Compare the functions below: f(x) = −3 sin(x − π) + 2
2 answers:
Given:
f(x) = - 3sin(x - π) + 2
h(x) = (x + 7)² - 1
g(x):
x: 0 1 2 3 4 5 6
g(x): 8 3 0 -1 0 3 8
For the range 0 ≤ x ≤ 6,
(a) f(x) takes a minimum value of -3 + 2 = -1, because the minimum value
for the sine function is -1.
(b) g(x) takes a minimum value of -1 according to the given table.
(c) h(x) takes a minimum value of 7^2 - 1 = 48 when x = 0.
A graph of f(x) and g(x) confirms the conclusions.
Answer: Both f(x) and g(x) have minimum values of -1.
f(x) = - 3sin(x - π) + 2
h(x) = (x + 7)² - 1
g(x):
x: 0 1 2 3 4 5 6
g(x): 8 3 0 -1 0 3 8
For the range 0 ≤ x ≤ 6,
(a) f(x) takes a minimum value of -3 + 2 = -1, because the minimum value
for the sine function is -1.
(b) g(x) takes a minimum value of -1 according to the given table.
(c) h(x) takes a minimum value of 7^2 - 1 = 48 when x = 0.
A graph of f(x) and g(x) confirms the conclusions.
Answer: Both f(x) and g(x) have minimum values of -1.
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Bear in mind that, is an isosceles right-triangle, so, one angle is 90°.
check the picture below.
check the picture below.
Answer:
The base and height of the solid is 5.5cm
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Step-by-step explanation:
Given
Required
Determine the dimensions that maximizes the volume
Let the base dimension be x and the height be h
The volume is calculated as:
181.5 =x^2h
The surface area (S) is calculated as this:
Substitute 181.5 for S
Make h the subject:
Substitute in
To get the maximum, we differentiate V with respect to t and set the differentiation to 0
Set to 0
Multiply through by 4
Recall that:
So, we have:
<em>Hence, the base and height of the solid is 5.5cm</em>