Answer:
y = 2 - ( x - 1)²/9
Step-by-step explanation: See Annex
As the parameter t increases, the value of x increases and the value of y decreases, we get the figure of the annex ( the arrow in the Annex indicates the way of the curve with t increasing.
b) to eliminate the parameter:
x = 1 + 3*t (1) y = 2 - t² (2)
Then from equation (1) t = ( x - 1 ) / 3
plugging that value in equation (2)
y = 2 - [ ( x - 1 ) / 3 ]²
y = 2 - ( x² + 1 - 2*x)/9
9*y = 18 - x² + 1 - 2*x or y = 2 - ( x - 1)²/9
The curve is a parabol
sry if my answer is wrong but I think it is the square root of nine
I don't know what the "six-step method" is supposed to be, so I'll just demonstrate the typical method for this problem.
Let <em>x</em> be the amount (in gal) of the 50% antifreeze solution that is required. The new solution will then have a total volume of (<em>x</em> + 60) gal.
Each gal of the 50% solution used contributes 0.5 gal of antifreeze. Similarly, each gal of the 30% solution contributes 0.3 gal of antifreeze. So the new solution will contain (0.5 <em>x</em> + 0.3 * 60) gal = (0.5 <em>x</em> + 18) gal of antifreeze.
We want the concentration of antifreeze to be 40% in the new solution, so we need to have
(0.5 <em>x</em> + 18) / (<em>x</em> + 60) = 0.4
Solve for <em>x</em> :
0.5 <em>x</em> + 18 = 0.4 (<em>x</em> + 60)
0.5 <em>x</em> + 18 = 0.4 <em>x</em> + 24
0.5 <em>x</em> - 0.4 <em>x</em> = 24 - 18
0.1 <em>x</em> = 6
<em>x</em> = 6/0.1 = 60 gal
Answer:the function representing profit, P = 3n + 200
Step-by-step explanation:
The function C = 2n + 200 represents his costs, in dollars, for producing n jars of salsa.
The revenue, or the amount he receives for selling n jars, can be represented by the function R = 5n.
Profit = revenue - cost or expenses.
Therefore,
The function representing Dominic's profit, P, for selling n jars of salsa will be
P = 5n - 2n + 200 = 3n + 200
Answer: The first 6 terms are = 8, 10, 12,14,16,18
Step-by-step explanation:
The NTH term of an Arithmetic Sequence is given as
an = a1 + (n - 1 ) d
where a1 = First term given as 8 and
d= common difference given as 2
Therefore We have that
the first term
an = a1 + (n - 1 ) d = 8+(1-1) 2
a1= 8
second term=
an = a1 + (n - 1 ) d= a2= 8 + (2-1) 2
= 8+ 2(1) = 10
3rd term
an = a1 + (n - 1 ) d= a3= 8 + (3-1) 2
= 8+ 2(2)= 8 + 4=12
4th term
an = a1 + (n - 1 ) d= a4= 8 + (4-1) 2
= 8+ 2(3)= 8+6=14
5th term
an = a1 + (n - 1 ) d= a5= 8 + (5-1) 2
= 8+ 2(4)=8+ 8=16
6th term
an = a1 + (n - 1 ) d= a6= 8 + (6-1) 2
= 8+ 2(5)=8 +10 =18
