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3 years ago

If 1/x + 1/3x equals 4 then what is x

Mathematics

1 answer:

Vikki [24]3 years ago

3 0

Answer:

$\huge\boxed{x=\dfrac{1}{3}}$

Step-by-step explanation:

$\dfrac{1}{x}+\dfrac{1}{3x}=4\\\\\text{Domain:}\ x\neq0\\\\\text{find LCD}=3x\\\\\dfrac{1\cdot3}{x\cdot3}+\dfrac{1}{3x}=4\\\\\dfrac{3}{3x}+\dfrac{1}{3x}=4\\\\\dfrac{3+1}{3x}=4\\\\\dfrac{4}{3x}=\dfrac{4}{1}\qquad\text{cross multiply}\\\\(3x)(4)=(4)(1)\\\\12x=4\qquad\text{divide both sides by 12}\\\\\dfrac{12x}{12}=\dfrac{4}{12}\\\\x=\dfrac{4:4}{12:4}\\\\x=\dfrac{1}{3}\in D$

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What are the domain range of f(x)= 1/5 power of x

Snowcat [4.5K]

Answer:

Domain: all real numbers

Range: all real numbers

Step-by-step explanation:

I'm assuming you mean the function $f(x)=x^{\frac{1}{5}}$ . That's usually written

f(x) = x^(1/5) with the ^ meaning "to the power of..." and the fraction exponent in parentheses so as not to be confused with x^1/5 which could mean x to the first power, divided by 5.

Fractional exponents are used to indicate roots. In this case, x is being raised to the 1/5 power, so this is the fifth root of x, written $\sqrt[5]{x}$ . The 5 is called the root index.

For odd roots, like this one, the domain is all real numbers--x can be any number at all. So the domain is all real numbers.

The range is also all real numbers. Attached is a graph of this function. It might not look like it, but the graph rises to the right to any height. The larger x gets, the larger the 5th root gets. A similar thing happens on the left--the smaller x gets, the smaller the 5th root gets.

EDIT: see the comment. For the function $f(x)=(1/5)^x$ , the domain is all real numbers. The range is positive real numbers. I'll attach a graph!

3 0

4 years ago

The shaded region R in diagram below is enclosed by y-axis, y = x^2 - 1 and y = 3.

Lostsunrise [7]

Cross sections of the volume are washers or annuli with outer radii x(y) + 1, where

y = x(y) ² - 1 ==> x(y) = √(y + 1)

and inner radii 1. The distance between the outermost edge of each shell to the axis of revolution is then 1 + √(y + 1), and the distance between the innermost edge of R on the y-axis to the axis of revolution is 1.

For each value of y in the interval [-1, 3], the corresponding cross section has an area of

π (1 + √(y + 1))² - π (1)² = π (2√(y + 1) + y + 1)

Then the volume of the solid is the integral of this area over [-1, 3]:

$\displaystyle\int_{-1}^3\pi y\,\mathrm dy = \frac{\pi y^2}2\bigg|_{-1}^3 = \boxed{4\pi}$

$\displaystyle\int_{-1}^3 \pi\left(2\sqrt{y+1}+y+1\right)\,\mathrm dy = \pi\left(\frac43(y+1)^{3/2}+\frac{y^2}2+y\right)\bigg|_{-1}^3 = \boxed{\frac{56\pi}3}$

8 0

3 years ago

Chic-ken Rulez is a food vendor at the state fair that only sells complete box meals which includes a sandwich (chicken or turke

sveta [45]

Answer:

This answer was provided through an attachment since it basically involves drawing a flow diagram.

Step-by-step explanation:

the question requires that we draw a flow diagram of the time and process of taking an order, making a drink, fixing a sandwich and also making fries.

please check the attachment for the processes #1 and #2.

the net process time minute for process#1

5+12+10 = 27 minutes

the net process time minute for process# 2

5 + 12 + 2 + 7

= 26 minutes

5 0

3 years ago

What is the integer that represents the temperature

Lerok [7]

The integer that represents the temperature is 7.

6 0

3 years ago

What is the area of the polygon below?

Lena [83]

Answer:

B.84 sq.units

Step-by-step explanation:

Adding both rectangles

12 + 72

84sq.units

pls Mark as brainliest

4 0

3 years ago