Answer:
See the attached figure.
Step-by-step explanation:
The given function is called piecewise function which is the function that can be in pieces, i.e: defined by multiple sub-functions.
So, need to graph 2x in the interval [3,∞)
And graph -(1/3) x + 7 in the interval (-∞,3]
We will find that f(3) at the function 2x will be equal f(3) at the function -(1/3) x + 7
Which mean the function is continuous.
The attached figure represents the graph of function, it was graphed using the tables on the graph.
Answer:
<h2>
1.5</h2>
Step-by-step explanation:
We are given two points. Let the points be A and B
A ( 8 , -2 ) ------> ( x1 , y1 )
B ( 12 , 4 ) ------> ( x2 , y2 )
Now, let's find the slope of the given points:
plug the values
When there is a ( - ) in front of an expression in parentheses , change the sign of each term in the expression
Subtract the numbers
Add the numbers
Reduce the fraction with 2
Hope this helps..
Best regards!!
2X + (2X+10)= 34
Width is 6, Length is 11
6 x 11 is 66
Area is 66
In an arithmetic sequence, the difference between consecutive terms is constant. In formulas, there exists a number 
such that
In an geometric sequence, the ratio between consecutive terms is constant. In formulas, there exists a number such that
So, there exists infinite sequences that are not arithmetic nor geometric. Simply choose a sequence where neither the difference nor the ratio between consecutive terms is constant.
For example, any sequence starting with
Won't be arithmetic nor geometric. It's not arithmetic (no matter how you continue it, indefinitely), because the difference between the first two numbers is 14, and between the second and the third is -18, and thus it's not constant. It's not geometric either, because the ratio between the first two numbers is 15, and between the second and the third is -1/5, and thus it's not constant.
1)
LHS = cot(a/2) - tan(a/2)
= (1 - tan^2(a/2))/tan(a/2)
= (2-sec^2(a/2))/tan(a/2)
= 2cot(a/2) - cosec(a/2)sec(a/2)
= 2(1+cos(a))/sin(a) - 1/(cos(a/2)sin(a/2))
= 2 (1+cos(a))/sin(a) - 2/sin(a)) (product to sums)
= 2[(1+cos(a) -1)/sin(a)]
=2cot a
= RHS
2.
LHS = cot(b/2) + tan(b/2)
= [1 + tan^2(b/2)]/tan(b/2)
= sec^2(b/2)/tan(b/2)
= 1/sin(b/2)cos(b/2)
using product to sums
= 2/sin(b)
= 2cosec(b)
= RHS
