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postnew [5]
3 years ago
9

Find the inverse of the function f(x)= 2x - 4 and show explain each step used to find the inverse.

Mathematics
1 answer:
pashok25 [27]3 years ago
4 0
F(x) is another way of saying y
Y=2x-4

For the inverse you trade the x and y

X=2y-4
Then get y by itself
Add 4 to both sides
X+4=2y

Divide both sides by 2
X+4/2Z
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How do you round 788.44-225.6? really need help:)
Igoryamba

Answer:

532.8

Step-by-step explanation:

3 0
3 years ago
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a box cost $2.48, but it is on sale for $1.49. How much do you save on one box when bought on sale? Now how much would you save
Thepotemich [5.8K]

Answer:

1. $0.99

2. $1.98

Step-by-step explanation:

1. From the question we have

Cost of box = $2.48

Selling price = $1.49

That is the box is discounted from $2.48 to $1.49

Therefore, amount saved = $2.48 - $1.49 = $0.99

2. The amount saved from buying a second box is hence;

2 × $0.99 = $1.98

Hence, as the number of boxes bought increases, the amount saved increases

5 0
4 years ago
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Evaluate the surface integral S F · dS for the given vector field F and the oriented surface S. In other words, find the flux of
Tomtit [17]

Apparently my answer was unclear the first time?

The flux of <em>F</em> across <em>S</em> is given by the surface integral,

\displaystyle\iint_S\mathbf F\cdot\mathrm d\mathbf S

Parameterize <em>S</em> by the vector-valued function <em>r</em>(<em>u</em>, <em>v</em>) defined by

\mathbf r(u,v)=7\cos u\sin v\,\mathbf i+7\sin u\sin v\,\mathbf j+7\cos v\,\mathbf k

with 0 ≤ <em>u</em> ≤ π/2 and 0 ≤ <em>v</em> ≤ π/2. Then the surface element is

d<em>S</em> = <em>n</em> • d<em>S</em>

where <em>n</em> is the normal vector to the surface. Take it to be

\mathbf n=\dfrac{\frac{\partial\mathbf r}{\partial v}\times\frac{\partial\mathbf r}{\partial u}}{\left\|\frac{\partial\mathbf r}{\partial v}\times\frac{\partial\mathbf r}{\partial u}\right\|}

The surface element reduces to

\mathrm d\mathbf S=\mathbf n\,\mathrm dS=\mathbf n\left\|\dfrac{\partial\mathbf r}{\partial u}\times\dfrac{\partial\mathbf r}{\partial v}\right\|\,\mathrm du\,\mathrm dv

\implies\mathbf n\,\mathrm dS=-49(\cos u\sin^2v\,\mathbf i+\sin u\sin^2v\,\mathbf j+\cos v\sin v\,\mathbf k)\,\mathrm du\,\mathrm dv

so that it points toward the origin at any point on <em>S</em>.

Then the integral with respect to <em>u</em> and <em>v</em> is

\displaystyle\iint_S\mathbf F\cdot\mathrm d\mathbf S=\int_0^{\pi/2}\int_0^{\pi/2}\mathbf F(x(u,v),y(u,v),z(u,v))\cdot\mathbf n\,\mathrm dS

=\displaystyle-49\int_0^{\pi/2}\int_0^{\pi/2}(7\cos u\sin v\,\mathbf i-7\cos v\,\mathbf j+7\sin u\sin v\,\mathbf )\cdot\mathbf n\,\mathrm dS

=-343\displaystyle\int_0^{\pi/2}\int_0^{\pi/2}\cos^2u\sin^3v\,\mathrm du\,\mathrm dv=\boxed{-\frac{343\pi}6}

4 0
4 years ago
100 POINTS PLEASE HELP ME I BEG 100 POINTS
Marrrta [24]

Answer:

see explanation

Step-by-step explanation:

(1)

Since FE = FG the triangle is isosceles with ∠ E = ∠ G, then

∠ E = \frac{180-106}{2} = \frac{74}{2} = 37°

(2)

Since all 3 sides are congruent then triangle is equilateral with the 3 angles being congruent, 60° each , then

12y = 60 ( divide both sides by 12 )

y = 5

(3)

The 3 angles are congruent then triangle is equilateral with the 3 sides being congruent, then

KL = JL , that is

4t - 8 = 2t + 1 ( subtract 2t from both sides )

2t - 8 = 1 ( add 8 to both sides )

2t = 9 ( divide both sides by 2 )

t = 4.5

(4)

Given ∠ B = ∠ C then triangle is isosceles with 2 legs being congruent , that is

AB = AC

4x + 1 = 9 ( subtract 1 from both sides )

4x = 8 ( divide both sides by 4 )

x = 2

Then

perimeter = AB + BC + AC = 4x + 1 + 2x + 3 + 9

                                            = 6x + 13

                                            = 6(2) + 13

                                            = 12 + 13

                                            = 25

7 0
2 years ago
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What is the angle of rotation of this regular octagon? what is the measure of an interior angle?
MrRissso [65]
Second question:
sum of all the interior angle     180*(8-2)=1080 degree
sum of one interior angle         1080/8=135 degree 
6 0
3 years ago
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