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}...
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...
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...
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.
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...
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...
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...
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?
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...
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
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...
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...
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)?
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...
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...
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...
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?
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...
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...
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...
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
=...
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?