David wants to install a fence around his garden. The garden is rectangular and has an area of 240 square feet. One side of the
garden is along the street and is 12 feet long. For this side of the garden, David will use fencing that costs $18 per linear foot. For the other three sides of the garden, David will use fencing that costs $15 per linear foot. What is the total cost of fencing? $756 $996 $1,032
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Answer:0.246 ft/s
Step-by-step explanation: As the worker starts moving and stops 10 feet away from the side rope connected to the load, it creates a right triangle, as illustrated in the image.
V = s/t... equation 1
S = distance the worker travels while pulling the rope = 10 ft
V = worker's velocity = 2 ft/s
T = time it takes for the worker to cover 10 ft = the same time the load takes to rise = 5 seconds
Using Pythagorean theorem to find the distance from the pulley to the new position of the worker
Square root of (40^2 + 10^2) = 41.23 ft
Distance covered by load = D = 41.23 - 40
= 1.23 ft
Load speed = D/t...equation 2
Substituting D and t into equation 2 gives us
Load speed = 1.23/5 = 0.246 ft/s
Answer:
Detailed explanation:
* Let’s clarify the procedure for solving this problem
- An exponential function can be expressed as , where
a signifies the starting amount (x = 0), and b denotes the growth factor
- If b > 1, it qualifies as an exponential growth function
- If 0 < b < 1, it is categorized as an exponential decay function
- Horizontal translation to the right by h units results in the new function being
- Conversely, if translated to the left by h units, the function modifies to
- A vertical upward shift by k units alters the function to
- A vertical downward shift by k units means the new function accounts for
* Now, let’s solve the problem
∵ f(x) is an exponential function
∵ The points (0, 1), (1, 10), (2, 100) are points of f(x)
- g(x) is the transformation of f(x)
∵ The points (3, 1), (4, 10), (5, 100) belong to g(x)
∵ The point (0, 1) on f(x) transforms to (3, 1) on g(x)
∵ The point (1, 10) on f(x) transforms to (4, 10) on g(x)
∵ The point (2, 100) on f(x) translates to (5, 100) on g(x)
∵ Notably, all y-coordinates of f(x) match those of g(x)
indicating no vertical translation
∴ Hence, no vertical translation occurred
∵ The x-coordinates of f(x) are increased by
3 units to yield the x-coordinates for g(x)
∴ This shows that f(x) is translated 3 units to the right
∵
∴
- Refer to the corresponding graph for greater clarity
# The red curve denotes f(x)
# The blue curve signifies g(x)
