multiplied by
= 75 hours
4 and a half hour repairs 6% of the entire boat so it is
4 1/2 multiplied by 6/100's inverse number
g(x) is a shift of 8 units to the left and 4 units of f(x), then the correct statement is B.
<h3>
Which statement compares the graph of the two functions?</h3>
First, a vertical shift of N units is written as:
g(x) = f(x) + N
- if N > 0 the shift is upwards.
- If N < 0 the shift is downwards.
A horizontal shift of N units is written as:
g(x) = f(x + N).
- if N < 0, the shift is to the right.
- If N > 0, the shift is to the left.
In this case, we have:
g(x) = f(x + 8) + 4
So g(x) is a shift of 8 units to the left and 4 units of f(x), then the correct statement is B.
If you want to learn more about translations:
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There are 12 inches in a foot, so 9ft = 108in. Also, 80% = 0.8. Therefore the formula is:
h(n) = 108 * 0.8^n.
To find the bounce height after 10 bounces, substitute n=10 into the equation:
h(n) = 108 * 0.8^10 = 11.60in (2.d.p.).
Finally to find how many bounces happen before the height is less than one inch, substitute h(n) = 1, then rearrage with logarithms to solve for the power, x:
108 * 0.8^x = 1;
0.8^x = 1/108;
Ln(0.8^x) = ln(1/108);
xln(0.8) = ln(1\108);
x = ln(1/108) / ln(0.8) = -4.682 / -0.223 = 21 bounces
x = 6
The average of 4 numbers is 6, which means that (3 + 5 + 10 + x) all divided by 4 is 6. That means that 3 + 5 + 10 + x = 24, because 24/4 is 6.
18 + x = 24, subtract 18 from 24 to get x = 6.
The maximum height the ball achieves before landing is 682.276 meters at t = 0.
<h3>What are maxima and minima?</h3>
Maxima and minima of a function are the extreme within the range, in other words, the maximum value of a function at a certain point is called maxima and the minimum value of a function at a certain point is called minima.
We have a function:
h(t) = -4.9t² + 682.276
Which represents the ball's height h at time t seconds.
To find the maximum height first find the first derivative of the function and equate it to zero
h'(t) = -9.8t = 0
t = 0
Find second derivative:
h''(t) = -9.8
At t = 0; h''(0) < 0 which means at t = 0 the function will be maximum.
Maximum height at t = 0:
h(0) = 682.276 meters
Thus, the maximum height the ball achieves before landing is 682.276 meters at t = 0.
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