Find the area of the rectangle shown.
914
323
323
914
The solution is

I'll use the integrating factor method for the first DE, and undetermined coefficients for the second one.

(a) Multiply both sides by exp(7t ):

exp(7t ) dx/dt + 7 exp(7t ) x = 5 exp(7t ) cos(2t )

The left side is now the derivative of a product:

d/dt [exp(7t ) x] = 5 exp(7t ) cos(2t )

Integrate both sides:

exp(7t ) x = 10/53 exp(7t ) sin(2t ) + 35/53 exp(7t ) cos(2t ) + C

Solve for x :

x = 10/53 sin(2t ) + 35/53 cos(2t ) + C exp(-7t )

(b) Solve the corresonding homogeneous DE:

d²x/dt ² + 6 dx/dt + 8x = 0

has characteristic equation

r ² + 6r + 8 = (r + 4) (r + 2) = 0

with roots at r = -4 and r = -2. So the characteristic solution is

x (char.) = C₁ exp(-4t ) + C₂ exp(-2t )

For the particular solution, assume an ansatz of the form

x (part.) = a cos(3t ) + b sin(3t )

with derivatives

dx/dt = -3a sin(3t ) + 3b cos(3t )

d²x/dt ² = -9a cos(3t ) - 9b sin(3t )

Substitute these into the non-homogeneous DE and solve for the coefficients:

(-9a cos(3t ) - 9b sin(3t ))

… + 6 (-3a sin(3t ) + 3b cos(3t ))

… + 8 (a cos(3t ) + b sin(3t ))

= (-a + 18b) cos(3t ) + (-18a - b) sin(3t ) = 5 sin(3t )

So we have

-a + 18b = 0

-18a - b = 5

==>   a = -18/65 and b = -1/65

so that the particular solution is

x (part.) = -18/65 cos(3t ) - 1/65 sin(3t )

and thus the general solution is

x (gen.) = x (char.) + x (part.)

x = C₁ exp(-4t ) + C₂ exp(-2t ) - 18/65 cos(3t ) - 1/65 sin(3t )

Answer:

87

Step-by-step explanation:

Given is a figure of cyclic quadrilateral.

Opposite angles of a cyclic quadrilateral are supplementary.

Therefore,

z° + 93° = 180°

z° = 180° - 93°

z° = 87°

z = 87

Answer:

x = 960.4

Step-by-step explanation:

980 = 1000[tex]e^{kt}[/tex]

.98 = [tex]e^{10 k}[/tex]

ln(.98) = 10k ln(e)

k = ln(.98)/10

k=-0.00202

~~~~~~~~~~~~~~

x = 1000[tex]e^{20 *-.00202}[/tex]

x = 960.4

The amount of the material right after 20 years will be x = 960.4.

Powers can simply be expressed in concise form using exponential expressions. The exponent shows how many times the base has been multiplied. Since 2 is the "base" and 5 is the "exponent," it can be represented as 2x2x2x2=25 for the number 32. This phrase should be understood as "two to the fifth power."

Given that radioactive material is known to decay at a yearly rate proportional to the amount at each moment. There were 1000 grams of the material 10 years ago. There are 980 grams right now.

The amount of the material will be calculated as,

980 = 1000

[tex]0.98 = e^{10k}[/tex]

ln(.98) = 10k ln(e)

k = ln(.98)/10

k=-0.00202

The value after 20 years will be,

[tex]x = 1000e^{20\times 0.00202}[/tex]

x = 960.4

Therefore, the amount of the material right after 20 years will be x = 960.4.

To know more about an exponential expression follow

https://brainly.com/question/2456547

#SPJ5

Answer:

0.7857

Step-by-step explanation:

Given :

Mean = 69 inches

Standard deviation, = 2.8 inches

The Zscore of a man who is 71.2 inches

The ZSCORE is obtained using the relation :

Zscore = (Score, x - mean) / standard deviation

Zscore = (71.2 - 69) / 2.8

Zscore = 2.2 / 2.8

Zscore = 0.7857

Step-by-step explanation:

You can conclude that 82% of all shoppers will do business with any retailer of any size aslong as they are on the internet.

82% of 2700 = 0.82 * 2700 =2214

which makes the other responder correct.

Answer:

Let the width of the garden =x meter

Then length=(x+4) meter

Half perimeter =36 m

So perimeter of garden =(2×36)=72 meters

According to the question

⇒2(l+b)=72

⇒2(x+x+4)=72

⇒2x+2x+4=74⇒4x=64⇒x=16 meters

Hence,the width of the garden =16 meters

The length of the garden =(16+4)=20 meters

Answer:

-7

Step-by-step explanation:

if you multiply by 7 positive it wont work because u cant cancel 7x out and a fraction wont work because theres no fraction involved in this so ur answer is A

Answer:

Hello good evening friend

This question is incomplete, the complete question is;

We know that the remainder R[tex]_n[/tex] will satisfy | R[tex]_n[/tex] | ≤ b[tex]_{ n + 1[/tex] = 1 / ( n + 1 )9[tex]^{ n + 1[/tex].

We must make n large enough so that this is less than 0.0001.

Rounding to five decimal places,

we have b₂ = _________ , b₃ =_________and b₄ =__________

Answer:

b₂ = 0.00617, b = 0.00046 and  b₄ = 0.00004

Step-by-step explanation:

Given the data in the question;

| R[tex]_n[/tex] | ≤ b[tex]_{ n + 1[/tex] = 1 / ( n + 1 )9[tex]^{ n + 1[/tex]

Now,

b[tex]_{ n + 1[/tex] = 1 / ( n + 1 )9[tex]^{ n + 1[/tex]

b₂ = b[tex]_{ 1 + 1[/tex] = 1 / ( 1 + 1 )9[tex]^{ 1 + 1[/tex] = 1 / (2)9² = 1 / 162 = 0.00617   { 5 decimal places }

b₃ = b[tex]_{ 2 + 1[/tex] = 1 / ( 2 + 1 )9[tex]^{ 2 + 1[/tex] = 1 / (3)9³ = 1 / 2187 = 0.00046 { 5 decimal places }

b₄ = b[tex]_{ 3 + 1[/tex] = 1 / ( 3 + 1 )9[tex]^{ 3 + 1[/tex] = 1 / (4)9⁴ = 1 / 19683 = 0.00004 { 5 decimal places }

Therefore, b₂ = 0.00062, b = 0.00046 and  b₄ = 0.00004

Answer:

6 and 2

Step-by-step explanation:

6+2= 8, so they can combine to equal 8. First box checked. Then, they can also be subtracted to get 4, half of 8. 8/2= 4 and 6-2=4. Second box checked.

Hope this helped :D

Step-by-step explanation:

Let's take the numbers as m and n and classify the info

m+n=8

m-n=4

So solving the sums Simultaneously you can get

2n=4

n=2

Substituting this value gives

2+m=8

m=6

Inorder to check if your answers are valid add them to the equations

6+2=8✅

6-2=4✅

Therefore the answers are valid

Answer:

3

Step-by-step explanation:

Answer:

1 : 4

Step-by-step explanation:

2 feet is 24 inches so we are finding the ratio between

6 and 24

Simplify

1 : 4

Answer:

Coefficient of skewness = 0.5785

Population standard deviation = 88.154

Step-by-step explanation:

Given the data:

Month Jan Feb Mar Apr May Jun Jul

Unit Sales 314 285 158 482 284 310 281

Reordered data : 158, 281, 284, 285, 310, 314, 482

The population mean of the data :

Mean, μ = Σx / n = 2114 / 7 = 302

The median :

1/2(n+1)th term

n = 7

1/2(8)th term

Median = 4th term = 285

The population standard deviation, s :

s = √(Σ(x - μ)²/n)

s = √[(158-302)^2 + (281-302)^2 + (284-302)^2 + (285-302)^2 + (310-302)^2 + (314-302)^2 + (482-302)^2] / 7

s= √(54398 / 7)

s = √7771.1428

s = 88.154

The Pearson Coefficient of skewness :

[3(μ - median)] / s

3(302 - 285) / 88.154

3(17) / 88.154

51 / 88.154

= 0.5785

Answer: hi your question is incomplete below is the complete question

Suppose we increase the overall number of doctors in the U.S. in all fields and specialties of medical practice by equal percentages, which would shift the supply curves in all the respective medical practice markets. Suppose we were to analyze two separate medical practice markets: Plastic Surgery Cardiology Which markets' price would be most impacted by this increase in the supply of doctors? Which markets' quantity would be most impacted by this increase in the supply of doctors?

answer :

Change in Market price = Cardiology

Change in Quantity = Plastic surgery

Step-by-step explanation:

Given that we are analyzing two separate markets with different levels of importance .

The demand for plastic surgery is more elastic when compared with Cardiology and this is due to the importance of Cardiology over plastic surgery.

The market price that will be affected by the increase in doctors supply is Cardiology market price while the Market quantity that would be affected by the increase is quantity of  Plastic surgery

Answer:

Parallel lines are lines that never intersect because they have the same slope (m). So, this means that they only possible difference in there equations is the y-intercept (b). ... The slope in each equation is one-half, but each equation has a different y-intercept.

Answer:

45 km por galón

60 galones en 2700 Km

Step-by-step explanation:

180 / 4

45 km por galón

900 / 45

20 galones

2700 / 45

60 galones en 2700 Km

Answer:

(-1, -6)

Step-by-step explanation:

This a term in this function is not negative, which would make it be flipped over the x-axis. Therefore this function takes the typical parabola shape, and it will have a minimum point.

To find the x-value of the minimum use the formula -b / 2a.

-12 / 2(6) = -1

Then plug in the x-value and find the y-value for this function

f(-1) = 6(-1)^2 + 12(-1) = -6

Answer:

0.9021 = 90.21% probability that 10 or fewer customers choose the leading brand

Step-by-step explanation:

For each customer, there are only two possible outcomes. Either they choose the leading brand, or they do not. The probability of a customer choosing the leading brand is independent of any other customer, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

The leading brand of dishwasher detergent has a 30% market share.

This means that [tex]p = 0.3[/tex]

A sample of 25 dishwasher detergent customers was taken.

This means that [tex]n = 25[/tex]

a. What is the probability that 10 or fewer customers choose the leading brand?

This is:

[tex]P(X \leq 10) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)[/tex]

In which

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{25,0}.(0.3)^{0}.(0.7)^{25} = 0.0001[/tex]

[tex]P(X = 1) = C_{25,1}.(0.3)^{1}.(0.7)^{24} = 0.0014[/tex]

[tex]P(X = 2) = C_{25,2}.(0.3)^{2}.(0.7)^{23} = 0.0074[/tex]

[tex]P(X = 3) = C_{25,3}.(0.3)^{3}.(0.7)^{22} = 0.0243[/tex]

[tex]P(X = 4) = C_{25,4}.(0.3)^{4}.(0.7)^{21} = 0.0572[/tex]

[tex]P(X = 5) = C_{25,5}.(0.3)^{5}.(0.7)^{20} = 0.1030[/tex]

[tex]P(X = 6) = C_{25,6}.(0.3)^{6}.(0.7)^{19} = 0.1472[/tex]

[tex]P(X = 7) = C_{25,7}.(0.3)^{7}.(0.7)^{18} = 0.1712[/tex]

[tex]P(X = 8) = C_{25,8}.(0.3)^{8}.(0.7)^{17} = 0.1651[/tex]

[tex]P(X = 9) = C_{25,9}.(0.3)^{9}.(0.7)^{16} = 0.1336[/tex]

[tex]P(X = 10) = C_{25,10}.(0.3)^{10}.(0.7)^{15} = 0.0916[/tex]

Then

[tex]P(X \leq 10) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) = 0.0001 + 0.0014 + 0.0074 + 0.0243 + 0.0572 + 0.1030 + 0.1472 + 0.1712 + 0.1651 + 0.1336 + 0.0916 = 0.9021[/tex]

0.9021 = 90.21% probability that 10 or fewer customers choose the leading brand

Answer:

The maximum number of possible combinations are 9.

Step-by-step explanation:

There are three types of juices :

Orange, Mango and Blue lemonade

There are three types of biscuits:

Oreo, Skyflakes and Rebisco

So, the number of possible combinations are

= (3 C 1) x (3 C 1)

= 3 x 3 = 9

The maximum number of possible combinations are 9.

Answer:

8x +15

Step-by-step explanation:

f(x) = 10 + 2x and g(x) = 6x + 5

(f+ g)(x) =  10 + 2x + 6x + 5

Combine like terms

              = 8x +15

Answer:

8x+15

Step-by-step explanation:

(f+g)(x) = f(x)+g(x)

= (10+2x) + (6x+5)

= 8x+15

hope it helped, please mark me brainliest.

Answer:

Step-by-step explanation:

Answer:9

Step-by-step explanation: 18/6=3 so 27/3 should equal the answer. If u know ur multiplication, the answer would be 9

Hello,

In a diginacci sequence, all term is the sum off digits of the 2 terms before.

Answer: 2,3

[tex]u_{-2}=1\\u_{-1}=1\\u_0=digit(u_{-2})+digit(u_{-1})=1+1=2\\u_1=1+2=3\\u_2=2+3=5\\u_3=3+5=8\\u_4=5+8=13\\u_5=8+1+3=12\\...\\u_{18}=11\\u_{19}=8\\u_{20}=10\\u_{21}=9\\u_{22}=10\\u_{23}=10\\u_{24}=2**********\\u_{25}=3**********\\2020=24*84+4\\u_{2020}=u_{4}=13\\[/tex]

We must begin with 13 , 10

Proof:

Dim a As Long, b As Long, c As Long, nb As Integer

a = 13

b = 10

nb = 1

Print nb, a

While nb < 2021

   nb = nb + 1

   c = somme&(a, b)

   a = b

   b = c

   '    Print nb, a

Wend

Print nb, a

End

Function somme& (a1 As Long, b1 As Long)

   Dim strA As String, strB As String, n As Long

   strA = LTrim$(Str$(a1))

   strB = LTrim$(Str$(b1))

   n = 0

   For i = 1 To Len(strA)

       n = n + Val(Mid$(strA, i, 1))

   Next i

   For i = 1 To Len(strB)

       n = n + Val(Mid$(strB, i, 1))

   Next i

   somme& = n

End Function

Answer:

0.5217

Step-by-step explanation:

P(more than 5 customer arrive):

P(X>=6)=1-P(X<=5)=  1-∑x=0x e-λ*λx/x!= 0.5217

Answer: this app help me

Step-by-step explanation: it is so fun the answers is it is so good

Answer:

1.25. It would be 1.25 if ur just talking about dividing in general which is pretty tough

Answer:

\dfrac54=-4c+\dfrac14 4 5 ​ =−4c+ 4 1 ​ start fraction, 5, divided by, 4, end fraction, equals, minus, 4, c, plus, start fraction, 1, divided by, 4, end fraction

Step-by-step explanation:

Step-by-step explanation:

Answer:

-15,625

Step-by-step explanation:

[tex]-5^6[/tex]  =   -15,625

Hope this helps.

Answer:

-15,625 ... be carful on this type question

the - sign does NOT get raised to the 6th power...

[tex](-5)^{6}[/tex] that would be + .... [tex]-5^{6}[/tex] is negative

Step-by-step explanation:

Answer:

11/12 cups

Step-by-step explanation:

2/3+1/4 = ( 2x4 + 3x1 )/( 3x4 ) = ( 8+3 )/12 = 11/12

Step-by-step explanation:

12/100=30/x

12x=3000

x=250

hiii! !!

Answer:

The quadrilateral is a rhombus

Step-by-step explanation:

Given

[tex]A = (2, 8)[/tex]

[tex]B = (3, 11)[/tex]

[tex]C = (4, 8)[/tex]

[tex]D=(3, 5)[/tex]

Required

The true statement

Calculate slope (m) using

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Calculate distance using:

[tex]d= \sqrt{(x_2 - x_1)^2 + (y_2 -y_1)^2}[/tex]

Calculate slope and distance AB

[tex]m_{AB} = \frac{11 - 8}{3 - 2}[/tex]

[tex]m_{AB} = \frac{3}{1}[/tex]

[tex]m_{AB} = 3[/tex] -- slope

[tex]d_{AB}= \sqrt{(3 - 2)^2 + (11 -8)^2}[/tex]

[tex]d_{AB}= \sqrt{10}[/tex] -- distance

Calculate slope and distance BC

[tex]m_{BC} = \frac{8 - 11}{4 - 3}[/tex]

[tex]m_{BC} = \frac{- 3}{1}[/tex]

[tex]m_{BC} = -3[/tex] -- slope

[tex]d_{BC} = \sqrt{(4-3)^2+(8-11)^2[/tex]

[tex]d_{BC} = \sqrt{10}[/tex] --- distance

Calculate slope CD

[tex]m_{CD} = \frac{5 - 8}{3 - 4}[/tex]

[tex]m_{CD} = \frac{- 3}{- 1}[/tex]

[tex]m_{CD} = 3[/tex] -- slope

[tex]d_{CD} = \sqrt{(3-4)^2+(5-8)^2}[/tex]

[tex]d_{CD} = \sqrt{10}[/tex] -- distance

Calculate slope DA

[tex]m_{DA} = \frac{8 - 5}{2 - 3}[/tex]

[tex]m_{DA} = \frac{3}{- 1}[/tex]

[tex]m_{DA} = -3[/tex] -- slope

[tex]d_{DA} = \sqrt{(2-3)^2 + (8-5)^2}[/tex]

[tex]d_{DA} = \sqrt{10}[/tex]

From the computations above, we can see that all 4 sides are equal, i.e. [tex]\sqrt{10}[/tex]

And the slope of adjacent sides are negative reciprocal, i.e.

[tex]m_{AB} = 3[/tex]  and [tex]m_{CD} = -3[/tex]

[tex]m_{CD} = 3[/tex] and [tex]m_{DA} = -3[/tex]

The quadrilateral is a rhombus