Answer:
see below
Step-by-step explanation:
prove: sin²x cos²y - cos²x sin²y ≡ sin²x - sin²y
we notice that the Right side only has sin² functions, hence we can start by trying to remove the cos² functions from the Left side.
Recall the identity: sin²α + cos²α = 1 , can be rearranged to give us:
cos²α = 1 - sin²a.
If we apply this to the left side of our equation, then
cos²y = 1-sin²y, and cos²x = 1-sin²x
Substituting these into the left side of the equation:
sin²x cos²y - cos²x sin²y
= sin²x (1-sin²y) - (1-sin²x ) sin²y
= sin²x - (sin²x sin²y) - sin²y + (sin²x sin²y)
= sin²x - sin²y
= Right Side of equation (Proven!)
Kenyan = k
$3.50 per pound
Sri Lankan = s
$5.60 per pound
6lbs of blend
$28.35
s+k = 6
3.50k + 5.60s = 28.35
where:
k = lbs of kenyan
s = lbs of Sri Lankan
Solve the system
s+k = 6
3.50k + 5.60s = 28.35
solve the first equation for s:
s = 6-k
Replace in the second equation:
3.50k + 5.60 (6-k) = 28.35
3.50k + 5.60(6)+ 5.60(-k) = 28.35
3.50k + 33.6 - 5.60k = 28.35
3.50k - 5.60k = 28.35-33.6
-2.1k= -5.25
k= -5.25/-2.1
k= 2.5 lbs
Replace k on any equation and solve for s
s+k= 6
s+ 2.5 = 6
s= 6-2.5
s= 3.5 lbs
Answer:
105.12 ft^2
Step-by-step explanation:
Area of a rectangle: bh
In this case 8*10.... so area of the rectangle is 80
Area of a circle: pir^2
Half it for a semicircle.
so 1/2 pi r^2
radius is 4 cuz its half of 8.
so 1/2(3.14)(4^2)=(0.5)(3.14)(16)=25.12
Now add up 80+25.12
Total is 105.12
Hope I helped :)
The hypotenuse formula is a^2+b^2=c^2
so each side a=1
b=1
1^2 +1^2=c^2
1+1= c^2 so the hypotenuse equals 2
