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3 years ago

Is the function y= sin(x)/x even, odd or neither

Mathematics

2 answers:

Bad White [126]3 years ago

8 0

The function is odd

dmitriy555 [2]3 years ago

5 0

By definition, a function f is even if f(−x)=f(x) . Since sin(−x)=−sinx , it implies that sinx is an odd function. That is why for example a half range Fourier sine series is said to be odd as well since it is an infinite sum of odd functions.

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Simplify this please

Ugo [173]

Answer:

$\frac{12q^{\frac{7}{3}}}{p^{3}}$

Step-by-step explanation:

Here are some rules you need to simplify this expression:

Distribute exponents: When you raise an exponent to another exponent, you multiply the exponents together. This includes exponents that are fractions. $(a^{x})^{n} = a^{xn}$

Negative exponent rule: When an exponent is negative, you can make it positive by making the base a fraction. When the number is apart of a bigger fraction, you can move it to the other side (top/bottom). $a^{-x} = \frac{1}{a^{x}}$ , and to help with this question: $\frac{a^{-x}b}{1} = \frac{b}{a^{x}}$ .

Multiplying exponents with same base: When exponential numbers have the same base, you can combine them by adding their exponents together. $(a^{x})(a^{y}) = a^{x+y}$

Dividing exponents with same base: When exponential numbers have the same base, you can combine them by subtracting the exponents. $\frac{a^{x}}{a^{y}} = a^{x-y}$

Fractional exponents as a radical: When a number has an exponent that is a fraction, the numerator can remain the exponent, and the denominator becomes the index (example, index here ∛ is 3). $a^{\frac{m}{n}} = \sqrt[n]{a^{m}} = (\sqrt[n]{a})^{m}$

$\frac{(8p^{-6} q^{3})^{2/3}}{(27p^{3}q)^{-1/3}}$ Distribute exponent

$=\frac{8^{(2/3)}p^{(-6*2/3)}q^{(3*2/3)}}{27^{(-1/3)}p^{(3*-1/3)}q^{(-1/3)}}$ Simplify each exponent by multiplying

$=\frac{8^{(2/3)}p^{(-4)}q^{(2)}}{27^{(-1/3)}p^{(-1)}q^{(-1/3)}}$ Negative exponent rule

$=\frac{8^{(2/3)}q^{(2)}27^{(1/3)}p^{(1)}q^{(1/3)}}{p^{(4)}}$ Combine the like terms in the numerator with the base "q"

$=\frac{8^{(2/3)}27^{(1/3)}p^{(1)}q^{(2)}q^{(1/3)}}{p^{(4)}}$ Rearranged for you to see the like terms

$=\frac{8^{(2/3)}27^{(1/3)}p^{(1)}q^{(2)+(1/3)}}{p^{(4)}}$ Multiplying exponents with same base

$=\frac{8^{(2/3)}27^{(1/3)}p^{(1)}q^{(7/3)}}{p^{(4)}}$ 2 + 1/3 = 7/3

$=\frac{\sqrt[3]{8^{2}}\sqrt[3]{27}p\sqrt[3]{q^{7}}}{p^{4}}$ Fractional exponents as radical form

$=\frac{(\sqrt[3]{64})(3)(p)(q^{\frac{7}{3}})}{p^{4}}$ Simplified cubes. Wrote brackets to lessen confusion. Notice the radical of a variable can't be simplified.

$=\frac{(4)(3)(p)(q^{\frac{7}{3}})}{p^{4}}$ Multiply 4 and 3

$=\frac{12pq^{\frac{7}{3}}}{p^{4}}$ Dividing exponents with same base

$=12p^{(1-4)}q^{\frac{7}{3}}$ Subtract the exponent of 'p'

$=12p^{(-3)}q^{\frac{7}{3}}$ Negative exponent rule

$=\frac{12q^{\frac{7}{3}}}{p^{3}}$ Final answer

Here is a version in pen if the steps are hard to see.

5 0

3 years ago

Please anyone help me

Ksju [112]

Answer:

-52

Step-by-step explanation:

plug 2 into u(x) which is equal to

2(5) + 1= 5

plug 5 into w(x) which is equal to

-2(5^2) - 2

-2(25) - 2

-50 - 2 = -52

3 0

3 years ago

(4 X 105) X 0.0375 how to solve this equation?

Flauer [41]

Answer:15.57

Step-by-step explanation:

1.bidmas

2.4x105=420

3.420x0.0375=15.57

7 0

3 years ago

Points W, K, and

Ksju [112]

Answer:

Points W, K, and J are collinear. Line CA and line YK intersect at point B. Point W is not contained on line m. The answers will be J,B,W

Step-by-step explanation:

Hope this helped :)

5 0

3 years ago

A triangular prism has a length of 5 inches, a base of 2 inches, a height of 2 inches, and sides of 2 inches and 3 inches. Find

riadik2000 [5.3K]

Volume of the Triangular prism = 1/2 (base*height*length)
V = 1/2 (2 * 2 * 5) 
V = 10 cubic inches. 

For the surface area, you can divide the prism into parts: 
It's made of three rectangles and two equal triangles. 

For the two triangles: 
The area of each of the triangles is 1/2(base x height) 
Area of each triangles = 1/2 (2 * 5) 
Area of each triangles = 5 inches^2. 

For the three rectangles: 
* one is equal to base x length, 
Rectangle1 = 2 x 5 
Rectangle1 = 10 inches^2. 

* another is equal to side 1 x length 
Rectangle2 = 3 x 5 
Rectangle2 = 15 inches^2 

* and the last is equal to side 2 x length. 
Rectangle3 = 3 x 5 
Rectangle3 = 15 inches^2 

Adding all the components up, 
10 + 15 + 15 + 5 + 5 = 50 inches^2 

Therefore, the surface area of the prism is greater than volume 50 > 10
hpe this helps:)

4 0

3 years ago