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soldier1979 [14.2K]
3 years ago
13

Find a unit vector in the direction of the vector left bracket Start 3 By 1 Matrix 1st Row 1st Column negative 8 2nd Row 1st Col

umn 7 3rd Row 1st Column negative 2 EndMatrix right bracket
−8
7
−2
.

A unit vector in the direction of the given vector is left bracket Start 3 By 1 Matrix 1st Row 1st Column nothing 2nd Row 1st Column nothing 3rd Row 1st Column nothing EndMatrix right bracket

?
?
?
.

​(Type exact​ answers, using radicals as​ needed.)
Mathematics
1 answer:
MrRissso [65]3 years ago
5 0

Answer:

\left[\begin{array}{c}-\frac{8}{\sqrt{117} } \\\frac{7}{\sqrt{117} }\\\frac{2}{\sqrt{117} }\end{array}\right]

Step-by-step explanation:

We are required to find a unit vector in the direction of:

\left[\begin{array}{c}-8\\7\\2\end{array}\right]

Unit Vector, \hat{a}=\dfrac{\overrightarrow{a}}{|\overrightarrow{a}|}

The Modulus of \overrightarrow{a} =\sqrt{(-8)^2+7^2+(-2)^2}=\sqrt{117}

Therefore, the unit vector of the matrix is given as:

\left[\begin{array}{c}-\frac{8}{\sqrt{117} } \\\frac{7}{\sqrt{117} }\\\frac{2}{\sqrt{117} }\end{array}\right]

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The sum of the 6th and seventh terms in a sequence of 12 numbers with a common difference is 16. What is the Sum of the number s
patriot [66]

Answer:

96

Step-by-step explanation:

commom difference = d

a₆ + a₇ = 16

a₅ + a₈ = (a₆ - d) + (a₇ + d) = a₆ + a₇ = 16

a₄ + a₉ = (a₆ - 2d) + (a₇ + 2d) = a₆ + a₇ = 16

Similarly,

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1 year ago
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qwelly [4]

Option D:

$y=\frac{5x-2}{x}

Solution:

Given function:

$y=\frac{-2}{x-5}

To find the inverse of the function.

<u>Inverse of a function:</u>

<em>If a function f(x) is mapping x to y, then the inverse function of f(x) maps y back to x.</em>

$y=\frac{-2}{x-5}

Interchange the variables x and y.

$x=\frac{-2}{y-5}

Now, solve for y.

Multiply both sides by (y - 5).

$x(y-5)=-\frac{2}{y-5}(y-5)

Cancel the common factors, we get

x(y-5)=-2

Divide by x on both sides.

$y-5=-\frac{2}{x}

Add 5 on both sides.

$y=-\frac{2}{x}+5

$y=-\frac{2}{x}+\frac{5}{1}

To make the denominator same, multiply the 2nd term by \frac{x}{x}.

$y=-\frac{2}{x}+\frac{5x}{x}

$y=\frac{-2+5x}{x}

$y=\frac{5x-2}{x}

Option D is the correct answer.

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The function f is continuous on the closed interval [1,15] and has the values shown on the table above. Let g(x) = ∫f(t) dt [1,x
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We're looking for the two values being subtracted here. One of these values is easy to find:

<span>g(1) = ∫f(t)dt = 0</span><span>
since taking the integral over an interval of length 0 is 0.
 
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</span><span>Each integral breaks down like so:

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So, the sum of all these integrals is 39, which means g(15)=39.
 
Then, g(15)-g(1)=39-0=39.
</span>
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