You set up was almost accurate. Remember the arc length formula:
If f'(y) is continuous on the interval [a,b], then the length of the curve x = f(y), a ≤ y ≤ b should be;
L = ∫ᵇ ₐ √1 + [f'(y)]^2 * dy
We have to find the length of the curve given x = √y - 2y, and 1 ≤ y ≤ 4. You can tell your limits would be 1 to 4, and you are right on that part. But f'(y) would be rather...
f'(y) = 1/(2√y) - 2
So the integral would be:
∫⁴₁ √1 + (1/(2√y) - 2)² dy
Using a calculator we would receive the solution 5.832. Their is a definite curve, as represented below;
Answer:
Answer is "No real Solution"
Answer:
If the directions say write an equation: 2n + 5 =25
If the directions say also to solve the equation and find the number: 10
Step-by-step explanation:
"The sum" means we're using adding. So what things are we adding together? The question says "twice a number" and 5. Well we've got the 5. And "twice" means two times. And "a number" means we don't know the number yet, so we choose a variable, like n.
"Twice a number" can be written 2n.
So far we have:
2n + 5 is 25
We use = for the "is" in this sentence.
2n + 5 = 25
Now we can solve it.
Subtract 5 from both sides.
2n = 20
Divide by 2 on both sides.
2n/2 = 20/2
n = 10
The number is 10.
