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3 years ago

Determine whether the vectors u and v are parallel, orthogonal, or neither. u = <6, -2>, v = <8, 24>

1 answer:

5 0

Because 6 * 8 + ( - 2 )* 24 = 48 - 48 = 0 , the vectora u and v are orthogonal ;
Two vectors are orthogonal if their dot product is zero.<span />

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Find all the zeros of the equation x^4-6x^2-7x-6=0

rusak2 [61]

Answer:

The zeros are

$x=-2,\:x=3,\:x=-\frac{1}{2}+i\frac{\sqrt{3}}{2},\:x=-\frac{1}{2}-i\frac{\sqrt{3}}{2}$

Step-by-step explanation:

We have been given the equation x^4-6x^2-7x-6=0

Use rational root theorem, we have

$a_0=6,\:\quad a_n=1$

$\mathrm{The\:dividers\:of\:}a_0:\quad 1,\:2,\:3,\:6,\:\quad \mathrm{The\:dividers\:of\:}a_n:\quad 1$

$\mathrm{Therefore,\:check\:the\:following\:rational\:numbers:\quad }\pm \frac{1,\:2,\:3,\:6}{1}$

$-\frac{2}{1}\mathrm{\:is\:a\:root\:of\:the\:expression,\:so\:factor\:out\:}x+2$

$=\left(x+2\right)\frac{x^4-6x^2-7x-6}{x+2}\\$

$=x^3-2x^2-2x-3$

Again factor using the rational root test, we get

$=\left(x+2\right)\left(x-3\right)\left(x^2+x+1\right)$

Using the zero product rule, we have

$x+2=0:\quad x=-2\\x-3=0:\quad x=3\\x^2+x+1=0\\\\x_{1,\:2}=\frac{-1\pm \sqrt{1^2-4\cdot \:1\cdot \:1}}{2\cdot \:1}\\\\=-\frac{1}{2}+i\frac{\sqrt{3}}{2},\:x=-\frac{1}{2}-i\frac{\sqrt{3}}{2}$

Therefore, the zeros are

$x=-2,\:x=3,\:x=-\frac{1}{2}+i\frac{\sqrt{3}}{2},\:x=-\frac{1}{2}-i\frac{\sqrt{3}}{2}$

4 0

3 years ago

Read 2 more answers

A distance is related to time according to the expression x = A sin(2πft), where A and f are constants. Find the dimensions of A

nika2105 [10]

Answer:

[M⁰L¹T⁰]

Step-by-step explanation:

given expression,

from the expression x = A sin (2 π f t),

A and f are constants

dimension of A =?

As the sine factor is dimensionless means that sine function will not have any dimension it is dimensionless.

so, remaining

x = A sin ()

so, the dimension of x is L

hence, the dimension of A also will be equal to L i.e [M⁰L¹T⁰]

5 0

3 years ago

Any answers? No need for an explanation if you want to sure, the answer would be appreciated!

KIM [24]

Answer:

Step-by-step explanation:

B: it is only a single equation

8 0

3 years ago

Which sentence would be a good counter example to this statement ?

ArbitrLikvidat [17]

Answer:

The answer is "Option D".

Step-by-step explanation:

A line is a horizontal 1D-dimensional representation without any thickness and extends in every way. It sometimes is also known as the straight line. The line, which connects two planes lies simultaneously on both planes, that's why in this question only "option D" is correct.

8 0

3 years ago

Expand 3(z+3) please help me solve this

mojhsa [17]

Answer:

3(z+3) = 3z + 9 if thats what your asking

Step-by-step explanation:

7 0

3 years ago