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Tema [17]
3 years ago
9

What is the justification for the first step in proving the formula for factoring the sum of cubes?

Mathematics
1 answer:
Anna11 [10]3 years ago
5 0

Explanation:

The formula isnt correctly written, it should state:

a^3+b^3 = (a+b)(a^2-ab+b^2)

You have to start from (a+b)(a^2-ab+b^2)  and end in a³+b³. On your first step, you need to use the distributive property.

(a+b)(a^2-ab+b^2) = a*(a^2-ab+b^2) + b*(a^2-ab+b^2)

This is equal to

a*a^2-a*(ab) + a*b^2 + b*a^2-b*(ab) + b*b^2 = a^3 - a^2b + ab^2 +ba^2 -b^2a +b^3

Note that the second term, -a²b, is cancelled by the fourth term, ba², and the third term, ab², is cancelled by the fifht term, -b²a. Therefore, the final result is a³+b³, as we wanted to.

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Two cylinders are shown below. Find the volume of each cylinder. Use 3.14 for pie. Enter your answers rounded to the nearest hun
Alchen [17]

Given:

For cylinder P: radius = 4.25 in. and height = 14 in.

For cylinder Q: radius = 7 in. and height = 8.5 in.

To find:

The volume of each cylinder.

Solution:

Volume of a cylinder is

V=\pi r^2h

where, r is radius and h is height. Use 3.14 for \pi.

Using the above formula, the volume of cylinder P is

V_P=(3.14)(4.25)^2(14)

V_P=794.0275

V_P\approx 794.03

Using the above formula, the volume of cylinder Q is

V_Q=(3.14)(7)^2(8.5)

V_Q=1307.81

Therefore, the volume of cylinder P is 794.03 sq. in. and volume of cylinder Q is 1307 sq. in.

7 0
3 years ago
A pizza parlor offers a choice of 16 different toppings. how may three-topping pizzas are possible
Mariulka [41]
48. 16 times 3 is 48:)

7 0
3 years ago
6j+8j+(5+5) Use the distributive property
vova2212 [387]

Hello!

Answer:

\boxed{14j+10}

Step-by-step explanation:

Distributive property: →→ a(b+c)=ab+ac

Order of operations stands for:

↓

Parenthesis

Exponent

Multiply

Divide

Add

Subtract

*Left to right*

Please Excuse My Dear Aunt Sally!

First, you remove parenthesis.

6j+8j+5+5

Then, you add by the numbers from left to right.

6+8=14

14j+5+5

5+5=10

<u><em>14j+10 is the final answer.</em></u>

Hope this helps!

Have a nice day! :)

:D

-Charlie

Thanks!

5 0
3 years ago
Abbie decides to start doing crunches as part of her daily workout. She decides to do 15 crunches the first day and then increas
Pavlova-9 [17]
For this case, the first thing we must do is define a variable.
 We have then:
 n: number of days.
 We now write the explicit formula that represents the problem.
 We have then:
 an = 4n + 15
 Where,
 15: crunches the first day
 4: increase the number 4 each day
 Answer:
 
An explicit formula for the number of crunches Abbie will do on day n is:
 
an = 4n + 15
3 0
3 years ago
An artist charges $980 for a portrait but gives a 5% discount. Calculate the cash price of the portrait.
Scrat [10]

Answer:

Step-by-step explanation:

1. A boutique is offering a 15% discount on a dress. Calculate the cash price for the dress if the marked price is $2300.

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7. Laura sees a summer dress in a store with a marked price of $1303. A discount of 9% is given on cash. What is the cash price of the summer dress?

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4 0
2 years ago
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