Solution :
We know, cot 2θ = 1/tan 2θ
Multiplying tan 2θ both side of the given equation.
tan²2θ - 3tan 2θ - 10 = 0
tan²2θ - 5tan 2θ + 2tan 2θ - 10 = 0
tan 2θ ( tan 2θ - 5 ) + 2 ( tan 2θ - 5 ) = 0
tan 2θ = -2 or tan 2θ = 5
Therefore,
or ![\theta = \dfrac{tan^{-1} (5)}{2}](https://tex.z-dn.net/?f=%5Ctheta%20%3D%20%5Cdfrac%7Btan%5E%7B-1%7D%20%20%285%29%7D%7B2%7D)
Hence, this is the required solution.
Answer:
$2.59 per pound of bark.
Step-by-step explanation:
Convert 3 tons to pound
1 ton = 2,000 pounds.
3 x 2,000 = 6,000
Now divide the $ and the pounds to find the $ per pound rate
6,000 ÷ 15,540 = 2.59
$2.59
Answer:
A' (6, -2)
B' (4, 2)
C' (10, 6)
Step-by-step explanation:
When you dilate by a scale factor of 2 about the origin, multiply each coordinate point by 2.
(3, -1) × 2 = (6, -2)
(2, 1) × 2 = (4, 2)
(5, 3) × 2 = (10, 6)
You must drive more than 40 miles to make option A the cheaper plan
<em><u>Solution:</u></em>
Two payment options to rent a car
Let "x" be the number of miles driven in one day
<em><u>You can pay $20 a day plus 25¢ a mile (Option A)</u></em>
25 cents is equal to 0.25 dollars
OPTION A : 20 + 0.25x
<em><u>You pay $10 a day plus 50¢ a mile (Option B)</u></em>
50 cents equal to 0.50 dollars
Option B: 10 + 0.50x
<em><u>For what amount of daily miles will option A be the cheaper plan ?</u></em>
For option A to be cheaper, Option A must be less than option B
Option A < Option B
![20 + 0.25x < 10 + 0.50x](https://tex.z-dn.net/?f=20%20%2B%200.25x%20%3C%2010%20%2B%200.50x)
Solve the inequality
Add -0.50x on both sides
![20 +0.25x -0.50x < 10 + 0.50x - 0.50x\\\\20 - 0.25x < 10](https://tex.z-dn.net/?f=20%20%2B0.25x%20-0.50x%20%3C%2010%20%2B%200.50x%20-%200.50x%5C%5C%5C%5C20%20-%200.25x%20%3C%2010)
Add - 20 on both sides,
![20 - 0.25x - 20 < 10 - 20\\\\-0.25x < -10](https://tex.z-dn.net/?f=20%20-%200.25x%20-%2020%20%3C%2010%20-%2020%5C%5C%5C%5C-0.25x%20%3C%20-10)
![\mathrm{Multiply\:both\:sides\:by\:-1\:\left(reverse\:the\:inequality\right)}](https://tex.z-dn.net/?f=%5Cmathrm%7BMultiply%5C%3Aboth%5C%3Asides%5C%3Aby%5C%3A-1%5C%3A%5Cleft%28reverse%5C%3Athe%5C%3Ainequality%5Cright%29%7D)
![0.25x > 10](https://tex.z-dn.net/?f=0.25x%20%3E%2010)
Divide both sides by 0.25
![x > 40](https://tex.z-dn.net/?f=x%20%3E%2040)
Thus you must drive more than 40 miles to make option A the cheaper plan
-0.1 - (x) = 0.3
-0.1 - (-0.4) = 0.3
-0.1 + 0.4 = 0.3
0.3 = 0.3 (true)
-0.4 is your answer
hope this helps