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2 years ago

How many unit cubes are on each layer of this cube

Mathematics

2 answers:

gogolik [260]2 years ago

8 0

There are 16 on each layer and 96 in total

serious [3.7K]2 years ago

4 0

I think the answer is the fist one!

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Sales at a book store increased from 5000 to 10000. This year sales dicreased to 5000 from 10000.

erastovalidia [21]

It's basically 5,000*2=10,000
and 10,000/2=5,000. your answer would be either they multiplied 5,000 by 2 and 10,000 divided by 2, they increased the sales by 5,000

6 0

3 years ago

Read 2 more answers

Consider the given function and the given interval. f$x$ = (x - 7)**2 text(, ) [5 text(, ) 11] (a) Find the average value fave

Jet001 [13]

a. $f$ has an average value on [5, 11] of

$f_{\rm ave}=\displaystyle\frac1{11-5}\int_5^{11}(x-7)^2\,\mathrm dx=\frac{(x-7)^3}{18}\bigg|_5^{11}=\frac{4^3-(-2)^3}{18}=4$

b. The mean value theorem guarantees the existence of $c\in(5,11)$ such that $f(c)=f_{\rm ave}$ . This happens for

$(c-7)^2=4\implies c-7=\pm2\implies c=9\text{ or }c=5$

8 0

3 years ago

What values of a and b make the equation true? StartRoot 648 EndRoot = StartRoot 2 Superscript a Baseline times 3 Superscript b

kramer

Option C: $a=3, b=4$ is the value of a and b

Explanation:

Given that the expression $\sqrt{648}=\sqrt{2^a\times3^b}$

We need to determine the value of a and b

Let us consider the term $\sqrt{648}$ and take the prime factorization of the term 648

Thus, we have,

648 divides by 2,

$648=2 \cdot 324$

324 divides by 2,

$648=2 \cdot 2 \cdot 162$

162 divides by 2,

$648=2 \cdot 2 \cdot 2 \cdot 81$

81 divides by 3,

$648=2 \cdot 2 \cdot 2 \cdot 3 \cdot 27$

27 divides by 3,

$648=2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 \cdot 9$

9 divides by 3,

$648=2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 \cdot 3 \cdot 3$

Thus, we have,

$\sqrt{648}=\sqrt{2^{3} \cdot 3^{4}}$

Therefore, equating the powers of 2 and 3, we get,

$a=3, b=4$

Hence, the value of a and b is 3 and 4

Thus, Option C is the correct answer.

4 0

3 years ago

Read 2 more answers

At noon, ship A is 50 km west of ship B. Ship A is sailing south at 10 km/h and ship B is sailing north at 20 km/h. How fast is

Lena [83]

So hmmm check the picture below

so, we're looking for dr/dt then at 4:00pm or 4 hours later

now, keep in mind that, the distance "x", is not changing, is constant whilst "y" and "r" are moving, that simply means when taking the derivative, that goes to 0

$\bf r^2=x^2+y^2\implies 2r\cfrac{dr}{dt}=0+2y\cfrac{dy}{dt}\implies \cfrac{dr}{dt}=\cfrac{y\frac{dy}{dt}}{r}\quad 
\begin{cases}
\cfrac{dy}{dt}=30\\
r=130\\
y=120
\end{cases}
\\\\\\
\cfrac{dr}{dt}=\cfrac{120\cdot 30}{130}$

6 0

3 years ago

Write the quadratic equation whose roots are 3 and -5, and whose leading coefficient is 2.

Rainbow [258]

$\begin{cases} x=3\implies &x-3=0\\ x=-5\implies &x+5=0 \end{cases}\qquad \implies\qquad a(x-3)(x+5)=\stackrel{0}{y} \\\\\\ a(\stackrel{F~O~I~L}{x^2+2x-15})=y\implies \stackrel{\textit{leading coefficient of 2}}{2(x^2+2x-15)}=y\implies 2x^2+4x-30=y$

Check the picture below.

5 0

2 years ago