Answer:
(0,-5)
Step-by-step explanation:
Terminal minus initial. (3-3, -7+2) = (0,-5)
A) cos a = (√22)/5; tan a = (√66)/22
B) sin a = (2√2)/3; tan a = 2√2
C) sin a = (√30)/6; cos a = (√6)/6
D) sin a = 3/5; tan a = 3/4
E) sin a = (5√26)/26; cos a = (√26)/26
F) sin a = 3/5; tan a = 3/4
Explanation
The ratio for sine is opposite/hypotenuse. This means the side opposite the angle is √3 and the hypotenuse is 5. Using the Pythagorean theorem to find the adjacent side,
(√3)² + A² = 5²
3+A² = 25
A² = 22
A=√22
This means that cos a = adjacent/hypotenuse = (√22)/5 and tan a = opposite/adjacent = (√3)/(√22) = (√66)/22.
B) The ratio for cosine is adjacent/hypotenuse; this means the side adjacent to the angle is 1 and the hypotenuse is 3. Using the Pythagorean theorem to find the side opposite the angle (p),
1² + p² = 3²
1+p² = 9
p² = 8
p=√8 = 2√2
This means that sin a = opposite/hypotenuse = (2√2)/3 and tan a = opposite/adjacent = (2√2)/1 = 2√2.
C) The ratio for tangent is opposite/adjacent; this means that the side opposite the angle is √5 and the side adjacent the angle is 1. Using the Pythagorean theorem to find the hypotenuse,
(√5)²+1² = H²
5+1=H²
6=H²
√6 = H
This means that sin a = opposite/hypotenuse = (√5)/(√6) = (√30)/6 and cos a = adjacent/hypotenuse = 1/(√6) = (√6)/6.
D) The ratio for cosine is adjacent/hypotenuse; this means that the side adjacent the angle is 4 and the hypotenuse is 5. Using the Pythagorean theorem to find the side opposite the angle, p:
4²+p²=5²
16+p²=25
p²=9
p=3
This means that sin a = opposite/hypotenuse = 3/5 and tan a = opposite/adjacent = 3/4.
E) The ratio for tangent is opposite/adjacent;; this means that the side opposite the angle is 5 and the side adjacent the angle is 1. Using the Pythagorean theorem to find the hypotenuse,
5²+1²=H²
25+1=H²
26=H²
√26 = H
This means that sin a = opposite/hypotenuse = 5/(√26) = (5√26)/26 and cos a = adjacent/hypotenuse = 1/(√26) = √26/26.
F) 0.8 = 8/10; The ratio for cosine is adjacent/hypotenuse. This means that the side adjacent the angle is 8 and the hypotenuse is 10. Using the Pythagorean theorem to find the side opposite the angle, p:
8²+p² = 10²
64+p² = 100
p² = 36
p=6
This means that sin a = opposite/hypotenuse = 6/10 = 3/5 and tan a = opposite/adjacent = 6/8 = 3/4.
Answer:
x=26
Step-by-step explanation:
3x +12 =90
subtract 12 from each side
3x=78
divide 3 from each side
x=26
Answer:
15
Step-by-step explanation:
hope this helps
Answers:
<em>How much did the temperature change from Sunday High to Mondays High?</em>
Change = 4 °C
<em>What was the difference between the high temperatures on Friday and Wednesday?</em>
Difference = 10 °C
Explanation:
Taking into account the graph, we get that the high temperature each day is:
Sunday: -10°C
Monday: -6 °C
Tuesday: - 4 °C
Wednesday: -6 °C
Thursday: 0 °C
Friday: 4 °C
Saturday: -2 °C
So, the change from Sunday High to Mondays High can be calculated as:
Change = Monday - Sunday
Change = -6 °C - (- 10 °C)
Change = -6 °C + 10 °C
Change = 4 °C
In the same way, the difference between the high temperatures on Friday and Wednesday can be calculated as:
Difference = Friday - Wednesday
Difference = 4 °C - (-6 °C)
Difference = 4 °C + 6 °C
Difference = 10 °C
Therefore, the answers are:
<em>How much did the temperature change from Sunday High to Mondays High?</em>
Change = 4 °C
<em>What was the difference between the high temperatures on Friday and Wednesday?</em>
Difference = 10 °C
