Answer:
1) x = 5√(1-sin^2t)
2) y = = -2+3t
Step-by-step explanation:
1)
Given rectangular equation:
x^2/25 + y^2 =1
Parametric equations y=-sint and x=?
Find parametric equation for x
Substituting value of y =-sint in given rectangular equation, we get
x^2/25 + (-sint )^2 =1
x^2/25 + sin^2t =1
x^2 + 25sin^2t = 25
x^2 =25 - 25sin^2t
taking square root on both sides
x= √(25 - 25sin^2t)
= √25(1-sin^2t)
= 5√(1-sin^2t)
2)
Given rectangular equation:
y=-3x+4
Parametric equations x=2-t and y=?
Find parametric equation for y
Substituting value of x=2-t in given rectangular equation, we get
y= -3(2-t) +4
= -6+3t+4
= -2+3t !
Answer:
(1, 1)
Step-by-step explanation:
We need to evaluate the given expression for each of the x-values and check if the y-value agrees with the y-value given in the pairs:
1) First point (-1,3): use x=-1 and check if y results in "3":
we obtained y=-7, so the point (-1,3) is Not on the graph of the function
2) Second point (0,2): use x=0 and check if y results in "2":
we obtained y=-2, so the point (0,2) is Not on the graph of the function
3) Third point (2,-2): use x=2 and check if y results in "-2":
we obtained y=2 (and not -2), so the point (2,-2) is Not on the graph of the function
4) Fourth point (1,1): use x=1 and check if y results in "1":
we obtained y=1 (the same y as in the given coordinate pair), so the point (1,1) IS on the graph of the function
<span>We move all terms to the left:
-840-(-15(-7x+7))=0
</span>We calculate terms in parentheses: -(-15(-7x+7)), so:
-15(-7x+7)
We multiply parentheses
105x-105
Back to the equation:
<span>
-(105x-105)
</span>
<span>We get rid of parentheses
-105x+105-840=0
We add all the numbers together, and all the variables
-105x-735=0
We move all terms containing x to the left, all other terms to the right
-105x=735
x=735/-105
x=-7
</span>
120.25 I just divided the figure into smaller shapes, found the value and then I added the areas together! :)
2 years
Tina planted a tree. It started at 6 feet and every year it grows another three feet. The expression representing this is 6 + 3x, where x represents years.
Tinas neighbor also planted a tree where each year (which we called x) it grows 6 feet. The expression to represent this is 6x.
If you want to know when they’ll be the same height, then you need to set the expressions equal to each other.
6 + 3x = 6x
To solve, first get the variable to one side
6 = 3x
Divide each side by 3
x = 2
The trees wi be the same height the 2nd year.
