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3 years ago

Distance between (-5, -5) And (-9, -2)

1 answer:

5 0

$d = \sqrt{(x_2 - x_1)^2+(y_2-y_1)^2} \\ d = \sqrt{(-9 - (-5))^2+(-2 - (-5))^2} \\ d = \sqrt{(-4)^2+(3)^2} \\ d = \sqrt{16 + 9} \\ d = \sqrt{25} = 5$

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A new DVD is available for sale in a store one week after its release. The cumulative revenue, $R, from sales of the DVD in this

AnnyKZ [126]

Solution :

It is given that :

$f'(t) = (350 \ln t)'$

$=350(\ln t)'$

$=\frac{350}{t}$

So, $f(5)=350 \ln (5) \approx 563$

$f'(5) = \frac{350}{5}$

$=70$

The relative change is then,

$\frac{f'(5)}{f(5)}=\frac{70}{350\ \ln(5)}$

$=\frac{1}{5\ \ln(5)}$

$\approx 0.12$

$=12\%$

This means that after 5 weeks, the revenue from the DVD sales in $563 with a rate of change of $70 per week and the increasing at a continuous rate of 12% per week.

3 0

3 years ago

The graph h = −16t^2 + 25t + 5 models the height and time of a ball that was thrown off of a building where h is the height in f

Thepotemich [5.8K]

Answer:

part 1) 0.78 seconds

part 2) 1.74 seconds

Step-by-step explanation:

step 1

At about what time did the ball reach the maximum?

Let

h ----> the height of a ball in feet

t ---> the time in seconds

we have

$h(t)=-16t^{2}+25t+5$

This is a vertical parabola open downward (the leading coefficient is negative)

The vertex represent a maximum

The x-coordinate of the vertex represent the time when the ball reach the maximum

Find the vertex

Convert the equation in vertex form

Factor -16

$h(t)=-16(t^{2}-\frac{25}{16}t)+5$

Complete the square

$h(t)=-16(t^{2}-\frac{25}{16}t+\frac{625}{1,024})+5+\frac{625}{64}$

$h(t)=-16(t^{2}-\frac{25}{16}t+\frac{625}{1,024})+\frac{945}{64}\\h(t)=-16(t^{2}-\frac{25}{16}t+\frac{625}{1,024})+\frac{945}{64}$

Rewrite as perfect squares

$h(t)=-16(t-\frac{25}{32})^{2}+\frac{945}{64}$

The vertex is the point $(\frac{25}{32},\frac{945}{64})$

therefore

The time when the ball reach the maximum is 25/32 sec or 0.78 sec

step 2

At about what time did the ball reach the minimum?

we know that

The ball reach the minimum when the the ball reach the ground (h=0)

For h=0

$0=-16(t-\frac{25}{32})^{2}+\frac{945}{64}$

$16(t-\frac{25}{32})^{2}=\frac{945}{64}$

$(t-\frac{25}{32})^{2}=\frac{945}{1,024}$

square root both sides

$(t-\frac{25}{32})=\pm\frac{\sqrt{945}}{32}$

$t=\pm\frac{\sqrt{945}}{32}+\frac{25}{32}$

the positive value is

$t=\frac{\sqrt{945}}{32}+\frac{25}{32}=1.74\ sec$

8 0

3 years ago

An option to buy a stock is priced at $150. If the stock closes above 30 next Thursday, the option will be worth $1000. If it cl

valentina_108 [34]

Answer:

Step-by-step explanation:

An option to buy a stock is priced at $150. If the stock closes above 30 next Thursday, the option will be worth $1000. If it closes below 20, the option will be worth nothing, and if it closes between 20 and 30, the option will be worth $200. A trader thinks there is a 50% chance that the stock will close in the 20-30 range, a 20% chance that it will close above 30, and a 30% chance that it will fall below 20.

a) Let X represent the price of the option

$1000 20/100 = 0.2

$200 50/100 = 0.5

$0 30/100 = 0.3

b) Expected option price

$= \sum x.P(X=x)\\\\ = 1000 * 0.2 + 200 * 0.5 + 0 = \$ 300$

Therefore expected gain = $300 - $150 = $150

c) The trader should buy the stock. Since there is an positive expected gain($150) in trading that stock option.

7 0

3 years ago

Rosa can run 4 miles in 56 minutes.How many miles does rosa run if she runs 42 minutes?

Alex Ar [27]

Rosa runs 3 miles in 42 minutes.

I divided 42 by 56 to get the percentage that will be multiplied to 4 miles to get the number of miles Rosa runs in 42 minutes.

42 / 56 = 0.75 * 100% = 75%

75% * 4 miles = 3 miles.

3 miles within 42 minutes

6 0

3 years ago

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The area of a parrellogram is 31.5ft and height is 6.3ft. What is the length of the base

Musya8 [376]

Answer:

Area = base × height

31.5 = base × 6.3

base = 5 ft

8 0

2 years ago

Read 2 more answers