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2 years ago

Create an algebraic expression to solve the following problems.

Mathematics

1 answer:

daser333 [38]2 years ago

7 0

Answer:

Step-by-step explanation:

x is the number of GB

f(x) is the cost in dollars

f(x) = 10x

Bill for 6 GB = f(6) = 60

:::::

f(x) = 8x+15

Bill for 8 GB = f(10) = 95

:::::

f(x) = 5x+30

Bill for 2 GB = f(2) = 40

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How do i find the volume of a cylinder?

mestny [16]

Hi there! The answer is 226 in^3

Like you've already written it down, the formula of the volume of a cylinder is
$volume \: = \: base \: \times \: height$

Since the base of any cylinder is a circle, we can find the area of this circle with the formula
$a \: = \pi \: {r}^{2}$
With r representing the radius.

Therefore, the volume of any cylinder can be found with the formula
$v \: = \pi \: {r}^{2} \: h$
With h representing the height.

Filling in this formula gives us the following
$v \: = \pi \times {3}^{2} \times 8 = 226.08$
Hence, the volume of this cylinder is about 226 in ^ 3.

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2 years ago

How is the expression (5 + y) ⋅8 described by its factors and terms?

quester [9]

The correct answer is D) it has two factors and the factor (5+y) has 2 terms.

The factors are what are multiplied to make the expression. In this expression, (5+y) and 8 are multiplied, so those are the 2 factors.

The factor (5+y) has two terms, 5 and y.

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3 years ago

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wolverine [178]

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2 years ago

HELP PLEASE<br><br> Which graph represents the system of inequalities?

Assoli18 [71]

Answer:

The answer to your question is in the picture below

Step-by-step explanation:

y + 3/4x < 2

y+ 3/4x = 2

y = -3/4x +2

Interceptions (0,2) and (8/3, 0) It's a dotted line and we are interested in the area below the line

y - 1 ≥ 2x

y - 1 = 2x

y = 2x + 1 Interception, it's not a dotted line with interceptions (0,1) and (-1/2, 0), we are interested in the area up the line.

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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.

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2 years ago