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Thepotemich [5.8K]

3 years ago

15

The cost of vacation to a cabin resort for a night is $95 for each person. Each cabin also has to pay a $25 recreational equipme

nt rental fee. Model the cost, C, for staying x nights at the resort.

2 answers:

Rom4ik [11]3 years ago

8 0

x=95x+ 25

Step-by-step explanation:

Blababa [14]3 years ago

7 0

(x) = 95x + 25 is correct, since the $25 cost is fixed, but the $95 cost increases as x increases.

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Step-by-step explanation:

because,THE MOON IS SMALLER ACROSS (IN DIAMETER) THAN THE UNITED STATES IS WIDE. If the Earth were hollow, about 50 moons would fit inside. a. THE MOON IS SMALLER THAN THE EARTH: FIFTY MOONS WOULD FILL THE EARTH.

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The difference of the square of a number and three times the sum of the number and 7 is more than the product of that number and

Pachacha [2.7K]

Answer:

x2 - 3(x + 7) > 15x

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6 0

3 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

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

Please help me. I suck at math

serg [7]

Answer:

Answer is ...Obtuse

Step-by-step explanation:

$\frac{m$

$\frac{5x + 4}{2} = \frac{3}{2} x + 21$

$\frac{5x + 4}{2} = \frac{3x + 42}{2}$

$5x + 4 = 3x + 42$

$5x - 3x = 42 - 4$

$2x = 38$

$x = 19$

$substituting \: x = 19 \: \:in \: \: \: \: \: \: \: \\ m$

We get,

m<ABC =

$(5 \times 19) + 4 = 99$

Hence <ABC is obtuse

4 0

3 years ago