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chubhunter [2.5K]
2 years ago
9

The Scale Factor of 1 2/3?

Mathematics
1 answer:
Ilya [14]2 years ago
8 0

Answer:

greater than 1

Step-by-step explanation:

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A filter filled with liquid is in the shape of a vertex-down cone with a height of 9 inches and a diameter of 6 inches at its op
Alina [70]

Answer: Level of the liquid dropping at 28.28 inch/second when the liquid is 2 inches deep.

Step-by-step explanation:

Since we have given that

Height = 9 inches

Diameter = 6 inches

Radius = 3 inches

So, \dfrac{r}{h}=\dfrac{3}{9}=\dfrac{1}{3}\\\\r=\dfrac{1}{3}h

Volume of cone is given by

V=\dfrac{1}{3}\pi r^2h\\\\V=\dfrac{1}{3}\pi \dfrac{1}{9}h^2\times h\\\\V=\dfrac{1}{27}\pi h^3

By differentiating with respect to time t, we get that

\dfrac{dv}{dt}=\dfrac{1}{27}\pi \times 3\times h^2\dfrac{dh}{dt}=\dfrac{1}{9}\pi h^2\dfrac{dh}{dt}

Now,  the liquid drips out the bottom of the filter at the constant rate of 4 cubic inches per second, ie \dfrac{dv}{dt}=-4\ in^3

and h = 2 inches deep.

-4=\dfrac{1}{9}\times \pi\times (2)^2\dfrac{dh}{dt}\\\\-9\pi =\dfrac{dh}{dt}\\\\-28.28=\dfrac{dh}{dt}

Hence, level of the liquid dropping at 28.28 inch/second when the liquid is 2 inches deep.

7 0
2 years ago
Solve the equation by using the quadratic formula.<br> 8x2 – 2x - 15 =0
ddd [48]

Answer:

x = 3/2 or x = -5/4

Step-by-step explanation:

Solve for x over the real numbers:

8 x^2 - 2 x - 15 = 0

Using the quadratic formula, solve for x.

x = (2 ± sqrt((-2)^2 - 4×8 (-15)))/(2×8) = (2 ± sqrt(4 + 480))/16 = (2 ± sqrt(484))/16:

x = (2 + sqrt(484))/16 or x = (2 - sqrt(484))/16

Simplify radicals.

sqrt(484) = sqrt(4×121) = sqrt(2^2×11^2) = 2×11 = 22:

x = (2 + 22)/16 or x = (2 - 22)/16

Evaluate (2 + 22)/16.

(2 + 22)/16 = 24/16 = 3/2:

x = 3/2 or x = (2 - 22)/16

Evaluate (2 - 22)/16.

(2 - 22)/16 = -20/16 = -5/4:

Answer: x = 3/2 or x = -5/4

4 0
2 years ago
3/5 of the 30 students are boys how many students are girls
anygoal [31]

if 3/5 are boys

1- 3/5

5/5 -3/5 = 2/5  are girls

2/5 * 30 = 60/5 = 12

12 are girls

6 0
2 years ago
Read 2 more answers
3. In a game, if you roll a 6 on a 6-sided number cube, you lose a turn.
dlinn [17]
Part A: The probability is 1/6. This is because there are six options in total, and only one of those options is 6.

Part B: The probability is 6/6, or alternatively 100%. This is because that the probability of rolling a 6 is 1/6, and the probability of rolling any of the other options is 5/6. Adding them together gives a probability of 6/6.

Part C: The probability is 5/6. This is because there are six options, and of those, five of them are not 6.
3 0
2 years ago
Read 2 more answers
Enter an expression for the perimeter of the given figure. Simplify the expression.
dlinn [17]

Answer:

4x + 28.4 in.

Step-by-step explanation:

perimeter = sum of lengths of sides

perimeter = x + 2 + x + 2 + x + 2 + x + 2 + 10.2 + 10.2

perimeter = 4x + 28.4

3 0
2 years ago
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