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3 years ago

Definition n of product rule

1 answer:

5 0

A product rule is a formal rule for differentiating problems where one function is multiplied by another.

Hope this helps!!! :)

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Consider this sphere inside the cylinder. Which statements are true? Check all that apply. NEED HELP ASAP

-Dominant- [34]

Option A: The height of the cylinder is equal to the diameter of the sphere.

Option C: The radius of the sphere is half the height of the cylinder.

Option E: The volume of the sphere is two-thirds the volume of the cylinder.

Solution:

The sphere is inside the cylinder.

Let r be the radius of the sphere.

Option A: The height of the cylinder is equal to the diameter of the sphere.

The sphere is fully occupied the cylinder.

If we draw the vertical line through enter of the sphere, which is equal to the height of cylinder.That is h = d. It is true.

Option B: The height of the cylinder is two times the diameter of the sphere.

That is h = 2d. From the above option, we know that h = d.

So, it is not true.

Option C: The radius of the sphere is half the height of the cylinder.

we know that diameter = 2 × radius (d = 2r)

From option A, we have h = d.

Substitute d = 2r, we get

⇒ h = 2r

Divide by 2 on both sides, we get

$$\Rightarrow \frac{h}{2}=r$

Therefore, it is true.

Option D: The diameter of the sphere is equal to the radius of the cylinder.

It is not true, because diameters of both cylinder and sphere are equal.

Option E: The volume of the sphere is two-thirds the volume of the cylinder.

Radius of cylinder and sphere = r

Height of cylinder h = 2r (by option C)

Volume of cylinder = Volume of sphere

$$\Rightarrow \pi r^2 h = \frac{4}{3} \pi r^3$ (formula)

$$\Rightarrow \pi r^2 (2r) = \frac{2\times2}{3} \pi r^3$

$$\Rightarrow 2 \pi r^3= \frac{2}{3} \times 2\pi r^3$

Hence it is true.

Option A, option C and option E are true.

6 0

4 years ago

Read 2 more answers

The width of a rectangle is 2/5 its length. Find the dimensions if the perimeter is 42<br> meters.

Olin [163]

The formula to find the perimeter of a rectangle is P= 2(l+w). By substituting what we now knowin to the equation:

•42=2(l+(2/5l)). We can have width represented at (2/5l) because it’s now 2/5 of the length. Now add them together to get a single coefficient for l.

•42= 2(7/5l). Multiplying 7/5 by 2.

42= (14/5l). Multiplying both sides by the reciprocal of 14/5, which is 5/14, to get l by itself.

•l= 15.

Now that we now know the value of l, we know that the length is 15m. To find the width of the answer, we then multiply 15 by 2/5, which equals 6. Therefore, the only third option is correct because the length is 15m and the width is 6m.

3 0

3 years ago

Personal Statement

leonid [27]

Well, as it says, your first statement needs to explain what interests you about the program.

If you feel you need multiple paragraphs, let the first be an introduction, around 4 or 5 sentences. Include, possibly what pushed you to apply for this program, what you're looking forward to, and a reason for them to hire you. You can add a thesis statement of sorts if that helps (a short statement, usually one sentence, that summarizes the main point or claim of a paper). The first paragraph can be short, it doesn't need to be too in-depth. You can talk more about that later in your statement.

The body paragraphs must include your goals and extracurricular interests (what courses would you like to take and why?).

As it states, you must list your GPA, what interests you about the Major and/or Minor/Workshop courses, and what you can contribute (you can build off of what you said in your first paragraph here).

It is very important to share additional details you think are important, such as accomplishments you are proud of, for example.

A conclusion would be nice, a short and sweet wrap-up of your overall statement (not too long).

Remember, the name of the game is to sound confident and prove to them that you are in fact a good fit for the program! Good luck! Stay focused ^^

7 0

3 years ago

You know only the given information about

katrin [286]

Since they are multiples if 12

The possibilities are

12, 12, 156

12,24,144

12,36,132

12,48,120

12,60,108

12,72,96

12,84,84

24,24,132

24,36,120

24,48,108

24,60,96

24,72,84

36,36,108

36,48,96

36,60,84

36,72,72

48,48,84

48,60,72

60,60,60

Hence the probability is 1/19 or 0.0526

6 0

4 years ago

If f(x) = 3x^2 + 2x, then find the value of y when x = -1.

loris [4]

Answer:

Step-by-step explanation:

-1 to the power of 2 is 1

1 times 3 is 3

2 times -1 is -2

3+(-2)=1

7 0

3 years ago