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3 years ago

9

In a fruit cocktail, for every 30 ml of orange juice you need 20 ml of apple juice and 50 ml of coconut milk. What proportion of

the cocktail is apple juice? Give your answer as a fraction in its simplest form.

1 answer:

Alex787 [66]3 years ago

5 0

Answer:

1/5

Step-by-step explanation:

Since we have given that

Quantity of orange juice = 30 ml

Quantity of apple juice = 20 ml

Quantity of coconut juice = 50 ml

Total quantity of cocktail = 100 ml

So, the ratio of orange juice to apple juice to coconut juice is given by

=30:20:50

= 3:2:5

Total ratio=3+2+5

=10

So, proportion of the cocktail of apple juice is given by

2/10×100

=1/5×100

=20%

Hence, the proportion of the cocktail is 1/5 apple juice

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2 years ago

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

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Answer:

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

Step-by-step explanation:

From the formula

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To differentiate the product,

Let r² = u, so that

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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

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

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Then,

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

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From the question

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

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

At the instant when $r = 99 m$

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

$180 \times 3 = 9801\pi h$

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

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

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

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

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

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

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

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

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