The line containing the vector <em>q</em> can be obtained by scaling <em>q</em> by an arbitrary scalar <em>t</em>. To make this line pass through the point <em>p</em>, translate this line by a vector <em>p</em> pointing from the origin to <em>p</em>.
So the line we want has equation
<em>r</em>(<em>t</em>) = <em>q</em><em>t</em> + <em>p</em> = (14, -8)<em>t</em> + (-4, 12) = (14<em>t</em> - 4, 12-8<em>t</em>)
where <em>t</em> is any real number.
(w - 6)(w + 2)
w^2 + 2w - 6w - 12 =
w^2 - 4w - 12 <===
Answer:
The diameter decreases at a rate of -0.0477 cm/min when it is 10 cm.
Step-by-step explanation:
Surface area of a snowball:
A snowball has a spheric format, which means that it's surface area is given by:
In which r is the radius, which is half the diameter. In function of the diameter, the area is given by:
Solving the question:
To solve this question, we have to implicitly derivate the area in function of t. So
Snowball melts so that its surface area decreases at a rate of 3 cm2/min
This means that
Find the rate at which the diameter decreases when the diameter is 10 cm.
This is when . So
The diameter decreases at a rate of -0.0477 cm/min when it is 10 cm.
Answer:
0.1393 = 13.93% probability that an order of 50 units will have one or more faulty units.
Step-by-step explanation:
Mean for a number of units, which means that the Poisson distribution is used to solve this question.
Poisson Distribution:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
In which
x is the number of sucesses
e = 2.71828 is the Euler number
is the mean in the given interval.
Mean:
3 defective for 1000, how many for 50?
3 - 1000
- 50
Applying cross multiplication:
What is the probability that an order of 50 units will have one or more faulty units?
This is:
In which
0.1393 = 13.93% probability that an order of 50 units will have one or more faulty units.