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1 year ago

Find the x- and y-intercepts for the following equation. Then use the intercepts to graph the equation.

Mathematics

1 answer:

kompoz [17]1 year ago

4 0

Answer:

Step-by-step explanation:

x int=2

y int=4

graph 2,0 and 0,4 as two points

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Sarah saw seven sharks while swimming now how many S is in the sentence

Katen [24]

Answer:

6 S's in the sentence

Step-by-step explanation:

5 0

3 years ago

What is the Laplace Transform of 7t^3 using the definition (and not the shortcut method)

Leokris [45]

Answer:

Step-by-step explanation:

By definition of Laplace transform we have

L{f(t)} = $L{{f(t)}}=\int_{0}^{\infty }e^{-st}f(t)dt\\\\Given\\f(t)=7t^{3}\\\\\therefore L[7t^{3}]=\int_{0}^{\infty }e^{-st}7t^{3}dt\\\\$

Now to solve the integral on the right hand side we shall use Integration by parts Taking $7t^{3}$ as first function thus we have

$\int_{0}^{\infty }e^{-st}7t^{3}dt=7\int_{0}^{\infty }e^{-st}t^{3}dt\\\\= [t^3\int e^{-st} ]_{0}^{\infty}-\int_{0}^{\infty }[(3t^2)\int e^{-st}dt]dt\\\\=0-\int_{0}^{\infty }\frac{3t^{2}}{-s}e^{-st}dt\\\\=\int_{0}^{\infty }\frac{3t^{2}}{s}e^{-st}dt\\\\$

Again repeating the same procedure we get

$=0-\int_{0}^{\infty }\frac{3t^{2}}{-s}e^{-st}dt\\\\=\int_{0}^{\infty }\frac{3t^{2}}{s}e^{-st}dt\\\\\int_{0}^{\infty }\frac{3t^{2}}{s}e^{-st}dt= \frac{3}{s}[t^2\int e^{-st} ]_{0}^{\infty}-\int_{0}^{\infty }[(t^2)\int e^{-st}dt]dt\\\\=\frac{3}{s}[0-\int_{0}^{\infty }\frac{2t^{1}}{-s}e^{-st}dt]\\\\=\frac{3\times 2}{s^{2}}[\int_{0}^{\infty }te^{-st}dt]\\\\$

Again repeating the same procedure we get

$\frac{3\times 2}{s^2}[\int_{0}^{\infty }te^{-st}dt]= \frac{3\times 2}{s^{2}}[t\int e^{-st} ]_{0}^{\infty}-\int_{0}^{\infty }[(t)\int e^{-st}dt]dt\\\\=\frac{3\times 2}{s^2}[0-\int_{0}^{\infty }\frac{1}{-s}e^{-st}dt]\\\\=\frac{3\times 2}{s^{3}}[\int_{0}^{\infty }e^{-st}dt]\\\\$

Now solving this integral we have

$\int_{0}^{\infty }e^{-st}dt=\frac{1}{-s}[\frac{1}{e^\infty }-\frac{1}{1}]\\\\\int_{0}^{\infty }e^{-st}dt=\frac{1}{s}$

Thus we have

$L[7t^{3}]=\frac{7\times 3\times 2}{s^4}$

where s is any complex parameter

5 0

3 years ago

2x+3y=1, -x+2y=-4 solve using substitution method

ollegr [7]

Step-by-step explanation:

1) 2x+3y-3y=1-3y. -x+2y= -4

2x/2=1-3y/2. -(1-3y/2)=-4

x=1-3y/2. -1+3y/2= -4

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

x=1+6/2 3y/2×2/3= -3×2/3

x=7/2 y= -2

S.s{ 7/3,-2}

2). -4x-6y+6y=7-6y. 4x+y= -2

-4x/-4=7-6y/-4. 4(-7-6y/4)+y= -2

x= -7-6y/4. -7-6y+y = -2

x= -7-6/4 -5y/5= 5/5

x=-13/4 y= 1

S.s { -13/4, 1 }

8 0

3 years ago

Minny has two coupons, but can use one of them. The first one is for $5 off an item; the second coupon is for 20% off an item. T

joja [24]

Let's first solve for the $5 off coupon,

$28 - 5 = 23$

The final total is $23.00 with $5 off.

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Now for the final price of the 20% off coupon,

$20\% = 0.2$

0.2 or 0.20 is decimal form of 20%. Easier to multiply than in percent form!

$0.2 \times 28 = 5.6$

$5.6 or $5.60 is 20% of 28, we're not done yet!

Lastly, subtract 20% off of 28 (5.6) from 28,

$28 - 5.6 = 22.4$
$22.4 or $22.40 is the final after 20% off!

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Q. Which is less after the discounts??

$23.00 or $22.40

A. $22.40 of course which was the 20% off.

Part A : Which coupon should she use ?

Answer : Well, to get a lower price, less to pay, the 20% off coupon is better!

Part B: How much money will she save by using the better coupon?

Answer : $5.6 / $5.60 is the amount she'll save!

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I hope that helps you out!!

Any more questions, please just ask me!!

~ Zoey

5 0

3 years ago

Please help me with this

Scilla [17]

The correct answers are the second option (Option B) and the last option (Option E).

The explanation is shown below:

1. By definition, a geometric sequence is a sequence of numbers each number, after the first one, is the result of multiply the previous number by a common ratio.

2. The Option B has the following common ratio:

(2/3) / (4/9)=1.5
1/(2/3)=1.5

r=1.5

3. The Option E has the following common ratio:

-15/3=-5
75/-15=-5

r=-5

6 0

3 years ago