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Cloud [144]
3 years ago
13

Carlos is 33 years younger than Kristen. 2 years ago, Kristen's age was 2 times Carlos's age. How old is Carlos now?

Mathematics
1 answer:
ale4655 [162]3 years ago
6 0

Answer:

Carlos is 35 years old now

Step-by-step explanation:

Assume that Carlos is x years old now

∵ Carlos is x years old now

∵ Carlos is 33 years younger than Kristen

- Kirsten's age is the sum of x and 33

∴ Kirsten is x + 33 years old now

2 years ago

∵ Carlos's age = x - 2

∵ Kristen's age = x + 33 - 2 = x + 31

∵ Kristen's age was 2 times Carlos's age

- Equate Kristen's age by 2 times Carlos's age

∴ x + 31 = 2(x - 2)

- Simplify the right hand side

∴ x + 31 = 2x - 4

- Subtract x from both sides

∴ 31 = x - 4

- Add 4 to both sides

∴ 35 = x

∵ x represents Carlos's age now

∴ Carlos is 35 years old now

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3 years ago
For f(x)=4sin(x2) between x=0 and x=3, find the coordinates of all intercepts, critical points, and inflection points to two dec
telo118 [61]

Answer:

Intercepts:

x = 0, y = 0

x = 1.77, y = 0

x = 2.51, y = 0

Critical points:

x = 1.25, y = 4

x = 2.17 , y = -4

x = 2.8, y = 4

Inflection points:

x = 0.81, y = 2.44

x = 1.81, y = -0.54

x = 2.52, y = 0.27

Step-by-step explanation:

We can find the intercept by setting f(x) = 0

4sin(x^2) = 0

sin(x^2) = 0

x^2 = n\pi where n = 0, 1, 2,3, 4, 5,...

x = \sqrt(n\pi)

Since we are restricting x between 0 and 3 we can stop at n = 2

So the function f(x) intercepts at y = 0 and x:

x = 0

x = 1.77

x = 2.51

The critical points occur at the first derivative = 0

f^{'}(x) = 4cos(x^2)2x = 8xcos(x^2) = 0

xcos(x^2) = 0

x = 0 or

cos(x^2) = 0

x^2 = \frac{\pi}{2} + n\pi where n = 0, 1, 2, 3

x = \sqrt{\pi(n+1/2)}

Since we are restricting x between 0 and 3 we can stop at n =  2

So our critical points are at

x = 1.25, y = f(1.25) = 4sin(1.25^2) = 4

x = 2.17 , y = f(2.17) = 4sin(2.17^2) = -4

x = 2.8, y = f(2.8) = 4sin(2.8^2) = 4

For the inflection point, we can take the 2nd derivative and set it to 0

f^[''}(x) = 8(cos(x^2) - xsin(x^2)2x) = 8cos(x^2) - 16x^2sin(x^2) = 0

cos(x^2) = 2x^2sin(x^2)

tan(x^2) = \frac{1}{2x^2}

We can solve this numerically to get the inflection points are at

x = 0.81, y = f(0.81) = 4sin(0.81^2) = 2.44

x = 1.81, y = f(1.81) = 4sin(1.81^2) = -0.54

x = 2.52, y = f(2.52) = 4sin(2.52^2) = 0.27

3 0
3 years ago
Michael bought 0.44 pound of slice turkey. what is the value of the digit in the hundredths place?
jarptica [38.1K]

Answer:

4

Step-by-step explanation:

You have 0.44

0 is in the ones place

4 is in the tenths place (0.4)

And the other 4 is in the hundredths place (0.04)

8 0
3 years ago
Read 2 more answers
Pls help i will give brainly
elixir [45]

Answer:

A

Step-by-step explanation:

If you look at the graph you can see that the turtle is -24 and the dolphin abt -35

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David charges $17 plus $7.00 per hour to mow lawns. Ari charges $11 plus $7.75 per hour to mow lawns. In what situations is Ari'
iren2701 [21]

Answer:

Ari's is less than Davids

Ari=18.75

David=24.00

Step-by-step explanation:

5 0
3 years ago
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