Answer:
θ is decreasing at the rate of 
units/sec
or 
(θ) = 
Step-by-step explanation:
Given :
Length of side opposite to angle θ is y
Length of side adjacent to angle θ is x
θ is part of a right angle triangle
At this instant,
x = 8 , 
= 7
( denotes the rate of change of x with respect to time)
y = 8 , 
= -14
( The negative sign denotes the decreasing rate of change )
Here because it is a right angle triangle,
tanθ = 
-------------------------------------------------------------------1
At this instant,
tanθ = 
= 1
Therefore θ = π/4
We differentiate equation (1) with respect to time in order to obtain the rate of change of θ or (θ)
(tanθ) = (y/x)
( Applying chain rule of differentiation for R.H.S as y*1/x)
θ(θ) = 
- 
-----------------------2
Substituting the values of x , y , , , θ at that instant in equation (2)
2(θ) = 
*(-14)- 
*7
(θ) =
Therefore θ is decreasing at the rate of units/sec
or (θ) =
The difference of the given functions is x^2 + 10
<h3>Difference of functions</h3>
Given the following functions
f(x) = 2x^2 + 3 and
g(x)=x^2-7
Take the difference
(f-g)(x) = 2x^2 + 3 - (x^2 - 7)
(f-g)(x) = 2x^2 - x^2 +3 + 7
(f-g)(x) = x^2 + 10
Hence the difference of the given functions is x^2 + 10
Learn more on difference of function here:brainly.com/question/17431959
#SPJ1
Answer:
Step-by-step explanation:
The number of students in each bus = s.
It is given that,
6 students traveled by car and the rest traveled in 11 buses.
So, the total number of students traveled = 11s + 6.
Since, the least number of students traveled is 450.
Thus, we get the inequality representing the situation is,
Answer:
Step-by-step explanation:
Given that Six cards numbered from 1 to 6 are placed in an empty bowl. First one card is drawn and then put back into the bowl; then a second card is drawn. If the cards are drawn at random
Since with replacement, repitition of numbers is possible
Possible drawings to give sum of 8 is
(2,6) (6,2) (3,5)(5,3)(4,4)
Out of this favourable events with 5 = (3,5) (5,3)
Hence required probability = 
Answer:
ec
(
x
)
=
√
13
3
Use the definition of secant to find the known sides of the unit circle right triangle. The quadrant determines the sign on each of the values.
sec
(
x
)
=
hypotenuse
adjacent
Find the opposite side of the unit circle triangle. Since the adjacent side and hypotenuse are known, use the Pythagorean theorem to find the remaining side.
Opposite
=
√
hypotenuse
2
−
adjacent
2
Step-by-step explanation:
