<h3>
Answer: ds/dt = 11</h3>
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Work Shown:
Before we can use derivatives, we need to find the value of s when (x,y) = (15,20)
s^2 = x^2+y^2
s^2 = 15^2+20^2
s^2 = 225+400
s^2 = 625
s = sqrt(625)
s = 25
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Now we can apply the derivative to both sides to get the following. Don't forget to use the chain rule.
s^2 = x^2 + y^2
d/dt[s^2] = d/dt[x^2 + y^2]
d/dt[s^2] = d/dt[x^2] + d/dt[y^2]
2s*ds/dt = 2x*dx/dt + 2y*dy/dt
2(25)*ds/dt = 2(15)*5 + 2(20)*(10)
50*ds/dt = 150 + 400
50*ds/dt = 550
ds/dt = 550/50
ds/dt = 11
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Side note: The information t = 40 is never used. It's just extra info.
The measure of m<JMO is 20 degrees
The triangle JOK is a 60 degrees equilateral triangle. Hence the measure of m<O at the center is 60 degrees.
<h3>Angle at a point</h3>
- The sum of the angle at a point is 360 degrees.
Since the base angles of triangle KOL and OLM are equal hence;
- m<KOL + m<MOL + m<JOM + m<JOK = 360 (angle at a point)
Substitute the base angles and the equilateral angles to get angle JOM
80 + 80 + m<JOM + 60 = 360
m<JOM = 360 - 360 - 220
m<JOM = 140 degrees
<h3>Sum of angles in a triangle</h3>
Since the sum of angle in the triangle JOM is 180 degrees, hence;
2m<JMO + m<JOM = 180
2m<JMO = 180 - 140
2m<JMO = 40
m<JMO = 20 degrees
Hence the measure of m<JMO is 20 degrees
Learn more on angles here: brainly.com/question/25770607
This is an exponential equation with a starting value of 12000 and an increase of 15% each years.
The following are true:
C. Each year, it increases by 15%
E. The painting's value was 12,000 at the time is was sold.
I hope you do well on your quiz or test!
Subtraction of a number from x represents a shift towards right. So this means g(x) has been shifted 4 units to right. Addition of a number to the function value represents a vertical shift. So g(x) has been shifted 3 units up to get f(x).
So, we can write f(x) as:
f(x) = g(x - 4) + 3
So, translate g(x) 4 units to right and 3 units up to get f(x).
Thus, option C is the correct answer