Answer:
Step-by-step explanation:
Given: A bushel contains 4 pecks and a peck contains 8 quarts.
i.e. A bush = 4 pecks
A peck = 8 quarts
Then, Number of quarts in 1 bush = 4 (8) =32
Let b = number of bushes and q = number of quarts
Number of quarts(q) in b bushes = 32b
hence, required equation: which describes the relationship between the number of b bushels and the number of q quarts.
Answer:
a) 5.83 cm
b) 34.45°
Step-by-step explanation:
a) From Pythagoras theorem of right triangles, given right triangle ABC:
AB² + BC² = AC²
Therefore:
AC² = 5² + 3²
AC² = 25 + 9 = 34
AC = √34
AC = 5.83 cm
b) From triangle ACD, AC = 5.83 cm, AD = 4 cm and ∠A = 90°.
From Pythagoras theorem of right triangles, given right triangle ACD:
AD² + AC² = DC²
Therefore:
DC² = 5.83² + 4²
DC² = 34 + 16 = 50
DC = √50
DC = 7.07 cm
Let ∠ACD be x. Therefore using sine rule: