See the picture attached to better understand the problem
we know that
a full circle is a 360 degrees
divided in 12 equals parts-------> 360/12-------> 30 degrees each part

<span>the smallest angle formed by the hands of a clock at 7 o'clock has 5 parts
so
5*30</span>°------> 150°

convert to radian
pi radians---------> 180°
x ---------------> 150°
x=150*pi/180--------> x=0.83*pi radians

the answer is
0.83*pi radians or 2.62 radians

5 0

3 years ago

A map has a scale of 1 in. 4 mi. You measure 3 inches between your house and the movie theatre. How many miles is it from your h

suter [353]

Hi!

1in:4m
3in:xm

3/1 = 3
4 x 3 = 12

1in:4m
3in:12m

The answer is 12

Hope this helps! :)

5 0

3 years ago

8÷2+(18−12)4−5×12 sos please help

Anuta_ua [19.1K]

-32

Explanation:
8/2 + (18-12)4-5•12
8/2 + (6)4 - 5 • 12
4 + 24 - 60
28 - 60
-32

Hope this helps!

7 0

3 years ago

A baseball diamond is a square with side 90 ft. A batter hits the ball and runs toward first base with a speed of 31 ft/s. (a) A

julsineya [31]

Answer:

a) -13.9 ft/s

b) 13.9 ft/s

Step-by-step explanation:

a) The rate of his distance from the second base when he is halfway to first base can be found by differentiating the following Pythagorean theorem equation respect t:

$D^{2} = (90 - x)^{2} + 90^{2}$ (1)

$\frac{d(D^{2})}{dt} = \frac{d(90 - x)^{2} + 90^{2})}{dt}$

$2D\frac{d(D)}{dt} = \frac{d((90 - x)^{2})}{dt}$

$D\frac{d(D)}{dt} = -(90 - x) \frac{dx}{dt}$ (2)

Since:

$D = \sqrt{(90 -x)^{2} + 90^{2}}$

When x = 45 (the batter is halfway to first base), D is:

$D = \sqrt{(90 - 45)^{2} + 90^{2}} = 100. 62$

Now, by introducing D = 100.62, x = 45 and dx/dt = 31 into equation (2) we have:

$100.62 \frac{d(D)}{dt} = -(90 - 45)*31$

$\frac{d(D)}{dt} = -\frac{(90 - 45)*31}{100.62} = -13.9 ft/s$

Hence, the rate of his distance from second base decreasing when he is halfway to first base is -13.9 ft/s.

b) The rate of his distance from third base increasing at the same moment is given by differentiating the folowing Pythagorean theorem equation respect t:

$D^{2} = 90^{2} + x^{2}$