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3 years ago

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Juan reads a book with 368 pages. savannah reads a book with 172 fewer pages than juan's book. how many pages are in the book sa

vannah reads?

2 answers:

krok68 [10]3 years ago

8 0

Answer: There are 196 pages in Savannah's book .

Step-by-step explanation:

Given : Juan reads a book with 368 pages.

Savannah reads a book with 172 fewer (less) pages than Juan's book.

Then, by using SUBTRACTION OPERATION, we have

The number of pages in Savannah's book = $368-172=196$

Hence, there are 196 pages in Savannah's book .

Step2247 [10]3 years ago

3 0

196 pages fewer than savannah

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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.

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3 years ago

Solve for [x]. The polygons in each<br> 2x-20<br> 16<br> 16<br> 8

Nataly_w [17]

$\quad \huge \quad \quad \boxed{ \tt \:Answer }$

$\qquad \tt \rightarrow \:x = 16$

____________________________________

$\large \tt Solution \: :$

If two polygons are similar, their corresponding sides ratios will be equal to each other.

$\qquad \tt \rightarrow \: \cfrac{8}{16} = \cfrac{2x - 20}{24}$

$\qquad \tt \rightarrow \: \cfrac{1}{2} = \cfrac{2x - 20}{24}$

$\qquad \tt \rightarrow \: 2x - 20 = \cfrac{24}{2}$

$\qquad \tt \rightarrow \: 2x = 12 + 20$

$\qquad \tt \rightarrow \: 2x = 32$

$\qquad \tt \rightarrow \: x = 16$

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

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144/11= 13.09

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