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3 years ago

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Mathematics

1 answer:

Levart [38]3 years ago

3 0

Answer:

Let us say x is a real number and z = a + ib is complex

|x| > 0

|z| = |a + ib| = square-root (a^2 + b^2)

Step-by-step explanation:

|x| > 0 the absolute value of a real number is a nonnegative real number

The |a + ib| = square-root of the sum of the squares of the real components of the complex number

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Premises: All good students are good readers. Some math students are good students. Conclusion: Some math students are good read

just olya [345]

Answer:

Therefore, the conclusion is valid.

The required diagram is shown below:

Step-by-step explanation:

Consider the provided statement.

Premises: All good students are good readers. Some math students are good students.

Conclusion: Some math students are good readers.

It is given that All good students are good readers, that means all good students are the subset of good readers.

Now, it is given that some math students are good students, that means there exist some math student who are good students as well as good reader.

Therefore, the conclusion is valid.

The required diagram is shown below:

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3 years ago

What is the length of the base of a right triangle with an area of 20 square meters and a height of 4 meters? 5 m 10 m 80 m 160

o-na [289]

You find the area of a triangle by using 1/2*b*h where b is the base and h is the height. since we already know the area is 20 and the height is for you plus them in so the problem would be 20= 1/2 (b) (4) then you multiply what you know together to get 20= 2b and then isolate the b by dividing both sides by two so the base should be 10 m

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3 years ago

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storchak [24]

The form f(x) = a(bx) equals a. The initial value of the function f(x) = a(bx) is always a. This is due to the fact that an is not reliant on x. As a result, if x changes, bx will change as well, but a will not.

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3 years ago

What is 100,000,000 written as a power of ten?<br> a. 10^8<br> b. 10^9<br> c. 10^10<br> d. 10^11

Minchanka [31]

$100,000,000 = 100 \times 10^6 = 1\times 10^8\\~~\underbrace{~~~~~~~~~~~~~~~}\\~~~~~~~~~8$

Your answer is a. 10^8

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3 years ago

You have just opened a new nightclub, Russ' Techno Pitstop, but are unsure of how high to set the cover charge (entrance fee). O

Neko [114]

Answer:

a)q(p)=-15p+ +300

b)R(p)=-15p²+300p

c)C(p)=-30p+1600

d.1)P(p)=-15p²+330p-1600

d.2)p=$11

Step-by-step explanation:

(a).Before getting started, we are going to consider the cartesian plane, where x-axis corresponds to the cover charge and y-axis corresponds to number of guests per night . There, we will locate the following coordinates according to the previous information:

(9,165) (10,150).

Remember that the slope-intercept form of the linear equation is y=mx+b where m is the slope and b is te intercept.

The slope can be calculated by the next formula:

$m=\frac{y2-y1}{x2-x1}$

In this case we will assign (9,165) as the first coordinate and (10,150) as the second one. The order does not matter. At the end we get the same value for m.

Therefore:

$m=\frac{150-165}{10-9} = -15$

Now, we have the slope and two poitns. According to this, and taking into account that point-slope form of the equation of a line is y-y1=m(x-x1), find a linear demand equation.

Any of two coordintates can be selected. In this case we will select the second one.

y-150=-15(x-10) equation 1

Solve equation 1 for y

y=-15x+150+150

y=-15x+300

Above we had defined x as cover charge (p) and y as number of guests (q). Thus, rewrite equation 1.

q(p)=-15p+ +300.

it equation shows the number of guests per night as a function of the cover charge,

(b). The nightly revenue can be calculated multplying the price of the cover charge by the number of guests. So, we just have to multiply the equation 1 by p.

p*q(p)=p*(-15p +300)

R(p)=-15p²+300p equation 2

(c) To get the cost function of the nightclub we just have to multiply the cost of the two non-alcoholic drinks by the number of the guests ( equation 1) and add to it nightly overheads.

C(p)=2*(-15p+300)+1000

C(p)= -30p+600+1000

C(p)=-30p+1600 equation 3

(d) In order to find the profit in terms of the cover charge we will subtract nightly costs ( equation 3) from nightly revenue (equation 2)

P(p)=R(p)-C(p)

P(p)=-15p²+300p - (-30p+1600)

P(p)=-15p²+300p+30p-1600

P(p)=-15p²+330p-1600

To determine that the entrance fee we should charge for a maximum profit we are going to use the first derivative test (y'(x)=0) in order to find an extremum point.

Compute the first derivative of P(p)

P'(p)=-30p+330=0

30p=330

p=330/30

p= $11

The entrance fee that we should charge for a maximum profit is p=$11 per guest.

5 0

3 years ago