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3 years ago

What is the value of the expression given below? (5+3i)-(5+3i)(5-5i)

Mathematics

1 answer:

snow_tiger [21]3 years ago

7 0

Answer:

Step-by-step explanation:

$i=\sqrt{-1}\to i^2=-1\\\\(5+3i)-(5+3i)(5-5i)\qquad\text{distribute}\\\\=(5+3i)(1-(5-5i))=(5+3i)(1-5-(-5i))=(5+3i)(-4+5i)\\\\\text{use}\ FOIL:\ (a+b)(c+d)=ac+ad+bc+bd\\\\=(5)(-4)+(5)(5i)+(3i)(-4)+(3i)(5i)\\\\=-20+25i-12i+15i^2=-20+13i+15(-1)\\\\=-20+13i-15=-35+13i$

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What is the surface area of the right cylinder below?

IgorLugansk [536]

Answer:

Ok to find the surface area of this cylinder first we need the circumference to find this we do C=πd

C=3.14*18

C=56.52

now we have to multiple this by the height of two

113.04

now we have to find the area of the bottom to do this we do A=πR^2

A=3.14*81

A=254.34

multiple this by two for the two sides we get

508.68

now we add this to 113.04 we get

621.72

since I used 3.14 instead of more digits of pie we can round this up so the answer is C.

Your Welcome

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2 years ago

I multiply my age by 5 and subtract 12

murzikaleks [220]

Let your age be x. The expression is :

5x - 12

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3 years ago

You need 3 sticks of butter for every 24 cookies you bake. How many sticks of butter for 16 cookies

Kay [80]

Answer: 2 sticks.

Step-by-step explanation:

Given statement: You need 3 sticks of butter for every 24 cookies you bake.

Using unitary method , the number of sticks of butter used to bake 1 cookie= $\dfrac{3}{24}=\dfrac{1}{8}$

Then the number of sticks of butter used to bake 1 cookie= $\dfrac{1}{8}\times16=2$

Hence, the number of sticks of butter used to bake 16 cookies= 2

3 0

3 years ago

Read 2 more answers

For the following linear system, put the augmented coefficient matrix into reduced row-echelon form.

Anni [7]

Answer:

The reduced row-echelon form of the linear system is $\left[\begin{array}{cccc}1&0&-5&0\\0&1&3&0\\0&0&0&1\end{array}\right]$

Step-by-step explanation:

We will solve the original system of linear equations by performing a sequence of the following elementary row operations on the augmented matrix:

Interchange two rows
Multiply one row by a nonzero number
Add a multiple of one row to a different row

To find the reduced row-echelon form of this augmented matrix

$\left[\begin{array}{cccc}2&3&-1&14\\1&2&1&4\\5&9&2&7\end{array}\right]$

You need to follow these steps:

Divide row 1 by 2 $\left(R_1=\frac{R_1}{2}\right)$

$\left[\begin{array}{cccc}1&3/2&-1/2&7\\1&2&1&4\\5&9&2&7\end{array}\right]$

Subtract row 1 from row 2 $\left(R_2=R_2-R_1\right)$

$\left[\begin{array}{cccc}1&3/2&-1/2&7\\0&1/2&3/2&-3\\5&9&2&7\end{array}\right]$

Subtract row 1 multiplied by 5 from row 3 $\left(R_3=R_3-\left(5\right)R_1\right)$

$\left[\begin{array}{cccc}1&3/2&-1/2&7\\0&1/2&3/2&-3\\0&3/9&9/2&-28\end{array}\right]$

Subtract row 2 multiplied by 3 from row 1 $\left(R_1=R_1-\left(3\right)R_2\right)$

$\left[\begin{array}{cccc}1&0&-5&16\\0&1/2&3/2&-3\\0&3/9&9/2&-28\end{array}\right]$

Subtract row 2 multiplied by 3 from row 3 $\left(R_3=R_3-\left(3\right)R_2\right)$

$\left[\begin{array}{cccc}1&0&-5&16\\0&1/2&3/2&-3\\0&0&0&-19\end{array}\right]$

Multiply row 2 by 2 $\left(R_2=\left(2\right)R_2\right)$

$\left[\begin{array}{cccc}1&0&-5&16\\0&2&3&-6\\0&0&0&-19\end{array}\right]$

Divide row 3 by −19 $\left(R_3=\frac{R_3}{-19}\right)$

$\left[\begin{array}{cccc}1&0&-5&16\\0&2&3&-6\\0&0&0&1\end{array}\right]$

Subtract row 3 multiplied by 16 from row 1 $\left(R_1=R_1-\left(16\right)R_3\right)$

$\left[\begin{array}{cccc}1&0&-5&0\\0&1&3&-6\\0&0&0&1\end{array}\right]$

Add row 3 multiplied by 6 to row 2 $\left(R_2=R_2+\left(6\right)R_3\right)$

$\left[\begin{array}{cccc}1&0&-5&0\\0&1&3&0\\0&0&0&1\end{array}\right]$

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3 years ago

Find the coordinates of the circumcenter for triangle DEF with coordinates D(1,3) E(8,3) and F(1,-5) show your work

nikklg [1K]

One leg is horizontal, on the line y=3. Another leg is vertical, on the line x=1. The point where these intersect, D(1, 3) is the vertex of a right angle. Any right triangle inscribed in a circle has its hypotenuse as the diameter of the circle.

Since the triangle is a right triangle, the circumcenter is the midpoint of the hypotenuse: ((8, 3) + (1, -5))/2 = (4.5, -1).

6 0

3 years ago