Let us assume that every vector in S_2 is a linear combination of vectors in S_1. Question: Does that mean that S_1 and S_2 are bases for the same subspace of V? I know that the...
Let us assume that every vector in S_2 is a linear combination of vectors in S_1. Question: Does that mean that S_1 and S_2 are bases for the same subspace of V? I know that the...
A fence 8 feet tall runs parallel to a tall building at a distance of 3 feet from the building. What is the length of the shortest ladder that will reach from the ground over the fence to...
triple integrals
It is continuous on [0,2] and differentiable on (0,2) f'(x)=3x^2-4x-2 The thing that I am stuck on is that f(a) does not equal f(b) f(0)=4 f(2)=0 I went ahead and plugged...
Consider the function f(x) = 4 x^3 - 4 x on the interval [ -4 , 4 ]. Find the average or mean slope of the function on this interval. By the Mean Value Theorem,...
A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y= 9-x^2. What are the dimensions of such a rectangle with the greatest possible area? width=...
A cylinder is inscribed in a right circular cone of height 2 and radius (at the base) equal to 4.5. What are the dimensions of such a cylinder which has maximum volume? width=??? height=...
If 1300 square centimeters of material is available to make a box with a square base and an open top, find the largest possible volume of the box.
I need help with the following homework problem and setting up the equations as well as how to solve them! (Bees collecting pollen and nectar - Optimization) Many bees collect...
0∫2(0∫¶/2 xsin(y)dy)dx
If the integral test applies, use it to determine whether the series converges or diverges. ∑ 1, ∞ (ln(n))2/n
When finding delta, use the absolute value of x-2 is less than 2 so that delta=min{2,__} This is what I've done so far: f(x)=1/x L=1/2 a=2 Find...
Find the inverse of x^3-2/x
∫1/4e^-.25x dx
How do you find the integral from 2 to infinity of (x2-1)-1/3dx and whether its divergent or convergent?
Include a diagram in your solution. I need help with this ASAP please!
Resolve the weight of the crate into the two rectangular components keeping it at rest. Include a vector diagram in your solution. I need help with this ASAP please!
ƒ'(x)=ax2+6x+b ƒ'(1)= 14 ƒ''(1)= 12 ∫12 f(x)dx=18
Find the distance in which the car can be brought to rest from 30 mph, assuming the same constant acceleration.
The function N(x) = −2x^3 + 180x^2 + 3000x + 20000 gives the number of items of a product that are sold for a given value of x, where x represents advertising expenditures in...