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Scrat [10]
2 years ago
15

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. x+y = 3, x = 4

−(y−1)^2; about the x-axis.
Mathematics
1 answer:
Ad libitum [116K]2 years ago
4 0
The intersection between the curves are
3, 0
0, 3
The volume of the solids is obtained by
V = ∫ π [ (4 - (y-1)²)² - (3 - y)²] dy with limits from 0 to 3
The volume is
V = 108π/5 or 67.86
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4 0
2 years ago
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A turtle walks 7/8 of a mile in 50 minutes. What is the unit rate when the turtle’s speed is expressed in miles per hour?
yKpoI14uk [10]

Answer:

21/20

Step-by-step explanation:

a) One hour is equivalent to 60 minutes.

So we can multiply 50 minutes by the fraction \frac{1 hour}{60 minutes}, so we could convert 50 minutes to hours.

It is:

50 minutes * \frac{1 hour}{60 minutes}=\frac{50}{60}hours

If we simplify the fraction, we have:

50 minutes = \frac{5}{6}hours

b) In order to express the turtle's speed in miles per hour, we have to divide

\frac{7}{8}miles by  \frac{5}{6}hours

So:

\frac{\frac{7}{8}miles }{\frac{5}{6}hours }

We simplify the expression by multiplying 7 mile by 6 and 8 by 5 hours:

\frac{\frac{7}{8}miles }{\frac{5}{6}hours}=\frac{42 miles}{40 hours} =\frac{21 miles}{20 hours}

4 0
2 years ago
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Tracie rides the bus home from school each day. The graph represents her distance from home relative to the number of minutes si
Semmy [17]

Step-by-step explanation:

Tracie’s bus travels towards her home at an average speed of StartFraction one-half EndFraction mile per minute.

4 0
1 year ago
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Which is a correct first step in solving the inequality –4(2x – 1) > 5 – 3x?distribute –4 to get –8x 4 > 5 – 3x.distribute
Leviafan [203]

Answer:

Option A is correct.

The first step in solving the inequality is:

to distribute -4 to get  -8x + 4> 5-3x

Step-by-step explanation:

The distributive property says that:

a\cdot(b+c) =a\cdot b + a\cdot c

Given the inequality:

-4(2x-1)> 5-3x

Apply the distributive property we have;

-4 \cdot (2x) -4\cdot (-1)> 5-3x

Simplify:

-8x + 4> 5-3x

Therefore, the first step in solving the inequality is:

to distribute -4 to get  -8x + 4> 5-3x

9 0
2 years ago
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A 3-gallon tub of ice cream yields about 90 scoops of ice cream. There are roughly 3785 cubic centimeters in 1 gallon. Determine
ASHA 777 [7]

Answer:

The radius of the scoop is r = 3.1 cm

Step-by-step explanation:

Since 3 gallons yields 90 scoops, and 1 gallon = 3785 cm³.

3 gallons = 3 × 3785 cm³ =  11355 cm³

So we have 11355 cm³ in 3 gallons which is also the volume of 90 scoops.

Since 90 scoops = 11355 cm³, then

1 scoop = 11355 cm³/90 = 126.2 cm³

Now, if each scoop is a sphere, the volume is given by V = 4πr³/3 where r is the radius of the scoop. Since we need to find the radius of the scoop, r, making r subject of the formula, we have

r = ∛(3V/4π)

Substituting V = 126.2 cm³, we have

r = ∛(3× 126.2 cm³/4π)

= ∛(378.6 cm³/12.57)

= ∛30.13 cm³

= 3.1 cm

So, the radius of the scoop is r = 3.1 cm

5 0
2 years ago
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