write the equation of a line in any form that is parallel 2y = 4x + 8 through the point of (1,3) plz and thank you

Answer:

The positive value of k that the function y = sin(kt) satisfies the differential equation y'' + 144y = 0 is +12

Step-by-step explanation:

To determine the positive values of k that the function y = sin(kt) satisfy the differential equation y''+144y=0.

First, we will determine y''.

From y = sin(kt)

y' = [tex]\frac{d}{dt}(y)[/tex]

y' = [tex]\frac{d}{dt}(sin(kt))\\[/tex]

y' = kcos(kt)

Now for y''

y'' = [tex]\frac{d}{dt}(y')[/tex]

y'' = [tex]\frac{d}{dt}(kcos(kt))[/tex]

y'' = [tex]-k^{2}sin(kt)[/tex]

Hence, the equation y'' + 144y = becomes

[tex]-k^{2}sin(kt)[/tex] + [tex]144(sin(kt))[/tex] [tex]= 0[/tex]

[tex](144 - k^{2})(sin(kt)) = 0[/tex]

[tex](144 - k^{2})= 0[/tex]

∴ [tex]k^{2} = 144\\[/tex]

[tex]k =[/tex] ±[tex]\sqrt{144}\\[/tex]

[tex]k =[/tex] ± [tex]12[/tex]

∴ [tex]k = +12[/tex] or [tex]-12[/tex]

Hence, the positive value of k that the function y = sin(kt) satisfies the differential equation y'' + 144y = 0 is +12

The positive value of k that satisfies the differential equation is k = 12.

To find the value of k that satisfies the equation, we differentiate the function y = sin(kt) twice to obtain y" and we insert it into the differential equation y" + 144y = 0.

So, y' = dy/dt

= dsin(kt)/dt

= kcos(kt)

y" = dy'/dt

y" = dkcos(kt)/dt

y" = -k²sin(kt)

So, substituting y and y" into the differential equation, we have

y" + 144y = 0

-k²sin(kt) + 144sin(kt) = 0

-k²sin(kt) = -144sin(kt)

k² = 144

k = ±√144

k = ±12

Since we require a positive value, k = 12

So, the positive value of k that satisfies the differential equation is k = 12.

Learn more about differential equations here:

https://brainly.com/question/18760518

Answer:

y=3x+25

Step-by-step explanation:

So to find the slope-intercept we need to find the slope and the y intercept. we already know the slope so to find the y intercept you subtract 2 from the x coordinate and 6 from the y, because the slope is 3. So the answer is y=3x+23

Answer:

y=3x+25

Step-by-step explanation:

We are given a point and the slope, so let's use the slope-intercept equation.

[tex]y-y_{1}=m(x-x_{1})[/tex]

where m is the slope and (x₁, y₁) is the point given. The slope is 3 and the point is (2,31). Therefore,

[tex]m= 3 \\x_{1}=2\\y_{1}=31[/tex]

Substitute the values into the equation.

[tex]y-31=3(x-2)[/tex]

We want the equation in slope intercept form: y=mx+b. We must isolate y on the left side of the equation.

First, distribute the 3. Multiply each term inside the parentheses by 3.

[tex]y-31= (3*x)+(3*-2)[/tex]

[tex]y-31=(3x)+(-6)[/tex]

[tex]y-31=3x-6[/tex]

Next, add 31 to both sides of the equation.

[tex]y-31+31=3x-6+31[/tex]

[tex]y=3x-6+31[/tex]

[tex]y=3x+25[/tex]

This equation is in slope intercept form, so our final answer is:

y= 3x+25 (slope⇒3 , y-intercept ⇒25)

Answer:

b) yes

The manufacturer has the right to state that the light bulbs last on average 400 hours

Step-by-step explanation:

Explanation:-

Given sample size 'n' = 64

Given standard deviation of the Population (σ)=100

Mean of the sample (x⁻) = 350 hours

95% of confidence interval is determined by

[tex](x^{-} -Z_{0.95} \frac{S.D}{\sqrt{n} } , x^{-} +Z_{0.95} \frac{S.D}{\sqrt{n} } )[/tex]

([tex](350 -1.96 \frac{100}{\sqrt{64} } , 350+1.96\frac{100}{\sqrt{64} } )[/tex]

(350-24.5 , 350+24.5)

(325.5 , 374.5)

Conclusion:-

Yes

The manufacturer has the right to state that the light bulbs last on average 400 hours

Answer:

1-70: Purple- 9/10= 0.18= 2 marbles

        Orange- 16/50= 0.32= 3 marbles

        Yellow- 6/50= 0.12= 1 marble

        Green- 19/50= 0.38= 4 marbles

1-71: Part A. 3/6= 1/2

       Part B. 4/6= 2/3

Answer:

The GCF of 30 and 45 is

15.

Hope it helps.

Answer:

The key features are

50ft³ = the volume

0.5ft³/min = rate

Time= 100 minutes

Step-by-step explanation:

Chiang is filling a 50ft container with water at a rate of 0.5 ft/ min.

50ft³ = the volume

0.5ft³/min = rate

There is a key future missing which is the time it will take to fill the 50 ft³ container

Time = volume/rate

Time= 50 ft³/0.5ft³/min

Time= 50/0.5 min

Time = 100 min

The key features are

50ft³ = the volume

0.5ft³/min = rate

Time= 100 minutes

Answer:

y = 12

Step-by-step explanation:

Use the equation y = kx

Plug in x and y to find k:

2 = k(16)

1/8 = k

Then, plug in 1/8 as k and 96 as x to find y:

y = 1/8(96)

y = 12

Answer:

97

Step-by-step explanation:

Answer:

Step-by-step explanation:

4x12-5x6-14=0, the highest power of the variable in this equation is 12 so to make it a quadratic equation we should replace x12 by y2. Hence to rewrite the given equation as quadratic just substitute x6=y.

Answer:

4/6=t/(t+1)

Step-by-step explanation:

4/6=t/(t+1)

Answer:

$133.4

Step-by-step explanation:

1. Find the increased pay:

29 * 1.15 = 33.35

2. Find how much she makes in 4 hrs

33.35 * 4 = 133.4

Answer:

35^8

Step-by-step explanation:

5^8 x 7^8

(5 x 7)^8

=35^8

Answer:

4/52 = 1/13

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given the set of datas 3, 7 and 2, we are to evaluate the folowing;

Σ2X – 2 and Σ(X – 1)² =where X are the individual datas.

We will substitute each of the data as value of X and ten take the sum as shown;

For Σ2X – 2

Σ2X – 2 = [2(3)-2]+[2(7)-2]+[2(2)-2]

Σ2X – 2 = (6-2)+(14-2)+(4-2)

Σ2X – 2 = 4+12+2

Σ2X – 2 = 18

For Σ(X – 1)² where x values are also 3, 7 and 2 we will have;

Σ(X – 1)² = (3 – 1)²+(7 – 1)²+(2 – 1)²

Σ(X – 1)² = 2²+6²+1²

Σ(X – 1)² = 4+36+1

Σ(X – 1)² = 41

Answer: The area  is 13[tex]\pi[/tex]ft^2 or  40.84 ft^2

Step-by-step explanation:

First find the area of the square and subtract it from the area of the circle.

The area of a square is  one of the side length squared.

A= 6^2

A = 36  

Now find the area of the whole circle.As it indicates that the diameter is 14ft and to find the area of a circle,we need square the radius and multiply it by pi.

Since the diameter is 14 divide it by 2 to find the radius.  14/2 = 7  

A= 7^2*[tex]\pi[/tex]  

A = 49[tex]\pi[/tex]   We will leave the area in terms of pi.

49[tex]\pi[/tex] - 36 = 13[tex]\pi[/tex]

Answer:

( x - y ) ( a - b ) = -1

Step-by-step explanation:

ax + by = c  and  bx + ay = 1 + c

ax + by = c  and  bx + ay - 1 = c

And now we set c equivalent

ax + by = bx + ay - 1

ax - bx + by - ay = -1

x (a - b) + -y (a - b) = -1

(x - y) ( a - b) = -1

So we can leave it like that, or we can solve for one of the variables.

If we solve for y:

(x - y) ( a - b) = -1

(x - y) = -1 / (a - b)

-y = (-1 / (a - b)) - x

y = (1 / (a-b)) + x

Cheers.

Answer:

ADD 4

Step-by-step explanation:

you want to get 2x by itself so you want to do opposite of -4 so you would do +4 and they cancel out, and what you do to one side you do to the other so

2x = 12 +4

2x = 16

and then you would divide the 2 on both sides so

x = 8 ... just in case you later need to know what x is :)

Answer:

Step-by-step explanation:

What is the probability that a randomly selected person with adequate lung capacity is a non-exerciser?

This depends on statistics given in the prior part of the question.

From this question, i can pick that there is an assumption or statement (in the full question) that exercisers have adequate lung capacity, in a population of both exercisers and non-exercisers.

Data that will help solve this include:

- Population Count or Total number of subjects in the population

- Number of exercisers

- Number of non-exercisers

- Number of subjects with adequate lung capacity

- Number of subjects with inadequate lung capacity

The formula to get the desired answer would be:

Number of non-exercisers

Number of persons with adequate lung capacity

The figure you get from this computation is the answer you seek!

Since it is a probability figure, it must lie between the values of 0 and 1.

Answer:

1/4 is greater than 1/10, 2/10, and 1/5 but not 4/5, and 2/4

Step-by-step explanation:

1/4 = 25%

4/5 = 80%

2/4 = 50%

1/10 = 10%

2/10 = 20%

1/5 = 20%

Answer:

  x ≤ -7

Step-by-step explanation:

Eliminate parentheses using the distributive property.

  -8 -2x ≥ 40 +6x +8

  -8 ≥ 48 +8x . . . . . . . . . add 2x

  -56 ≥ 8x . . . . . . . . . . . subtract 48

  -7 ≥ x . . . . . . . . . . . . . . divide by 8

The solution is x ≤ -7.

Answer:

Rachel has 27

Hong has 51

Manuel has 17

Step-by-step explanation:

Let R represent Rachel, H represent Hong, and M represent Manuel.

They combined have a total of 95. Thus:

[tex]R+H+M=95[/tex]

Hong has 3 times what Manuel has. Therefore:

[tex]H=3M[/tex]

Rachel has 10 more than Manuel. Therefore:

[tex]R=10+M[/tex]

Substitute:

[tex]R+H+M=95\\(10+M)+(3M)+M=95[/tex]

Combine like terms:

[tex]5M+10=95[/tex]

Subtract 10 from both sides:

[tex]5M=85[/tex]

Divide by 5:

[tex]M=17[/tex]

Therefore, Manuel has 17.

Now, find Rachel and Hong's money.

[tex]H=3M\\H=3(17)=51[/tex]

So, Hong has 51.

And for Rachel:

[tex]R=10+M\\R=10+17=27[/tex]

Rachel has 27.

Answer:

  y = x

Step-by-step explanation:

The slopes of parallel lines are the same, so we know the equation will be ...

  y = x + constant

We can find the constant by using the given point's values for x and y:

  2 = 2 + constant

Obviously, the constant is zero.

The equation of the parallel line through (2, 2) is y = x.

Answer:

4

just go with it the explaining  would take to long

Step-by-step explanation:

Answer:

The correct answer would be 54 hundreds

Step-by-step explanation:

If we are considering how many hundreds something has, we can simply take away two 0's and use that number.  We take the two 0's off and then we have the right number of hundreds

Answer:

Hey there!

Five-thousand four-hundred can be expressed as fifty-four hundred.

Let me know if this helps :)

Answer:

Y varies directly as X.

y=kx.

6=K72.

x=6/72.

x=0.08.

Y=0.08x.

when y=?, x=8.

y=0.08×8=0.64.

Answer:

Approximately

Height of screen= 7.1 meters

Step-by-step explanation:

Angle of elevation= 18°

Angle of depression= 58°

Distance of Goran from screen= 5 m

Height of screen from the attachment below

X+y

First let's determine angle a and b

a= 180-90-18

a= 72°

b= 180-90-48

b= 43°

Using sine formula

5/sin a= x/sin 18

5/sin 72= x/sin18

(5*sin 18)/sin 72= x

1.6246 = x

X= 1.6246 m

Y/sin 48= 5/sin b

Y= (5*sin 48)/sin 43

Y= (5*1.08965779)

Y= 5.4483 m

Height of screen= x+y

Height of screen= 1.6246+5.4483

Height of screen= 7.0729

Approximately

Height of screen= 7.1 meters

Answer:

Hey!

Your answer is 15,360!

Step-by-step explanation:

4% of 16,000 is 640

SO...

To find out the last year's amount of voters we have to minus 640 from 16,000...

16,000 - 640 = 15,360

HOPE THIS HELPED!!

Answer:

Your friends data

Step-by-step explanation:

The rule of statistics is: the more exact the data, the better.

It looks like you just rounded your data to the nearest tenth. This is good, but not nearly as good as rounding it to the nearest hundredth.

This is because when you have data that is more exact, you get a better estimation for mean, median, etc. This can help make patterns in your data.

This means that your friend had better data than you.

Hope this helped!

Answer:

Yes, it means that both of you obtain a result with the same precision and accuracy.

Step-by-step explanation:

It is provided that two different people took measurements in order to find the length of a rod.

The first person took 30 measurements.

The second person took 20 measurements.

Both the people got the same average length, i.e. L₀.

In statistics, a larger sample leads to an error free result.

So, for the first person the larger sample helped reducing the chance of any sort of error that may be present.

For the second person, the average is same as the first even when their sample size is less than the first.

This may happen because the sample was selected with a certain precision and accuracy.

Thus, both of them obtain a result with the same precision and accuracy.