Let us check the transformations. The first step is regarding the argument of the function, the -2x part. So, first of all, the minus sign implies that the function is reflected along the y-axis since f(x) is replaced with f(-x). However, cosx is symmetric along that axis so there is no change on the graph. Also, the 2 factor means that the function is compressed along the x-axis, since now f(2) corresponds to f(1) etc. (if we substitute 1 in the cos(2x), it is as if substituting 2 in the origninal function cosx). Finally, we have that the factor 3 in front of cos, implies that the function is dilated along the y-axis; the highs become 3 times higher and the lows 3 times low.
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Answer:
Step-by-step explanation:
A quadratic function y=ax^2 +bx +c is symmetric about the vertical line x=-b/(2a). That is the x-coordinate of the vertex (maximum or minimum).
Here, we have ...
h = -16t^2 +44t +5
t = -44/(2(-16)) = 11/8 = 1.375
It takes 1.375 seconds for the ball to reach its maximum height.
The height at that time is ...
h = (-16(11/8) +44)(11/8) +5 = (-22 +44)(11/8) +5 = 121/4 +5 = 141/4 = 35.25
The maximum height is 35.25 feet.
Answer:
6.93 lbs.
Step-by-step explanation:
The weight on the moon is approximately 16.5% of what you would weigh on Earth. Using this information, we can say that 16.5% of 42 lbs would equal how much the object would weigh on the moon.
I prefer to convert percentages the decimal way, so let's do it that way. 16.5% is 0.165 as a decimal, so now all we have to do is multiply 0.165 by 42 (since we are saying 16.5% of 42 lbs), and we get 6.93 lbs.
Hope this helps! :)
Answer:
The expression for c is
Step-by-step explanation:
The given equation is
To find an expression that represents,c we need to make c the subject.
Add b to both sides
We now divide both sides by 'a'
Simplify the LHS to get:
Answer:
Step-by-step explanation:
area=1/2×24×10=120 ft²
