If a point
(
x
,
y
)
is written as
(
r
,
θ
)
in polar coordinates, then
x
=
r
o
s
θ
and
y
=
r
sin
θ
.
As such in polar form equation
x
=
−
3
can be written as
r
cos
θ
=
−
3
or
r
=
−
3
cos
θ
Answer:
55°
Step-by-step explanation:
if an angle is bisected, it get divided into two equal angles .
so, each resulting angle will be half of the angle which is bisected.
hence, measure of each angle formed is
110° / 2 = 55°
He will mix some 20% solution and some 70% solution to make 60% solution.
Let x = number of liters of 20% solution.
Let y = number of liters of 70% solution.
He wants to make 50 liters of 60% solution, so
x + y = 50 First Equation
The amount of acid in x amount of 20% solution is 20% of x, or 0.2x
The amount of acid in y amount of 70% solution is 70% of y, or 0.7y
The amount of acid in 50 liters of 60% solution is 60% of 50 liters, or 0.6 * 50 = 30
Now we add the amounts of acid.
0.2x + 0.7y = 30 Second Equation
x + y = 50
0.2x + 0.7y = 30
-0.2x - 0.2y = -10
0.2x + 0.7y = 30
------------------------
0.5y = 20
y = 40
x + y = 50
x + 40 = 50
x = 10
Answer: He needs 10 liters of 20% solution and 40 liters of 70% solution.
<span>We have this equation:
</span>

and we need to find the value of x.
First of all, we multiply the whole equation for 1/2, so our goal is to isolate x, therefore:
Next step we must do is to apply <span>logarithms:
</span>

Next, we have to apply identities and then to solve the equation:




Finally, we have the value of x which was our goal. This is the answer for the question above:
Half the perimeter is equal to the length plus the width.
326 /2 = 163
Length + width = 163
87 + width = 163
Width = 163 - 87
Width = 76 meters