<span>\int_c\vec f\cdot d\vec r, in two ways, directly and using stokes' theorem. the vector field \vec f = 5 y\vec i - 5 x\vec j and c is the boundary of s, the part of the surface z = 16 -x^2-y^2 above the xy-plane, oriented upward.</span>
<h3>
Answer: k = 0 or k = 3</h3>
Explanation:
If you have repeated x values, then you wont have a function. For example, the points (1,5) and (1,6) mean we don't have a function since the input x = 1 leads to multiple outputs y = 5 and y = 6 simultaneously. For a function to be possible, we must have any input lead to exactly one output only.
What we do is set the x coordinates (k^2 and 3k) equal to each other and solve for k
k^2 = 3k
k^2-3k = 0
k(k-3) = 0 .... factoring
k = 0 or k-3 = 0 .... zero product property
k = 0 or k = 3
If k = 0, then (k^2,5) becomes (0,5). Also, (3k,6) becomes (0,6). The two points (0,5) and (0,6) mean the graph fails the vertical line test.
Similarly, if k = 3, then (k^2,5) becomes (9,5) and (3k,6) = (9,6). Another vertical line test failure happens here to show we don't have a function.
Answer:
17.8 meters
Step-by-step explanation:
Given:
before expansion railroad rail= 4 km
expansion= 16 cm
railroad makes an isosceles triangle at the center of the rail when it expands
The base of the triangle=4 km
As 1km=100,000 cm
thus 16 cm= 16/100,000 km
each side of this triangle= (4 + 16/100,000) / 2 = 4.0001 / 2 = 2.00008 km
One half of the isosceles triangle makes a right triangle with one of the side =4 / 2 = 2 km
and the hypotenuse = 2.00008 km
Using Pythagoras theorem to find the third side of this right angles triangle:
c^2=a^2+b^2
2.00008^2= 2^2 + b^2
2.00008^2 - 2^2=b^2
b=0.0178 km
b= 17.8 m
hence, approximately 17.8 meters would the center of the rail rise above the ground!
Answer:
Step-by-step explanation:
Hope it helps you
This kind of situation is modelled by Bernoulli's formula. It applies everytime there is an experiments with two possible outcomes repeated n times. Each repetition is independent on the others, and we know the probability of the two outcomes p and 1-p. If we want the outcome with probability p to appear k times, the probability is
In your case, you run the "experiment" 4 times (you choose 4 printers) and want that all of them to be non-defective. A printer is non-defective with probability 1/2, since there are 5 defective and 5 non-defective printers.
So, our model is built with n = k = 4, p = 1-p = 1/2. The probability is
