Let f (x) = -1/2(x + 2)+ 5
1 answer:
Answer:
Rate of change = -1
Step-by-step explanation:
Given:
f(x) = -½(x + 2)² + 5
Required:
Average rate of change from x = -3 to x = 1
Solution:
Rate of change =
Where,
a = -3,
f(a) = f(-3) = -½(-3 + 2)² + 5 = -½(-1)² + 5 = 4.5
b = 1,
f(b) = f(1) = -½(1 + 2)² + 5 = -½(9) + 5 = 0.5
Plug in the values into the formula:
Rate of change =
Rate of change =
Rate of change = -1
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The trigonometric function gives the ratio of different sides of a right-angle triangle. The measure of ∠C is 28°. And the value of b and c is 7.06 and 3.76, respectively.
<h3>What are Trigonometric functions?</h3>The trigonometric function gives the ratio of different sides of a right-angle triangle.
where perpendicular is the side of the triangle which is opposite to the angle, and the hypotenuse is the longest side of the triangle which is opposite the 90° angle.
The sum of all the angles can be written as,
∠A + ∠B + ∠C = 180°
90° + 62° + ∠C = 180°
∠C = 28°
Sin(∠B) = AC/BC
Sin(∠B) = b/8
b = 8 × Sin(62°)
b = 7.06
Cos(∠B) = AB/BC
Cos(∠B) = c/8
c = 8 × Cos(62°)
c = 3.76
Hence, the measure of ∠C is 28°. And the value of b and c is 7.06 and 3.76, respectively.
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Answer: V = 193.25π
Step-by-step explanation: The method to calculate volume of a solid of revolution is given by an integral of the form:
V =
f(x) is the area is the function that rotated forms the solid.
For f(x)=y= and solid delimited by x = 2 and x = 4:
V =
V =
V =
V =
V = 193.25π
The volume of a solid formed by y = and delimited by x = 2 and x = 4
is 193.25π cubic units.