Need help with 7 and 8
1 answer:
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Answer:
Step-by-step explanation:
The given equation is
We substitute the ordered pairs to see which ones satisfies the equation.
For (-1,-8), we put x=-1 and y=-8 to get:
This is not true.
For we put x=-1 and
to get
This is true
For (3,3/2) we have 2(3)+6(3/2)=15
This implies 6+9=15
15=15
This is also True
For (-5,25/6), we have 2(-5)+6(25/6)=-10+25=15
This is also true.
Answer:
x= 23.0 (nearest tenth)
Step-by-step explanation:
Please see the attached picture for the full solution.
A suitable vector calculator can perform this arithmetic directly, as can many graphing or scientific calculators that are capable of handling complex numbers. Mine says
(8, 2π/3) - (4, π/3) = (4√3, 5π/6)
The distance is 4√3 ≈ 6.9282.
If you cannot use your calculator for this purpose, you can use the Law of Cosines. You have two sides of the triangle (4 and 8) and the angle between them (2π/3 - π/3), so you have all the information needed.
c² = a² + b² -2ab·cos(C)
c² = 4² + 8² - 2·4·8·cos(π/3)
c² = 16 + 64 - 32 = 48
c = √48 = 4√3
Or, you can simply recognize that the two vectors have the ratio 1:2 and the angle between them is 60°. That is, they are one leg and the hypotenuse of a 30°-60°-90° triangle, so the other leg is 4√3.
(8, 2π/3) - (4, π/3) = (4√3, 5π/6)
The distance is 4√3 ≈ 6.9282.
If you cannot use your calculator for this purpose, you can use the Law of Cosines. You have two sides of the triangle (4 and 8) and the angle between them (2π/3 - π/3), so you have all the information needed.
c² = a² + b² -2ab·cos(C)
c² = 4² + 8² - 2·4·8·cos(π/3)
c² = 16 + 64 - 32 = 48
c = √48 = 4√3
Or, you can simply recognize that the two vectors have the ratio 1:2 and the angle between them is 60°. That is, they are one leg and the hypotenuse of a 30°-60°-90° triangle, so the other leg is 4√3.