Answer: 8
Step-by-step explanation:
Here we have the equation of a vertical ellipse (this means the major axis is in the y-axis) with a center in the form:
Where is the semimajor axis and is the semiminor axis, being the major axis .
So, if we have this given equation:
Then:
Hence:
This is the major axis of the ellipse
Answer:
Problem 20)
Problem 21)
A)
The velocity function is:
The acceleration function is:
B)
Step-by-step explanation:
Problem 20)
We want to differentiate the equation:
We can take the natural log of both sides. This yields:
Since ln(aᵇ) = bln(a):
Take the derivative of both sides with respect to <em>x: </em>
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Implicitly differentiate the left and use the product rule on the right. Therefore:
Simplify:
Simplify and multiply both sides by <em>y: </em>
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Since <em>y</em> = (cos x)ˣ:
Problem 21)
We are given the position function of a particle:
A)
Recall that the velocity function is the derivative of the position function. Hence:
Differentiate:
The acceleration function is the derivative of the velocity function. Hence:
Differentiate:
B)
The position at <em>t</em> = 0 will be:
The velocity at <em>t</em> = 0 will be:
And the acceleration at <em>t</em> = 0 will be:
Answer:
229.2
Step-by-step explanation:
Remark
There's a lot in this question. The x is not just any x. It is defined and limited by its relationship with the sine function.
The Sin is defined as Opposite over Hypotenuse in a right triangle. The 670 is the Hypotenuse. You know that by the definition of Sine.
So one thing you should always keep in mind: the x because of where it is in the definition, will always be smaller than the Hypotenuse. So you should get a value less than 670.
Formula
Just as you have it
Sin(20) = x / 670
Solution
Multiply both sides by 570
670 * sin(20) = x
sin(20) = 0.3420
x = 670 * 0.3420
x = 229.2
Answer:
Trapezoid
Step-by-step explanation:
The two sloped opposite sides are congruent. The two uncongruent opposite sides are parallel. There are no right angles. You can do this by finding the distance and slopes of the lines.
Not triangle because has four vertices.
Answer:
A = 33.33
Step-by-step explanation:
P = 0.006A^2 - 0.02A + 120
*** P = 126 ***
126 = 0.006A^2 - 0.02A + 120
126 = (3/500)A^2 - (1/50)A + 120
*** multiplied with 500 on both sides ***
63000 = 3A^2 - 10A + 60000
63000 - 3A^2 + 10A - 60000 = 0
3000 - 3A^2 + 10A = 0
3A^2 - 10A - 3000 = 0
3A^2 + 90A - 100A - 3000 = 0
3A(A + 30) - 100(A + 30) = 0
(A + 30)(3A - 100) = 0
A + 30 = 0 | 3A - 100 = 0
A = -30 | 3A = 100
A = -30 | A = 100/3
Human age cannot be negative so
A = 100/3 = 33.33