25,270 Answered Questions for the topic calculus

12/20/23

Check orthogonality of these curves
How do you check orthogonality condition for these curves, I know only the answer that they are but I can't seem to move forward with the solution. I appreciate your help.
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Calculus Physics

12/20/23

Non-Constant Acceleration of a Car Drag Racing on a Quarter Mile Track. What am I doing wrong?

I'm a retired engineer and my hobby is racing my Cadillac at the local quarter mile track. Being a numbers geek by training I decided to write an Excel program that could take my time slip and spit... more
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Calculus

12/20/23

calculus derivatives
g(x)=e^root x
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Calculus

12/19/23

optimization circuit
The average cost function, denoted as a(x), is defined as a(x) = c(x) / x, where c(x) represents the cost function, and x represents the number of units produced. The cost function is given as c(x)... more
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Calculus

12/19/23

on the closed interval [0, 2pi], find the max value of the function f(x) = 4 sin x - 3 cos x
a. 3 b. 4 c. 24/5d. 5 e. none of theseI went about solving this by: finding f'(x): I got 4 cos (x) + 3 sin (x) then setting f'(x) to zero: 0 = 4 cos (x) + 3 sin (x) simplifying the equation to:... more
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Calculus

12/19/23

suppose lim x-> 0 [g(x)-g(0)]/x = 1 it follows that ...
a.) g is not defined at x = 0 b.) g is not continuous at x = 0 c.) The limit of g(x) as x approaches 0 equals 1 d.) 𝑔 ′ (0) = 1 e.) 𝑔 ′ (1) = 0I'm not sure which answer is correct, i'm tied between... more
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Calculus Math Geometry

12/19/23

Find the area bounded by y= (x-12)/ (x^2 -4x -32), x=5, x=6 and y=0. For reference, previous answers to similar questions were very small, between 1 and 2.

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Calculus Math Physics

12/19/23

The velocity of a particle moving along a line is a function of time given by v(t) = 88 / (t^2 +9t +8). Find the distance that the particle has traveled after t=7 seconds if it started at t=0 seconds.
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Calculus

12/19/23

f(x) = 1/(x^2+1) and g(x) = sqrt (x), what is derivative of f(g(x))
my questions is do I evaluate f(g(x)) and then solve for the derivative. OR do I solve for the derivative using the f'(g(x)) * g'(x) rule?
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Calculus Math

12/19/23

The cost to produce c(q) = q^2 (√q - 2) items is dollars. Find the marginal cost.
Just to be clear, this is what the question actually looks like:
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Calculus

12/19/23

Which of the following statements are true?
𝑓(𝑥) = { 𝑥^2 − 1, 𝑥 ≠ 1 4, 𝑥 = 1which of the following statements are/is true?a) the limit as x -> 1 existsb) f(1) existsc) f is continuous at x = 1I said that a) and b)... more
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Calculus Math

12/19/23

Find Lamé coefficients for the following curves
How do you find lame coefficients for the following curves. I've been trying without getting any success. Would highly appreciate your help.
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Calculus Math

12/19/23

How fast is the balloon rising up?
A hot air balloon is rising 200 ft above ground while a person viewing the balloon has a height of 6 feet has a view of 45 degrees to the hot air balloon. If the distance between the balloon and... more
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Calculus Math Algebra 1

12/19/23

Algebra- please help
There were 8 fewer boys than girls in Mr. Taylor’s Algebra class. If he had 40 pupils, how many were girls?
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Calculus Math Algebra 1

12/19/23

I need help with this please
Jane and Sophia went to the corner store where packages of gum cost 54¢ each and candy bars cost 88¢ each. They spent $26.38 total and bought 35 items total. How many candy bars did they buy?
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Calculus

12/19/23

Determine the length of r = θ 0 ≤ θ ≤ 1 . This is polar coordinates.
Determine the length of r = θ 0 ≤ θ ≤ 1
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12/19/23

Calculus Differentiation Question
A conical pile of rocks increases in volume at a rate of 16pi/3 cubic feet per minute. When the height of the pile is 30 feet, the radius is 10 feet. What is the rate of change of the height of the... more
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Calculus Math Geometry

12/19/23

Find the area bounded by y = (x-16) / (x^2 - 3x - 28), x=2, and y=0.
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Calculus Math

12/18/23

Consider the curve given by x2 + sin(xy) + 3y = C, where Cis a constant. The point (1, 1) lies on this curve. Use the tangent line approximation to approximate the y-coordinate when x = 1.01
round to the nearest thousanth
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Calculus Math Physics

12/18/23

The velocity of a particle moving along a line is a function of time given by v(t) = 72 / (t^2 + 12t + 35). Find the distance that the particle has traveled after t=8 seconds if it started at t=0 secs
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Calculus Math

12/18/23

Find the slope of the tangent line to the graph of the equation xy+12=0 at (-2, 6)
I got m = -3
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Calculus Math

12/18/23

A particle's position (in meters) is given by the equation s(t) = 5x sin(2x), on the interval [-1, 4] minutes. What is its instantaneous velocity at t=0
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Calculus Math

12/18/23

A particle's position (in meters) is given by the equation s(t) = 5x sin(2x), on the interval [-1, 4] minutes. What is its instantaneous velocity at t=0
It should be 0 right because t = 0?
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Calculus Math

12/18/23

An equation of the line tangent to the graph of f(x) = (4x2-8x+3)4 at the point where x = 1is
 A. x=1 B. y=1 C. y-81 384(x-1) D. y-1=3.37497(x-1) E. y=5(x-1)thinking its B cant be sure though
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Calculus Precalculus

12/18/23

Related Rates / Conical Tank
A right conical tank with the point oriented down, a height of 18 feet, and a radius of 4 feet has sprung a leak. How fast is the volume of water in the tank changing when the water is 13 feet high... more
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