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3 years ago

What is the kinetic energy, in joules, of an object that has a mass of 100 kilograms and moves with a velocity of 10 m/s?

Mathematics

1 answer:

Over [174]3 years ago

6 0

Given, an object with a mass of 100kg.

The velocity given 10m/s.

Kinetic energy is directly proportional to the mass of the object and to the square of its velocity.

The formula to find Kinetic energy is

K.E = 1/2 × m × v² ( where m = mass and v = velocity)

= 1/2 × (100) × (10)²

= 1/2 × (100) × (100)

= 1/2 × (10000)

= 5000

We have got the required answer.

The required kinetic energy is 5000 joules.

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Find the surface area of the part of the circular paraboloid z=x^2+y^2 that lies inside the cylinder X^2+y^2=1

hichkok12 [17]

Answer:

$\mathbf{\dfrac{\pi}{6}[5 \sqrt{5}-1]}$

Step-by-step explanation:

Given that:

The surface area (S.A) $z = x^2 +y^2$

Hence the S.A is of form z = f(x,y)

Then the S.A can be represented with the equation

$A(S) = \iint _D \sqrt{1+ (\dfrac{\partial z}{\partial x})^2+ (\dfrac{\partial z}{\partial y})^2} \ dA$

where :

D = cylinder $x^2 +y^2 =1$

In polar co-ordinates:

D = {(r, θ): 0≤ r ≤ 1, 0 ≤ θ ≤ 2π)

Similarly, $\dfrac{\partial z}{\partial x} = 2x$ and $\dfrac{\partial z}{\partial y} = 2y$

Therefore;

$S.A = \iint_D \sqrt{1+4x^2+4y^2} \ dA$

$= \iint_D \sqrt{1+4(x^2+y^2)} \ dA$

$= \int^{2 \pi}_{0} \int^{1}_{0} \sqrt{1+4r^2} \ r \ dr \d \theta$

$= [\theta]^{2 \pi}_{0} \dfrac{1}{8}\times \dfrac{2}{3}\begin {bmatrix} (1+4r^2)^{\dfrac{3}{2}}\end {bmatrix}^1_0$

$= 2 \pi \times \dfrac{1}{12}[5^{\dfrac{3}{2}} - 1]$

$\mathbf{=\dfrac{\pi}{6}[5 \sqrt{5}-1]}$

6 0

3 years ago

The number forty one to the power of negative start fraction two over five end fraction end power can be written in the form sta

Fantom [35]

From the description we can infer that we have the expression: $41^{- \frac{2}{5} }$ .
Now, to write our expression as a as a root, we are going to apply the law of exponents: $x^{-n}= \frac{1}{x^n}$ first
$41^{- \frac{2}{5} }= \frac{1}{41^{ \frac{2}{5} }}$

Next, we are going to apply the law about fractional exponents: $x^{ \frac{m}{n}}= \sqrt[n]{x^m}$
$\frac{1}{41^{ \frac{2}{5} }}= \frac{1}{ \sqrt[5]{41^2} }$

We can conclude that the value of B is 2.

3 0

3 years ago

Blain is two years older than three times Jillians age. Jillian is also 16 years younger than Blain. How old is Blain?

Ipatiy [6.2K]

The age of Blain is 23 years old

<h3><u>Solution:</u></h3>

Let the age of Blain be "a" and age of Jillian be "b"

Given that Blain is two years older than three times Jillians age

So we can frame a equation as:

age of blain = 2 + 3(age of Jillian)

a = 2 + 3b ----- eqn 1

Also given that Jillian is also 16 years younger than Blain

Age of Jillain = Age of Blain - 16

b = a - 16 ---- eqn 2

Substitute eqn 2 in eqn 1

a = 2 + 3(a - 16)

a = 2 + 3a - 48

a - 3a = -46

-2a = -46

a = 23

Thus the age of Blain is 23 years old

4 0

3 years ago

Which angles are corresponding angles?

Reptile [31]

Answer:

1 and 3

15 and 13

15 and 7

1 and 9

Step-by-step explanation:

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2 years ago

Ralph sold brownies for $0.28 a piece in order to earn money for baseball cards. if the cards cost $0.60 per pack, and if ralph

lara [203]

he nbeeds to have atleast sold 3

7 0

2 years ago

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