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3 years ago

Factorize (x-3y)^3+27y^3 With explanation Will mark Brainliest for the best one...

Mathematics

1 answer:

drek231 [11]3 years ago

7 0

Use the identity: a^3 + b^3 = (a + b)(a^2 - ab + b^2)
Replace b^3 by 27y^3
x^3 + 27b^3 = (x + 3y)(x^2 - 3xy + 9y^2)

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The radius of the cone is 1.25 inches, and its height is 2.75 inches. If the diameter of the bubble gum ball is 0.5 inches, what

nasty-shy [4]

<h2>Explanation:</h2><h2></h2>

The volume of a cone can be found as:

$V=\frac{1}{3}\pi r^2 h \\ \\ \\ Where: \\ \\ V:Volume \\ \\ r:radius \ of \ base \\ \\ h:height$

Given the radius and height, we can find the volume of the cone:

$V=\frac{1}{3}\pi r^2 h \\ \\ V=\frac{1}{3}\pi (1.25)^2(2.75) \\ \\ V=\frac{1}{3}\pi(1.5625)(2.75) \\ \\ V\approx 4.5in^3$

The volume of a sphere is:

$V=\frac{4}{3}\pi r^3 \\ \\ \text{Each gum ball has a diameter of 0.5in, so the radius is:} \\ \\ r=\frac{0.5}{2}=0.25in$

So, for each gum ball the volume is:

$V=\frac{4}{3}\pi r^3 \\ \\ V=\frac{4}{3}\pi (0.25)^3 \\ \\ V=0.065in^3$

Therefore, the he closest approximation of the volume of the cone that can be filled with flavored ice is:

$4.5-0.065=4.43in^3$

Conclusion: The volume of the cone that can be filled with flavored ice is 4.43 cubic inches.

3 0

4 years ago

Can someone help me ?

Alex Ar [27]

All you need to do is divide 2.25 by 2!

The answer is 1.125!

I hope this helps! :)

5 0

3 years ago

HELP ME PLEASE PLEASE

olga_2 [115]

i really thinks its 6.9*10 to the power of 2

4 0

2 years ago

The measures of two complementary angles are 4x+6 and 5x+3. Find x.

Juliette [100K]

4x + 6 + 5x + 3 = 90

9x +9 = 90

( Subtract 9 from 9 and 90 )

9x = 81

( Divide 9x and 81 by 9 )

x = 9

Hope this helps.

6 0

3 years ago

Solve the simultaneous equation y-2x+1=0 and 4x^2+3y^2-2xy=7

Lapatulllka [165]

The first equation is $y-2x+1=0$

$y=2x-1$ (Equation 1)

The second equation is $4x^{2}+3y^{2}-2xy=7$ (Equation 2)

Putting the value of x from equation 1 in equation 2.

we get,

$4x^{2}+3(2x-1)^{2}-2x(2x-1)=7$

$4x^{2}+3(4x^{2}+1-4x)-4x^{2}+2x=7$

by simplifying the given equation,

$12x^{2}-10x-4=0$

$6x^{2}-5x-2=0$

Using discriminant formula,

$D=b^{2}-4ac$

$D=25-4 \times 6 \times -2 = 73$

Now the formula for solution 'x' of quadratic equation is given by:

$x=\frac{-b+\sqrt{D}}{2a} and x=\frac{-b-\sqrt{D}}{2a}$

$x=\frac{5+\sqrt{73}}{12} and x=\frac{5-\sqrt{73}}{12}$

Hence, these are the required solutions.

8 0

3 years ago