To answer this question, first
let ∫ √(t³+1) dt = g(t) + C
<span>Then g'(t) = √(t³+1) </span>
<span>F(x) = ∫₀ˣ √(t³+1) dt = g(t) |₀ˣ = g(x) - g(0) </span>
<span>Now g(x) is some function of x, while g(0) is a constant </span>
<span>F(x) = g(x) - g(0) </span>
<span>Differentiate both sides: </span>
<span>F'(x) = g'(x) - 0 = √(x³+1) </span>
<span>So you are correct, in this case, we simply replace t with x (this is not always the case) </span>
<span>F'(2) = √(2³+1) = √9 = 3 </span>
<span>You MUST remember that when dealing with square roots, we have: </span>
<span>x² = 4 -----> x = -2 or 2 </span>
<span>x = √4 ----> x = 2 </span>
<span>That's why in the quadratic formula: x = (-b ± √(b²-4ac)) / (2a), we use a ± sign in front of square root, otherwise, if we could willy-nilly assign positive and negatives value to √(b²-4ac), then we would have no need for the ± sign. </span>
<span>Also, when solving x² = 4, we usually have intermediate step </span>
<span>x = ± √4, where +√4 (or simply √4) = 2, and -√4 = 2
</span>
Answer:
0.26
Step-by-step explanation:
26=100x
Do the inverse operation of multiplication.
-- Division.
26/100 = 0.26
x = 0.26
Answer:
2/5
Step-by-step explanation:
perpendicular line means the two lines' slope when multiplied together gives a answer of -1.
hence, we just need to find the slopw of the line connecting the 2 points and form an equation with -1 to get the slope the question wants.
slope of the line PQ:
(7-5)/(-3-2) = -2/5 (slope formula)
slope of the perpendicular line:
-2/5 x slope = -1
slope = (-1)/(-2.5) = 2/5
Answer: -2
Step-by-step explanation:
