34% written in decimal form is .34 (by moving the decimal 2 places left).
.34 written as a fraction is 34/100. Reduce the fraction by dividing numerator and denominator by 2 to get 17/50.
The ratio is 17:50
Volume of the cone is 117.5 π ft³
<u>Step-by-step explanation:</u>
Lateral area of the cone = πrs
s is the slant height = 15 ft
From the above formula, we can find the radius as, 5 ft.
Volume of the cone = π r² h/3
s = √ (5²+ h²)
Squaring on both sides, we will get,
s² = 15² = (5² + h²)
15² - 5² = h²
225 - 25 = 200 = h²
h = √200 = 14.1 ft
Volume = π × 5² × 14.1 / 3 = 117.5 π ft³
(x,y)
to be a function
for every x, ther must be only 1 y to corespond to it
basically, x must NEVER repeat with a different y
list them
ah, we see (1,1) an d(1,-1)
also (4,2) and (4,-2)
double offense
1 repeats with 1 and -1
4 repeats with 2 and -2
not a function
domain is all x values
range is all y values
if they repeat, don't list them
domain=(0,1,4)
range=(-2,-1,0,1,2)
The question is already solved, but I am adding a response so it won't show up on the unanswered list.
Answer:
The rate at which the distance between them is changing at 2:00 p.m. is approximately 1.92 km/h
Step-by-step explanation:
At noon the location of Lan = 300 km north of Makenna
Lan's direction = South
Lan's speed = 60 km/h
Makenna's direction and speed = West at 75 km/h
The distance Lan has traveled at 2:00 PM = 2 h × 60 km/h = 120 km
The distance north between Lan and Makenna at 2:00 p.m = 300 km - 120 km = 180 km
The distance West Makenna has traveled at 2:00 p.m. = 2 h × 75 km/h = 150 km
Let 's' represent the distance between them, let 'y' represent the Lan's position north of Makenna at 2:00 p.m., and let 'x' represent Makenna's position west from Lan at 2:00 p.m.
By Pythagoras' theorem, we have;
s² = x² + y²
The distance between them at 2:00 p.m. s = √(180² + 150²) = 30·√61
ds²/dt = dx²/dt + dy²/dt
2·s·ds/dt = 2·x·dx/dt + 2·y·dy/dt
2×30·√61 × ds/dt = 2×150×75 + 2×180×(-60) = 900
ds/dt = 900/(2×30·√61) ≈ 1.92
The rate at which the distance between them is changing at 2:00 p.m. ds/dt ≈ 1.92 km/h
