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DedPeter [7]
3 years ago
12

50 POINTS!!!!

Mathematics
1 answer:
tatiyna3 years ago
6 0

Answer:

90 cubic inches

Step-by-step explanation:

V = 1/3 · area of base · height

V = 1/3 · 18 · 15

V = 6 · 15

V = 90

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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 gym employee is paid monthly. After working for three months, he had earned $4,500. To
Leto [7]

Answer:

$9000

Step-by-step explanation:

A gym employee has earned in 3 months =$4500

Then his monthly salary =$4500/3 =$1500

After six months he will earn = 6 × his monthly salary

= 6×$1500=$9000

5 0
3 years ago
PLEASE HELP!!!!
frozen [14]
A) \frac{2 \frac{1}{4}}{ \frac{1}{2}}
b)\frac{1}{2} • 2 = 1
so \frac{9}{4} • 2 = \frac{9}{2} cups (which is 4 \frac{1}{2} )
5 0
3 years ago
Help me out:)i need an answer as soon as possible!!!
kifflom [539]
Answer is c , got it right
5 0
3 years ago
The volume of a solid right pyramid with a square base is v units3 and the length of the base edge is y units. Write the express
Wewaii [24]

Answer:

h = V/y^2

Step-by-step explanation:

The volume of a right pyramid is given by the expression = Area of base × height.

Area of base = Area of square at the base

= y × y = y^2.

Now, we substitute these values:

V = y^2 × height

height = V/y^2

6 0
3 years ago
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