Slope intercept form of y-3=2/3(x+5)
1 answer:
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The volume of a cone is 
where r = radius and h = height. If the cone has a volume of 94.2 cm³ (I assume you didn't mean m³ because that would be ridiculously huge) and a height of 10 cm, we can plug these values into the formula to find the radius. Don't do any rounding.
Now we know that's going to be the radius of our <em>new </em>cone as well since we're keeping the diameter the same. The volume is going to be double 94.2 which is 188.4. Let's solve for the height.
Now we know that's going to be the radius of our <em>new </em>cone as well since we're keeping the diameter the same. The volume is going to be double 94.2 which is 188.4. Let's solve for the height.
9514 1404 393
Answer:
±√58 ≈ ±7.616
Step-by-step explanation:
The linear combination of sine and cosine functions will have an amplitude that is the root of the sum of the squares of the individual amplitudes.
|x| = √(3² +7²) = √58
The motion is bounded between positions ±√58.
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Here's a way to get to the relation used above.
The sine of the sum of angles is given by ...
sin(θ+c) = sin(θ)cos(c) +cos(θ)sin(c)
If this is multiplied by some amplitude A, then we have ...
A·sin(θ+c) = A·sin(θ)cos(c) +A·cos(θ)sin(c)
Comparing this to the given expression, we find ...
A·cos(c) = 3 and A·sin(c) = -7
We know that sin²+cos² = 1, so the sum of the squares of these values is ...
(A·cos(c))² +(A·sin(c))² = A²(cos(c)² +sin(c)²) = A²(1) = A²
That is, A² = (3)² +(-7)² = 9+49 = 58. This tells us the position function can be written as ...
x = A·sin(θ +c) . . . . for some angle c
x = (√58)sin(θ +c)
This has the bounds ±√58.
