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navik [9.2K]
3 years ago
15

A wheel rolling at a constant speed has a radius of 15 inches and takes 30

Mathematics
1 answer:
dezoksy [38]3 years ago
6 0

Answer:

152.87 degree/seconds

Step-by-step explanation:

1 rotation = Circumference of a circle = 2πr

r = 15 inches

1 rotation = 2 × 3.14 × 15

94.2 inches.

We are told in the question that it takes 30 seconds to roll 100 feet along the ground

Convert feet to inches

1 feet = 12 inches

100 feet =

100 × 12 = 1200 inches.

Hence, if

94.2 inches = 1 rotation

1200 inches = X

Cross multiply

94.2 × X = 1200 × 1

94.2X = 1200

X = 1200/94.2

X = 12.738853503 rotations

Formula for Angular velocity = Number of rotations × 2π/time in seconds

Time = 30 seconds

12.738853503 × 2 × 3.14/30

= 2.6666666667 rotations per second

Converting Angular velocity to degree per second

= 2.6666666667 × 180/ π

= 2.6666666667 × 180/3.14

= 152.86624204 degree/seconds

Approximately to 2 decimal places

= 152.87 degree/seconds

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Paladinen [302]

Answer:

\frac{140}{3}, \frac{140}{3}, \frac{140}{3}

Step-by-step explanation:

Let the numbers be x, y\ and\ z.

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Open bracket

f(x,y) = 140xy - x^2y - xy^2

Differentiate w.r.t x and y

f_x=140y - 2xy - y^2

f_y=140x - x^2 - 2xy

Since the products are maximum, then f_x = f_y = 0

For f_x=140y - 2xy - y^2

140y - 2xy - y^2 = 0

Factorize:

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For f_y=140x - x^2 - 2xy

140x - x^2 - 2xy = 0

---------------------------------------------------

Substitute y = 0

140x - x^2 -2x*0 = 0

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Factorize

x(140 - x)= 0

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x = 0\ or\ x = 140

---------------------------------------------------

Substitute y = 140 - 2x

140x - x^2 - 2xy = 0

140x - x^2 - 2x(140 - 2x) = 0

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Re-arrange

4x^2 -x^2 +140x - 280x = 0

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Factor x out

x(3x - 140) = 0

Divide through by x

3x - 140 = 0

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Recall that: y = 140 - 2x

y = 140 - 2 * \frac{140}{3}

y = 140 - \frac{280}{3}

Take LCM

y = \frac{140*3-280}{3}

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Recall that:

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z = 140 - \frac{140}{3} - \frac{140}{3}

Take LCM

z =  \frac{3 * 140- 140 - 140}{3}

z =  \frac{140}{3}

Hence, the numbers are:

\frac{140}{3}, \frac{140}{3}, \frac{140}{3}

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