Answer:
2.3 units
Step-by-step explanation:
The unknown side is opposite the given angle 50 degrees, and the length of the hypotenuse is 3 units.
Since sin Ф = opp / hyp, we have here sin 50° = x/3, or x = 3 sin 50°.
Using a calculator, we find that the sine of 50° is 0.776.
Therefore, x = 3(0.766) = 2.298 units, or approximately 2.3 units
Answer:
The rate at which both of them are moving apart is 4.9761 ft/sec.
Step-by-step explanation:
Given:
Rate at which the woman is walking,
= 3 ft/sec
Rate at which the man is walking,
= 2 ft/sec
Collective rate of both, 
= 5 ft/sec
Woman starts walking after 5 mins so we have to consider total time traveled by man as (5+15) min = 20 min
Now,
Distance traveled by man and woman are 
and 
ft respectively.
⇒ 
⇒ 
As we see in the diagram (attachment) that it forms a right angled triangle and we have to calculate 
.
Lets calculate h.
Applying Pythagoras formula.
⇒ 
⇒ 
Now differentiating the Pythagoras formula we can calculate the rate at which both of them are moving apart.
Differentiating with respect to time.
⇒
⇒ 
⇒ 
...as 
⇒ Plugging the values.
⇒ 
...as 
ft/sec
⇒ 
ft/sec
So the rate from which man and woman moving apart is 4.9761 ft/sec.
Let "x" represent the number of units
5x = the number of tomato plants in Inessa's garden
6x = the number of tomato plants in Ralph's garden
the question says that half (1/2 x (5x)) of Inessa's tomato plants are taken from her garden and put into Ralph's garden
this means that Ralph has a total of 850 tomato plants in his garden
using all of this information, we get the following (which we have to solve):
(1/2)(5x) + 6x = 850
when we solve for "x", we find that:
"x" = 100
so, going back to the original statement, if Ralph started out with (6x) tomato plants, and "x" = 100, we have to multiply 6 by 100
doing so gives us our final answer:
Ralph had 600 tomato plants in the beginning
