Mary Beth would like to buy a more fuel-efficient vehicle instead of driving her mom's gas-guzzler. Assuming she can find a car
1 answer:
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Answer:
x = 41.2
Step-by-step explanation:
Assuming the dotted line at the top is parallel to the segment with length x, it follows from the alternate interior angles theorem that the interior angle of the triangle (marked in diagram) is also 27º.
Using SOH-CAH-TOA, we get that tan(27º) = 21/x, so x = 21/tan(27º), which is approximately equal to 41.2.
Answer:
a) is the equation of the curve that makes an angle π/3.
b) is the equation of line through the point (4,4).
Step-by-step explanation:
Given:
A line from origin which makes an angle of with x-axis.
A vertical line from .
We have to write the equation of the curves in Polar or Cartesian format.
Step wise:
a) A line from origin which makes an angle of with x-axis.
To write the equation of the above line in Polar coordinates is more desirable as the angles could be defined well in polar form.
So,
⇒ ...equation (i)
⇒ ...here
is the slope
The slope in terms of (angle) can be written as,
⇒
Plugging the values of the angle, .
⇒ ...equation (ii)
Now re-arranging the equation (i) we can write it as,
⇒
b) A vertical line from .
<em>Note:</em>
<em>The equation of a vertical line always takes the form x = k, where k is any number and k is also the x-intercept .</em>
To write the above point in Cartesian coordinate is more acceptable and easy for us.
⇒
Then,
y = sq-rt(3) x is the equation of the curve that makes an angle π/3.
and x = 3 is the equation of line through the point (4,4).