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3 years ago

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A satellite radio company charges a one time fee of $36 for installation. The company also charges $42 per month for use. based

upon this information complete this table showing the total cost of using the satellite radio after each month listed.

1 answer:

Greeley [361]3 years ago

5 0

Answer:

<em>Table shown below</em>

Step-by-step explanation:

<u>Linear Modeling</u>

It consists of finding and using the equation of a line to represent the behavior of a real situation in numerical terms.

We are given the model of the charges for a satellite radio company that charges a fixed fee of $36 for installation and a variable fee of $42 per month for use.

The model is written as:

C(m) = 36 + 42m

Where m is the number of months.

For m=1:

C(1) = 36 + 42(1)=$78

For m=2:

C(2) = 36 + 42(2)=$120

For m=3:

C(3) = 36 + 42(3)=$162

For m=4:

C(4) = 36 + 42(4)=$204

For m=5:

C(5) = 36 + 42(5)=$246

The calculations are resumed in the table shown below.

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ella [17]

$30 + $35 = $65

Assuming tax is on whole sale not each item:
$65 * 0.06 (6%) = $3.90 (6% of $65)

$65 + $3.90 = $68.90 ($65 + 6%)

OR

You could combine both of these steps and just use this working:
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4 years ago

Find an equation of the plane with the given characteristics. The plane passes through the points (4, 3, 1) and (4, 1, -7) and i

Minchanka [31]

Answer:

$3x - 4y + z = 1$

Step-by-step explanation:

Given

$Point\ 1 = (4,3,1)$

$Point\ 2 = (4,1,-7)$

Perpendicular to $8x + 7y + 4z = 18$

Required

Determine the plane equation

The general equation of a plane is:

$a(x-x_1) + b(y - y_1) + c(z-z_1) = 0$

For $n =$

$(x_1,y_1,z_1) = (4,3,1)$

$(x_2,y_2,z_2) = (4,1,-7)$

First, we need to determine parallel vector $V_1$

$V_1 =$

$V_1 =$

$V_1 =$

$V_1$ is parallel to the required plane

From the question, the required plane is perpendicular to $8x + 7y + 4z = 18$

Next, we determine vector $V_2$

$V_2 =$

This implies that the required plane is parallel to $V_2$

Hence: $V_1$ and $V_2$ are parallel.

So, we can calculate the cross product $V_1 * V_2$

$V_1 =$

$V_2 =$

$n = V_1 * V_2$

$V_1 * V_2 =\left[\begin{array}{ccc}i&j&k\\0&2&8\\8&7&4\end{array}\right]$

The product is always of the form + - +

So:

$V_1 * V_2 = i\left[\begin{array}{cc}2&8\\7&4\end{array}\right]$ $-j\left[\begin{array}{cc}0&8\\8&4\end{array}\right]$ $+k\left[\begin{array}{cc}0&2\\8&7\end{array}\right]$

Calculate the product

$V_1 * V_2 = i(2*4- 8*7) - j(0*4- 8*8) + k(0*7 - 2 * 8)$

$V_1 * V_2 = i(8- 56) - j(0- 64) + k(0 - 16)$

$V_1 * V_2 = i(-48) - j(- 64) + k(- 16)$

$V_1 * V_2 = -48i +64j - 16k$

So, the resulting vector, n is:

$n =$

Recall that:

$n =$

By comparison:

$a = -48$ $b = 64$ $c = -16$

Substitute these values in $a(x-x_1) + b(y - y_1) + c(z-z_1) = 0$

$-48(x-x_1) + 64(y - y_1) -16(z-z_1) =0$

Recall that: $(x_1,y_1,z_1) = (4,3,1)$

So, we have:

$-48(x-4) + 64(y - 3) -16(z-1) =0$

$-48x + 192 + 64y -192 - 16z +16 = 0$

Collect Like Terms

$-48x + 64y - 16z = 0 - 192 + 192 - 16$

$-48x + 64y - 16z = -16$

Divide through by -16

$3x - 4y + z = 1$

<em>Hence, the equation of the plane is</em> $3x - 4y + z = 1$ <em></em>

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Answer:

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Step-by-step explanation:

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9 = 3 x 3
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