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tekilochka [14]

3 years ago

15

Solve the equation . cos2x−cosx=0. on the interval [0,2π)

1 answer:

Charra [1.4K]3 years ago

6 0

Cos <span>2</span><span>x </span><span>= </span><span>2</span><span>cos^</span><span>2</span><span>(</span><span>x</span><span>) </span><span>− </span><span>1</span>
2<span>cos^</span><span>2 </span><span>(</span><span>x</span><span>) </span><span>− </span><span>1 </span><span>− </span><span>cos</span><span>(</span><span>x</span><span>) </span><span>≡ </span><span>2</span><span>cos^</span><span>2</span><span>(</span><span>x</span><span>) </span><span>− </span><span>cos</span><span>(</span><span>x</span><span>) </span><span>− </span><span>1</span>
Let <span>cos</span><span>(</span><span>x</span><span>) </span><span>= </span><span>y</span>
2<span>y^</span><span>2 </span><span>− </span><span>y </span><span>− </span><span>1
</span><span>(</span><span>2</span><span>y </span><span>+ </span><span>1</span><span>) </span><span>(</span><span>y </span><span>− </span><span>1</span><span>) </span>y <span>= </span><span>−</span><span>1/2
</span><span>y </span><span>= </span><span>1</span>
y <span>= </span><span>cos</span><span>(</span><span>x)</span>
∴ <span>cos</span><span>(</span><span>x</span><span>) </span><span>= </span><span>−</span><span>1/</span><span>2 ; </span><span>cos</span><span>(</span><span>x</span><span>) </span><span>= </span><span>1</span>
x <span>= </span><span>2/</span><span>3 </span><span>π ;</span><span> </span><span>x </span><span>= </span><span>0</span>
solutions;x <span>= </span><span>2/</span><span>3 </span><span>π</span><span>, </span><span>x </span><span>= </span><span>0</span><span>, </span><span>x </span><span>= </span><span>4/</span><span>3 </span><span>π</span><span>, </span><span>x </span><span>= </span><span>2</span><span>π</span>

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Plz show work and solve quick please need help!!!!!

Simora [160]

Surface area is just the area of all these 4 triangles plus the rectangle.

First we can find the area of the rectangle.

$\sf A=lw$

Half of the length is 28 cm, so the full length must be 28 * 2 = 56 cm.

$\sf A=(56)(27)$

$\sf A=1512cm^2$

The base for the left and right triangles are 27. The heights would be the net length minus half the length of the rectangle:

$\sf 82.8-28=54.8\? cm$

Calculate the area:

$\sf A=\dfrac{1}{2}bh$

$\sf A=\dfrac{1}{2}(27)(54.8)$

$\sf A=739.8\?cm^2$

We have two of these triangles.

$\sf 739.8\times 2=1479.6\? cm^2$

Now do the other two pair of triangles. The bases for them are 28 + 28 = 56 cm. The heights would be the net width minus the width of the rectangle:

$\sf 81.2-27=54.2\?cm$

Now find the area:

$\sf A=\dfrac{1}{2}bh$

$\sf A=\dfrac{1}{2}(56)(54.2)$

$\sf A=1517.6\? cm^2$

We have two of these triangles.

$\sf 1517.6\times 2=3035.2\?cm^2$

Add all the areas together:

$\sf 1512+1479.6+3035.2=\boxed{\sf 6026.80\? cm^2}$

7 0

3 years ago

Express the series using sigma notation.<br><br> 4 + 16 + 64 + 256 + 1,024

Hatshy [7]

Answer:

EASSYYY

Step-by-step explanation:

1364

3 0

2 years ago

Read 2 more answers

HA=2-bA , solve the equation for A

yaroslaw [1]

HA + bA = 2
A(h+b) = 2
A = 2/h+b

7 0

2 years ago

Read 2 more answers

Aiden's mom calculated that in the previous month, their family had used 40% of the monthly income for

Natali5045456 [20]

Answer:

The money left after gasoline expenses was <u>$622.50</u>.

Step-by-step explanation:

Given:

Last month, family had used 40% of the monthly income for gasoline, and 63% of that gasoline was consumed by the family's SUV.

The family's SUV used $261.45 worth of gasoline previous month.

Now, to find the money left of the family monthly income after gasoline expenses.

Let the total money spend on gasoline be $g.$

As, given:

The family's SUV used $261.45 worth of gasoline, which was 63% of the gasoline that was consumed.

According to question:

$63\%\ of\ g=$261.45.\\\\$

$\frac{63}{100} \times g=261.45\\\\0.63\times g=261.45$

<em>Dividing both sides 0.63 we get:</em>

$g=\$415.$

<u><em>The total money spend on gasoline = $415.</em></u>

Now, 40% of the monthly income is used for gasoline.

Let the total monthly income be $x.$

So, to get the monthly income we put an equation:

$40\%\ of\ x=\$415\\\\\frac{40}{100}\times x=415\\\\0.40\times x=415$

<em>Dividing both sides by 0.40 we get:</em>

$x=\$1037.50.$

<u><em>The total monthly income = $1037.50.</em></u>

Now, to get the money left after gasoline expenses we subtract the total money spend on gasoline from the total monthly income:

$\$1037.50-\$415\\\\=\$622.50.$

Therefore, the money left after gasoline expenses was $622.50.

6 0

3 years ago

What type of polynomial is this and what is its degree?<br> 5b3 - 3 + 6b

Dmitry_Shevchenko [17]

Answer:

3rd degree trinomial

Step-by-step explanation:

the highest power is 3 and there are 3 terms so its a 3rd degree trinomial

3 0

3 years ago