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2 years ago

If the original volume of a cone is 32cm^3 and the height is tripled, what is the resulting volume of the new cone?

Mathematics

1 answer:

yarga [219]2 years ago

3 0

Answer:

Step-by-step explanation:

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What is the quotient (125 – 8x3) ÷ (25 + 10x + 4x2)? –2x + 5 2x – 5 –2x – 5 2x + 5

juin [17]

ANSWER

$\frac{125 - 8 {x}^{3} }{ 25 + 10x + 4 {x}^{2} } = - 2x+5$

EXPLANATION

We have been given the quotient,

$\frac{125 - 8 {x}^{3} }{ 25 + 10x + 4 {x}^{2} }$
to simplify.

We need to rewrite the numerator as difference of two cubes.

$\frac{125 - 8 {x}^{3} }{ 25 + 10x + 4 {x}^{2} } = \frac{ {5}^{3} - ( {2x})^{3} }{ 25 + 10x + 4 {x}^{2} }$

We need to make use of the difference of cubes formula,

${a}^{3} - {b}^{3} = (a - b)( {a}^{2} + ab + {b}^{2} )$

We now let,
$a = 5 \: and \: b = 2x$

Then the numerator becomes,

$\frac{125 - 8 {x}^{3} }{ 25 + 10x + 4 {x}^{2} } = \frac{ (5 - 2x)(25 + 5 (2x) + {(2x)}^{2}) }{ 25 + 10x + 4 {x}^{2} }$

This simplifies to,

$\frac{125 - 8 {x}^{3} }{ 25 + 10x + 4 {x}^{2} } = \frac{ (5 - 2x)(25 + 10x + 4 {x}^{2}) }{ 25 + 10x + 4 {x}^{2} }$

We cancel out common factors to obtain,

$\frac{125 - 8 {x}^{3} }{ 25 + 10x + 4 {x}^{2} } = \frac{ (5 - 2x)}{ 1}$

$\frac{125 - 8 {x}^{3} }{ 25 + 10x + 4 {x}^{2} } = 5 - 2x$

8 0

2 years ago

Read 2 more answers

(3 x 6) = 10 x _____ = ____

nataly862011 [7]

Answer:

1.8

Step-by-step explanation:

$(3 \times 6) = 10 \times 1.8 = 18$

4 0

2 years ago

Need help with this?

Scilla [17]

Answer:

Measurements.

Step-by-step explanation:

Measurements are important because they help us in our every day lives such as cooking and baking, construction and many other things but measurements also help us find out our weight and height, or even what size shoe we have. So basically measurements are important in every part of our every day lives.

Hope it helps!

OwO

3 0

2 years ago

the legs of a right triangle are 10 centimeters and 24 centimeters long. what is the length of the hypotenuse?

igomit [66]

Pytharorean therum...can only be used on right triangles
a^2 + b^2 = c^2...a and b r ur legs and c is ur hypotenuse
10^2 + 24^2 = c^2
100 + 576 = c^2
676 = c^2
sqrt 676 = c
26 = c <== ur hypotenuse is 26 cm

6 0

2 years ago

Read 2 more answers

Please help me I will mark BRAINLIEST!!! Find the value of x

Basile [38]

Answer:

x = 2√3 ≈ 3.464

Step-by-step explanation:

The side marked x is opposite the given 30° angle. The side marked 6 is adjacent to that angle. The trig function relating opposite and adjacent sides of a right triangle is ...

Tan = Opposite/Adjacent

Filling in values, we have ...

tan(30°) = x/6

Multiplying by 6 gives ...

x = 6tan(30°) = 6(√3/3)

x = 2√3 ≈ 3.464

6 0

2 years ago