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3 years ago

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E-Z View cable company charges a flat rate of $40 per month for service and $4.95 for each pay per view movie. View the Best cha

rges a flat rate of $25 per month and $5.95 for each pay per view. Using the given equations, how many pay per views will generate equal monthly bills from the two companies?

1 answer:

kkurt [141]3 years ago

6 0

E-Z View: 40 + 4.95x
View the best: 25 + 5.95x

Equal monthly bills:

40 + 4.95x = 25 + 5.95x

5.95x - 4.95x = 40 - 25

x = 15

Answer: 15

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A body moves s metres in a time t seconds so that s = t3 – 3t2 + 8. Find:

Lady bird [3.3K]

Using derivatives, it is found that:

i) $v(t) = 3t^2 - 6t$

ii) 9 m/s.

iii) $a(t) = 6t - 6$

iv) 6 m/s².

v) 1 second.

<h3>What is the role of derivatives in the relation between acceleration, velocity and position?</h3>

The velocity is the derivative of the position.

The acceleration is the derivative of the velocity.

In this problem, the position is:

$s(t) = t^3 - 3t^2 + 8$

item i:

Velocity is the <u>derivative of the position</u>, hence:

$v(t) = 3t^2 - 6t$

Item ii:

$v(3) = 3(3)^2 - 6(3) = 27 - 18 = 9$

The speed is of 9 m/s.

Item iii:

Derivative of the velocity, hence:

$a(t) = 6t - 6$

Item iv:

$a(2) = 6(2) - 6 = 6$

The acceleration is of 6 m/s².

Item v:

t for which a(t) = 0, hence:

$6t - 6 = 0$

$6t = 6$

$t = \frac{6}{6}$

$t = 1$

Hence 1 second.

You can learn more about derivatives at brainly.com/question/14800626

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2 years ago

Archimedes is making waves as he showers in his bath.

ch4aika [34]

Answer:

Step-by-step explanation

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2 years ago

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The volume of a cylinder can is 1.54 litre and area of base is 77cm^2 Find its height

goblinko [34]

Answer:

The height is 20 cm.

Step-by-step explanation:

First, we have to know that the volume formula is V = πr²h and the base area of cylinder is a circle. So we can let πr² be 77 cm² . Then we have to substitute the following values into the formula :

$v = 1.54 \: l$

$v = 1540 \: {cm}^{3}$

$v = \pi \times {r}^{2} \times h$

Let πr² be 77,

Let v be 1540,

$1540 = 77 \times h$

$77h = 1540$

$h = 1540 \div 77$

$h = 20 \: cm$

5 0

3 years ago

Luden [163]

Cone details:

height: h cm

radius: r cm

Sphere details:

radius: 10 cm

================

From the endpoints (EO, UO) of the circle to the center of the circle (O), the radius is will be always the same.

<u>Using Pythagoras Theorem</u>

(a)

TO² + TU² = OU²

(h-10)² + r² = 10² [insert values]

r² = 10² - (h-10)² [change sides]

r² = 100 - (h² -20h + 100) [expand]

r² = 100 - h² + 20h -100 [simplify]

r² = 20h - h² [shown]

r = √20h - h² ["r" in terms of "h"]

(b)

volume of cone = 1/3 * π * r² * h

===========================

$\longrightarrow \sf V = \dfrac{1}{3} * \pi * (\sqrt{20h - h^2})^2 \ ( h)$

$\longrightarrow \sf V = \dfrac{1}{3} * \pi * (20h - h^2) (h)$

$\longrightarrow \sf V = \dfrac{1}{3} * \pi * (20 - h) (h) ( h)$

$\longrightarrow \sf V = \dfrac{1}{3} \pi h^2(20-h)$

To find maximum/minimum, we have to find first derivative.

(c)

<u>First derivative</u>

$\Longrightarrow \sf V' =\dfrac{d}{dx} ( \dfrac{1}{3} \pi h^2(20-h) )$

<u>apply chain rule</u>

$\sf \Longrightarrow V'=\dfrac{\pi \left(40h-3h^2\right)}{3}$

<u>Equate the first derivative to zero, that is V'(x) = 0</u>

$\Longrightarrow \sf \dfrac{\pi \left(40h-3h^2\right)}{3}=0$

$\Longrightarrow \sf 40h-3h^2=0$

$\Longrightarrow \sf h(40-3h)=0$

$\Longrightarrow \sf h=0, \ 40-3h=0$

$\Longrightarrow \sf h=0,\:h=\dfrac{40}{3}$ <u />

<u>maximum volume:</u> <u>when h = 40/3</u>

$\sf \Longrightarrow max= \dfrac{1}{3} \pi (\dfrac{40}{3} )^2(20-\dfrac{40}{3} )$

$\sf \Longrightarrow maximum= 1241.123 \ cm^3$

<u>minimum volume:</u> <u>when h = 0</u>

$\sf \Longrightarrow min= \dfrac{1}{3} \pi (0)^2(20-0)$

$\sf \Longrightarrow minimum=0 \ cm^3$

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2 years ago

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The average speed of one team in a relay race is about 10 miles per hour. What is the speed in feet per second?

ki77a [65]

10 miles per second in feet per second is 14.67 feet per second

Step-by-step explanation:

The average speed of one team in a relay race = 10 miles per hour.

We need to find the speed in feet per second.

The conversion rule is:

1 mile per hour = 1.467 feet per second

So, Speed in feet per second is:

1 mile per hour = 1.467 feet per second

10 miles per hour = 10*1.467 feet per second

= 14.67 feet per second

So, 10 miles per second in feet per second is 14.67 feet per second

Keywords: Conversion of units

Learn more about Conversion of units at:

#learnwithBrainly

5 0

3 years ago