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Dennis_Churaev [7]
3 years ago
5

Grace uses 9.8 pints of blue paint and white paint to paint her bedroom walls. 4/5

Mathematics
1 answer:
igor_vitrenko [27]3 years ago
5 0
4/5 * 9.8 = 7.84 pints of blue paint
9.8 - 7.84 = 1.96 pints of white paint
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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
A stadium floor that is in the shape of a circle has a diameter with a length of 50 yards. What is the area of the circle on the
barxatty [35]

Step-by-step explanation:

as diameter=50 yards

radius (r)=50/2=25 yards

ar of circle = π r r

π=22/7

22÷7×25×25

1974.285714

3 0
3 years ago
Read 2 more answers
What’s the area all sides meet at right angles
Marina86 [1]

Answer: 54

Step-by-step explanation: I separated it into 3 areas in my head and then added up 21+21+12 to get 54

7 times 3 is 21

7 times 3 is 21

and

3 times 4 is 12

sorry if i am wrong i just did this in my head

8 0
2 years ago
6. If n (E) = 40, n (A) = 22, n (ANB) = 8 and n ((AUB)') = 6, determine n(B)​
Dimas [21]

Answer:

4

Step-by-step explanation:

First n(AUB)=n(E) - n((AUB)')

So n(AUB) = 40 - 6 = 34

Now all u hv to do is use the formulae,

n(AUB) = n(A) + n(B) - n(ANB)

So when u substitute above values,

34=22 + n(B) - 8

So,

n(B) = 4

4 0
3 years ago
Which is the equation of a line that has a slope of -2/3 and passes through point (-3,-1)
DiKsa [7]

Answer:

y = -2/3x - 3

Step-by-step explanation:

y = mx + b

m = slope

(-3,-1) = (x,y)

<em>Plus in the coordinates</em>

-1 = -2/3(-3) + b

<em>negative times negative = positive</em>

-2/3 * -3 = 2

-1 = 2 +b

<em>Use inverse operations</em>

-2 --2

-3 = b

y = -2/3x - 3

5 0
2 years ago
Read 2 more answers
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