What is the surface area of the cylinder with height 4 km and radius 2 km? Round

A scatterplot is produced to compare the size of a lake to the number of fish that are in it. There are 15 data points, each rep

alukav5142 [94]

Answer:

Since there is no cluster formed in the scatterplot, the two variables are not related. Therefore, based on the data shown in the scatterplot, the number of fish in a lake is not dependent on the size of the lake.

Step-by-step explanation:

5 0

2 years ago

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A triangle has angle measures of 18° and 57°. What is the measure of the third angle?

Pachacha [2.7K]

Answer:

105°

Step-by-step explanation:

Measure of the third angle

= 180° - 18° - 57° (angle sum of triangle)

= 105°

5 0

1 year ago

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

2 years ago

Select the correct answer.<br> What are the solutions of this quadratic equation?<br> 25x^2 + 1 = 0

Llana [10]

Answer:

no solution because the square root of a negative number is not a real number d=-100

4 0

2 years ago

Jesse recorded the temperatures at which two oils freeze: Oil Temperature Sesame oil −6.2 °C Peanut oil 3.1 °C Which statement a

AVprozaik [17]

Answer: C. Sesame oil freezes at a lower temperature than peanut oil because −6.2 °C < 3.1 °C

Step-by-step explanation:

Given that:

Freezing point of sesame oil = - 6.2°C

Freezing point of peanut oil = 3.1°C

Comparing the two temperatures :

Freezing(when a substance turns to solid) usually occurs at low temperatures. The temperature of sesame oil(-6 2°C) is lower than that of peanut oil(3.1°C).

Hence, it can be concluded that Sesame oil freezes at lower temperature than peanut oil.

Mathematically,

-6.2°C < 3.1°C

6 0

2 years ago

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