Determine mrs chaukes annual income if she earns R32040 per month

I don't know what table you have as reference, but I suspect it includes the following transforms:

[tex]1 \leftrightarrow \dfrac1s[/tex]

[tex]e^{at} \leftrightarrow \dfrac{1}{s-a}[/tex]

[tex]\cos(at) \leftrightarrow \dfrac{s}{s^2+a^2}[/tex]

[tex]\sin(at) \leftrightarrow \dfrac{a}{s^2+a^2}[/tex]

[tex]\cosh(at) \leftrigharrow \dfrac{s}{s^2-a^2}[/tex]

[tex]\sinh(at) \leftrigharrow \dfrac{a}{s^2-a^2}[/tex]

It probably also includes some more general properties, like

[tex]t f(t) \leftrightarrow -F'(s)[/tex]

[tex]e^{at} f(t) \leftrightarrow F(s-a)[/tex]

where F(s) is the Laplace transform of f(t).

Beyond these, you should also know the following identities:

[tex]\cosh(t) = \dfrac{e^t + e^{-t}}2[/tex]

[tex]\cosh^2(t) = \dfrac{1 + \cosh(2t)}2[/tex]

[tex]\cos^2(t) = \dfrac{1 + \cos(2t)}2[/tex]

[tex]\sin^2(t) = \dfrac{1 - \cos(2t)}2[/tex]

[tex]\sin(2t) = 2 \sin(t) \cos(t)[/tex]

[tex]\sin(t \pm T) = \sin(t) \cos(T) \pm \cos(t) \sin(T)[/tex]

Putting everything together, we have

• (a)

[tex]\cosh(t) \sin(t) = \dfrac{e^t + e^{-t}}2 \times \sin(t) = \dfrac12 e^t \sin(t) + \dfrac12 e^{-t} \sin(t)[/tex]

and the Laplace transform is

[tex]\dfrac12 F(s - 1) + \dfrac12 F(s + 1)[/tex]

where F(s) is the transform of sin(t),

[tex]F(s) = \dfrac{1}{s^2 + 1}[/tex]

Then

[tex]\cosh(t) \sin(t) \leftrightarrow \dfrac{\frac1{(s-1)^2+1} + \frac1{(s+1)^2+1}}2 = \boxed{\dfrac{s^2+2}{s^4+4}}[/tex]

• (b)

[tex]\sin^2(t) = \dfrac12 \left(1 - \cos(2t)\right)[/tex]

and the transform is

[tex]F(s) = \dfrac12 \left(\dfrac1s - \dfrac{s}{s^2+4}\right) = \boxed{\dfrac{2}{s^3+4s}}[/tex]

• (c)

[tex]\cos^2(2t) = \dfrac12 \left(1 + \cos(4t)\right)[/tex]

with transform

[tex]F(s) = \dfrac12 \left(\dfrac1s + \dfrac{s}{s^2+16}\right) = \boxed{\dfrac{s^2+8}{s^3+16s}}[/tex]

• (d)

[tex]\cosh^2(t) = \dfrac12 \left(1 + \cosh(2t)\right)[/tex]

with transform

[tex]F(s) = \dfrac12 \left(\dfrac1s + \dfrac{s}{s^2-4}\right) = \boxed{-\dfrac2{s^3-4s}}[/tex]

• (e)

[tex]t\sinh(2t) \leftrightarrow -F'(s)[/tex]

where F(s) is the Laplace transform of sinh(2t),

[tex]F(s) = \dfrac{2}{s^2 - 4} \implies -F'(s) = \boxed{\dfrac{4s}{(s^2-4)^2}}[/tex]

• (f)

[tex]\sin(t) \cos(t) = \dfrac12 \left(2\sin(t) \cos(t)\right) = \dfrac12 \sin(2t)[/tex]

with transform

[tex]F(s) = \dfrac12 \times \dfrac{2}{s^2+4} = \boxed{\dfrac1{s^2+4}}[/tex]

• (g)

[tex]\sin\left(t+\dfrac\pi4\right) = \sin(t) \cos\left(\dfrac\pi4\right) + \cos(t) \sin\left(\dfrac\pi4\right) = \dfrac1{\sqrt2} \left(\sin(t) + \cos(t)\right)[/tex]

with transform

[tex]F(s) = \dfrac1{\sqrt2} \left(\dfrac1{s^2+1} + \dfrac{s}{s^2+1}\right) = \boxed{\dfrac{s+1}{\sqrt2 (s^2+1)}}[/tex]

The last two are trivial and follow directly from the properties listed above.

• (h)

[tex]\cos(2t) - \cos(3t) \leftrightarrow \dfrac{s}{s^2+4} - \dfrac{s}{s^2+9} = \boxed{\dfrac{5s}{s^4 + 13s^2 + 36}}[/tex]

• (i)

[tex]\sin(2t) + \cos(4t) \leftrightarrow \dfrac2{s^2+4} + \dfrac{s}{s^2+16} = \boxed{\dfrac{s^3+2s^2+4s+32}{s^4+20s^2+64}}[/tex]

Answer:

77ft ?

Step-by-step explanation:

Applying the expression for speed, we found that the time taken for the bucket to hit the bottom of the well is 15 seconds

Given Data

Speed = 2 meters per second

Distance = 30 meters

Time = ??

We know that the expression for the relationship between speed, distance and time is given as

Speed = Distance/Time

substituting we have

2 = 30/t

cross  multiplying

2t = 30

divide both sides by 2

t = 30/2

t = 15 seconds

Answer 15 seconds

Learn more about speed and distance here:

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Answer:

a: 3/10 + 3/10 =6/10

b: 3/10 + 4/10 = 7/10

c:

Answer:I believe its this

Step-by-step explanation:

you can see the step by step in the attached image as well as the result

Answer:

y = 2x

the formula for linear equations are y = mx+c,

where m is the gradient,

and c is the y-intercept

to find m (the gradient):

1. pick to points on the graph (eg. -2,-4 and 2,4)

2 substitute the values into the formula for gradient y2-y1/x2-x1.

m = y2-y1/x1-x2

= -4 -4/-2-2

= -8/-4

= 2

to find c (y-intercept):

- the y-intercept is where the graph cuts the y axis

- in this graph, the y-intercept is 0

hence,

c = 0

substitute m = 2 and c = 0 to y = mx+c,

y = 2x + 0

y = 2x

hence, the equation that best represents the relationship shown in the graph is y = 2x.

Answer:

x - 6 = 0

Step-by-step explanation:

x - 6 = ?

If x = 6, then

6 - 6 = 0

Answer:

i think 66.5 miles per hour

Step-by-step explanation:

Answer:

205.295 miles divided by 3.12 hours = 65.8 miles per hour

Step-by-step explanation:

Answer:

6a +6a +3 + 6a

12a +3 +6a

18a +3

Answer:

a) 52

Step-by-step

49+52=101

which makes the equation true

101>100

51 will make it equal

53 and 54 its more than 52 that meants it wont be  the smallest whole number

Step-by-step explanation:

[tex](x + y) {}^{2} - 1[/tex]

[tex](x + y - 1)(x + y + 1)[/tex]

Answer:

here's your answer hope it helps.

Step-by-step explanation:

1. decimal:

39/50=0.78

2. percentage:

39/50=78%

9/50 to a decimal is 0.78 and a percent is 78%.

To convert fraction into decimal, divide the top of the fraction by the bottom number (39/50) here 39 is the top of the fraction and 50 is bottom of the fraction.

39/50 = 0.78

To convert fraction into percent, divide the top of the fraction by the bottom number then multiple the result by 100 here 39 is the top of the fraction and 50 is bottom of the fraction then multiple the result(0.78) by 100.

39/50 = 0.78 * 100 = 78.

Therefore, 39/50 to a decimal is  0.78 and a percent is 78%.

Learn more about decimal and percent here:

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Answer:

There are no solutions to the system because the equations represent parallel lines.

Step-by-step explanation:

Answer:

What does 0 = −12 mean regarding the solution to the system? There are no solutions to the system because the equations represent parallel lines.

Given :

To Find :-

Solution :-

From the given figure we can see that the prism is made up of

And the base and height of each triangle is ,

And the dimensions of each rectangle is ,

Therefore , the Total surface area is ,

→ TSA = 2( area of each ∆) +3(area of each rectangle)

→ TSA = 2 ( 1/2 * 7 * 5)in.² + 3(13*6.1) in.²

→ TSA = 2 * 35/2 in.² + 3* 79.3 in.²

→ TSA = 35 in.² + 237.9 in.²

→ TSA = 272.9 ≈ 273 in.²

Hence the TSA of prism is 273 in.² .

I hope this helps.

Answer:

Step-by-step explanation:

Total weight of apples:

The weight of fresh apples:

Total Weight of Apples

[tex] \frac{30}{4}=7.5pounds [/tex]

Weight of Fresh Apples

[tex]7.5 - 3 = 3.5pounds[/tex]

Hope it helps youuuu :)

Answer:

3 days

Step-by-step explanation:

Kali runs 10 laps around a track each day, and each lap is 400 meters. So, the first step would be:

10 • 400 = 4,000

That means Kali runs 4,000 meters each day.

Now, there are 1,000 meters in 1 kilometer. This means he runs 4 kilometers each day, and we're trying to get to 12 kilometers.

The final step is to divide. 12/4 = 3

So, it would take 3 days for him to run a total of 12 kilometers.

Answer:

Kali will run 3 days

Step-by-step explanation: took quiz

Answer:

See below.

Step-by-step explanation:

(4x^2-3x^3)+(2x^2+4x^3)

6x^2-x^3

(-8x^2-2x+7)+(x^2-3x+2)

-7x^2-5x+9

-hope it helps

Answer:

0.8x - y = -1.8, x-int = 2.25, y-int = -1.8

Step-by-step explanation:

(-4, -5) and (1, -1)

slope = [(-5) - (-1)] / [(-4) - 1] = -4 / -5 = 4/5 = 0.8

Let y = 0.8 x + b

Sub (-4, -5) into it

-5 = 0.8 * (-4) + b = -3.2 + b

b = -5 + 3.2 = -1.8

The equation is y = 0.8x - 1.8

standard form: 0.8x - y = -1.8

let y = 0, 0.8x - 1.8 = 0

x = 1.8/0.8 = 2.25   (x-intercept)

let x = 0, y = -1.8    (y-intercept)

The slope of a linear regression is the rate of change of the line of the best fit

The linear regression is given as:

y = -1.62x + 18

Where

Using the above representations, the slope means that the wait time per staff is 1.62 minutes

Also, the slope value is realistic because time can be measured in decimals

Read more about linear regressions at:

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Answer:

[tex]x= 4[/tex]

Step-by-step explanation:

[tex]\frac{\sqrt{2x}}{\sqrt{x-2}\:}=2[/tex]                       [ bring √(x - 2) to the opposite side ]

[tex]\sqrt{2x} = 2\sqrt{x-2}[/tex]          

[tex](\sqrt{2x} )^{2} = (2\sqrt{x-2})^2[/tex]      [ square both sides ]

[tex]2x = 4(x-2)[/tex]  

[tex]2x=4x-8[/tex]

[tex]2x - 4x = -8[/tex]

[tex]-2x = -8[/tex]

[tex]x= 4[/tex]

Answer:

x=4

Step-by-step explanation:

[tex]\dfrac{\sqrt{2x} }{\sqrt{x-2}}=2[/tex]

Multiply both sides by [tex]\sqrt{x-2}[/tex] :

[tex]\implies \sqrt{2x}=2\sqrt{x-2}[/tex]

Square both sides:

[tex]\implies 2x=4(x-2)\\\\\implies 2x=4x-8[/tex]

Add 8 to both sides:

[tex]\implies 2x+8=4x[/tex]

Subtract [tex]2x[/tex] from both sides:

[tex]\implies 8=2x[/tex]

Divide both sides by 4:

[tex]\implies x=4[/tex]

[tex] \: \: \: [/tex]

[tex] \: \: \: [/tex]

[tex] \: \: \: [/tex]

The Value Of x Is 5.

Answer:

x = 5

Step-by-step explanation:

5x = 25

x = 25/5

x = 5

Hope it helps ⚜

Answer:

4 + 7 = 11

4 + 7(3) = 25

4 + 21 = 25

first number is 4, second is 7

I hope this helped!

Step-by-step explanation:

Rearranging the question,

SOLVE FOR Y IN TERMS OF X:

x - 2y = 4

Move 2y to the other side

x=2y+4

Move 4 to the other side and flip the equation

2y=x-4

Divide both sides by two:

-Hunter

Answer:

y = 1/2x - 2

(You need to rearrange x-2y=4)

Answer:

25

Step-by-step explanation:

To find the mean, sum up the five data points and divide this sum by 5:

125

----- = 25

  5

The mean is 25.

Answer:

The answer is below, y = 2x - 2

Step-by-step explanation:

2x - y > 2

-2x       -2x

-y > 2 - 2x

/-1     / -1

y < -2 + 2x, also written as y < 2x - 2

This is where we got our answer: y = 2x - 2

*There is an invisible 1 before the variable (y)*

*When dividing an inequality with a negative number, the sign flips (from < to >, or from ≤ to ≥)*

I'm going to share a little tip:

< or ≤ = below the line

> or ≥ = above the line

Hope that helps

Answer:

12 m

Step-by-step explanation:

If 1 m = 3.3 feet, then,

1 feet = 1/3.3 m

So,

39.6 feet

= 39.6/3.3

Multiplying by 10....

= 396/33

= 12 m

Hope it helps ⚜

Answer:

Yellow

Step-by-step explanation:

y= -f(x) reflects over the x-axis which is what this graph shows. When you complete the factor of

-(x+3)(x-1)

Use the FOIL method to solve

(First, Outer, Inner, last) This will equal to the

y= -x^2-2x+3 as shown in the yellow box

Answer:

Step-by-step explanation:

4x^2 -3x  for x = -4

4(-4)^2 - 3(-4)

4 (16) - (-12)

64 + 12

76

Hope this helps!

Answer:

76

Step-by-step explanation:

It is easier to do x square first which gives you 16

Then do 16 times 4 which is 64

Then do x times -3 which is -12

Then do the sum 64-(-12)

which gives you the answer of 76

Hope This Helps