Answer:
Explanation:
Power P = V² / R
a ) The resistance is changed to 2.90R
Power will become 1 / 2.9 times .
b )The voltage of the battery is now 2.90V, but the resistance is R
P = (2.9V)² / R
= 8.41 x V² / R
So power becomes 8.41 times
c )The resistance is 2.90R and voltage is 2.90V
Power P = (2.9V)² / 2.9 R
= 2.9 V²/R
So power becomes 2.9 times
d ) The resistance is 2.90R and the voltage is V/2.90
Power P = ( V/2.90)² x 1 / 2.90R
1 / ( 2.9 )³ x V² / R
= 1 / 24.389 x V² / R
So power becomes 1 / 24.389 times .
Answer:
Third Option
Explanation:
If we have a vector A = ax + by we know that by definition
cA = cax + cby
Where c is a constant.
In this case we have two vectors
You may notice that vector B has an opposite direction to vector A.
You may also notice that | Ax | is the double of | Bx | and | Ay | is double of |By |
That is to say
So the equation that relates to vectors A and B is:
.
You can verify this relationship by performing the operation
Answer:
Diabetes
Explanation:
Insulin is an important hormone that helps the body convert sugar, starches, and other foods into energy.
A microwaveable cup-of-soup package needs to be constructed in the shape of a cylinder to hold 600 cubic centimeters of soup. The sides and bottom of the container will be made of styrofoam costing 0.02 cents per square centimeter. The top will be made of glued paper, costing 0.05 cents per square centimeter. Find the dimensions for the package that will minimize production costs.
h: height of the cylinder, r: radius of the cylinder
The volume of a cylinder: V=πr2h
Area of the sides: A=2πrh
Area of the top/bottom: A=πr2
The cost of packaging, C=2πrh*0.02+ πr^2*0.02+ πr^2*0.05 subject to the constraint πr^2h=600
C=πr(0.04h+.07r) and the constraint implies h=600/ πr^2
So C=πr(24/πr^2+.07r)=24/r+.07πr^2
C'=-24/r^2+0.14πr=0
r^3=24/0.14π r=3.79 cm
h=600/πr^2=13.3 cm
C=π*3.79*(0.04*13.3+.07*3.79)=9.48cents
C''=0.14π+48/r^3>0 for all r>=0 so our solution is indeed a minimum.
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This is a projectile motion problem, so, we use the formula for trajectory:
y =xtanα + gx^2/2v^2(cosα)^2
where
y is the vertical distance (y = 50 m)
x is the horizontal distance (x=90 m)
α is the angle of trajectory; since it levels of HORIZONTALLY, α = 0°
v is the initial velocity
g is the acceleration due to gravity which is 9.81 m/s^2
Substituting to the formula,
50 =90tan(0°) + (9.81)(90)^2/2v^2(cos0°)^2
v = 28.2 m/s
