Answer: 
Step-by-step explanation:
Given
The diameter of a circle is 
So, the radius is 
The circumference is given by 
Insert the values
Thus, the circumference of the circle is
Answer: 3
Step-by-step explanation:
Katie, Let the number of nickles = N Since there are 7 more dimes than nickles, the number of dimes D = N + 7 Since there are 4 more quarters than nickles, the number of quarters Q = N + 4 Since quarters = $0.25, dimes = $0.10, and nickles = $0.05 and all added together = $4.90 ⇒ 0.25·Q + 0.10·D + 0.05·N = 4.90 Now multiply through by 100 to eliminate the decimal: 25Q + 10D + 5N = 490 Substitute for Q and D 25(N+4) + 10(N+7) + 5N = 490 25N + 10N + 5N +100 +70 = 490 40N + 170 = 490 ⇒ 40N = 320 ⇒ N = 320/40 N = 8, D = N+7 = 15 Q = N+4 = 12 Check: 25(12) + 10(15) + 5(8) = 300 + 150 + 40 = 490
Answer:
34 ft
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you of the relationship between adjacent and opposite sides of a right triangle and the trig function of the associated angle. Here, the relevant relation is ...
Tan = Opposite/Adjacent
tan(10°) = (height of lifeguard)/(distance from shore)
Then the distance from shore is ...
distance from shore = (height of lifeguard)/tan(10°) ≈ (6 ft)/(0.17633)
distance from shore ≈ 34 ft
