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lorasvet [3.4K]
3 years ago
7

Find the general solution of

qrt%7B2%7D" id="TexFormula1" title="2cos(2x + \frac{\pi }{4} ) = \sqrt{2}" alt="2cos(2x + \frac{\pi }{4} ) = \sqrt{2}" align="absmiddle" class="latex-formula"> =

Mathematics
1 answer:
Aleks04 [339]3 years ago
5 0

Answer:

\large\boxed{x=-\dfrac{\pi}{4}+k\pi\ \text{or}\ x=k\pi\ \text{for}\ k\in\mathbb{Z}}

Step-by-step explanation:

2\cos\left(2x+\dfrac{\pi}{4}\right)=\sqrt2\qquad\text{divide both sides by 2}\\\\\cos\left(2x+\dfrac{\pi}{4}\right)=\dfrac{\sqrt2}{2}\to2x+\dfrac{\pi}{4}=\pm\dfrac{\pi}{4}+2k\pi\\\\2x+\dfrac{\pi}{4}=-\dfrac{\pi}{4}+2k\pi\ \vee\ 2x+\dfrac{\pi}{4}=\dfrac{\pi}{4}+2k\pi\qquad\text{subtract}\ \dfrac{\pi}{4}\ \text{from all sides}\\\\2x=-\dfrac{2\pi}{4}+2k\pi\ \vee\ 2x=2k\pi\qquad\text{divide all sides by 2}\\\\x=-\dfrac{\pi}{4}+k\pi\ \vee\ x=k\pi\ \text{for}\ k\in\mathbb{Z}

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Factor tree<br>67344 using prime numbers​
Aleksandr-060686 [28]

Answer:

2^4*3*23*61

Step-by-step explanation:

\begin{array}{c|c}67344&2\\33672&2\\16836&2\\8418&2\\4209&3\\1403&23\\61&61\\1&\\\end{array}

8 0
3 years ago
Someone help me please !!!
KIM [24]

Answer:

1. 10

2. 12

3. Sqrt 130

4. Sqrt 45

Step-by-step explanation:

To find the missing side of a right triangle, use the Pythagorean Theorem. The Pythagorean Theorem is a^2+b^2=c^2 where a and b are the legs with a being the smallest and c is the hypotenuse.

1. a=6, b=8, c=?

6^2+8^2=c^2\\36+64=c^2\\100=c^2\\10=c

2. a=5, b=?, c=13

5^2+b^2=13^2\\25+b^2=169\\169-25=b^2\\144=b^2\\12=b

3. a=7, b=9, c=?

7^2+9^2=c^2\\49+81=c^2\\130=c^2\\\sqrt{130}=c

4. a=2, b=?, c=7

2^2+b^2=7^2\\4+b^2=49\\49-4=b^2\\45=b^2\\\sqrt{45}=b

5 0
3 years ago
Given: 315/1575. Write the prime fractorization of the numerator and the denominator, then write the fraction in lowest terms.
Ne4ueva [31]
The prime factorization of the numerator, 315, is 5 x 3 x 3 x 7. That of the denominator, 1575 is 5 x 5 x 3 x 3 x 7. To convert the fraction to its lowest form, cancel all the factors that appear to both the numerator and denominator. We will be left with 1/5. 
3 0
3 years ago
Given that 1 x2 dx 0 = 1 3 , use this fact and the properties of integrals to evaluate 1 (4 − 6x2) dx. 0
Debora [2.8K]

So, the definite integral  \int\limits^1_0 {(4 - 6x^{2} )} \, dx= - 74

Given that

\int\limits^1_0 {x^{2} } \, dx = 13

We find

\int\limits^1_0 {(4 - 6x^{2} )} \, dx

<h3>Definite integrals </h3>

Definite integrals are integral values that are obtained by integrating a function between two values.

So, Integral \int\limits^1_0 {(4 - 6x^{2} )} \, dx

So, \int\limits^1_0 {(4 - 6x^{2} )} \, dx = \int\limits^1_0 {4} \, dx - \int\limits^1_0 {6x^{2} } \, dx \\=  4[x]^{1}_{0}    - \int\limits^1_0 {6x^{2} } \, dx \\=  4[x]^{1}_{0}    - 6\int\limits^1_0 {x^{2} } \, dx \\= 4[1 - 0]    - 6\int\limits^1_0 {x^{2} } \, dx\\= 4[1]    - 6\int\limits^1_0 {x^{2} } \, dx\\= 4    - 6\int\limits^1_0 {x^{2} } \, dx

Since

\int\limits^1_0 {x^{2} } \, dx = 13,

Substituting this into the equation the equation, we have

\int\limits^1_0 {(4 - 6x^{2} )} \, dx = 4 - 6\int\limits^1_0 {x^{2} } \, dx\\= 4 - 6 X 13 \\= 4 - 78\\= -74

So, \int\limits^1_0 {(4 - 6x^{2} )} \, dx= - 74

Learn more about definite integrals here:

brainly.com/question/17074932

4 0
2 years ago
What does the number 3.1968e+22 mean?
sattari [20]
You add them and then it would be 30.6898033492
8 0
3 years ago
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