Answer:
20
Step-by-step explanation:
using pythagorean theorem to find the hypotenuse gives √20, so the measure of the side of the square is also √20, square that to give the area of square, which is 20
To simplify the function, we need to know some basic identities involving exponents.
1. b^(ax)=(b^x)^a=(b^a)^x
2. b^(x/d) = (b^x)^(1/d) = ((b^(1/d)^x)
Now simplify f(x), where
f(x)=(1/3)*(81)^(3*x/4)
=(1/3)(3^4)^(3*x/4) [ 81=3^4 ]
=(1/3)(3^(4*3*x/4) [ rule 1 above ]
=(1/3) (3^(3*x)
=(1/3)(3^(3x)) [ or (1/3)(27^x), by rule 1 ]
(A) Initial value is the value of the function when x=0, i.e.
initial value
= f(0)
=(1/3)(3^(3x))
=(1/3)(3^(3*0))
=(1/3)(3^0)
=(1/3)(1)
=1/3
(B) the simplified base base is 3 (or 27 if the other form is used)
(C) The domain for an exponential function is all real values ( - ∞ , + ∞ ).
(D) The range of an exponential function with a positive coefficient and without vertical shift is ( 0, + ∞ ).
Answer:
I found it! It's over here!!
Now what do I do with it?
Answer:
Step-by-step explanation:
The vertex form of a parabola:
(h, k) - vertex
We have the vertex at (3, 2) → h = 3 and k = 2.
Substitute:
The point (4, 6) is on athe parabola. Put the coordinates of this point to the equation:
<em>subtract 2 from both sides</em>
Finally:
<em>vertex form</em>
<em>use (a - b)² = a² - 2ab + b²</em>
<em>use the distributive property</em>
<em>standard form</em>
