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Hoochie [10]
3 years ago
8

Any help with an explanation would be appreciated!

Mathematics
1 answer:
Lilit [14]3 years ago
5 0

Problem 1

We'll use the product rule to say

h(x) = f(x)*g(x)

h ' (x) = f ' (x)*g(x) + f(x)*g ' (x)

Then plug in x = 2 and use the table to fill in the rest

h ' (x) = f ' (x)*g(x) + f(x)*g ' (x)

h ' (2) = f ' (2)*g(2) + f(2)*g ' (2)

h ' (2) = 2*3 + 2*4

h ' (2) = 6 + 8

h ' (2) = 14

<h3>Answer: 14</h3>

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

Problem 2

Now we'll use the quotient rule

h(x) = \frac{f(x)}{g(x)}\\\\h'(x) = \frac{f'(x)*g(x)-f(x)*g'(x)}{(g(x))^2}\\\\h'(2) = \frac{f'(2)*g(2)-f(2)*g'(2)}{(g(2))^2}\\\\h'(2) = \frac{2*3-2*4}{(3)^2}\\\\h'(2) = \frac{6-8}{9}\\\\h'(2) = -\frac{2}{9}\\\\

<h3>Answer:  -2/9</h3>

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

Problem 3

Use the chain rule

h(x) = f(g(x))\\\\h'(x) = f'(g(x))*g'(x)\\\\h'(2) = f'(g(2))*g'(2)\\\\h'(2) = f'(3)*g'(2)\\\\h'(2) = 3*4\\\\h'(2) = 12\\\\

<h3>Answer:  12</h3>
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If you are moving the center of circle 2 to the the center of circle 1, then the translation rule is (x,y) ---> (x+4, y+10). 
Note how x = 1 turns into x = 5. So we add 4
Also, y = -2 turns into y = 8. We add 10

The scale factor to turn the radius r = 4 into r = 8 is 2. Basically we double the radius. We can divide the two radii to see 8/4 = 2

----------------------------------

Summary:
To go from circle 2 to circle 1, we apply these two transformations
translation: (x,y) ---> (x+4, y+10)
dilation: scale factor 2

note: 
if you want to go backwards, go from circle 1 to circle 2, then undo the transformations above
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3 years ago
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Fynjy0 [20]

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Step-by-step explanation:

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z=12

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3 years ago
hosting a dinner party for 38 people, you plan to serve peach pie for dessert. Each pie has 8 slices. how many pies must your bu
dem82 [27]

Answer:

4.75 or round up to 5.

Step-by-step explanation:

if each pie has 8 slices, then you must do 8+8+8... and so on until u reach 38. However you wont get exactly 38 because 8 doesn't add up evenly into 38. You can find the exact number by divding the amount of people, 38, by the number of slices per pie, 8. The answer will be 4.75 but you can not buy a fraction of a pie so you must round up to 5 whole pies. There will be extra left over in the end, but you cant round down because 4 pies would not be enough, so you must buy 5.

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Suppose that the length of a phone call in minutes is an exponential random variable with parameter λ = 1/ 8. If someone arrives
Elis [28]

Answer:

a) P=0.535

b) P=0.204

c) P=0.286

Step-by-step explanation:

The exponential distribution is expressed as

F(x>t)=e^{-\lambda t}

In this example, λ=1/8=0.125 min⁻¹.

a) The probability of having to wait more than 5 minutes

F(x>5)=e^{-0.125*5}=e^{-0.625}=0.535

b) The probability of having to wait between 10 and 20 minutes

F(1020)=e^{-0.125*10}-e^{-0.125*20}\\\\F(10

c) The exponential distribution is memory-less, so it is independent of past events.

If you have waited 5 minutes, the probability of waiting more than 15 minutes in total is the same as the probability of waiting 15-5=10 minutes.

F(x>15|t^*=5)=F(x>15)/F(x>5)=\frac{e^{-0.125*15}}{e^{-0.125*5}}=e^{-0.125*(15-5)}\\\\ F(x>15|t^*=5)=e^{-0.125*(10)}=F(x>10)=0.286

5 0
3 years ago
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