geno3141

Lateral surface area of a cylinder  =  pi x diameter x height

                                              LSA  =  pi x 6 x 4  ft² 

                                             LSA  =  24pi   =  75.36 ft²  (approximately)

(percent x amount) + (percent x amount)  =  final percent x final amount

                                  0.40 · x  +  0.50 · 6  =  0.46 · (x + 6)      [x is the unknown number of liters of the 40% solution]

                                             0.40x + 3.00  =  0.46x + 2.76

subtract 0.40x from both sides:         3.00  =  0.06x + 2.76

subtract 2.76 from both sides:           0.24  =  0.06x

divide both sides by 0.06:                       4  =  x

Since the slope is -3/7, every time the y-value decreases by three, the x-value will increase by 7

If the start with a y-value of 18, you can make 6 decreases (of three each time) to get to the x-axis.

So, increase the original x-value (zero) 6 times:  6 x 7  =  42.

Therefore, the x-intercept will be (42,0)

tan( pi / 3 )  =  sqrt( 3 )

So, the answer is "no."

There are six different ways the cars can finish (turquoise = a; teal = b, aquamarine = c):

a-b-c     a-c-b     b-a-c     b-c-a     c-a-b     c-b-a

Since it's completely random, 1/3^rd of the time the turquoise car will finish ahead of the other two cars.

Probability = 0.333

If the arithmetic sequence has an initial term of a and a common difference of d,

the fifth term will be a + 4d,

the ninth term will be a + 8d,

the fifteenth term will be a + 15d.

Since these three terms are the first three terms of a geometric sequence, call the common ratio r.

Therefore, (a + 4d)r  =  a + 8d  and  (a + 8d)r  =  a + 15d.

(a + 4d)r  =  a + 8d     --->   ar + 4dr  =  a + 8d     --->   ar  =  a + 8d - 4dr

(a + 8d)r  =  a + 15d   --->   ar + 8dr  =  a + 15d   --->   ar  =  a + 15d - 8dr

Combining these two equations into one equation:  a + 8d - 4dr  =  a + 15d - 8dr

                                                                                --->   8d - 4dr  =  15d - 8dr   

                                                                                 --->          4dr  =  7d   

                                                                                 --->            4r  =  7 

                                                                                  --->             r  =  7/4

Since we know that  (a + 4d)r  =  a + 8d   --->   (a + 4d)·(7/4)  =  a + 8d

                                                                  --->          7a + 28d  =  4a + 32d

                                                                  --->                     3a  =  4d

                                                                  --->                       d  = (3/4)·a

This leads to an infinite set of solutions: for example, if  a = 4  and  d = 3, you get the answers  16, 28, 49

and, if a = 8 and d = 6, you get the answers  32, 56, 98.

On the first day you save $0.01, on the second day you save $0.02, on the third day you save $0.03, etc.

Thus, on the n^th day, you save 0.01·n.

This is an arithmetic sequence because each number is 0.01 greater than the previous number.

The formula for the sum of an arithmetic sequence is:  Sum  =  N(F + L)/2

where  N = number of terms,  F = value of the first term,  L = value of the last term.

a)  N = 100, F = 0.01, L = 0.01·N = 1.00    --->     Sum  =  100(0.01 + 1.00)/2     --->     Sum  =  $50.50.

b)  N  = n, F = 0.01, L = 0.01n, Sum = 500.00     --->     500.00  =  n(0.01 + 0.01n)/2

     --->     1000.00  =  n(0.01 + 0.01n)   

     --->     1000.00  =  0.01n + 0.01n²

     --->     100,000  =  n + n²

     --->     n² + n - 100,000  =  0

Using the quadratic formula with a = 1, b = 2, and c = -100,000   --->  n = 316 (approximately)

If it is a parabola, it's equation is:  y - k  =  a(x - h)²  where (h, k) is it's vertex.

Substituting  h = -3  and  y = -13:  y - -13  =  a(x - -3)²     --->     y + 13  =  a(x + 3)²  

y-intercept = -4  -->  x = 0  and  y = -4     --->     -4 + 13  =  a(0 + 3)²     --->     9  =  9a     --->    a  = 1

Solution:  y + 13  =  1(x + 3)²     --->     y + 13  =  (x + 3)²  

Stage 1: the two captains are called  -->  total number = 2

Stage 2: four new players are called  -->  total number = 6

Stage 3: eight new players are called  -->  total number = 14

Stage 4: sixteen new players are called  -->  total number = 30

Stage 5: twenty new players are called  -->  total number = 50

Being a cubic polynomial, it has the form:  P(x)  =  ax³ + bx² + cx + d

Since P(0) = -3   --->   P(0)  =  a(0)³ + b(0)² + c(0) + d  =  -3   --->   d = -3

Since P(1) = 4   --->  P(1)  =  a(1)³ + b(1)² + c(1) + -3  =  a + b + c - 3  =  4   --->   a + b + c  =  7

Using long division, I divided  ax³ + bx² + cx - 3  by  x² + x + 1  and I got

a quotient of  ax + (b - a)  and  a remainder of  (c - b)x + (a - b - 3)

Since the problem said that the remainder was  2x - 1   --->   (c - b)x + (a - b - 3)  =  2x - 1

which means that  c - b  =  2  and  a - b - 3  =  -1    --->   c  =  b + 2   and   a  =  b + 2

Combining  a + b + c  =  7  and  c = b + 2  and  a = b + 2

--->   a = 3   and   b = 1   and  c = 3

Since the quotiet was  ax + (b - a)  and  a = 3  and  b = 1,

replace to determine the answer.