25,270 Answered Questions for the topic calculus

Calculus Math

10/27/23

Optimization problom
A box is to have an open top, vertical sides, a square bottom, and a volume of 108 m^3.Find the dimensions that minimize the surface area of the box.Height= ????Length=????
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Calculus

10/27/23

I need this calculus 2 question answered reallt soon! I did it 4 times and I still havent gotten the answer
A tank contains 400 L of water. A solution with a salt concentration of 0.4 kg/L is added at a rate of 5 L/min. The solution is kept mixed and is drained from the tank at a rate of 3 L/min.... more
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Calculus

10/26/23

Question: What are the key steps to improve my understanding of calculus, and how can a tutor assist me in this process?
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Calculus

10/26/23

Can anyone help me solve this related rates problem? I have been stuck on it for hours and don't really know how to start it.
A searchlight rotates at a rate of 2 revolutions per minute. The beam hits a wall located 9 miles away and produces a dot of light that moves horizontally along the wall. How fast (in miles per... more
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Calculus Math Precalculus

10/26/23

sin²x (1 + cot²x) = 1
sin²x (1 + cot²x) = 1LHS: sin²x (1 + cot²x)= sin²x (csc²x) (what rule)= sin²x (1 / sin²x) (what rule)= 1 (what rule)(Algebra, Reciprocal, Quotient, Pythagorean, or Odd/Even)
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Calculus Math Precalculus

10/26/23

cot²x (sec²x - 1)
LHS: cot²x (sec²x - 1)= cot²x (tan²x) (find the rule)= cos²x/sin²x ⋅ sin²x/cos²x (find the rule)= 1 (find the rule)(Algebra, Reciprocal, Quotient, Pythagorean, or Odd/Even)
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Calculus

10/26/23

Linear Approximation

Use linear approximation , i.e the tangent line, to approximate 3sqrt 8.02 as follow. Left f(x)=3sqrtx and find the equation of the tangent line to f(x) at x=8 in the fo9rm y=mx+b. m = b = using... more
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10/26/23

Please show work and fully answer the question

Five points, not necessarily different, are selected on the number line between and possibly including 0 and 1. After I calculate the distance between each pair of points, I add all ten distances.... more
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Calculus Math

10/26/23

Definition of the Derivative
No calculator is allowed on this question.The average rate of change of a function, f, on the interval [1, 1+Δx] is given by sin(Δx) + 3-5*deltax.Find f'(1).
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Calculus Math Precalculus

10/26/23

cot²x (sec²x - 1) = 1
LHS: cot²x (sec²x - 1)= cot²x (tan²x) (find the rule)= cos²x/sin²x ⋅ sin²x/cos²x (find the rule)= 1 (find the rule)(Algebra, Reciprocal, Quotient, Pythagorean, Odd/Even)
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Calculus Math Precalculus

10/26/23

(1 - cosx)(1 + cosx) = sin²x
LHS: (1 - cosx)(1 + cosx)= 1 - cos²x (find the rule)= sin²x (find the rule)(Algebra, Reciprocal, Quotient, Pythagorean, Odd/Even)
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Calculus

10/26/23

Find critical Values

Find all critical values for the function f(x)=x ^5/11(x-5)^2 and then list them
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Calculus

10/26/23

Using differentials

Use differentials ( or equivalently , a linear approximation ) to approximate sin ( 55 degree ) as follows : Let f(x)= sin (x) and find the equation of the tangent line to f(x) at a " nice" point... more
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10/26/23

chemistry basic calculation
there is about 50.109 of gold atoms in one drop of a sea water. how many grams of gold can be obtained from 1 tonne of sea water, if we know that the mass of 1 drop is 33 mg.
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Calculus Math

10/26/23

Calc BC Mean Value Theorem
Let f be a twice-differentiable function such that f'(2)=0. The second derivative of f is given by f''(x)=x2e2-x -1 forUse the Mean Value Theorem on the closed interval [2,4] to show that f'(4)... more
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Calculus Precalculus

10/26/23

section 3.7 calculus 1550
A graphing calculator is recommended.A particle moves according to a law of motion s = f(t), t ≥ 0, where t is measured in seconds and s in feet. (If an answer does not exist, enter DNE.)f(t)... more
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Calculus

10/25/23

Find the critical values f(x) on the given interval. f(x)= x/x^2-x+9, [0,9]
Find the critical values f(x) on the given interval. f(x)= x/x^2-x+9, [0,9]
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Calculus

10/25/23

A kite 100ft above the ground moves horizontally at a speed of 8 ft/s. At what rate is the angle between the string and the horizontal decreasing when 150 ft of string has been let out?

A kite 100ft above the ground moves horizontally at a speed of 8 ft/s. At what rate is the angle between the string and the horizontal decreasing when 150 ft of string has been let out?
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Calculus

10/24/23

derrivative calculus
Two straight roads diverge from an intersection at an angle of 60°. Two cars leave the intersection at the same time, the first traveling down one road at 44 mi/h and the second traveling down the... more
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Calculus

10/24/23

We will evaluate the following improper integral
We will evaluate the following improper integral:∫ x/(x^2 + 4)^2 dx from 3 to ∞ First we will do the indefinite integral ∫ x/(x^2 + 4)^2 dx(a) Use the substitution u=x^2+4 to formulate as an... more
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Calculus

10/24/23

You will integrate the following rational function
You will integrate the following rational function:∫ (−2 x^2 −24 x +138)/(x−5)^2 (x+3) dxTo do this, start by writing (−2 x^2 −24 x +138)/(x−5)^2 (x+3) = A/x−5 + B/(x−5)^2 + C/x+3(a) Put the... more
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10/24/23

A scientist begins with 250 grams of a radioactive substance. After 250 minutes, the sample has decayed to 30 grams.

1.) Write an exponential equation f(t) representing this situation. (Let t be the amount of radioactive substance in grams and t be the time in minutes.)2.) To the nearest minute, what is the... more
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Calculus

10/23/23

Consider the equation below. f(x)=e^6x+e^-x
Consider the function below. f(x)=e^6x+e^-x (a) Find the intervals on which f is increasing. (Enter your answer using interval notation.) Ans: (-ln(6)/7,infinity) Find the interval on which f is... more
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Calculus Precalculus

10/23/23

Use implicit differentiation
9. y' of sec²(x) + csc²(y) = 9ans. y'= tan(x) sec²(x) / cot(y) csc²(y)
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Calculus Precalculus

10/23/23

Use implicit differentiation to find the derivative of: Write the solution of each number

10. y - Arccot(xy) = 3
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