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4 years ago

5

A ball bearing is shaped like a sphere and has a diameter os 2.5 centimeters l. What is the volume contained inside the ball bea

ring? Use 3.14 pi. Round your answer to the nearest hundredth

1 answer:

blondinia [14]4 years ago

6 0

Okay, so the volume of a sphere is 4/3 x pi x r^3.

The diameter of the sphere is 2.5, so the radius is 1.25cm. This cubed is 1.953125.
Multiply that by 3.14 to get 6.1328125. And finally, multiply by 4/3 to get 8.1770. To the nearest hundredth, we get that the volume of the sphere is 8.18cm^3.

Hope this helps:)

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Please help me with these calculus bc questions

zhannawk [14.2K]

4. Compute the derivative.

$y = 2x^2 - x - 1 \implies \dfrac{dy}{dx} = 4x - 1$

Find when the gradient is 7.

$4x - 1 = 7 \implies 4x = 8 \implies x = 2$

Evaluate $y$ at this point.

$y = 2\cdot2^2-2-1 = 5$

The point we want is then (2, 5).

5. The curve crosses the $x$ -axis when $y=0$ . We have

$y = \dfrac{x - 4}x = 1 - \dfrac4x = 0 \implies \dfrac4x = 1 \implies x = 4$

Compute the derivative.

$y = 1 - \dfrac4x \implies \dfrac{dy}{dx} = -\dfrac4{x^2}$

At the point we want, the gradient is

$\dfrac{dy}{dx}\bigg|_{x=4} = -\dfrac4{4^2} = \boxed{-\dfrac14}$

6. The curve crosses the $y$ -axis when $x=0$ . Compute the derivative.

$\dfrac{dy}{dx} = 3x^2 - 4x + 5$

When $x=0$ , the gradient is

$\dfrac{dy}{dx}\bigg|_{x=0} = 3\cdot0^2 - 4\cdot0 + 5 = \boxed{5}$

7. Set $y=5$ and solve for $x$ . The curve and line meet when

$5 = 2x^2 + 7x - 4 \implies 2x^2 + 7x - 9 = (x - 1)(2x+9) = 0 \implies x=1 \text{ or } x = -\dfrac92$

Compute the derivative (for the curve) and evaluate it at these $x$ values.

$\dfrac{dy}{dx} = 4x + 7$

$\dfrac{dy}{dx}\bigg|_{x=1} = 4\cdot1+7 = \boxed{11}$

$\dfrac{dy}{dx}\bigg|_{x=-9/2} = 4\cdot\left(-\dfrac92\right)+7=\boxed{-11}$

8. Compute the derivative.

$y = ax^2 + bx \implies \dfrac{dy}{dx} = 2ax + b$

The gradient is 8 when $x=2$ , so

$2a\cdot2 + b = 8 \implies 4a + b = 8$

and the gradient is -10 when $x=-1$ , so

$2a\cdot(-1) + b = -10 \implies -2a + b = -10$

Solve for $a$ and $b$ . Eliminating $b$ , we have

$(4a + b) - (-2a + b) = 8 - (-10) \implies 6a = 18 \implies \boxed{a=3}$

so that

$4\cdot3+b = 8 \implies 12 + b = 8 \implies \boxed{b = -4}$ .

5 0

2 years ago

On a test, shelly got approximately 93% of the items correct. she got 76 questions right. how many questions were on the test? a

svetlana [45]

You multiply 76 by 0.93. That is 70.68 which rounds to 71. To check, (71/76) = ~93.

8 0

3 years ago

Vikentia [17]

Answer:

The answer would be 70.2.

Step-by-step explanation:

You just have to replace the x in the equation with a 2 because x=2.

5 0

3 years ago

Helppp me pleaseee!!!!!!!

kenny6666 [7]

Answer:

V=πr2h

3=π·72·9

3≈461.81412

Step-by-step explanation:

Mark me the brainliest PLZ.

7 0

4 years ago

There are 751 identical plastic chips numbered through 751 in a box.

den301095 [7]

Answer:

1.1331

Step-by-step explanation:

Divided 100 by 751

7 0

3 years ago