6 4/5 as improper fraction is 34/5
5 3/4 as improper fraction is 23/4
3 1/3 by 25/4 is 8/15
14/3 by 3 1/2 is 4/3
3 1/4 by 5 1/2 is 13/22
Take the derivative with respect to t

the maximum and minimum values occur when the tangent line is zero so we set the derivative to zero

divide by w

we add sin(wt) to both sides

divide both sides by cos(wt)

OR

(wt)=2(n*pi-arctan(2^0.5))
(wt)=2(n*pi+arctan(2^-0.5))
where n is an integer
the absolute max and min will be

since 2npi is just the period of cos

substituting our second soultion we get

since 2npi is the period

so the maximum value =

minimum value =
Answer:
6/25 km in 1 min; or 0.24 km/min
Step-by-step explanation:
The info about Angel is not necessary.
Jayden runs 3 laps in 5 mins
Each lap is 2/5 km, so Jayden runs 3 x (2/5 km) in 5 min = 6/5 km in 5 min.
Distance = rate x time
6/5 km = rate (5 min)
We want to isolate r (rate), so divide both sides by 5 min
6/5 km ÷ 5 min = r
6/5 km (1/5 min) = r
6/25 km/min = r (notice how the units worked out correctly to km/min)
So, Jayden runs 6/25 km in 1 min.
Answer:
18.0
Step-by-step explanation:
==>Given:
Triangle with sides, 16, 30, and x, and a measure of an angle corresponding to x = 30°
==>Required:
Value of x to the nearest tenth
==>Solution:
Using the Cosine rule: c² = a² + b² - 2abcos(C)
Let c = x,
a = 16
b = 30
C = 30°
Thus,
c² = 16² + 30² - 2*16*30*cos 30°
c² = 256 + 900 - 960 * 0.8660
c² = 1,156 - 831.36
c² = 324.64
c = √324.64
c = 18.017769
x ≈ 18.0 (rounded to nearest tenth)
Answer:
1. 12
2. the prism with a length of 7 1/2 will have a shorter width, with a width of 6