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1 year ago

5

Help solving this problem, the second problem not the third

1 answer:

yawa3891 [41]1 year ago

7 0

Given:

1 Van and 4 buses filled with 195 students.

1 Van and 5 buses filled with 241 students.

Let x and y be the number of students in Van and number of students in bus.

$\begin{gathered} x+4y=195\ldots\text{ (1)} \\ x+5y=241\ldots\text{ (2)} \end{gathered}$

Subtract equation (1) from equation (2)

$\begin{gathered} x+5y-x-4y=241-195 \\ y=46 \end{gathered}$

Substitute y=46 in equation (1)

$\begin{gathered} x+4(46)=195 \\ x+184=195 \\ x=195-184 \\ x=11 \end{gathered}$

Number of students that van can carry is 11.

Number of students that bus can carry is 46

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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

What is equivalent to 7^13/7^7

Deffense [45]

The equivalent expression to 7^13/7^7 would be 7^6.

<h3>What are equivalent expressions?</h3>

Those expressions that might look different but their simplified forms are the same expressions are called equivalent expressions.

To derive equivalent expressions of some expression, we can either make it look more complex or simple. Usually, we simplify it.

We have given an expression as 7^13/7^7

The equivalent expression;

$\dfrac{7^{13}}{7^7} \\\\7^{13-7}\\\\7^6$

Hence, The equivalent expression to 7^13/7^7 would be 7^6.

Learn more about expression;

brainly.com/question/22246485

#SPJ1

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2 years ago

What is the % of 7/10

Delicious77 [7]

7/10=70/100=70%, so the answer is seventy-percent.

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3 years ago

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2 years ago

A phone is 35 percent off which is now worth 78 pounds what was the original price

Black_prince [1.1K]

Answer:

120 pounds

Step-by-step explanation:

65% of y= 78 pounds

$\frac{65}{100}$ × y = 78 pounds

65y = 78 × 100=7800

y= 7800/65= 120 pounds

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3 years ago