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VashaNatasha [74]
3 years ago
8

the pendulum on a grandfather clock swings from side to side once every second. If the length of the pendulum is 3 feet and the

angle through which it swings is 10 degrees, how far does the tip of the pendulum travel in 1 second?

Mathematics
1 answer:
bogdanovich [222]3 years ago
3 0
Check the picture below

thus \bf s=\cfrac{r\theta\pi }{180}\qquad 
\begin{cases}
s=\textit{arc's length}\\
r=radius\\
\theta=\textit{angle in degrees}\\
----------\\
r=3\\
\theta=10
\end{cases}\implies s=\cfrac{3\cdot 10\cdot \pi }{180}

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CAN I GET HELP PLEASE!
Mila [183]

Answer:

0.30 of a book / hour or 3/10 of a book per hour.

Step-by-step explanation:

Usually I tell people to put the numbers into decimals. Unfortunately for this question, it won't work. So we have any choice but to do it with fractions.

r = amount / time

amount = 1/4

time = 5/6

r = \frac{\frac{1}{4} }{\frac{5}{6} }

Invert the denominator and multiply

r = \frac{1}{4} * \frac{6}{5}

r = 6 * 1 / (5*4) = 6/20 = 3/10

The answer is 3/10 of a book per hour

5/6 of an hour is almost an hour.

1/4 of a book is 0.25 of a book.

3/10 of a book is 0.30 of a book. So it looks like it is just about right.

4 0
3 years ago
Shaq painted 600 portraits in 8 hours at that rate how many portraits would he paint in 4 minutes?
Deffense [45]

Answer: In 4 minutes he will make 5 portraits

Step-by-step explanation:

\large \boldsymbol{} 600p-8h=480 min  \\\\ x \ p-4  min   \\\\ x=\dfrac{600\cdot 4}{480} =\dfrac{2400}{480} =5  \ portraits \\\\ \rm Answer : 5

3 0
3 years ago
Find the distance between the origin and the point (10,45,57)
Marina86 [1]

Answer:

Step-by-step explanation:

3D space  (x, y, z)  = (10, 45, 57)

I will use  x² + y² = (2D Hyp)²  and (2D Hyp)² + z² = (3D Hyp)²

which is just x² + y²  + z² = (3D Hyp)²

10² + 45²  + 57² = (3D Hyp)²

100 + 2025 + 3249    =  5374   =   (3D Hyp)²    the destance from the origin

                                                   =  73.31    the destance from the origin

3 0
3 years ago
Given the speeds of each runner below determine who runs the fastest
Liula [17]

Answer:

Stephanie ran the fastest at 15 feet per second

Step-by-step explanation:

Frank ran the second fastest at 13.2 feet per second because it took him 60 seconds to run 792 feet, and 792/60 = 13.2

Debbie ran the third fastest at 12.08 feet per second because it took her 23 seconds to run 278 feet, and 278/23=12.086

Noah gets last place because it took him 551 seconds to run a mile, or 5280 feet, and 5280/551=9.58 feet per second

4 0
3 years ago
A forest ranger is in a forest 2 miles from a straight road. A car is located c miles down the road. The forest ranger can walk
Tcecarenko [31]

Answer:

  • T(x) = (√(4+x^2))/2 +(c -x)/4
  • (a) x = 1.155 miles
  • (b) x = 1/2 mile

Step-by-step explanation:

The straight line distance from the starting point to the point x on the road is given by the Pythagorean theorem:

  d1 = √(2²+x²)

The time required to walk that distance in the woods (at 2 miles per hour) is ...

  time = distance / speed

  t1 = √(4+x²)/2

The remaining distance along the road to the car is ...

  d2 = c - x . . . . . for c > x

and the corresponding time at 4 mph is ...

  t2 = (c -x)/4

Then the total time is ...

  T(x) = t1 +t2

  T(x) = √(4+x²)/2 +(c -x)/4

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(a) The value of x that minimizes total time is the one that makes the derivative zero.

  T'(x) = x/(2√(4+x²)) -1/4

  0 = (2x -√(4+x²))/(4√(4+x²))

  √(4+x²) = 2x . . . . . fraction is zero when numerator is zero; add radical

  4 +x² = 4x² . . . . . . square both sides

  4/3 = x² . . . . . . . . . subtract x², divide by 3

  x = (2/3)√3 ≈ 1.1547

If c = 9 miles, x = 1.1547 miles.

__

(b) For c < (2/3)√3, the shortest travel time will be along the straight-line path to the car.

If c = 1/2 mile, x = 1/2 mile.

8 0
3 years ago
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