5 students made an A in their Math quiz, 10 students made an B, 6 students made an C,

The length of the minute hand is 150% of the length of the hour hand. In 1 hour, how much farther does the tip of the minute han

tatiyna

Answer:

17(pi)r/6

Step-by-step explanation:

Since neither hand length is known, you can have an answer in terms of one of the hands, but you cannot get just a number.

Let r = the length of the hour hand.

Then, the length of the minute hand is 150% of r = 1.5r.

The minute hand is the radius of the circle drawn by the tip of the minute hand. In 1 hour, the minute hand rotates one full revolution, so the tip of the minute hand moves the circumference of the circle drawn by the tip of the minute hand.

Now we find the circumference of the circle of the tip of the minute hand.

C = 2 * pi * r,

but the radius here is 1.5r, so we get

C_minute_hand = 2 * pi * (1.5)r

C_minute_hand = 3(pi)r

The hour hand rotates a full revolution in 12 hours, so it rotates 1/12 of a revolution in 1 hour. The radius is r.

C_hour_hand = 2 * pi * r * 1/12

C_hour_hand = (pi)r/6

The difference in how much each tip travels is

3(pi)r - (pi)r/6 = (pi)r(3 - 1/6) = 17(pi)r/6

5 0

3 years ago

A tree initially measured 38 1/2 feet tall. Over the next 5 1/2 years, it grew to a final height of 49 1/2 feet. During those 5

polet [3.4K]

Answer:

2feets per year

Step-by-step explanation:

49,5-38,5=11feets --->this is how much it grew in 5,5years

11/5,5=2feets/year --->this is the yearly rate

4 0

3 years ago

Read 2 more answers

Determine the exact value

adell [148]

Answer:(theta) =π only

Step-by-step explanation:

-4cos(theta)+1=5

Subtract 1 from both sides

-4cos(theta)+1-1=5-1

-4cos(theta)=4

Divide both sides by -4

-4cos(theta) ➗ -4=4 ➗ -4

cos(theta)=-1

(theta)=cos(inverse)(-1)

(theta)=180

(theta)=π

6 0

3 years ago

How many quarters are thee in 4 1/2

Neko [114]

Hi there!

quarter:18

1.Find common denominator in 4 and 1/2:

$4=\frac{1}{4}$

$\frac{1}{2}=\frac{2}{4}$

2.Convert 4 2/4 into mixed number:

$4\frac{2}{4}=\frac{18}{4}$

3.Divide 18/4 by 1/4:

$\frac{18}{4}*\frac{1}{4}=18$

Therefore, there is 18 quarters in 4 1/2.

4 0

2 years ago

If sin(x) = 5/13, and x is in quadrant 1, then tan(x/2) equals what?

Rufina [12.5K]

$x$ is in quadrant I, so $0$ , which means $0$ , so $\dfrac x2$ belongs to the same quadrant.

Now,

$\tan^2\dfrac x2=\dfrac{\sin^2\frac x2}{\cos^2\frac x2}=\dfrac{\frac{1-\cos x}2}{\frac{1+\cos x}2}=\dfrac{1-\cos x}{1+\cos x}$

Since $\sin x=\dfrac5{13}$ , it follows that

$\cos^2x=1-\sin^2x\implies \cos x=\pm\sqrt{1-\left(\dfrac5{13}\right)^2}=\pm\dfrac{12}{13}$

Since $x$ belongs to the first quadrant, you take the positive root ( $\cos x>0$ for $x$ in quadrant I). Then

$\tan\dfrac x2=\pm\sqrt{\dfrac{1-\frac{12}{13}}{1+\frac{12}{13}}}$

$\tan x$ is also positive for $x$ in quadrant I, so you take the positive root again. You're left with

$\tan\dfrac x2=\dfrac15$

4 0

3 years ago