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3 years ago

What is the volume of the cylinder height 12cm length 4cm

Mathematics

1 answer:

erica [24]3 years ago

6 0

Answer:

$192\pi \: {cm}^{3}$

Step-by-step explanation:

h = 12 cm, r = 4 cm

$V_{cylinder} = \pi {r}^{2} h \\ = \pi \times {4}^{2} \times 12 \\ = \pi \times 16 \times 12 \\ V_{cylinder}= 192\pi \: {cm}^{3}$

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Licemer1 [7]

Answer:

y + 1 = 4 (x + 3)

Step-by-step explanation:

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2 years ago

David is planning to attend a public university after he graduates from high school in 3 years. He is devising a plan to save mo

allochka39001 [22]

Answer:

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3 years ago

How much sugar syrup would you get by:<br> Making 70% sugar syrup using 350g sugar?

zvonat [6]

Answer:

You will get 500g of sugar syrup.

I already answered this question.

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75/100 = 350/x

Therefore x = 500g of sugar syrup

8 0

2 years ago

How do I simplify (6^-2)(3^-3)(3 x 6)^4? Not the answer, just the simplified expression.

Mazyrski [523]

The simplification form of the provided expression is 108 after applying the integer exponent properties.

<h3>What is integer exponent?</h3>

In mathematics, integer exponents are exponents that should be integers. It may be a positive or negative number. In this situation, the positive integer exponents determine the number of times the base number should be multiplied by itself.

We have an expression:

$=\left(6^{-2}\right)\left(3^{-3}\right)\left(3\:\cdot \:6\right)^4$

$=\dfrac{1}{36}\cdot \dfrac{1}{27}\left(3\cdot \:6\right)^4$

$=\dfrac{1}{36}\cdot \dfrac{1}{27}\cdot \:81\cdot \:1296$

$=\dfrac{1}{36}\cdot \dfrac{1}{27}\cdot \dfrac{104976}{1}$

$=\dfrac{104976}{972}$

= 108

Thus, the simplification form of the provided expression is 108 after applying the integer exponent properties.

Learn more about the integer exponent here:

brainly.com/question/4533599

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5 0

1 year ago

. The indicated function y1(x) is a solution of the associated homogeneous equation. Use the method of reduction of order to nd

Blababa [14]

The question is:

The indicated function y1(x) is a solution of the associated homogeneous equation. Use the method of reduction of order to find a second solution y2(x) of the homogeneous equation

x²y'' - 7xy' + 16y = 0; y1 = x^4

Answer:

The second solution y2 is

A(x^4)lnx

Step-by-step explanation:

Given the homogeneous differential equation

x²y'' - 7xy' + 16y = 0

And a solution: y1 = x^4

We need to find a second solution y2 using the method of reduction of order.

Let y2 = uy1

=> y2 = ux^4

Since y2 is also a solution to the differential equation, it also satisfies it.

Differentiate y2 twice in succession with respect to x, to obtain y2' and y2'' and substitute the resulting values into the original differential equation.

y2' = u'. x^4 + u. 4x³

y2'' = u''. x^4 + u'. 4x³ + u'. 4x³ + u. 12x²

= u''. x^4 + u'. 8x³ + u. 12x²

Now, using these values in the original equation,

x²(u''. x^4 + u'. 8x³ + u. 12x²) - 7x(u'. x^4 + u. 4x³)+ 16(ux^4) = 0

x^6u'' + 8x^5u' + 12x^4u - 7x^5u' - 28x^4u + 16x^4u = 0

x^6u'' + x^5u' = 0

xu'' = -u'

Let w = u'

Then w' = u''

xw' = -w

w'/w = -1/x

Integrating both sides

lnw = -lnx + C

w = Ae^(-lnx) (where A = e^C)

w = A/x

But w = u'

So,

u' = A/x

Integrating this

u = Alnx

Since

y2 = uy1

We have

y2 = (Alnx)x^4 = (Ax^4)lnx

Therefore, the second solution y2 is

A(x^4)lnx

6 0

3 years ago