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uranmaximum [27]
3 years ago
13

18. Let z = a + bi represent a general complex number. As noted in the lesson, the conjugate of z, abbreviated conj(z) or conj(a

+ bi) is the complex number a-bi. Also, the modulus of z, modulus(z) is the "size" of z, or √(a2 + b2). Which of the following is true for all complex numbers?
A) All of the following
B) z*conj(z) = [modulus(z)]2
C) z + conj(z) = 2a
D) z - conj(z) = 2bi
E) None of the above
19. Using the definition of "size" of z from problem #18, which of the following is largest?
A) 3i
B) -7
C) 4
D) -2i
E) 4 + 4i
F) None of the above
Mathematics
1 answer:
AnnyKZ [126]3 years ago
5 0

Question (18):

Answer: (A) All of the following

(I am using z^* in place of conj(z)

z*z^*=(a+ib)(a-ib)=a^2-(ib)^2= a^2+b^2=\mbox{modulus(z)}^2

z+z^*=a+ib+a-ib=2a\\z-z^*=a+ib-a+ib=2bi


Question (19):

Answer: (B) -7

modulus of -7 is sqrt(49)=7

the other choices are all < 7


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The number of salmon swimming upstream to spawn is approximated by the following function:
umka2103 [35]

Answer:

The water temperature that produces the maximum number of salmon swimming upstream is approximately 12.305 degrees Celsius.

Step-by-step explanation:

Let S(x) = -x^{3}+2\cdot x^{2}+405\cdot x +4965, for 6 \leq x \leq 20. x represents the temperature of the water, measured in degrees Celsius, and S is the number of salmon swimming upstream to spawn, dimensionless.

We compute the first and second derivatives of the function:

S'(x) = -3\cdot x^{2}+4\cdot x +405 (Eq. 1)

S''(x) = -6\cdot x +4 (Eq. 2)

Then we equalize (Eq. 1) to zero and solve for x:

-3\cdot x^{2}+4\cdot x +405 = 0

And all roots are found by Quadratic Formula:

x_{1} \approx 12.305\,^{\circ}C, x_{2}\approx -10.971\,^{\circ}C

Only the first root is inside the given interval of the function. Hence, the correct answer is:

x \approx 12.305\,^{\circ}C

Now we evaluate the second derivative at given result. That is:

S''(12.305) = -6\cdot (12.305)+4

S''(12.305) = -69.83

According to the Second Derivative Test, a negative value means that critical value leads to a maximum. In consequence, the water temperature that produces the maximum number of salmon swimming upstream is approximately 12.305 degrees Celsius.

5 0
3 years ago
Apex Grocery wants to build a warehouse that is exactly five miles from each of the routes between stores L, M, and N. Which con
Elanso [62]

Answer: Option C - Construction Y because point E is the circumcentre of triangle LMN.

Point E is the best location for the warehouse as it is exactly equidistant from the three stores at L, M and N.

Step-by-step explanation:

Before solving an algebra problem, it sometimes helps to get a geometric picture of what's happening. Geometry says that three points determine a circle - in other words, given three points that are not

all on the same line, there is exactly one circle which passes through all 3. Finding the point equidistant from the 3 points is the same thing as finding the center of the circle that passes through all of them (since all points on a circle are equidistant from the center).

Our points are L, M and N. Draw the lines LM, LN and MN to form a triangle. Now construct the perpendicular bisectors of any two of the lines, and their intersection, point E, will be the center of this circle.

As shown in the Construction Y because E is the circumcentre of triangle LMN.

This is the best location for the warehouse as it is exactly equidistant from the three stores at L, M and N.

QED!

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3 years ago
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mr Goodwill [35]

Answer:

y = 8x

Step-by-step explanation:

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3 years ago
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Answer:

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Step-by-step explanation:

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2 years ago
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Answer:

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Your slope should be -2/5

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Hope I helped

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3 years ago
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