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faltersainse [42]
3 years ago
11

A cinema sold 1000 tickets on a Saturday evening. Adult tickets cost £9, children's

Mathematics
1 answer:
Alla [95]3 years ago
3 0

Answer:

Step-by-step explanation:

a + c = 1000

9a + 5c = 6680

------------------------------

9a + 9c = 9000

9a+ 5c = 6680

------------------------------

4c         = 2320

c           = 580

------------------------------------------------------------

a+ 580 = 1000

a = 420

A = 420

C = 580

If you substitute the numbers into 9a + 5c = 6680, that should give you the right answer.

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Assume z = x + iy, then find a complex number z satisfying the given equation. d. 2z8 – 2z4 + 1 = 0
kodGreya [7K]

Answer: complex equations has n number of solutions, been n the equation degree. In this case:

Z=\frac{\sqrt[8]{2} }{\sqrt[4]{2}} e^{i11,25°}

Z=\frac{\sqrt[8]{2} }{\sqrt[4]{2}} e^{i101,25°}

Z=\frac{\sqrt[8]{2} }{\sqrt[4]{2}} e^{i191,25°}

Z=\frac{\sqrt[8]{2} }{\sqrt[4]{2}} e^{i281,25°}

Z=\frac{\sqrt[8]{2} }{\sqrt[4]{2}} e^{i78,75°}

Z=\frac{\sqrt[8]{2} }{\sqrt[4]{2}} e^{i168,75°}

Z=\frac{\sqrt[8]{2} }{\sqrt[4]{2}} e^{i258,75°}

Z=\frac{\sqrt[8]{2} }{\sqrt[4]{2}} e^{i348,75°}

Step-by-step explanation:

I start with a variable substitution:

Z^{4} = X

Then:

2X^{2}-2X+1=0

Solving the quadratic equation:

X_{1} =\frac{2+\sqrt{4-4*2*1} }{2*2} \\X_{2} =\frac{2-\sqrt{4-4*2*1} }{2*2}

X=\left \{ {{0,5+0,5i} \atop {0,5-0,5i}} \right.

Replacing for the original variable:

Z=\sqrt[4]{0,5+0,5i}

or Z=\sqrt[4]{0,5-0,5i}

Remembering that complex numbers can be written as:

Z=a+ib=|Z|e^{ic}

Using this:

Z=\left \{ {{{\frac{\sqrt{2}}{2} e^{i45°} } \atop {{\frac{\sqrt{2}}{2} e^{i-45°} }} \right.

Solving for the modulus and the angle:

Z=\left \{ {{\sqrt[4]{\frac{\sqrt{2}}{2} e^{i45}} = \sqrt[4]{\frac{\sqrt{2}}{2} } \sqrt[4]{e^{i45}} } \atop {\sqrt[4]{\frac{\sqrt{2}}{2} e^{i-45}} = \sqrt[4]{\frac{\sqrt{2}}{2} } \sqrt[4]{e^{i-45}} }} \right.

The possible angle respond to:

RAng_{12...n} =\frac{Ang +360*(i-1)}{n}

Been "RAng" the resultant angle, "Ang" the original angle, "n" the degree of the root and "i" a value between 1 and "n"

In this case n=4 with 2 different angles: Ang = 45º and Ang = 315º

Obtaining 8 different angles, therefore 8 different solutions.

3 0
3 years ago
For the region bounded by y=2x​, the​ x-axis, and x=1​, determine which of the following is​ greater: the volume of the solid ge
telo118 [61]

Answer:

The correct answer B) The volumes are equal.

Step-by-step explanation:

The area of a disk of revolution at any x about the x- axis is πy² where y=2x. If we integrate this area on the given range of values of x from x=0 to x=1 , we will get the volume of revolution about the x-axis, which here equals,

\int\limits^1_0 {(pi)y^{2} } \, dx

which when evaluated gives 4pi/3.

Now we have to calculate the volume of revolution about the y-axis. For that we have to first see by drawing the diagram that the area of the CD like disk centered about the y-axis for any y, as we rotate the triangular area given in the question would be pi - pi*x². if we integrate this area over the range of value of y that is from y=0 to y=2 , we will obtain the volume of revolution about the y-axis, which is given by,

\int\limits^2_0 {pi - pix^{2} } \, dy = \int\limits^2_0 {1 - y^{2}/4 } \, dy

If we just evaluate the integral as usual we will get 4pi/3 again(In the second step i have just replaced x with y/2 as given by the equation of the line), which is the same answer we got for the volume of revolution about the x-axis. Which means that the answer B) is correct.

7 0
3 years ago
How many hours are in a week
blondinia [14]
There are 168 hours in one week.
Hope this helps! >.<
4 0
3 years ago
Read 2 more answers
the dimensions of the oven tray is 600mm by 500mm. Each cake tin is 25cm in diameter. How many cake tins can be fit on the oven
gulaghasi [49]

That's 60cm by 50cm

so that would be 4 cake tins

8 0
3 years ago
Read 2 more answers
Use the square to answer the question.
Studentka2010 [4]

Answer:

20 inches

Step-by-step explanation:

The correct answer is 20 because there is 4 sides and each side is worth of the length 5 so 5 times 4 - is what 20 . So the answer 20 is right . Hope this helps, you are welcome.

8 0
3 years ago
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