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1. Integral optimization

Homework Statement A circular disk of radius r is used in an evaporator and is rotated in a vertical plane. If it is to be partially submerged in the liquids as to maximize the exposed wetted area of the disk, show that the center of the disk should be positioned at a height r/ \sqrt{1+\pi^2}...
2. Inverse trig functions

Homework Statement Determine sin(arctan(3)) The Attempt at a Solution I do not know how to start this. No special triangles : (.
3. Trig ratios

Homework Statement Find the trigonometric ratios sin\theta, cos\theta, tan\theta for the angle \theta = 14\pi. If a ratio does not exist or is undefined, write "DNE". The Attempt at a Solution I know that the other equivalent angle for 15pi is just pi. But I do not know how to write the...
4. What volume of this solution is required to make 1.25 L

Homework Statement An aqueous stock solution is 85.0% H2SO4 by mass and its density is 1.83 g/mL. What volume of this solution is required to make 1.25 L of 2.75 mol/L H2SO4(aq)? Give your answer in millilitres, accurate to three significant figures. Homework Equations c1v1=c2v2 The...
5. Neutralization reaction

Homework Statement what volume of 0.350 mol/L NaOH(aq) is required to completely neutralize 54.5 mL of 1.31 mol/L H3PO4(aq)? Homework Equations c1v1 = c2v2 The Attempt at a Solution You would just solve for v2 but I am not getting the right answer for some reason.
6. Inverse ln function

Homework Statement Determine f^{-1}(0) of f(x) = ln (4-7x) + ln(-7-5x) Homework Equations f(x) = ln (4-7x) + ln(-7-5x) The Attempt at a Solution What I did was y = ln (4-7x)(-7-5x) Then I swapped x and y to attempt to make the inverse function x = ln (4-7y)(-7-5y) and I start to...
7. Optimizing speed and cost.

Homework Statement The cost of fuel per kilometre for a truck travelling v kilometres per hour is given by the equation C(v) = \frac{v}{100}+\frac{25}{v}. Assume the driver is paid \$40/h. What speed would give the lowest cost, including fuel and wagesm for a 1000-km trip? Homework Equations...
8. Maximum area ratios

Homework Statement A Norman window has the shape of a rectangle with a semicircular top. Assume that the semicircular portion of the peripmeter is three times as costly to build per metre as the straight edges. For a given area, what ratio of heigh to radius would minimize the cost. Homework...
9. More than one tangent

Homework Statement Show that the tangent to the curve y=(x^2+x-2)^2+3 at the point where x =1 is also tangent to the curve at another point. Homework Equations y=(x^2+x-2)^2+3 The Attempt at a Solution y'=2(x^2+x-2)(2x+1) y'(1)=0 0=2(2x+1)(x+2)(x-1) x= -1/2, -2, 1 Would this be correct?
10. Power rule

Homework Statement Find two straight lines that are perpendicular to y=0.25x and tangent to the curve f(x) = 1/x. Homework Equations y=0.25x f(x) = 1/x. The Attempt at a Solution What I did was equate y and f(x) and determined when they equal which is 2 and -2. The points are (2, 1/2) and...
11. Sound loudness

Homework Statement How many decibels does the loudness of a sound increase if its intensity increases 25 times? Homework Equations dB = 10 log\frac{I_{b}}{I_{a}} The Attempt at a Solution \frac{I_{b}}{I_{a}} = \frac{25}{1} dB = 10 log\frac{25}{1} dB = 13.98
12. Trig derivatives

Homework Statement Find the maximum value and minimum value of the function f(x) = cos 2x + 2sinx 0 \leq x \leq \frac{3\pi}{4} Homework Equations f(x) = cos 2x + 2sinx The Attempt at a Solution f(x) = cos 2x + 2sinx f'(x) = -2sin2x + 2cosx 0=-2sin2x + 2 cosx...
13. Optimization math help

Homework Statement A piece of wire 8 cm long is cut into two pieces. One piece is bent to form a circle, and the other is bent to form a square. How should the wire be cut if the total enclosed area is to be small as possible? Keep \pi in your answer. Homework Equations A= \pi r^{2} A= lw...
14. Two undetermined constants

Homework Statement If s(0) = 0, v(1) = 24 and a(t) = 24t+6 find s(t) Homework Equations The Attempt at a Solution I know a(t) is s''(t) and v(t) is s'(t). however, How can I find s(t)?
15. Determining perpendicular tangent line

Homework Statement Determine the coordinates of the points on the graph of f(x) = \sqrt {2x+1} where the tangent line is perpendicular to the line 3x+y+4 = 0 Homework Equations f(x) = \sqrt {2x+1} 3x+y+4 = 0 The Attempt at a Solution For this, I was going to find the...
16. When does this derivative equal 7

Homework Statement Solving a derivative for when it equals to 7. Homework Equations p'(t) = {88t+210}/{2\sqrt{44t^{2}+210t} The Attempt at a Solution 7(2\sqrt{44t^{2}+210t}) = {88t+210} This is where I get stuck. Do I divied both sides by 7 then again by 2? then I would...
17. Quotient rule

Homework Statement For some reason, I cannot seem to get the derivative for this. Homework Equations f(a) =\frac {(2500+0.2t)(1+t)}{\sqrt {0.5t+2}} The Attempt at a Solution f(a) =\frac {(2500+0.2t)(1+t)}{\sqrt {0.5t+2}} \frac {(2500+0.2t)}{\sqrt {0.5t+2}} (1+t) From...
18. Piecewise functions

Homework Statement We started piecewise functions in calculus and I'm finding it rather difficult. This question has had me stumped for a while. I'm quite well at finding domain and range, however :). For what value of k is the following a continuous function Homework Equations f(x)=...

Homework Statement Differentiate using the product rule Homework Equations (2t^2+t^{(1/3)})(4t-5) The Attempt at a Solution h'(t) = f'(t)g(t)+f(t)g'(t) (4t+\frac {1}{3}t^{\frac {-2}{3}})(4t-5)+(2t^2+t^{(1/3)})(4) \frac {-5}{3t^{2/3}}+24t^{2}-20t+\frac {16}{3}t^{1/3} Why is this wrong?
20. Product Rule on a triangle

Homework Statement Question: the base b and height h change with a time t in such a way that b= (t+1)^{2} and h= t^{2}+1 Determine the rate of change of the area of the triangle when t=3 Homework Equations A=\frac {1}{2}(b)(h) The Attempt at a Solution I am not sure what to do...
21. Power rule

Homework Statement I promise this will be my last one :p For this function: f(x)=-4x^{3}+\frac{3}{x}+\sqrt{x}-2 What would be the derivative using the power rule? Homework Equations f(x)=-4x^{3}+\frac{3}{x}+\sqrt{x}-2 The Attempt at a Solution...
22. Determining slope of the tangent line.

Homework Statement I've never seen such a problem before: Find the two straight lines that are perpendicular to y=0.25x and tanget to the curve f(x)=1/x Homework Equations y=0.25x ; f(x)=1/x The Attempt at a Solution Using the power rule, I found the derivatives of: f(x)=-x^{-2} and y=0.25...
23. Derivative question.

Homework Statement Find the rate of change of depth D with respect to time t Find the rate of change of depth when the depth is 22.5 m Homework Equations D=10(2-(t/14))^2 The Attempt at a Solution I know I need to determine the derivative for both. dy/dx =10(2-(t/14))^2 =...
24. Schools University application

In two months, university application will start. So I have this little time to decide what to do. I don't think it is a possibility to do everything I want so I have to narrow it down to one. What can I do?