90° about point X, resulting in

Bumek [7]

the correct answer is your third choice.

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nasty-shy [4]

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3 years ago

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A stadium has a total of 18,000 seats. Of these, 9,500 are field seats, and the rest are grandstand seats. Complete an equation

Angelina_Jolie [31]

Answer:

Wow, thanks for all the points!

Step-by-step explanation:

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3 years ago

Solve the following compound inequality: x is greater than or equal to 2 or x is less than 2

Troyanec [42]

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3 years ago

Help me asap! I will give you marks

Law Incorporation [45]

Recall the binomial theorem.

$(a+b)^n = \displaystyle \sum_{k=0}^n \binom nk a^{n-k} b^k$

1. The binomial expansion of $\left(1+\frac x3\right)^7$ is

$\left(1 + \dfrac x3\right)^7 = \displaystyle\sum_{k=0}^7 \binom 7k 1^{7-k} \left(\frac x3\right)^k = \sum_{k=0}^7 \binom 7k \frac{x^k}{3^k}$

Observe that

$k = 1 \implies \dbinom 71 \left(\dfrac x3\right)^1 = \dfrac73 x$

$k = 2 \implies \dbinom 72 \left(\dfrac x3\right)^2 = \dfrac73 x^2$

When we multiply these by $8-9x$ ,

• $8$ and $\frac73 x^2$ combine to make $\frac{56}3 x^2$

• $-9x$ and $\frac73 x$ combine to make $-\frac{63}3 x^2 = -21x^2$

and the sum of these terms is

$\dfrac{56}3 x^2 - 21x^2 = \boxed{-\dfrac73 x^2}$

2. The binomial expansion is

$\left(2a - \dfrac b2\right)^8 = \displaystyle \sum_{k=0}^8 \binom 8k (2a)^{8-k} \left(-\frac b2\right)^k = \sum_{k=0}^8 \binom 8k 2^{8-2k} a^{8-k} b^k$

We get the $a^6b^2$ term when $k=2$ :

$k=2 \implies \dbinom 82 2^{8-2\cdot2} a^{8-2} b^2 = 28 \cdot2^4 a^6 b^2 = \boxed{448} \, a^6b^2$

6 0

1 year ago