Answer:
Solutions:
Step-by-step explanation:
Expanding the factored form:
Factoring the second-degree polynomial:
This is true for
KC has a piece of gum stuck to her bike tire, which applies a forward torque (i.e. a force to roll forwards) on the tire's movem
ent. The torque varies in a periodic way that can be modeled approximately by a trigonometric function. When the gum is on the front of the tire, its weight is pulling forwards with a maximum torque of 0.01\text{ Nm}0.01 Nm0, point, 01, start text, space, N, m, end text (Newton metre, the SI unit for torque), and when it's on the back of the tire, it's pulling backwards with a minimum torque of -0.01\text{ Nm}−0.01 Nmminus, 0, point, 01, start text, space, N, m, end text. The maximum torque is reached once in every rotation, which is every 1.21.21, point, 2 meters. The first time it reaches its maximum torque is 0.30.30, point, 3 meters into the race.
Find the formula of the trigonometric function that models the torque \tauτtau the gum applies on the tire ddd meters into the race. Define the function using radians.
Find the formula of the trigonometric function that models the torque \tauτtau the gum applies on the tire ddd meters into the race. Define the function using radians.
2 answers:
Answer:
t(d) = 0.01cos(5π(d-0.3)/3)
Step-by-step explanation:
Since we are given the location of a maximum, it is convenient to use a cosine function to model the torque. The horizontal offset of the function will be 0.3 m, and the horizontal scaling will be such that one period is 1.2 m. The amplitude is given as 0.01 Nm.
The general form is ...
torque = amplitude × cos(2π(d -horizontal offset)/(horizontal scale factor))
We note that 2π/1.2 = 5π/3. Filling in the given values, we have ...
t(d) = 0.01·cos(5(d -0.3)/3)
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Answer:
30 ft
Step-by-step explanation:
This is a classic right triangle problem, where the length of the ladder represents the hypotenuse, where the ladder is lengthwise from the building is the base of the triangle, and what we are looking for is the height of the triangle. Pythagorean's Theorem will help us find this length.
so
1024 - 100 = y^2 and
y = 30.4 so 30 feet
To solve this, we are going to use the compound interest formula: 
where
is the final amount after 
years
is the initial investment
is the interest rate in decimal form
is the number of times the interest is compounded per year
For the first 4 years we know that:
, 
, 
, and since the problem is not specifying how often the interest is communed, we are going to assume it is compounded annually; therefore, 
. Lest replace those values in our formula:
Now, for the next 6 years the intial investment will be the final amount from our previous step, so
. We also know that: 
, 
, and . Lets replace those values in our formula one more time:
We can conclude that Collin will have <span>£3691.41 in his account after 10 years.</span>
where
For the first 4 years we know that:
Now, for the next 6 years the intial investment will be the final amount from our previous step, so
We can conclude that Collin will have <span>£3691.41 in his account after 10 years.</span>