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2 years ago

Help me answer this question

Mathematics

2 answers:

vovangra [49]2 years ago

8 0

Answer: I think 128 cubes

Step-by-step explanation:

We are given: Volume of rectangular prism = 2 units³ and Cube with edge = 1/4 unitWe must find: The number of cubes that can fill the prismFirstly, find the volume of 1 cube:Volume = 1/4 x 1/4 x 1/4Volume = 1/64 units³Next find the number of cubes that can go into the prism:Number of cubes = 2 ÷ 1/64Number of cubes = 128Therefore 128 cubes can fit in.

ad-work [718]2 years ago

4 0

Answer:

128 cubes can fit in.

Step-by-step explanation:

We are given: Volume of rectangular prism = 2 units³ and Cube with edge = 1/4 unit

We must find: The number of cubes that can fill the prism

Firstly, find the volume of 1 cube:

Volume = 1/4 x 1/4 x 1/4

Volume = 1/64 units³

Next find the number of cubes that can go into the prism:

Number of cubes = 2 ÷ 1/64

Number of cubes = 128

Therefore 128 cubes can fit in.

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Show that the function f(x)=sin3x + cos5x is periodic and it’s period.

lbvjy [14]

The period of $f(x)$ is $\boxed{2\pi}$ .

Recall that $\sin(x)$ and $\cos(x)$ both have periods of $2\pi$ . This means

$\sin(x + 2\pi) = \sin(x)$

$\cos(x + 2\pi) = \cos(x)$

Replacing $x$ with $3x$ , we have

$\sin(3x + 2\pi) = \sin\left(3 \left(x + \dfrac{2\pi}3\right)\right) = \sin(3x)$

In other words, if we change $x$ by some multiple of $\frac{2\pi}3$ , we end up with the same output. So $\sin(3x)$ has period $\frac{2\pi}3$ .

Similarly, $\cos(5x)$ has a period of $\frac{2\pi}5$ ,

$\cos(5x + 2\pi) = \cos\left(5 \left(x + \dfrac{2\pi}5\right)\right) = \cos(5x)$

We want to find the period $p$ of $f(x)$ , such that

$f(x + p) = f(x)$

$\implies \sin(3x + p) + \cos(5x + p) = \sin(3x) + \cos(5x)$

On the left side, we have

$\sin(3x + p) = \sin(3x + 2\pi + p - 2\pi) \\\\ ~~~~~~~~ = \sin(3x+2\pi) \cos(p-2\pi) + \cos(3x+2\pi) \sin(p-2\pi) \\\\ ~~~~~~~~ = \sin(3x) \cos(p-2\pi) + \cos(3x) \sin(p - 2\pi)$

and

$\cos(5x + p) = \cos(5x + 2\pi + p - 2\pi) \\\\ ~~~~~~~~ = \cos(5x+2\pi) \cos(p-2\pi) - \sin(5x+2\pi) \sin(p-2\pi) \\\\ ~~~~~~~~ = \cos(5x) \cos(p-2\pi) - \sin(5x) \sin(p-2\pi)$

So, in terms of its period, we have

$f(x) = \sin(3x) \cos(p - 2\pi) + \cos(3x) \sin(p - 2\pi) \\\\ ~~~~~~~~ ~~~~+ \cos(5x) \cos(p - 2\pi) - \sin(5x) \sin(p - 2\pi)$

and we need to find the smallest positive $p$ such that

$\begin{cases} \cos(p - 2\pi) = 1 \\ \sin(p - 2\pi) = 0 \end{cases}$

which points to $p=2\pi$ , since

$\cos(2\pi-2\pi) = \cos(0) = 1$

$\sin(2\pi - 2\pi) = \sin(0) = 0$

3 0

1 year ago

What is 5.76 rounded to the nearest tenth?

Llana [10]

Answer:

5.76 rounded to the nearest tenth is 5.8 or 5.80.

7 0

2 years ago

Read 2 more answers

Which problem can be solved using the equation y=8×+50 ?

vladimir2022 [97]

Answer:

x will equal 6.25

Step-by-step explanation:

all you have to do is divide both sides by 8

6 0

3 years ago

Stephanie took a science exam that had two parts. Part 1: She got 16 questions correct, which was 45 of the number of part 1 que

nasty-shy [4]

Answer:

Step-by-step explanation:

Let x and y be the total number of questions in part 1 and part 2 exams respectively.

For part 1:

Number of correct question = 4/5 of the total number of question in part 1

$\Rightarrow 16=\frac{4}{5}\times x$

$\Rightarrow x=20$

For part 2:

Number of corrected question = 2/3 of total number of question in part 2

$\Rightarrow 16=\frac{2}{3}\times x$

$\Rightarrow x=24$

So, the total umbers of the questions on Stephanie's exam

=x+y

=20+24

=44

Hence, the total umbers of the questions on Stephanie's exam was 44.

3 0

3 years ago

How do you write 3x-y=14 in slope intercept form

Ede4ka [16]

Y=3x-14 or 3x-14=Y
This is because you want to keep y positive, and so you add Y on both sides and get 3x=14+y, then you want to get y alone so you subtract 14 on both sides and get 3x-14=Y

3 0

3 years ago