Answer:
Step-by-step explanation:
Given that,
f(3) = 2
f'(3) = 5.
We want to estimate f(2.85)
The linear approximation of "f" at "a" is one way of writing the equation of the tangent line at "a".
At x = a, y = f(a) and the slope of the tangent line is f'(a).
So, in point slope form, the tangent line has equation
y − f(a) = f'(a)(x − a)
The linearization solves for y by adding f(a) to both sides
f(x) = f(a) + f'(a)(x − a).
Given that,
f(3) = 2,
f'(3) = 5
a = 3, we want to find f(2.85)
x = 2.85
Therefore,
f(x) = f(a) + f'(a)(x − a)
f(2.85) = 2 + 5(2.85 - 3)
f(2.85) = 2 + 5×-0.15
f(2.85) = 2 - 0.75
f(2.85) = 1.25
2
Divide both the top and bottom by 2 and you get 2/3
Answer:
B
Step-by-step explanation:
An equation of a circle:
(x - a)² + (y - b)² = r²
(a; b) - a coordinates of a center
r - a radius
r = 5; P(6; 1) ⇒ a = 6 and b = 1
therefore
(x - 6)² + (y - 1)² = 5²
check:
A) Q(1; 11)
L = (1 - 6)² + (11 - 1)² = (-5)² + 10² = 25 + 100 = 125
R = 25
L ≠ R
B) R(2; 4)
L = (2 - 6)² + (4 - 1)² = (-4)² + 3² = 16 + 9 = 25
R = 25
L = R - CORRECT
C) S(4; -4)
L = (4 - 6)² + (-4 - 1)² = (-2)² + (-5)² = 4 + 25 = 29
R = 25
L ≠ R
D) T(9; -2)
L = (9 - 6)² + (-2 - 1)² = 3² + (-3)² = 9 + 9 = 18
R = 25
L ≠ R
Answer: B) R(2; 4).
Answer:
800$
Step-by-step explanation:
640/80=8
8=1% so
8x100=800
100%=800
![\\ \\ ={ \left[ -\frac { { 2x }^{ 2+1 } }{ 2+1 } -\frac { 5{ x }^{ 1+1 } }{ 1+1 } +3x \right] }_{ -3 }^{ \frac { 1 }{ 2 } }](https://tex.z-dn.net/?f=%5C%5C%20%5C%5C%20%3D%7B%20%5Cleft%5B%20-%5Cfrac%20%7B%20%7B%202x%20%7D%5E%7B%202%2B1%20%7D%20%7D%7B%202%2B1%20%7D%20-%5Cfrac%20%7B%205%7B%20x%20%7D%5E%7B%201%2B1%20%7D%20%7D%7B%201%2B1%20%7D%20%2B3x%20%5Cright%5D%20%20%7D_%7B%20-3%20%7D%5E%7B%20%5Cfrac%20%7B%201%20%7D%7B%202%20%7D%20%20%7D)
![\\ \\ ={ \left[ -\frac { 2{ x }^{ 3 } }{ 3 } -\frac { 5{ x }^{ 2 } }{ 2 } +3x \right] }_{ -3 }^{ \frac { 1 }{ 2 } }](https://tex.z-dn.net/?f=%5C%5C%20%5C%5C%20%3D%7B%20%5Cleft%5B%20-%5Cfrac%20%7B%202%7B%20x%20%7D%5E%7B%203%20%7D%20%7D%7B%203%20%7D%20-%5Cfrac%20%7B%205%7B%20x%20%7D%5E%7B%202%20%7D%20%7D%7B%202%20%7D%20%2B3x%20%5Cright%5D%20%20%7D_%7B%20-3%20%7D%5E%7B%20%5Cfrac%20%7B%201%20%7D%7B%202%20%7D%20%20%7D)
