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disa [49]
3 years ago
7

Solve each of the following literal equations for c: (c/b) - x = 2d and ac + bd = x

Mathematics
1 answer:
maks197457 [2]3 years ago
8 0
(c/b) - x = 2d
(c/b) = 2d + x
c = b(2d + x)
c = 2db + bx

ac + bd = x
ac = x - bd
c = (x - bd) / a OR c = (x/a) - (bd/a)
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66.64 rounded to the nearest cent
Zolol [24]
It would just be 66.6
4 0
3 years ago
Evaluate the expression when x = 3.<br><br> x² + 6x - 3
Black_prince [1.1K]

Answer:

X=3

{3}^{2}  + 6(3) - 3 \\ 9 + 18 - 3 \\ 27 - 3 \\  = 24

3 0
2 years ago
(a) Find a vector parallel to the line of intersection of the planes −4x+2y−z=1 and 3x−2y+2z=1.
valentinak56 [21]

Find the intersection of the two planes. Do this by solving for <em>z</em> in terms of <em>x</em> and <em>y </em>; then solve for <em>y</em> in terms of <em>x</em> ; then again for <em>z</em> but only in terms of <em>x</em>.

-4<em>x</em> + 2<em>y</em> - <em>z</em> = 1   ==>   <em>z</em> = -4<em>x</em> + 2<em>y</em> - 1

3<em>x</em> - 2<em>y</em> + 2<em>z</em> = 1   ==>   <em>z</em> = (1 - 3<em>x</em> + 2<em>y</em>)/2

==>   -4<em>x</em> + 2<em>y</em> - 1 = (1 - 3<em>x</em> + 2<em>y</em>)/2

==>   -8<em>x</em> + 4<em>y</em> - 2 = 1 - 3<em>x</em> + 2<em>y</em>

==>   -5<em>x</em> + 2<em>y</em> = 3

==>   <em>y</em> = (3 + 5<em>x</em>)/2

==>   <em>z</em> = -4<em>x</em> + 2 (3 + 5<em>x</em>)/2 - 1 = <em>x</em> + 2

So if we take <em>x</em> = <em>t</em>, the line of intersection is parameterized by

<em>r</em><em>(t)</em> = ⟨<em>t</em>, (3 + 5<em>t</em> )/2, 2 + <em>t</em>⟩

Just to not have to work with fractions, scale this by a factor of 2, so that

<em>r</em><em>(t)</em> = ⟨2<em>t</em>, 3 + 5<em>t</em>, 4 + 2<em>t</em>⟩

(a) The tangent vector to <em>r</em><em>(t)</em> is parallel to this line, so you can use

<em>v</em> = d<em>r</em>/d<em>t</em> = d/d<em>t</em> ⟨2<em>t</em>, 3 + 5<em>t</em>, 4 + 2<em>t</em>⟩ = ⟨2, 5, 2⟩

or any scalar multiple of this.

(b) (-1, -1, 1) indeed lies in both planes. Plug in <em>x</em> = -1, <em>y</em> = 1, and <em>z</em> = 1 to both plane equations to see this for yourself. We already found the parameterization for the intersection,

<em>r</em><em>(t)</em> = ⟨2<em>t</em>, 3 + 5<em>t</em>, 4 + 2<em>t</em>⟩

3 0
3 years ago
In a sample of n = 6 scores, 5 of the scores are each above the mean by one point. Where is the 6th score located relative to th
den301095 [7]

The mean of a dataset is the sum of all data elements divided by the count of the elements.

The location of the 6th score relative to the mean is 5 points below the mean

Let:

\bar x \to<em> Mean</em>

a \to<em> 5 scores</em>

b \to<em> 6th scores</em>

Given that:

n = 6

The 5 scores that are 1 above the mean implies that:

a = \bar x + 1

The mean of a dataset is calculated using:

\bar x = \frac{\sum x}{n}

So, we have:

\bar x =\frac{5a + b}{6}

\bar x =\frac{5(\bar x + 1) + b}{6}

Open brackets

\bar x =\frac{5\bar x + 5 + b}{6}

Multiply both sides by 6

6\bar x =5\bar x + 5 + b

Make b the subject

b = 6\bar x -5\bar x - 5

b = \bar x - 5

This means that the 6th score is 5 points below the mean

Read more about mean at:

brainly.com/question/17060266

3 0
3 years ago
Often sales of a new product grow rapidly at first and then level off with time. This is the case with the sales represented by
True [87]

Answer:

Here we have the function:

S(t) = 500 - 400*t^(-1)

Then the rate of change at the value t, will be:

S'(t) = dS(t)/dt

This differentiation will be:

S'(t) = -400/t^2

Then:

a) the rate of change at t = 1 is:

S'(1) =  -400/1^2 = -400

The rate of change after one year is -400

b) t = 10

S'(10) = -400/10^2 = -400/100 = -4

The rate of change after 10 years is -4, it reduced as the years passed, as expected.

7 0
3 years ago
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