Deflection and rotation of simple beam with uniform and concentrated loads
7 years 5 months ago
Find the area of the largest rectangle that can be inscribed in the ellipse x^2/25 + y^2/16 = 1.
7 years 5 months ago
A ship lies 6 miles from a straight shore, and opposite a point 10 miles farther along the shore, another ship lies 18 miles offshore.
7 years 5 months ago
A wall 10 ft high along the property line is 8 ft from a house.
7 years 5 months ago
A triangle has a variable sides x, y, and z subject to the constraint that the perimeter P is fixed to 18 cm. What is the maximum possible area of the triangle?
7 years 5 months ago
A corner lot, triangular in shape, has perpendicular sides measuring 90 m and 120 m, respectively.
7 years 5 months ago
If 1200 cm^2 of material is available to make a box with a square base and open top, find the largest possible volume of the box.
7 years 5 months ago
A closed cylindrical tank having a volume of 71.57 m^3 is to be constructed. If the surface area is to be minimum, what is the required diameter of the tank?
7 years 5 months ago
Two vertices of a rectangle are on the positive x-axis. The other two vertices are on the lines y = 4x and y = 6 - 5x. What is the maximum possible area of the rectangle?
7 years 5 months ago
A Norman window has the shape of a rectangle surmounted by a semicircle.
7 years 5 months ago
A cylindrical can is to be made to hold 1 liter of oil. Find the radius that will minimize the cost of the metal to manufacture the can.
7 years 5 months ago
A farmer has 2400 ft of fencing and wants to fence off a rectangular field that borders a straight river.
7 years 5 months ago
Find the area of the largest rectangle that can be inscribed in a right triangle with legs of length 3 cm and 4 cm if two sides of the rectangle lie along the legs.
7 years 5 months ago
A steel pipe is being carried down a hallway 9 ft wide.
7 years 5 months ago
Common Maxima and Minima Problems
7 years 5 months ago
Quiz: Common Optimization Problems
7 years 5 months ago
A certain bacterial culture doubles in number every day. If there were 1000 bacteria at the end of the 1st day, how many will there be after 10 days?
7 years 5 months ago
Find the 7th term of the geometric sequence beginning with 6, 9, 27/2, …
7 years 5 months ago
Find the sum of the arithmetic sequence 2, 4, 6, 8, 10, 12.
7 years 5 months ago
A pyramid of blocks has 26 blocks in the bottom row and 2 fewer blocks in each successive row thereafter. How many blocks are there in the pyramid?
7 years 5 months ago
The sequence 1, 1, 2, 3, 5, 8, 13 is called the Fibonacci sequence. What is then the tenth term?
7 years 5 months ago
Compute the sum of the integers from 1 to 1000.
7 years 5 months ago
Compute the following: $\displaystyle \sum_{j = 1}^6 \left[ -3 + 5(j - 1) \right]$.
7 years 5 months ago
Compute the following: $\displaystyle \sum_{n = 1}^3 \left( \dfrac{n + 1}{n} \right) - \sum_{n = 1}^3 \left( \dfrac{n}{n + 1} \right)$.
7 years 5 months ago
Find $\displaystyle \sum_{n = 1}^4 (2k + 1)$.
7 years 5 months ago
Find $\displaystyle \sum_{n = 1}^5 S_n$ where $S_n = 2/n$.
7 years 5 months ago
Find the 6th term of $1, ~ 2, ~ 5, ~ ... \, , ~ \frac{1}{2}(1 + 3^{n - 1})$.
7 years 5 months ago
Find the 8th term of the sequence $-3, ~ 4, ~ 5/3, ~ … \, , ~ \dfrac{n + 2}{2n - 3}$.
7 years 5 months ago
In the figure, $\varphi$ represents the angle subtended by a 5 ft picture when viewed from point P that is 7 ft below the picture and 14 ft away from the wall on which the picture hangs.
7 years 5 months ago
Solve for $x$ if $\arcsin (x + 2) = \pi/6$.
7 years 5 months ago
Find the exact value of $\arccos (\tan 45^\circ)$
7 years 5 months ago
Evaluate the $\tan (\arctan 3 + \arctan 4)$.
7 years 5 months ago
Evaluate the $\tan (\arctan 3 - \arctan 2)$.
7 years 5 months ago
Find the exact value of $\cos [ \, \arcsin (2/3) \, ]$.
7 years 5 months ago
At a point A that is 50 m from the base of a monument, the angle of elevation to the top of the monument is twice as large as the angle of elevation from a point B that is 150 m from the monument.
7 years 5 months ago
From the following figure, which of the following is equal to $\tan (\theta/2)$?
7 years 5 months ago
Solve for b as shown in the figure.
7 years 5 months ago
If $\theta$ is an acute angle of a right triangle where $\sin \theta = x/2$, compute the value of $\sin 2\theta$ in terms of $x$.
7 years 5 months ago
Find $\tan \beta$ from the given figure.
7 years 5 months ago
From the given right triangle what is the value of $3 \sin^2 \varphi \, \sec \varphi$ in terms of $x$.
7 years 5 months ago
Area outside equilateral triangle available for grazing by the goat.
7 years 5 months ago
Find the area of the sector inside the square ABCD.
7 years 5 months ago
Find the value of $x = \sin^2 \varphi - \cos^2 \varphi$ if $\varphi$ is $\pi / 4$ or $45^\circ$.
7 years 5 months ago
Which of the following is equal to $\dfrac{\sin \theta}{1 + \cos \theta}$.
7 years 5 months ago
Find the value of x if $x = \dfrac{1 + \tan^2 \phi}{\tan \phi \, \csc^2 \phi}$.
7 years 5 months ago
Solve for x if ln (x + 1) = 1 + ln x.
7 years 5 months ago
A bacterial culture is growing according to the formula y = 10,000e^{0.6x) where x is the time in days. Estimate the number of bacteria after one week.
7 years 5 months ago
A radioactive substance is decaying (it is changing into another element) according to the formula y = Ae^(-0.2x)
7 years 5 months ago
Solve for x if log_x (2x)^(3x) = 4x.
7 years 5 months ago
Solve for x if (x + 2) log_b b^x = x.
7 years 5 months ago