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3 years ago

#10

Mathematics

1 answer:

amm18123 years ago

3 0

Answer:

There are 3 green marbles in the box.

Step-by-step explanation:

15% = 0.15

To figure out how much 15% of 21 is, you must multipl the decimal form of the percentage by the whole number. This will give you how much of that number that percentage is.

0.15 * 21 = 3.15

But you can't have 0.15 of a marble, so you must round as well.

3 green marbles in the box.

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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

3.50 rounded to the nearest whole ounce

Maslowich

Answer:

Step-by-step explanation:

Look at the tenths place to round.

4 and below, round down.

5 and above, round up.

In this case, it’s 5 so round up.

3.50 -> 4

5 0

3 years ago

For which pair of triangles would you use AAS to prove the congruence of the 2 triangles

DerKrebs [107]

Answer:

The correct option is B.

Step-by-step explanation:

According to AAS congruence rule, two triangles are congruent if two angles and a non included side are congruent to corresponding angles and side of another triangle.

We need two angles and a non included side, to use AAS postulate.

In option A, two sides and their inclined angle are congruent, therefore these triangles are congruent by SAS postulate and option A is incorrect.

In option B, two angles and a non included side are congruent, therefore these triangles are congruent by AAS postulate and option B is correct.

In option C, two angles and their included side are congruent, therefore these triangles are congruent by ASA postulate and option C is incorrect.

In option D, all sides are congruent, therefore these triangles are congruent by SSS postulate and option D is incorrect.

8 0

3 years ago

Read 2 more answers

A circular garden has a circumference of 63 yards. Lars is digging a straight line along a diameter of the garden at a rate of 5

Harrizon [31]

Answer:

4 hours

Step-by-step explanation:

If the circumference of the circular garden =63 yards

Circumference of a Circle =2πr=πd (d=diameter)

Therefore:

πd= 63

diameter of the circular garden =63/3.14=20 yards

If he digs at a rate of 5 yards per hour, the time required to dig across the garden will be:

20 yards/5 yard per hours = 4 hours

It will take him 4 hours to dig across the circular garden.

6 0

3 years ago

If C = 2m2 + m and D = 2 – 6m + 2m², find an expression that equals<br> 2C - 2D in standard form.

lidiya [134]

C = 2m^2 + m
D = 2 - 6m + 2m^2

2C = 2(2m^2 + m) = 4m^2+2m
2D = 2(2-6m+2m^2) = 4-12m+4m^2

2C - 2D =
4m^2+2m-(4-12m+4m^2) =
4m^2+2m-4+12m-4m^2 =
0m^2 + 14m -4 =
14m - 4

3 0

3 years ago