75a^2b/25ab^2
= 75x axaxb /25xaxbxb
=3a/b
The y intercept occurs when x = 0 so in the case of the first function it is y = 3
g(x) = 3 cos 2x + 1
when x = 0 g(x) = 3 cos 0 + 1 = 3*1 + 1 = 4
so the answer is g(x)
The sine ratio is basically a fraction of the opposite side over the hypotenuse. Since the hypotenuse is always the longest side, this means the fraction cannot exceed 1. If it did,then that would lead to the opposite side being larger than the hypotenuse but again the hypotenuse is the longest side. The largest the sine ratio can get is 1.
Answer:
Step-by-step explanation:
Height: h(t)= -0.2t^2+2t = 2t(-0.1t + 1)
-0.2t^2+2t is a quadratic expression with a = -0.2 and b = 2.
The ball reaches its max height at t = -b/(2a).
Here, t = -2 / (2·[-0.2] ), or t = 2/0.4 = 5 (sec)
The ball reaches its max height at at 5 sec.
The max ht. of the ball is h(5) = -0.2(5 sec)^2 + 2(5 sec) = (-5 + 10) sec, or 5 ft.
To determine after how many sec the ball reaches the ground, we set h(t) = 0 and solve for t:
h(t)= -0.2t^2+2t = 0 = 2t(-0.1t + 1). Thus, t = 0 sec or t = 10 sec
The ball reaches the ground again after 10 sec.
Answer:
There are two possibilities:
and
and
Step-by-step explanation:
Mathematically speaking, the statement is equivalent to this 2-variable non-linear system:
First, is cleared in the first equation:
Now, the variable is substituted in the second one:
And some algebra is done in order to simplify the expression:
Roots are found by means of the General Equation for Second-Order Polynomials:
and
There are two different values for :
There are two possibilities:
and
and