Image 170k

Tried to create a video for this answer, but status stayed in perpetual "preparing room...". Student requested help on writing...

Image 170k

Tried to create a video for this answer, but status stayed in perpetual "preparing room...". Student requested help on writing...

Evaluate and simplify (answer)

Hi Michelle, Hopefully you see how to get to here: 3 3 -------- - ---- (7+h) 7 -------------------- ...

Hi Neal, One technique to try is writing the difference between successive terms to see if a pattern develops. For example the difference between 3 and 0 is 3, the difference between 8 and 3 is 5, between 15 and 8, 7. So we have 3, 5, 7... Checking one more difference...

(9x)/(4-(sqrt(6x-38))) (answer)

6x - 38 must be greater than 0 too, because otherwise taking the square root of a negative number. Check out this graph: https://www.desmos.com/calculator/qgvcaurvrk

Double integral - calculating area (answer)

Hi Claire, Take a look at this graph to get the idea of what is happening. This problem is an example of the "area between two curves". To find the height of a "typical rectangle" use "top" - "bottom". https://www.desmos.com/calculator/mmynniltq1 Hopefully...

Another option for finding the area of any triangle when you know all three sides is to use Heron's formula. First make sure that the numbers a,b,c (sides of the triangle) actually form a triangle. The sum of any two sides must be greater than the 3rd side. Find the...

Dice experiment (answer)

Hi Jovan, One way to look at it: You might try drawing a tree diagram where Even has a probability of 1/2 and Odd has a probability of 1/2. Some possible outcomes {E,E,E}, {O,O,O}, {E,O,E}, etc. The probability of each of those outcomes is (1/2)(1/2)(1/2)=...

Hi Huja, Look up Heron's formula for finding the area of a triangle given the length of each side. Using this formula requires you to first find the "semi-perimeter" of the triangle. In Heron's formula the semi-perimeter is usually represented by the letter "s"...

Hi Ariana, If you solve the first equation for y, you will have slope-intercept form (y=6x+1). That means the slope of the given line is 6. Parallel lines have the same slope. Use point-slope form to write the equation of the parallel line. y - (-11) = 6 (x-3) See...

Create the "hole" at x= 5 by introducing a factor of (x-5) in both numerator and denominator of rational function. Do create a vertical asymptote at x=-6, introduce a factor of (x+6) in the denominator. In order to have a horizontal asymptote at y=7 the reduced function (after...

Hi Cayce, To determine the slope of the line passing through two points use the formula for slope. The following graph shows the results of two different ways to do the calculation. https://www.desmos.com/calculator/5pvn8xfhg7 The graph...

Optimisation (answer)

Hi Vans, Here are some ideas to get you started. Let x = the height of a locker. Let y = the width. Then the area of one locker will be A = xy. The trick is to come up with a relationship between x and y so that A can be written as the...

Optimisation (answer)

Hi Vans, You need a function that determines the length of the wire for any given point at which the wires are staked between 0 and 24 meters. The assumption is that this point is on the line connecting the bases of the two poles. If you draw a sketch you will see that the two separate...

Confusing Problem (answer)

Hi Karen, Imagine two piles of coffee. One contains 10 pounds and each pound is worth $5. So that pile is worth $50. The second pile we do not know the number of pounds so let's call that x. That pile is worth $8 for each pound. If we multiply x by 8 we will have the...

Find an area bounded by a graph (answer)

Hi Vagif, First thing I would recommend is to use specific values for a, b, c to get an idea of what is going on. The following graph has sliders for a,b,c so you can adjust them to get different pictures: https://www.desmos.com/calculator/2gzw4cq72y Notice...

volume of this solid (answer)

Hi Marcio, The easiest way to solve this problem is to use the washer method, but integrating along the y-axis. The problem has already solved the for x in terms of y. Remember "outer radius squared minus inner radius squared". This graph should give you the...

Hi Billy, It is the 4th choice that is similar for the two constructions. The 3 angle bisectors of a triangle meet at a common point. After constructing two of them, that point is the center of the inscribed circle. You still have to construct a perpendicular through...

Hi Lexie, The idea behind logarithmic differentiation is to simplify finding y' when complicated product/quotient rule is required. Take the natural log of both sides, use properties of logarithms to expand the ln f(x) into separate terms, then take the derivative of both sides...

Find y-values. (answer)

Hi Madeline, You might want to start using the Desmos online graphing calculator to help answer questions like this. Here is a graph containing the parent function (y=|x|), a vertical stretch for the parent (y=3|x|), and the function for this question. https://www...

Hi Jenna, I assume the rest of the question went something like "what was the scale factor for this dilation"? Do you see a number that you can multiply each coordinate of the first three points that maps to the coordinates of the 2nd three points? For...