1) If y=kx, where k is a constant, and y=128 when x=16, what is the value of y when x is increased by 25%?
(I got 160?)
2) Aaron calculates using a certain foot and line spacing, that each page of a typed document contains at least 240 words and at most 260 words. What is the least number of pages needed for a 12,000-word document?
(I got 50 pages)
3) How many solutions to the equation 4 cos x=1 lie between x=0 and x=3(pi)
A)2
B)3
C)4
D)6
(^I don't understand this)
cosx=.25
sketch the cosine curve over two cycles.
well, you really want to look at only 1.5 cycles. How often does it equal .25? I see three in my sketch.
how do you draw cycles? Or graph/sketch the equation?
Are number 1 and 2 correct?
1) To find the value of y when x is increased by 25% in the equation y = kx, we first need to determine the value of k.
Given that y = 128 when x = 16, we can substitute these values into the equation:
128 = k * 16
To isolate k, divide both sides of the equation by 16:
k = 128 / 16 = 8
Now that we know the value of k is 8, we can find the new value of y when x is increased by 25%.
Since x is increased by 25%, the new x value is 1.25 times the original x value:
new x = 16 * 1.25 = 20
Substituting into the equation y = kx:
y = 8 * 20 = 160
So, the correct answer is y = 160.
2) To determine the number of pages needed for a 12,000-word document, knowing that each page contains at least 240 words and at most 260 words, we can find the minimum and maximum number of pages, and then use the average to get the closest possible integer value.
The minimum number of pages is obtained by dividing the total number of words (12,000) by the maximum words per page (260):
min pages = 12,000 / 260 = 46.15
The maximum number of pages is obtained by dividing the total number of words (12,000) by the minimum words per page (240):
max pages = 12,000 / 240 = 50
Since we cannot have a fraction of a page, we need to round up the minimum number of pages to the nearest whole number. So, the least number of pages needed is 47.
Therefore, the correct answer is 47 pages.
3) To determine the number of solutions to the equation 4 cos(x) = 1 that lie between x = 0 and x = 3π, we need to find the values of x that satisfy the equation within this interval.
The equation 4 cos(x) = 1 represents a cosine function. The graph of cosine oscillates between -1 and 1. In the given equation, we have cos(x) = 1/4.
To find the solutions within the interval [0, 3π], we need to consider the values of x where the cosine function equals 1/4.
First, we need to find the inverse of the cosine function, called arccos or cos^(-1), to solve for x.
arccos(1/4) = 1.318116071.
Now, we have to determine the solutions between 0 and 3π where x = 1.318116071.
Within the interval, there are two solutions where cos(x) = 1/4:
x ≈ 1.318116071 and x ≈ 5.963788443.
Therefore, the correct answer is A) 2 solutions.