Immediately, by definition of cotangent, we find
tan(α) = 1/cot(α) = 1/(-√3)
⇒ tan(α) = -√3
Given that π/2 < α < π, we know that cos(α) < 0 and sin(α) > 0. In turn, sec(α) < 0 and csc(α) > 0.
Recall the Pythagorean identity,
cos²(α) + sin²(α) = 1
Multiplying both sides by 1/sin²(α) recovers another form of the identity,
cot²(α) + 1 = csc²(α)
Solving for csc(α) above yields
csc(α) = + √(cot²(α) + 1) = √((-√3)² + 1) = √4
⇒ csc(α) = 2
⇒ sin(α) = 1/2
Solve for cos(α) using the first form of the Pythagorean identity:
cos(α) = - √(1 - sin²(α)) = - √(1 - (1/2)²) = - √(3/4)
⇒ cos(α) = -√3/2
⇒ sec(α) = -2/√3
Answer:
See below.
If the correct sum is 1155, then Ken had 495 stamps, and Henry had 660 stamps.
Step-by-step explanation:
Henry had h stamps.
Ken had k stamps.
After giving away 2/3 of his stamps, Henry ended up with 1/3 of his stamps, or h/3.
After giving away 3/4 of his stamps, ken ended up with 1/4 of his stamps, or k/4.
h/3 = k/4
h + k = 1156
4h = 3k
h = 1156 - k
4(1156 - k) = 3k
4624 - 4k = 3k
4624 = 7k
k = 4624/7
Stamps left: 0.25 × 4624/7 = 1156/7
h = 1156 - k
h = 1156 - 4624/7
h = 8092/7 - 4624/7
h = 3468/7 =495.43
Stamps left: 1/3 × 3468/7 = 1156/7
Total number of stamps left: 1156/7 + 1156/7 = 2312/7 = 330.29
The problem is solved correctly, but the numbers given must be incorrect since you cannot have a fraction of a stamp.
Answer:
j = 5.352
Step-by-step explanation:
Simplifying
0.602 = j + -4.75
Reorder the terms:
0.602 = -4.75 + j
Solving
0.602 = -4.75 + j
Add '-1j' to each side of the equation.
0.602 + -1j = -4.75 + j + -1j
Combine like terms: j + -1j = 0
0.602 + -1j = -4.75 + 0
0.602 + -1j = -4.75
Add '-0.602' to each side of the equation.
0.602 + -0.602 + -1j = -4.75 + -0.602
Combine like terms: 0.602 + -0.602 = 0.000
0.000 + -1j = -4.75 + -0.602
-1j = -4.75 + -0.602
Combine like terms: -4.75 + -0.602 = -5.352
-1j = -5.352
Divide each side by '-1'.
j = 5.352
Answer:
7.50h+0.75s 63.75 30
Step-by-step explanation:
7.50 x how many hours + 0.75 x how many sunglasses he sold
7.50 x 6 + 0.75 x 25= 63.75
7.50x8= 60 0.75x40=30 60+30=90
Take the second equation already set to y and substitute it into the first equation for y...
3x + (6 - 4x) = 1 ... now we simplify
3x + 6 - 4x = 1 .....now combine like terms
-x + 6 = 1 .....