<h3>
Answer: approximately 1560.1 foot-pounds</h3>
Explanation:
Refer to the diagram below. The angle theta is the angle of elevation formed between the horizontal line and the diagonal force being applied (the pulling force). Let x be the horizontal component pulling force, which is the horizontal portion of the right triangle. We know the hypotenuse of this triangle is 55 pounds as it is the force applied.
Use the cosine ratio to help solve for x. Make sure your calculator is in degree mode.
cos(angle) = adjacent/hypotenuse
cos(19) = x/55
x/55 = cos(19)
x = 55*cos(19)
x = 52.0035216579624 which is approximate
Roughly 52.0035216579624 pounds of force is being applied in a pure horizontal direction. The cart moves 30 feet, so,
work = (force)*(displacement)
work = (52.0035216579624)*(30)
work = 1560.10564973888
work = 1560.1 foot-pounds
A foot-pound is a unit of work, similar to how a joule is as well (though a joule measures in kilograms and meters)
(y + z)³
in expanded form: (y + z) (y + z) (y + z)
y(y + z) + z(y + z) 1st and 2nd set
y² + yz + yz + z² product of 1st and 2nd set
(y² + 2yz + z²)(y + z) multiply with 3rd set
y(y² + 2yz + z²) + z(y² + 2yz + z²)
y³ + 2y²z + yz² + y²z + 2yz² + z³
y³ + 2y²z + y²z + yz² + 2yz² + z³ Group like terms.
y³ + 3y²z + 3yz² + z³ Product of 1st, 2nd, and 3rd set ...2nd CHOICE
Answer:
Step-by-step explanation:
Let the rate at which the bacteria grow be represented by the exponential equation
P(t) = P0e^kt
P(t) is the population of the bacteria after time t
P0 is the initial population
k is the constant of variation
t is the time
If the initial Population is 160 bacteria's, them the equation becomes;
P(t) = 160e^kt
b) if After 5 hours there will be 800 bacteria, this means
at t = 5 p(t) = 800
Substitute and get k
800 = 160e^5k
800/160 = e^5k
5 = e^5k
Apply ln to both sides
Ln5 = lne^5k
ln5 = 5k
k = ln5/5
k = 0.3219
Next is to calculate the population after 7hrs i.e at t = 7
P(7) = 160e^0.3219(7)
P(7) = 160e^2.2532
P(7) = 160(9.5181)
P(7) = 1522.9
Hence the population after 7houra will be approximately 1523populations
c) To calculate the time it will take the population to reach 2790
When p(t) = 2790, t = ?
2790 = 160e^0.3219t
2790/160 = e^0.3219t
17.4375 = e^0.3219t
ln17.4375 = lne^0.3219t
2.8587 = 0.3219t
t = 2.8587/0.3219
t = 8.88 hrs
Hence it will take approximately 9hrs for the population to reach 2790
Here is an attachment with the answer. I hope this helps.
Answer:
7 songs costs $8.4
Step-by-step explanation:
6/5= $1.2 for each song
1.2 times 7= $8.4
7 songs costs $8.4
