The question is an illustration of solving equations using estimates.
The student's strategy makes sense because he uses estimation to solve the given equation
The correct sequence of equation is as follows:
We have:
Add 0 to the equation
Express 0 as 1 - 1
Add another 0
Express 0 as 3 - 3
Rewrite as:
Solve
Read more about estimation and equations at:
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Answer:
y=1/3x -3
Step-by-step explanation:
Slope intercept form is y=mx+b, where m is the <u>slope </u>and b is the <u>y-intercept, </u>or the y-value at which the line intersects the y-axis.
Your slope is 1/3, and your y-int. is -3, so substitute those values in:
y=<u>1/3</u>(x) <u>- 3</u>
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Answer:
90 mph
Step-by-step explanation:
Against wind DATA:
distance = 600 miles ; time = 5 hrs. ; rate = 600/5 = 120 mph
With wind DATA:
distance = 600 miles ; time = 2 hrs ; rate = 600/2 = 300 mph
Equations:
p + w = 300
p - w = 120
2p = 420
p = 210 mph (speed of the plane in still air)
Since p+w = 300, w = 300-210 = 90 mph (speed of the wind)
I'm only going to alter the left hand side. The right side will stay the same the entire time
I'll use the identity tan(x) = sin(x)/cos(x) and cot(x) = cos(x)/sin(x)
I'll also use sin(x+y) = sin(x)cos(y)+cos(x)sin(y) and cos(x+y) = cos(x)cos(y)-sin(x)sin(y)
So with that in mind, this is how the steps would look:
tan(x+pi/2) = -cot x
sin(x+pi/2)/cos(x+pi/2) = -cot x
(sin(x)cos(pi/2)+cos(x)sin(pi/2))/(cos(x)cos(pi/2)-sin(x)sin(pi/2)) = -cot x
(sin(x)*0+cos(x)*1)/(cos(x)*0-sin(x)*1) = -cot x
(0+cos(x))/(-sin(x)-0) = -cot x
(cos(x))/(-sin(x)) = -cot x
-cot x = -cot x
Identity is confirmed
