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3 years ago

Find f(3) if f(x)=2x+4

Mathematics

1 answer:

solong [7]3 years ago

3 0

Answer:

f(3) = 10

Step-by-step explanation:

If x = 3 then fill in the x's on the original equation and solve;

f(x) = 2x + 4

f(3) = 2(3) + 4

2 x 3 = 6

6 + 4 = 10

So, f(3) = 10

Hope this helps!!!

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Fit a trigonometric function of the form f(t)=c0+c1sin(t)+c2cos(t)f(t)=c0+c1sin⁡(t)+c2cos⁡(t) to the data points (0,5.5)(0,5.5),

larisa86 [58]

Answer

$f(t)=-0.2+4.1sin(t)+4cos(t)$

Step-By-Step Explanation

Given the function $f(t)=c_0+c_1sin(t)+c_2cos(t)$ .

For each pair (t, f(t)) in the data points (0,5.5), (π/2,0.5), (π,−2.5), (3π/2,−7.5)

$f(0)=c_0+0c_1+c_2=5.5$ .

$f(\pi /2)=c_0+c_1+0c_2=0.5$ .

$f(\pi)=c_0+0sin(t)-c_2=-2.5$ .

$f(3\pi /2)=c_0-c_1+0c_2=-7.5$ .

Expressing this as a system of linear equations in matrix form AX=B

$\left(\begin{array}{ccc} 1 & 0 & 1 \\ 1 & 1 & 0 \\ 1 & 0 & -1 \\ 0 & -1 & 0 \end{array} \right)\left( \begin{array}{c} c_{0} \\ c_{1} \\ c_{2}\\ \end{array} \right)=\left(\begin{array}{c} 5.5 \\ 0.5 \\ -2.5 \\ -7.5 \end{array} \right)$

Where

$A=\left(\begin{array}{ccc} 1 & 0 & 1 \\ 1 & 1 & 0 \\ 1 & 0 & -1 \\ 0 & -1 & 0 \end{array} \right)$ ,

$B=\left(\begin{array}{c}5.5\\0.5\\-2.5\\-7.5\end{array} \right)$

$X=\left(\begin{array}{c}c_0\\c_1\\c_2\end{array}\right)$

To determine the values of X, we use the expression

$X=(A^{T}A)^{-1}A^{T}B$

$A^{T}A= \left(\begin{array}{ccc} 3 & 1 & 0 \\ 1 & 2 & 0 \\ 0 & 0 & 2 \end{array} \right)$

$(A^{T}A)^{-1}= \left(\begin{array}{ccc} 0.4 & -0.2 & 0 \\ -0.2 & 0.6 & 0 \\ 0 & 0 & 0.5 \end{array} \right)$

$A^{T}B=\left(\begin{array}{c} 3.5 \\ 8 \\ 8 \end{array} \right)$

Therefore:

$X=\left(\begin{array}{ccc} 0.4 & -0.2 & 0 \\ -0.2 & 0.6 & 0 \\ 0 & 0 & 0.5 \end{array} \right)\left( \begin{array}{c} 3.5 \\ 8 \\ 8 \end{array} \right)$

$X=\left(\begin{array}{c}c_0\\c_1\\c_2\end{array}\right)=\left(\begin{array}{c} -0.2 \\4.1\\4\end{array}\right)$

Therefore, the trigonometric function which fits to the given data is:

$f(t)=-0.2+4.1sin(t)+4cos(t)$

8 0

3 years ago

Can someone please help me with this ? Dew in 5 mins .. I clicked the first answer on accident btw ..

Alexxx [7]

Answer:

B The equation is 4x = -48. Ben's point total is -12.

Step-by-step explanation:

Ben's total + Olive's total = -48

x + 3x = -48

4x = -48

x = -48 ÷ 4

Ben's total (x) = -12

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3 years ago

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Someone plz answer this with an actual answer

azamat

Answer:

12,7

Step-by-step explanation:

6 0

3 years ago

Suppose the radius of a circle is 2. What is its area?

Mila [183]

The area would be 12.57
Hope that helps you! :)

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3 years ago

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The table represents a linear function. What is the slope of the function?

dybincka [34]

Answer: 3

Step-by-step explanation:

In theory we know that the equation of a linear function is expressed as

Eq.(1): y = m*x + c,

where m is the slope and c is a constant.

From the table we know the values of x and y, so we can use any of those, but in this case lets use the first and third rows of the table and substituting in Eq.(1) we obtain a 2-equation system as follow:

Point (-2,-2) gives: -2 = (-2)*m + c Eq.(2)

Point (0,4) gives: 4 = (0)*m + c Eq.(3)

Now rearranging Eq.(2) we get: -2 = -2*m + c <=> -2 - c = -2m Eq.(4)

Then rearranging Eq.(3) we get: 4 = 0 + c <=> c = 4

Plugging the value of c in Eq.(4) we get:

-2 = -2m + 4 <=> -2 - 4 = - 2m <=> -6 = -2m <=> m = 3

So finally and from Eq.(1) we obtain

y = 3x + c

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3 years ago

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