# Calculus homework help

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### The table below gives the depth of water across a river measured at one metre intervals between ...

**$**The table below gives the depth of water across a river measured at one metre intervals between banks.

Distance (m) 0 1 2 3 4

Water depth (m) 0 0.5 1.6 0.9 0

(a) Use the …

*How We Cough*When we cough, the trachea (windpipe) contracts to increase the velocity of the air going out. This raises the question of how much it should contract to maximize the …what is the gradient function of the equation: Y = 3X^3 + 2X

Use linear approximation, i.e. the tangent line, to approximate (1.4)^(1/3)

The count in a bacteria culture was 500 after 20 minutes and 1900 after 30 minutes. a)What was the initial size of the culture? =? b)Find the doubling period. =? c)Find the population …

Let f(t) be the weight (in grams) of a solid sitting in a beaker of water. Suppose that the solid dissolves in such a way that the rate of change (in grams/minute) of the weight of the solid at …

Find the Taylor expansion of the function up to x^4 about x0=0 f(x)=ln(sinx/x)

Find slopes of all lines tangent to the graph of the relation y^3+(2x^12)(y^2) - 35y = 84 - 84x^5 at the points on its graph where x = 1.

Find ∫ √(a^2 + x^2) dx with limits 0 to t using the substitution x = a sinh u

The line y = 2x + 5 intersects the curve y = x^2 + 2x + 2 at the points P and Q

1. Find the coordinates of P and Q, giving your answers in surd form.

2. Find the area of the shaded …### maths

**$34**how long before i get an order to work on?

If an annuity pays out at a rate of c(t) = $1,000t+35,000 per year, what is the present value of this annuity over 20 years if there is an inflation rate of 5% per year.

The sum of the length and the girth (perimeter of a cross section) of a package carried by a delivery service cannot exceed 108 inches. Find the dimensions of the rectangular package of …

Using calculus, find the equation of the line through the point (3, 5) that cuts off the least area from the first quadrant. Show all steps and define variables when appropriate. Use …

The rate of decay of a strain of bacteria is proportional to the number of bacteria remaining. Show this as a differential equation and give an example of its solution with chosen …

Can someone please explain how summing quantities of x^2 equals (1/3)x^3?

This summation process can be eliminated by using (1/3)x^3. Can you please show me the process in detail that …Investigate Newton’s law of cooling describing in words the principle it is based on and showing mathematical equation that results. Give one example of its use with selected numerical.

Describe an application of business calculus you see in sales daily work. What is the situation in which calculus could be applied and what is your estimate of the function you would use?