<h3>
Answer: -35</h3>
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Explanation:
Let y = -3*f(-3) + 2*f(3)
The goal is to find the value of y as some single numeric value.
We know that f(x) is an odd function. This means that
f(-x) = -f(x)
For all x in the domain of f(x).
Based on that, we can say
f(-3) = -f(3)
and,
y = -3*f(-3) + 2f(3)
-1*y = -1*(-3*f(-3) + 2*f(3)) ... multiply both sides by -1
-y = 3*f(-3) - 2*f(3)
-y = 3*f(-3) + 2*(-f(3))
-y = 3*f(-3) + 2*f(-3)
-y = 3*7 + 2*7 .... f(-3) replaced with 7
-y = 21+14
-y = 35
y = -35
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Here's a slightly different approach
f(-3) = 7
-f(3) = 7
Since f(-3) = -f(3)
We can then transform -f(3) = 7 into f(3) = -7 after multiplying both sides by -1
Therefore,
y = -3*f(-3) + 2f(3)
y = -3*7 + 2(-7)
y = -21 - 14
y = -35
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There are probably other routes to solve this problem.
Whichever path you take, you should find that -3*f(-3) + 2f(3) = -35
Answer:
7
Step-by-step explanation:
The x-intercept is the x-value when y=0, so we plug in y=0,
x=-2(0)+7
x=0+7
x=7
So the x-intercept is 7
Step-by-step explanation:
substitution:
7x-9= 3x-1
4x= 8
x=2
One meter is 100 centimeters. 100 meters is then 100*100, that's 10000, or ten thousand centimeters.
The surface area of the figure is 96 + 64π ⇒ 1st answer
Step-by-step explanation:
* Lats revise how to find the surface area of the cylinder
- The surface area = lateral area + 2 × area of one base
- The lateral area = perimeter of the base × its height
* Lets solve the problem
- The figure is have cylinder
- Its diameter = 8 cm
∴ Its radius = 8 ÷ 2 = 4 cm
- Its height = 12 cm
∵ The perimeter of the semi-circle = πr
∴ The perimeter of the base = 4π cm
∵ The area of semi-circle = 1/2 πr²
∴ The area of the base = 1/2 × π × 4² = 8π cm²
* Now lets find the surface area of the half-cylinder
- SA = lateral area + 2 × area of one base + the rectangular face
∵ LA = perimeter of base × its height
∴ LA = 4π × 12 = 48π cm²
∵ The dimensions of the rectangular face are the diameter and the
height of the cylinder
∴ The area of the rectangular face = 8 × 12 = 96 cm²
∵ The area of the two bases = 2 × 8π = 16π cm²
∴ SA = 48π + 16π + 96 = 64π + 96 cm²
* The surface area of the figure is 96 + 64π