Answer:
The actual speed = 27.12 mi/h
Direction = 36.5° in NE(north of east)
Step-by-step explanation:
As given , A hot air balloon is flying at a constant speed of 20 mi/h at a bearing of N 36° E.
⇒θ = 36°
Let v₀ be the constant speed, then v₀ = 20
Let vₓ be the speed in East direction
be the speed in North direction
So,
vₓ = v₀ sin(θ) = 20 sin(36°) + 10 ( As given, There is a 10mi/h cross wind blowing due east.)
⇒vₓ = 20(0.588) + 10 = 11.76 + 10 = 21.76 mi/h
and = v₀ cos(θ) = 20 cos(36°) = 20(0.809) = 16.18 mi/h
Now,
the actual speed = √(vₓ)² + ()²
= √(21.76)² + (16.18)²
= √473.498 + 261.792
= √735.29 = 27.12
⇒The actual speed = 27.12 mi/h
Now,
Direction = θ = 
⇒ Direction = 36.5° in NE(north of east)
Answer:
287.1 inches of the canvas.
Step-by-step explanation:
To solve this, we need to first figure out the total area of the canvas. To do that, multiply width by height.
29*33=957
Now set up your equation for solving for the area of the canvas that the rose covers.
x/957=30/100
We did it where: x is the area of the rose covers, 957 is the amount of inches that the canvas takes up, and the right side of the equation is the percent.
Now cross multiply.
100x=28,710
Now divide both sides by 100.
x=287.1
The red rose covers 287.1 inches of the canvas.
John has x amount of dogs. Solve for x to find how many dogs john has.
Let,
f(x) = -2x+34
g(x) = (-x/3) - 10
h(x) = -|3x|
k(x) = (x-2)^2
This is a trial and error type of problem (aka "guess and check"). There are 24 combinations to try out for each problem, so it might take a while. It turns out that
g(h(k(f(15)))) = -6
f(k(g(h(8)))) = 2
So the order for part A should be: f, k, h, g
The order for part B should be: h, g, k f
note how I'm working from the right and moving left (working inside and moving out).
Here's proof of both claims
-----------------------------------------
Proof of Claim 1:
f(x) = -2x+34
f(15) = -2(15)+34
f(15) = 4
-----------------
k(x) = (x-2)^2
k(f(15)) = (f(15)-2)^2
k(f(15)) = (4-2)^2
k(f(15)) = 4
-----------------
h(x) = -|3x|
h(k(f(15))) = -|3*k(f(15))|
h(k(f(15))) = -|3*4|
h(k(f(15))) = -12
-----------------
g(x) = (-x/3) - 10
g(h(k(f(15))) ) = (-h(k(f(15))) /3) - 10
g(h(k(f(15))) ) = (-(-12) /3) - 10
g(h(k(f(15))) ) = -6
-----------------------------------------
Proof of Claim 2:
h(x) = -|3x|
h(8) = -|3*8|
h(8) = -24
---------------
g(x) = (-x/3) - 10
g(h(8)) = (-h(8)/3) - 10
g(h(8)) = (-(-24)/3) - 10
g(h(8)) = -2
---------------
k(x) = (x-2)^2
k(g(h(8))) = (g(h(8))-2)^2
k(g(h(8))) = (-2-2)^2
k(g(h(8))) = 16
---------------
f(x) = -2x+34
f(k(g(h(8))) ) = -2*(k(g(h(8))) )+34
f(k(g(h(8))) ) = -2*(16)+34
f(k(g(h(8))) ) = 2
