Dice and Derivatives
The function f(x) = x2-8x-9 . It contains the points (1,-16) and (7,-16). Find the intersection of the tangent lines for x = 1 and x = 7
Point is (4,-34)
The lines in point slope form are -6(x-1)-16 and 6(x-7)-16
Add 16 and divide both sides by 6 to get –(x-1) = x-7
Solve to get that x = 4 then use that in one equation to get that y = -34
Find the Surface area of a 4x4x4 cube
96 = 4x4x6 or 6a^2 where a = 4
Find the value of the expression below
51 + 42 + 33 + 24 + 15
5+16+27+16+1 = 65
Find Z using the equations below
H = P – Q + 2R
Z = H/50
It is known that P = 7500 Q = 1800 and R = -1900
2R-Q = 4600 and P – 4600 = 2900 = H
H\50 = 58
Find the value of QUIT
-2Q = U
1 - 3I = T
U + I = 5
U-T = 18
Q = 1
U = -2
I = 7
T = -20
QUIT = 280
Find the 2nd derivative of f(x) where f(x) is given below
f(x) = x7-x6+x5+2x4-5x3
f''(x) = 42x5-30x4+20x3+24x2-30x
Find the surface area of a 3 by 7 by 11 rectangular prism
Find area of each face then add then together or do
(3*7 + 7*11 + 3*11)*2 = 262 units
Find J using the equations below
A = 1, B = A+3, C = 2B, D = -C, E = D + 5, F = 2D, G = F +10, H = 4G, I = H -20, J = I/2
B = 4, C = 8, D = -8, E = -3, F = -6, G = 4, H = 16, I = -4, J = -2
Z = X + Y where X and Y are the x and y coordinates of the minimum of f(x) where f(x) is shown below
f(x) = x2-14x+24
f(x) = (x-2)(x-12) when factored out X = 7, Y = -25 at the minimum so Z = 7-25 = -18
Find the value of Q+U+I+T
4U = T
Q-U= I
T+I = -1
Q – T = 13
Q = 5
U = -2
I = 7
T = -8
Q + U + I + T = 2
Two fair 6 sided dice are rolled and their sum is computed. Find the probability that their sum is divisible by 3 or 4 (fractions are fine as an answer)
3,4,6,8,9 and 12 are the sums that work and there is a 2/36 chance for a 3, a 3/36 chance for a 4, a 4/36 chance for a 9, 5/36 chance for a 6 and 8 each, and a 1/36 chance for a 12 totaling to 20/36 chance and 5/9.
Find the area of the triangle formed by the x axis and the lines y=4(x-2) and y= 2(4-x)
Base is from 2,0 to 4,0 and is 2 units, lines intercept at 8/3,8/3, so our height is 8/3 do base * height over 2 to get 8/3 as our answer
8/3
Find the sum of all terms below
{7, 9, -3, 16, 2, 5, 11, 1, 8, -13}
Sum is 43
Find Z where Z is equal to the expression below
2-2+25+23+2-1+21+2-2+20+22
48
Find the value of the expression Q+U+I+T
2T+1 = Q
I - 6 = U
Q + 6 = U
5T+1 = I
Q = 9
U = 15
I = 21
T = 4
Final answer is 49
Find the 2nd derivative of f(x) where f(x) = log(sin(x2))
1st derivative (1/sin(x2)) * cos(x2) * 2x = cot(x2)*2x
2nd derivative 2cot(x2)- csc2(x2)*4x2
Find the area of the trapezoid formed by the lines y = 4, y = x, y = 10 – x and the x axis
Area = ½*h*(b1+b2)
B1 = 10 b2 = 2 and h = 4
Area = 24
Find the average of all terms below
{7, 19, 4, 11, 1, 12, 9, 2, 10, 5}
8 there are 10 terms and the sum of the terms is 80
Z is the value of the expression below where i is the imaginary number
(5i6)2+7i74+(3i110)3-30i50+9i16-15i100
Z = 15 , 25 – 7 – 27 +30 + 9 – 15
Find the value of QUIT/6
Q+U = 1
T-I = 1
4I – 1 = Q
8+U = I
Q = 7
U = -6
I = 2
T = 3
QUIT/6 = -42
Two fair 10-sided dice are rolled are their product is computed. Find the probability that the product is divisible by 6? (Hint there are 100 possible outcomes and each one has a 1% chance of occurring)
If one of the die is a 6 the product is automatically divisible by 6 and there are 19 ways that can happen. But we can still get a number that is divisible by 6 from multiplying 3 or 9 by another even number and there are 16 ways to do that. So we have a 35 ways and a 35% chance this will happen
Find the area under the curve of the function y = x3 - x from x = 2 to x = 4
Take the integral from 2 to 4 or use two separate ones to get 56 – 2 and 54 as our answer
Find the Product of all terms below
{4, 6, 1/8, 14, 1/7, 9, 2/3, 10, 3/5, 1/2}
4*6*1/8 = 3, 14*1/7*1/2 =1, 9*2/3 = 6 and 10*3/5 = 6
108
Find Z where Z is the value of the f(x) when integrated form 0 to 2
f(x) = 10x4+2x3+18x+6
This evaluates to 2x5+x4/2+9x2+6x and that evaluated at 0 is 0 and at 2 is 120 so Z = 120
Find the value of Q – U – I – T
Q = 3(U + 1)
T = U - I
T = 1 – 3I
T = 2U-5
Q = 30
U = 9
I = -4
T = 13
Q-U-I-T = 12