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Mrac [35]
3 years ago
12

100 points , please help. I am not sure if I did this correct if anyone can double-check me thanks!

Mathematics
1 answer:
Nookie1986 [14]3 years ago
8 0

Step-by-step explanation:

\lim_{n \to \infty} \sum\limits_{k=1}^{n}f(x_{k}) \Delta x = \int\limits^a_b {f(x)} \, dx \\where\ \Delta x = \frac{b-a}{n} \ and\ x_{k}=a+\Delta x \times k

In this case we have:

Δx = 3/n

b − a = 3

a = 1

b = 4

So the integral is:

∫₁⁴ √x dx

To evaluate the integral, we write the radical as an exponent.

∫₁⁴ x^½ dx

= ⅔ x^³/₂ + C |₁⁴

= (⅔ 4^³/₂ + C) − (⅔ 1^³/₂ + C)

= ⅔ (8) + C − ⅔ − C

= 14/3

If ∫₁⁴ f(x) dx = e⁴ − e, then:

∫₁⁴ (2f(x) − 1) dx

= 2 ∫₁⁴ f(x) dx − ∫₁⁴ dx

= 2 (e⁴ − e) − (x + C) |₁⁴

= 2e⁴ − 2e − 3

∫ sec²(x/k) dx

k ∫ 1/k sec²(x/k) dx

k tan(x/k) + C

Evaluating between x=0 and x=π/2:

k tan(π/(2k)) + C − (k tan(0) + C)

k tan(π/(2k))

Setting this equal to k:

k tan(π/(2k)) = k

tan(π/(2k)) = 1

π/(2k) = π/4

1/(2k) = 1/4

2k = 4

k = 2

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If one three-digit number ( 0 cannot be a left digit) is chosen at random from all those that can be made from the following set
Oksana_A [137]

The probability of choosing a number that is not a multiple of 2 is P = 0.44

<h3 /><h3>How to find the probability?</h3>

We need to count the number of options for each digit.

  • For the first digit, we have 8 options {1, 2, 3, 4, 5, 6, 7, 8}
  • For the second digit, we have 9 options {0 ,1, 2, 3, 4, 5, 6, 7, 8}
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The total number of combinations is the product between the numbers of options:

C = 8*9*9 = 648

If we want our number to not be a multiple of 2 then it must end in a odd digit, the combinations that meet that condition are:

  • For the first digit, we have 8 options {1, 2, 3, 4, 5, 6, 7, 8}
  • For the second digit, we have 9 options {0 ,1, 2, 3, 4, 5, 6, 7, 8}
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C = 8*9*4 = 288

Then the probability of selecting a 3 digit number that is not a multiple of 2 is:

P = 288/648 = 0.44

If you want to learn more about probability, you can read:

brainly.com/question/251701

8 0
2 years ago
Can someone please help me I'm confused as to what I'm supposed to do.
kobusy [5.1K]
I hope this helps you


(fog)(5)=f (g (5))=?



x= 5 g (5)=-4.5+3=-20+3=-17




f (g(5))=f (-17)=-2. (-17)-7




f (-17)=34-7




f (-17)=27
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