Answer:
The slope of the curve at (3,1) is 3.
Step-by-step explanation:
The given differential equation is
It is given that the solution curve is passing through the point (3,1).
The slope of a curve y(t) at a point (a,b) is the value of y'(t) at (a,b).
We need to find the slope of the curve at (3,1).
Substitute t=3 and y=1 in the above equation, to find the slope.
Therefore the slope of the curve at (3,1) is 3.
Answer:
A non-calculus solution follows afterward.
For a calculus solution, the gradient is the first derivative with the point put in.
y = -x²+3x
dy/dx or y’ = -2x +3 is the gradient at any point.
but the tangent is at x = 2 so put it in
y’ = -(2*2)+3 = -1 is the gradient of the tangent at point (2,2)
Non-calculus solution:
y = -x²+3x 1️⃣but slope of tangent m = (y-2)/(x-2)2️⃣
put 1️⃣ into 2️⃣ and rearrange ⟹ mx-2m+x²-3x+2 = 0
or x²+(m-3)x+2–2m =0
but for a tangent the discriminant b²-ac = 0
(m-3)²-4*1*(2–2m) = 0
m²+2m+1 = 0
(m+1)(m+1) = 0
m = -1 is the is the gradient of the tangent at point (2,2)
Step-by-step explanation:
Answer:
x=10
Step-by-step explanation:
$52-$22=$30
$30/3=$10=x
This may not be correct but Georgia will be about nine if u subtract 6 from 15... And as for Jerry, if he swims for 4 hours, at 2 miles, he might be swimming 480 miles.. 2x60 (aka and hour x 2) 120.. Do that 4 times and u end up with about 480.. So sorry if I'm wrong
Answer:
10.0499
Step-by-step explanation:
Input Data :
Point 1 (
x
A
,
y
A
) = (-2, 3)
Point 2 (
x
B
,
y
B
) = (8, 2)
Objective :
Find the distance between two given points on a line?
Formula :
Distance between two points = √
(
x
B
−
x
A
)
2
+
(
y
B
−
y
A
)
2
Solution :
Distance between two points = √
(
8
− −
2
)
2
+
(
2
−
3
)
2
= √
10^2
+
(
−
1
)
2
= √
100
+
1
= √
101 = 10.0499
Distance between points (-2, 3) and (8, 2) is 10.0499