1. What is the volume of the cube?

2 answers:

6 0

A cube volume is side legnth=x x^3
so assuming that 15 is the side legnth then
15^3=15 times 15 times 15=3375mm^3 which is D

andrew11 [14]4 years ago

5 0

I'm guessing 15 mm is the side length.

V = a^3

Where 'a' is the side length.

V = 15^3

V = 3375

So the volume of the cube is 3375 mm^3.

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Matt worked m hours each week. Nate worked n hours each week. The equation n = 4m – 6 describes the relationship between the num

Tasya [4]

Answer:

Linear relationship

Step-by-step explanation:

This is a linear relationship as it is expressed in the form y= mx+b

Here y= n b = -6 and x= m

A linear equation corresponds to a straight line hence it shows a linear relationship.

There is a correspondence between algebra and geometry through co ordinate system. We can convert a point into a pair of numbers and vice versa.

If we are given the value of y we can determine x and vice versa.

n = 4m – 6

In the given equation suppose x = 5 so y will be 14

n= 4(5)- 6

n= 20-6= 14

Also if we have y= 18 x will be 6

n = 4m – 6

18 + 6= 4m

24/4= m

m= 6

6 0

3 years ago

Evaluate the integral using the indicated trigonometric substitution. (use c for the constant of integration.) x^3 / sqrt x^2 +

slava [35]

$\displaystyle\int\frac{x^3}{\sqrt{x^2+49}}\,\mathrm dx$

Taking $x=7\tan\theta$ gives $\mathrm dx=7\sec^2\theta\,\mathrm d\theta$ , so that the integral becomes

$\displaystyle\int\frac{(7\tan\theta)^3}{\sqrt{(7\tan\theta)^2+49}}(7\sec^2\theta)\,\mathrm d\theta$
$=\displaystyle7^4\int\frac{\tan^3\theta\sec^3\theta}{\sqrt{49\tan^2\theta+49}}\,\mathrm d\theta$
$=\displaystyle7^3\int\frac{\tan^3\theta\sec^3\theta}{\sqrt{\tan^2\theta+1}}\,\mathrm d\theta$
$=\displaystyle7^3\int\frac{\tan^3\theta\sec^3\theta}{\sqrt{\sec^2\theta}}\,\mathrm d\theta$
$=\displaystyle7^3\int\frac{\tan^3\theta\sec^3\theta}{|\sec\theta|}\,\mathrm d\theta$

When $\sec\theta>0$ , we have

$=\displaystyle7^3\int\frac{\tan^3\theta\sec^3\theta}{\sec\theta}\,\mathrm d\theta$
$=\displaystyle7^3\int\tan^3\theta\sec^2\theta\,\mathrm d\theta$

and from here we can substitute $u=\tan\theta$ to proceed from here.

Quick note: When we set $x=7\tan\theta$ , we are implicitly enforcing $-\dfrac\pi2$ just so that the substitution can be undone later via $\theta=\tan^{-1}\dfrac x7$ . But note that over this domain, we automatically guarantee that $\sec\theta>0$ , so the absolute value bars can be dropped immediately.

6 0

3 years ago

What is the area of triangle IHC?

madam [21]

Answer:

$28 cm^2$