Answer:
a) the product is equal to 953.
b) the product is greater than 443.
c) the product is greater than 181.
Step-by-step explanation:
a) 953 × 63/63 = 953
Therefore, the product is equal to 953.
b) 443 × 86/79 = 482.25
Therefore, the product is greater than 443.
c) 181 × 30/28 = 193.93
Therefore, the product is greater than 181.
Hope this helps =)
A. The range is equal to the highest value minus the lowest value. Since the table given in part A is already in terms of range, then there is no need for a solution. The range of temperature for each month is as it is.
B. For this question, find the largest value which would represent the all-time high. That would be on February at 95°F. The lowest value would also represent the all-time low. That would be on July at 50°F.
C. The range of part B is just the difference of the all-time high and all-time low temperatures.
Range = 95°F - 50°F = 45°F
Step-by-step explanation:
Left hand side:
4 [sin⁶ θ + cos⁶ θ]
Rearrange:
4 [(sin² θ)³ + (cos² θ)³]
Factor the sum of cubes:
4 [(sin² θ + cos² θ) (sin⁴ θ − sin² θ cos² θ + cos⁴ θ)]
Pythagorean identity:
4 [sin⁴ θ − sin² θ cos² θ + cos⁴ θ]
Complete the square:
4 [sin⁴ θ + 2 sin² θ cos² θ + cos⁴ θ − 3 sin² θ cos² θ]
4 [(sin² θ + cos² θ)² − 3 sin² θ cos² θ]
Pythagorean identity:
4 [1 − 3 sin² θ cos² θ]
Rearrange:
4 − 12 sin² θ cos² θ
4 − 3 (2 sin θ cos θ)²
Double angle formula:
4 − 3 (sin (2θ))²
4 − 3 sin² (2θ)
Finally, apply Pythagorean identity and simplify:
4 − 3 (1 − cos² (2θ))
4 − 3 + 3 cos² (2θ)
1 + 3 cos² (2θ)
