A street light is mounted at the top of a 15-ft-tall pole. A man 6 ft tall walks away from the pole with a speed of 7 ft/s along
a straight path. How fast is the tip of his shadow moving when he is 30 ft from the pole?
2 answers:
Answer:
Since only his speed affects how fast his shadow moves, then we calculate for the speed which is 11.67ft/s
Step-by-step explanation:
Assuming similar triangle
(y-x)/y = 6/15
15(y-x) = 6y
15y - 15x = 6y
(15 -6)y = 15x
9y = 15x
y = (5/3)x
By differentiating both sides with respect to time t
dy/dt = 5/3 (dx/dt)
But (dx/dt) is 7 ft/s
Therefore dy/dt = 5/3 * 7 = 35/3 = 11.67ft/s
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To solve this, we are going to use the surface are of a sphere formula: 
where
is the surface area of the sphere
is the radius of the sphere
We know for our problem that
and 
, so lets replace those vales in our formula:
Now, we just need to solve our equation for:
or
Since the radius of a sphere cannot be a negative number,.
We can conclude that the radius of a sphere with surface area <span>2,122.64 </span>
is 13 in.
where
We know for our problem that
Now, we just need to solve our equation for
Since the radius of a sphere cannot be a negative number,
We can conclude that the radius of a sphere with surface area <span>2,122.64 </span>
Answer:
2000 ml
Step-by-step explanation:
Given: Sarai pours all the liquid from a full small beaker into a larger beaker.
The liquid fills the large beaker to 15% of its capacity.
The small beaker holds 300 ml.
Lets assume capacity of large beaker to hold be "x".
As given, Sarai pours all the liquid from a full small beaker into a larger beaker
∴
⇒
Dividing both side by 0.15
⇒
∴
Hence, the large beaker can hold 2000 ml of liquid.