First we use sin(a+b)= sinacosb+sinbcosa
and cos(a+b)=cosa cosb -sinasinb
tan(x+pi/2)= sin(x+pi/2) / cos(x+pi/2)
and sin(x+pi/2) = sinxcospi/2 + sinpi/2cosx =cosx,
<span>cos(x+pi/2) = cosxcospi/2- sinxsinpi/2= - sinx,
</span> because <span>cospi/2 =0, </span>and <span>sinpi/2=1
</span><span>=tan(x+pi/2)= sin(x+pi/2) / cos(x+pi/2)= cosx / -sinx = -1/tanx = -cotx
</span>from where <span>tan(x+pi/2)=-cotx</span>
Using S = ut + 1/2gt², from rest, u = 0
S = 1/2gt², g ≈ 9.8 m/s²
S = <span>1/2 *9.8*3²
</span>S = 0.5<span> *9.8*3*3
</span>
<span>S ≈ 44.1 m</span>
Answer:
Freezer A is better option as price per cubic foot is less for Freezer A
Step-by-step explanation:
Data provided in the question:
Measure of Freezer A = 1 ft × 1 ft × 5 ft
Measure of Freezer B = 1.5 ft × 1.5 ft × 4 ft
Price of Freezer A = $300
Price of Freezer B = $600
Now,
Volume of Freezer A = 1 ft × 1 ft × 5 ft
= 5 ft³
Volume of Freezer B = 1.5 ft × 1.5 ft × 4 ft
= 9 ft³
Now,
Price per cubic foot for Freezer A = $300 ÷ 5 ft³
= $60/ft³
Price per cubic foot for Freezer B = $600 ÷ 9 ft³
= $66.67/ft³
Hence,
Freezer A is better option as price per cubic foot is less for Freezer A
Answer:
For the first 30 minutes, we will have a line with a given steepness, this will represent the 30 minutes riding at a fast pace.
Then he stops for 20 minutes, we will represent this with a constant line.
Then he again moves for another 30 minutes, but with a slower pace than in the first 30 minutes, then this line will be less steep than the first line.
A sketch of this situation can be seen below.
