A circle is a geometric object that has symmetry about the vertical and horizontal lines through its center. When the circle is a unit circle (of radius 1) centered on the origin of the x-y plane, points in the first quadrant can be reflected across the x- or y- axes (or both) to give points in the other quadrants.
That is, if the terminal ray of an angle intersects the unit circle in the first quadrant, the point of intersection reflected across the y-axis will give an angle whose measure is the original angle subtracted from the measure of a half-circle. Since the measure of a half-circle is π radians, the reflection of the angle π/6 radians will be the angle π-π/6 = 5π/6 radians.
Reflecting 1st-quadrant angles across the origin into the third quadrant adds π radians to their measure. Reflecting them across the x-axis into the 4th quadrant gives an angle whose measure is 2π radians minus the measure of the original angle.
Answer:
Stacy made £25.2 from the 18 loaves of bread. So She made £5.20 as a profit.
Step-by-step explanation:
18 loaves of bread × £1.4 = £25.2 Round it up = £25
£25.20 - £20 = £5.20 Round it up = £5
Stacy Made about £5 as profit.
Answer: 
Step-by-step explanation:
First, we need to find the common denominator
The easiest way to do this is by multiplying the two given denominators, which are 2 and 5.
2 × 5 = 10
So, our common denominator is 10. Then, multiply the numerators of the two fractions by 2 and 5. Here's why:
= 
We multiplied the top and bottom by 2 to make sure our new fraction stays equivalent to the original fraction.
Do the same thing for the other one:
= 
Finally, subtract the two fractions to find the difference between the two times:
=
The reason we used the common denominator is because we can only add or subtract fractions if they have the same denominator.
Answer:
[See Below]
Step-by-step explanation:
✦ So it must add up to 360dg so add:
✧ 115dg + 85dg + 60dg = 260dg
✦ Now subtract:
✧ 360dg - 260dg = 100dg
So X would be 100 degrees.
~<em>Hope this helps Mate. If you need anything feel free to message me. </em>
Answer:
y = 1/e
y = 0.37
Step-by-step explanation:
y = (ln x)/x; (e, 1/e)
Step 1
Find the point of tangency.
It's given as (e,1/e) or (2.72,0.37)
Step 2
Find the first derivative, and evaluate it at x=e
Using product rule.
d(uv) = udv + vdu
Where u = lnx and v = 1/x
du = 1/x , dv = -1/x^2
f'(x) = -lnx/x^2 +1/x^2
f'(x) = (1-lnx)/x^2
At x = e
f'(e) = (1-lne)/e^2
f'(e) = 0
The slope of the tangent line at this point is m= 0
Step 3
Find the equation of the tangent line at (e,1/e) with a slope of m=0
y−y1 = m(x - x1)
y-(1/e) = 0(x-1)
y = 1/e
y = 0.37
