A school bus has 12 rows of seats and 4 s students can be seated in each row how many students are riding the bus if 11 Rosenfel
d the students and two students are writing in the 12 row?
Number 2
Number 2
2 answers:
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Answer:
a) f(x) = 4 - x²
The linear approximation of the function at a=1 is
L(x) = 5 - 2x at a = 1
b) The graph of the function and the linear approximation at that point is attached to this solution.
The curve represent the real function,
f(x) = 4 - x²
The straight line represents the linear approximation of the function at a=1.
L(x) = 5 - 2x
The curve and the function evidently cross paths at x=1 and understandably so.
c) Using the linear approximation obtained at a = 1.
f(1.1) = 2.8
Using the actual function, the actual value of f(1.1) = 2.79
d) Percent error = 0.358%
Step-by-step explanation:
f(x) = 4 - x²
a) The linear approximation of the function at the given point is given as
L(x) = f(a) + f'(a) [x - a]
f(x) = 4 - x²
a = 1
f(a) = 4 - 1² = 3
f'(x) = -2x
f'(a) = -2(1) = -2
L(x) = f(a) + f'(a) [x - a]
L(x) = 3 + (-2)(x - 1)
L(x) = 3 -2x + 2
L(x) = 5 - 2x
L(x) = -2x + 5
f(x) = 4 - x²
L(x) = 5 - 2x at a = 1
b) The graph of the function and the linear approximation at that point is attached to this solution.
The curve represent the real function,
f(x) = 4 - x²
The straight line represents the linear approximation of the function at a=1.
L(x) = 5 - 2x
The curve and the function evidently cross paths at x=1 and understandably so.
c) Use the linear approx. to estimate the given fxn value.
f(1.1)
L(x) = 5 - 2x
L(1.1) = 5 - 2(1.1) = 2.8
Using the function, the actual value of f(1.1) = 4 - 1.1² = 2.79
d) Compute the percent error in your approximation, 100*Iapprox-exactI/IexactI, where the exact value is given by a calculator
Percent error
= 100% × (|approx - exact|)/exact
Approximated value = 2.8
Exact value = 2.79
Percent error = 100% × (2.8-2.79)/2.79
Percent error = 0.358%
Hope this Helps!!!
We can draw a right triangle to easily visualize the given problem. Since the ski jumper is 2650 ft from the base of the ski jump, we can consider this as one of the right triangle's legs.
What we're looking for is the height of the ski jump or the other leg of the right triangle. Since the ski jumper looks up at an angle of elevation of 26°, we can use the tangent function to find the missing height. You may refer to the image below to better understand the problem.
Recall that tanθ = (opposite side facing the angle)/(side adjacent to the angle). For this case, we have
Hence, the height of the ski jump (rounded off the nearest whole foot) is 1292 feet.
Answer: 1292 feet
What we're looking for is the height of the ski jump or the other leg of the right triangle. Since the ski jumper looks up at an angle of elevation of 26°, we can use the tangent function to find the missing height. You may refer to the image below to better understand the problem.
Recall that tanθ = (opposite side facing the angle)/(side adjacent to the angle). For this case, we have
Hence, the height of the ski jump (rounded off the nearest whole foot) is 1292 feet.
Answer: 1292 feet