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alexgriva [62]
3 years ago
5

Find the values of x and

Mathematics
1 answer:
SVEN [57.7K]3 years ago
4 0

Answer:

x+2jsvwb w gskcbs shihdks sjixn

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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
Find the product : 2p (4p² + 5p + 7)
Ber [7]
<h3>Answer: 8p^3 + 10p^2 + 14p</h3>

Explanation:

The outer term 2p is distributed among the three terms inside the parenthesis. We will multiply 2p by each term inside

2p times 4p^2 = 2*4*p*p^2 = 8p^3

2p times 5p = 2*5*p*p = 10p^2

2p times 7 = 2*7p = 14p

The results 8p^3, 10p^2 and 14p are added up to get the final answer shown above. We do not have any like terms to combine, so we leave it as is.

6 0
3 years ago
What is the answer to this
LekaFEV [45]
4 \dfrac{3}{5} \times \dfrac{5}{12} =

= \dfrac{23}{5} \times \dfrac{5}{12}

You changed the mixed numeral into a fraction correctly.
Now you need to multiply the fractions.
Multiply the numerators together, and multiply the denominators together.

= \dfrac{23 \times 5}{5 \times 12}

Now we could multiply out the numerator and denominator, and then we'd need to reduce the fraction, but before we multiply, we see there is a factor of 5 both in the numerator and in the denominator, so we can reduce before we multiply.

= \dfrac{23 \times 5}{12 \times 5}

= \dfrac{23}{12}

= 1 \dfrac{11}{12}
6 0
3 years ago
A cab charges $1.75 for the first mile and $0.25 for each additional mile. Write and solve an inequality to determine how many m
Margaret [11]
A. 1.75+0.25x<15;x,53miles

sorry, i could not put in the or equal to signs
                       
4 0
3 years ago
At the end of the school year a school system has a table with the total absences and tardies in its 10 schools what is the best
enot [183]

Answer:

A

Step-by-step explanation:

3 0
2 years ago
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