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Maru [420]
3 years ago
13

A grading machine can grade 96 multiple

Mathematics
1 answer:
weqwewe [10]3 years ago
8 0

Answer:

6.25 minutes or 375 seconds

Step-by-step explanation:

We can solve the following problem through the Proportion method.

Here,

we may take the time taken by the machine as x

96 : 2 : : 300 : x\\96x= 2 *300\\96x=600\\x=600/96\\x=6.25\ minutes

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The radius of a cone is increasing at a constant rate of 7 meters per minute, and the volume is decreasing at a rate of 236 cubi
storchak [24]

Answer:

The rate of change of the height is 0.021 meters per minute

Step-by-step explanation:

From the formula

V = \frac{1}{3}\pi r^{2}h

Differentiate the equation with respect to time t, such that

\frac{d}{dt} (V) = \frac{d}{dt} (\frac{1}{3}\pi r^{2}h)

\frac{dV}{dt} = \frac{1}{3}\pi \frac{d}{dt} (r^{2}h)

To differentiate the product,

Let r² = u, so that

\frac{dV}{dt} = \frac{1}{3}\pi \frac{d}{dt} (uh)

Then, using product rule

\frac{dV}{dt} = \frac{1}{3}\pi [u\frac{dh}{dt} + h\frac{du}{dt}]

Since u = r^{2}

Then, \frac{du}{dr} = 2r

Using the Chain's rule

\frac{du}{dt} = \frac{du}{dr} \times \frac{dr}{dt}

∴ \frac{dV}{dt} = \frac{1}{3}\pi [u\frac{dh}{dt} + h(\frac{du}{dr} \times \frac{dr}{dt})]

Then,

\frac{dV}{dt} = \frac{1}{3}\pi [r^{2} \frac{dh}{dt} + h(2r) \frac{dr}{dt}]

Now,

From the question

\frac{dr}{dt} = 7 m/min

\frac{dV}{dt} = 236 m^{3}/min

At the instant when r = 99 m

and V = 180 m^{3}

We will determine the value of h, using

V = \frac{1}{3}\pi r^{2}h

180 = \frac{1}{3}\pi (99)^{2}h

180 \times 3 = 9801\pi h

h =\frac{540}{9801\pi }

h =\frac{20}{363\pi }

Now, Putting the parameters into the equation

\frac{dV}{dt} = \frac{1}{3}\pi [r^{2} \frac{dh}{dt} + h(2r) \frac{dr}{dt}]

236 = \frac{1}{3}\pi [(99)^{2} \frac{dh}{dt} + (\frac{20}{363\pi }) (2(99)) (7)]

236 \times 3 = \pi [9801 \frac{dh}{dt} + (\frac{20}{363\pi }) 1386]

708 = 9801\pi \frac{dh}{dt} + \frac{27720}{363}

708 = 30790.75 \frac{dh}{dt} + 76.36

708 - 76.36 = 30790.75\frac{dh}{dt}

631.64 = 30790.75\frac{dh}{dt}

\frac{dh}{dt}= \frac{631.64}{30790.75}

\frac{dh}{dt} = 0.021 m/min

Hence, the rate of change of the height is 0.021 meters per minute.

3 0
3 years ago
A parallelogram has sides 17.3 m and 43.4 m long. The height corresponding to the 17.3-m base is 8.7 m. Find the height, to the
Anvisha [2.4K]

Answer:

3.5m

Step-by-step explanation:

A parallelogram has sides 17.3 m and 43.4 m long.

The height corresponding to the 17.3-m base is 8.7 m.

The area of a parallelogram = base × height

= 8.7m × 17.3m

= 150.51m²

Both parallelograms have the same area

Hence, the height, to the nearest tenth of a meter, corresponding to the 43.4-m base is calculated as:

= 150.51m²/43.4m

= 3.4679723502m

Approximately = 3.5m

7 0
3 years ago
Which property refers to "regrouping" the terms in the expression 9 (2-x) = 18 - 9x ?
Aliun [14]
The answer is C- Distributive Property because you times everything in the bracket by the value connected to it:
9 times 2=18
9 times x = 9x
= 18 - 9x
3 0
3 years ago
Read 2 more answers
When Riley goes bowling, her scores are normally distributed with a mean of 160 and
e-lub [12.9K]

Answer:

The interval that would represent the middle 68% of the scores of all the games that Riley bowls is (147, 173).

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

Approximately 68% of the measures are within 1 standard deviation of the mean.

Approximately 95% of the measures are within 2 standard deviations of the mean.

Approximately 99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean of 160, standard deviation of 13.

Middle 68% of the scores of all the games that Riley bowls.

Within 1 standard deviation of the mean, so:

160 - 13 = 147.

160 + 13 = 173.

The interval that would represent the middle 68% of the scores of all the games that Riley bowls is (147, 173).

6 0
3 years ago
Pls help me ASAP!!!!!!!!!!!!!
Nikolay [14]

Sound the same but have totally different meanings.

5 0
3 years ago
Read 2 more answers
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