Decompose 3/8 as the sum of unit fractions

Anvisha [2.4K]

Answer:

Step-by-step explanation:

We'll take this step by step. The equation is

$8-3\sqrt[5]{x^3}=-7$

Looks like a hard mess to solve but it's actually quite simple, just do one thing at a time. First thing is to subtract 8 from both sides:

$-3\sqrt[5]{x^3}=-15$

The goal is to isolate the term with the x in it, so that means that the -3 has to go. Divide it away on both sides:

$\sqrt[5]{x^3}=5$

Let's rewrite that radical into exponential form:

$x^{\frac{3}{5}}=5$

If we are going to solve for x, we need to multiply both sides by the reciprocal of the power:

$(x^{\frac{3}{5}})^{\frac{5}{3}}=5^{\frac{5}{3}}$

On the left, multiplying the rational exponent by its reciprocal gets rid of the power completely. On the right, let's rewrite that back in radical form to solve it easier:

$x=\sqrt[3]{5^5}$

Let's group that radicad into groups of 3's now to make the simplifying easier:

$x=\sqrt[3]{5^3*5^2}$ because the cubed root of 5 cubed is just 5, so we can pull it out, leaving us with:

$x=5\sqrt[3]{5^2}$ which is the same as:

$x=5\sqrt[3]{25}$

8 0

3 years ago

Help me with this problem? 15 points

kobusy [5.1K]

Answer:

See explanation

Step-by-step explanation:

Since 12 is 3 times greater than 4, you simply need to divide all of the ingredients by 3.

Cactus chunks: 4 1/2 divided by 3 is 3/2 or 1 1/2

Crushed Tumbleweed: 8/3 is just 8/3 or 2 2/3

Cactus Juice: 10/4 or 2 1/2

Lizard eggs: 4

Crumbled Flower Petals: 7/4 or 1 3/4

Water: 10/3 or 3 1/3

Hope this helps!

5 0

3 years ago

What is the surface area of this rectangular pyramid?

Alexxx [7]

Answer:

304m^2

Step-by-step explanation:

First find the surface area of the base by multiplying the length by the width.

(12m) (8m)= 96m^2

Second, find the surface area of the front and back triangles using the formula 1/2 (base) (height). Use the length for the base.

1/2 (12m) (10m)= 60m^2

Next, find the surface area of the side triangles using the formula 1/2 (base) (height). Use the width as the base.

1/2 (8m) (11m)= 44m^2

Last, add the surface area of each section. Make sure you add the area of each face.(we only solved for 1 of the front/ back triangles and 1 of the side triangles) To make it easier to understand I wrote out an equation to show how I added the surface areas.

base=a, front/ back triangles= b, side triangles=c

SA= a + 2b +2c or SA= a +b +b +c +c

Using one of the equations above solve for the total surface area.

SA= (96m^2) + (60m^2) +(60m^2) +(44m^2) +(44m^2)

or

SA= (96m^2) + 2(60m^2) +2(44m^2)

SA= (96m^2) +(120m^2) +(88m^2)

SA= 304m^2

7 0

3 years ago

a chessboard has 64 squares at a chess tournament 84 chessboards were used how many squares are there on 85 chessboards

jasenka [17]