# Search results

1. ### Kayak Question

Homework Statement A woman lives on an island 2km from the mainland. Her fitness club is 4km along the shore from the point closest to the island. To get to the fitness club, she paddles her kayak at 2km/h. Once she reaches the shore she jogs at 4km/h. Determine where she should land to reach...
2. ### Minimize Distance

Homework Statement Mike, who i standing on the deck of a yacth that is travelling due west at 6km/h, sees a sailboat sailing southwestat 4km/h, 3km northwest of the yacht. How close to each other do these boats get? Homework Equations The Attempt at a Solution My drawing is: |...
3. ### Really hard related rates problem

Homework Statement A trough has an isosceles trapezoidal cross section as shown in the diagram. Water is draining from the trough at 0.2m^3/s At what rate is the surface rea of the water decreasing? Dimensions are: base width=0.4m, top width= 0.8m...
4. ### Finding closest distance

Homework Statement Ship A, sailing due east at 8 km/h, sights ship B 5km to the southeast when ship B is sailing due north at 6km/h. How close to each other will the two ships get? Homework Equations The Attempt at a Solution I drew the picture. Ship a distance is 8t and B is 6t...
5. ### Rates of Change in business

Homework Statement A Real estate office manages 50 apartments in a downtown building. When the rent is $900 per month, all the units are occupied. For every$25 increase in rent, one unit becomes vacant. On average, each unit requires \$75 in maintenance and repairs each month. How much rent...
6. ### Keep getting an indeterminate answer for limit

Homework Statement Determine the limit: lim as x->-2 [1/(1+x)+1]/[2x+x^2] Homework Equations The Attempt at a Solution I can't seem to work around it, I keep getting an indeterminate answer.
7. ### Explaining the chain rule

Homework Statement The question is: How would you explain the chain rule to a classmate? My teacher wants: 1.a graph, 2. in words, 3. using math Homework Equations The Attempt at a Solution I said: for the function y=f[g(x)], the chain rule is d/dx[g(x)]. Whats the graph like?
8. ### Exponential Derivative

How do you find the derivative of: y=x(3x)^x^2 ? I though it was yprime=(1)3x^x^2+x(3x^x^2)ln(1+3x)(2x)
9. ### Chain rule Derivative help

Given: h=f\circ g , g(2)=5, g\prime(2)=3, and f\prime(5)=-2 Determine h\prime(2)
10. ### Find two lines through the point (2,8) and tangent to y = x^3

Find two lines that pass through the point(2,8) and are tangent to the curve y=x^3 I found the first equation which is y=12x-16 by finding the derivative of y=x^3 which is y=3x^2. I then plugged in (2,8) into y=mx+b along with the slope of 12. But how can there be more than one slope at...
11. ### Average rate of change of a sphere

the Volume of a sphere is given by V(r) = \frac{4}{3}\pi(r)^3 Find the average rate of change of volume with respect to radius as the radius changes from 10 cm to 15 cm. Ok what I tried is: \lim_{r\rightarrow 15} \frac{V(r)-V(a)}{r-a} P(a,V(a))=(15,14 137)\\ Let\ r=10 \lim_{r\rightarrow 15}...
12. ### Rate of movement of glacier

The movement of a certain glacier can be modelled by d(t)=0.01t^2+0.5t where d is the distance in metres that a stake on the glaciers has moved, relative to a fixed position, t days after measurements began. Find the rate at which the glacier is moving after 20 days. What is the question...
13. ### Limits of polynomial functinos

Invent a function and sketch its graph to satisfy each situation lim_x-0+ f(x)=3 and lim_x-0- f(x)=-2 I can't figure out an equation for that
14. ### Trouble with Tangent of a Line

I tried many thigns with this one: Determine the equation of the line that is perpendicular to the tangent to y=5x^2 at (1,5) What I did was use the formula for instantaneous rate of change finding the equation of the secant. (5x^2-5)/(x-1) from there I found that the slope of the...
15. ### Inverse expressions

yea ok but wait how do u find the inverse of like y=(x)^(1/3) y=3(2)^x whats the formula is not in the book BTW i can't do those equations in latex...
16. ### Exponential Growth etc

the question is how do I solve (1.024)^t=2.857 and find "t" without using logarithms
17. ### Solve for X

Solve for X: 3(2)^x = 4(^x^+^1) I did: xlog3(2)=(x+1)log4 and got the wrong answer
18. ### Logarithm's and Such

There are initially 200 bacteria in a culture. After five minutes, the population has grown to 4080 bacteria. Estimate the doubling period. I DID THIS: 4080=200(k)^5\\\frac{4080}{200}=k^5\\k=1.82 IS THIS CORRECT?
19. ### Logarithm's and Such

There are initially 200 bacteria in a culture. After five minutes, the population has grown to 4080 bacteria. Estimate the doubling period. I DID THIS: 4080=200(k)^5 4080/200=k^5 k=1.82 IS THIS CORRECT?
20. ### Logarithm Proofs

Can't start: (log_{a}b)(log_{b}a) =1
21. ### Dimensions of Box

Sponge Bob Square Pants makes an open-topped box from a 30-cm by 30-cm piece of cardboard by cutting out equal squares from the corners and folding up the flaps to make the sides. What are the dimensions of each square, to the nearest hundredth of a centimetre, so that the volume of the...
22. ### Roots of Polynomial

The Roots and degree of a polynomial function are given. Write the function in standard form. b) 2, -2i, degree 4 obviously i know there is a function with x^4 and it should have 4 x answers so I dont know how to do this...I know that (x-2) is a factor
23. ### Finding the dimensions

A box has dimensions that are linear factors of (x^3-7x^2+14x-8) cubic centimetres. What dimensions give a volume of 12 cm cubed? I started it off by moving 12 to the left side giving the equation: x^3-7x^2+14x-20=0 then from then I don't know....If I substitute 5, the equation is...
24. ### Polynomials math homework

What are the ROots: x^4+4x^3+14x^2=-4x-13 ok the 13 really causes a problem because you can't factor that. So I move the right side to the left and then you can't find a number that fits so that it equals zero so I tried factoring it somehow but can't do it can someone help?
25. ### Determine Roots

What are the ROots: x^4+4x^3+14x^2=-4x-13 ok the 13 really causes a problem because you can't factor that. So I move the right side to the left and then you can't find a number that fits so that it equals zero so I tried factoring it somehow but can't do it can someone help?
26. ### Solving Polynomial Equations

A box has dimensions that are linear factors of (x^3-7x^2+14x-8) cubic centimetres. What dimensions give a volume of 12 cm cubed? I started it off by moving 12 to the left side giving the equation: x^3-7x^2+14x-20=0 then from then I don't know....If I substitute 5, the equation is...
27. ### Easy Question

Let f = {(-4.4),(-2,4),(1,3),(3,5),(4,6)} and g = {(-4,2),(-2,1),(0,2),(1,2),(2,2),(4,4)} Determine a)f + g
28. ### Geometry-Sequences with unlimited repeated values

Here is the question I cannot get it.... In a series of license plates, the first three symbols are any of the 26 letters in the alphabet and the last three are any of the 10 digits from 0 to 9. How many plates can be formed in which at least one symbol is repeated? - --------I know that...
29. ### Help with a Proof

Prove that the sum of the exterior angles at opposite vertices of any quadrilateral es equal to the sum of the interior angles at the other two vertices. THIS question is REAly really really really getting me frustrated... The way we're suppost to do it is like this.... 180n-360 is the...
30. ### Completing the Square

Ok so can you please tell me where I go wrong here. I want to put y=3x^2+2x-1 into y=a(x-h)^2+K ax^2-2ah+ah^2+k=3x^2-2x+ah^2-1 ax^2=3x^2 -----> a=3 -2ahx=-2x -2(3)hx=-2x ----->h=1/3 K=----->-1 Therefore: y=3(x-1/3)^2-1 But I think it's suppost to be: y=3(x+1/3)^2-4/3 Is...