SOMEONE PLEASE HELP ME ASAP PLEASE!!!​

Answer:

  (x, y) = (7, 4) meters

Step-by-step explanation:

The area of the floor without the removal is x^2, so with the smaller square removed, it is x^2 -y^2.

The perimeter of the floor is the sum of all side lengths, so is 4x +2y.

The given dimensions tell us ...

  x^2 -y^2 = 33

  4x +2y = 36

From the latter equation, we can write an expression for y:

  y = 18 -2x

Substituting this into the first equation gives ...

  x^2 -(18 -2x)^2 = 33

  x^2 -(324 -72x +4x^2) = 33

  3x^2 -72x + 357 = 0 . . . . write in standard form

  3(x -7)(x -17) = 0 . . . . . factor

Solutions to this equation are x=7 and x=17. However, for y > 0, we must have x < 9.

  y = 18 -2(7) = 4

The floor dimension x is 7 meters; the inset dimension y is 4 meters.

Answer:

-0.28

Step-by-step explanation:

(1/5) : (-5/7)=(1*5)/(5*(-5))=-(7/25)=-0.28

Answer:

[tex]-7/25[/tex]

Step-by-step explanation:

[tex]1/5 \div -5/7[/tex]

Do the reciprocal of the second fraction.

[tex]1/5 \times 7/-5[/tex]

Multiply the first fraction by the reciprocal of the second fraction.

[tex]7/-25=-0.28[/tex]

The answer in decimal form is -0.28.

Answer:

Sry, i dont know all of the numbers. Hope this helps!

Here are the first:

Step-by-step explanation:

3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408128481117450284102701938521105559644622948954930381964428810975665933446128475648233786783165271201909145648566923460348610454326648213393607260249141273724587006606315588174881520920962829254091715364367892590360011330530548820466521384146951941511609433057270365759591953092186117381932611793105118548074462379962749567351885752724891227938183011949129833673362440656643086021394946395224737190702179860943702770539217176293176752384674818467669405132000568127145263560827785771342757789609173637178721468440901224953430146549585371050792279689258923542019956112129021960864034418159813629774771309960518707211349999998372978049951059731732816096318595024459455346908302642522308253344685035261931188171010003137838752886587533208381420617177669147303598253490428755468731159562863882353787593751957781857780532171226806613001927876611195909216420198938095257201065485863278865936153381827968230301952035301852968995773622599413891249721775283479131515574857242454150695950829533116861727855889075098381754637464939319255060400927701671139009848824012858361603563707660104710181942955596198946767837449448255379774726847104047534646208046684259069491293313677028989152104752162056966024058038150193511253382430035587640247496473263914199272604269922796782354781636009341721641219924586315030286182974555706749838505494588586926995690927210797509302955321165344987202755960236480665499119881834797753566369807426542527862551818417574672890977772793800081647060016145249192173217214772350141441973568548161361157352552133475741849468438523323907394143334547762416862518983569485562099219222184272550254256887671790494601653466804988627232791786085784383827967976681454100953883786360950680064225125205117392984896084128488626945604241965285022210661186306744278622039194945047123713786960956364371917287467764657573962413890865832645995813390478027590099465764078951269468398352595709825822620522489407726719478268482601476990902640136394437455305068203496252451749399651431429809190659250937221696461515709858387410597885959772975498930161753928468138268683868942774155991855925245953959431049972524680845987273644695848653836736222626099124608051243884390451244136549762780797715691435997700129616089441694868555848406353422072225828488648158456028506016842739452267467678895252138522549954666727823986456596116354886230577456498035593634568174324112515076069479451096596094025228879710893145669136867228748940560101503308617928680920874760917824938589009714909675985261365549781893129784821682998948722658804857564014270477555132379641451523746234364542858444795265867821051141354735739523113427166102135969536231442952484937187110145765403590279934403742007310578539062198387447808478489683321445713868751943506430218453191048481005370614680674919278191197939952061419663428754440643745123718192179998391015919561814675142691239748940907186494231961567945208095146550225231603881930142093762137855956638937787083039069792077346722182562599661501421503068038447734549202605414665925201497442850732518666002132434088190710486331734649651453905796268561005508106658796998163574736384052571459102897064140110971206280439039759515677157700420337869936007230558763176359421873125147120532928191826186125867321579198414848829164470609575270695722091756711672291098169091528017350671274858322287183520935396572512108357915136988209144421006751033467110314126711136990865851639831501970165151168517143765761835155650884909989859982387345528331635507647918535893226185489632132933089857064204675259070915481416549859461637180270981994309924488957571282890592323326097299712084433573265489382

Pls mark Brainliest

Answer:

D. No, because the differential equation does not have constant coefficients.

Step-by-step explanation:

The undetermined coefficient method cannot be applied to non homogeneous variables. The differential equation does not have constant variables therefore the method of undetermined superposition can not be applied. To complete a solution of non homogeneous equation the particular solution must be added to the homogeneous equation.

Answer:

[tex]y(x)=c_1e^{2ix}+c_2e^{-2ix}[/tex]

Step-by-step explanation:

You have the following differential equation:

[tex]3y''+12y=0[/tex]     (1)

In order to find the solution to the equation, you can use the method of the characteristic polynomial.

The characteristic polynomial of the given differential equation is:

[tex]3m^2+12=0\\\\m^2=-\frac{12}{3}=-4\\\\m_{1,2}=\pm2\sqrt{-1}=\pm2i[/tex]

The solution of the differential equation is:

[tex]y(x)=c_1e^{m_1x}+c_2e^{m_2x}[/tex]   (2)

where m1 and m2 are the roots of the characteristic polynomial.

You replace the values obtained for m1 and m2 in the equation (2). Then, the solution to the differential equation is:

[tex]y(x)=c_1e^{2ix}+c_2e^{-2ix}[/tex]

Answer:

54

Step-by-step explanation:

The pink parts are 9 out of total 11 parts.

9/11

Multiply with 66.

9/11 × 66

= 54

Hey there! :)

Answer:

P(Pink) = 54.

Step-by-step explanation:

Begin by calculating the possibility of the spinner landing on pink:

[tex]P(pink) = \frac{pink}{total}[/tex]

Therefore:

[tex]P(Pink) = \frac{9}{11}[/tex]

In this question, the spinner was spun 66 times. Since we have solved for the probability, we can set up ratios to find the probability of the spinner landing on pink out of 66.

[tex]\frac{9}{11}= \frac{x}{66}[/tex]

Cross multiply:

594 = 11x

Divide both sides by 11:

x = 54.

P(Pink) = 54.

Answer:

c. The data are continuous because the data can take on any value in an interval.

Step-by-step explanation:

A variable is said to be continuous if it can take on any value in an interval. Examples are lengths, temperature, etc

A discrete variable, on the other hand, can only take on specific values. Examples of discrete variables are the number of students and age.

The exact lengths (in kilometers) of the ocean coastlines of different countries is a continuous variable because it can take on any value in an interval.

A stated earlier, Lengths are in general, continuous variables.

Answer:

the step-by-step explanation for height first :

[tex]h=\sqrt{h^{2} } +r^{2} =26[/tex]

[tex]h=\sqrt{h^{2} } +10^{2} =676[/tex]

[tex]h=\sqrt{h^{2} } + 100 = 676[/tex]

[tex]100-100 = 0[/tex]

[tex]676-100=576[/tex]

[tex]\sqrt{576}[/tex]

[tex]height =[/tex] 24 m

________________

step-by-step explanation for the problem :

FORMULA :  [tex]v = \frac{1}{3}[/tex] · [tex]\pi[/tex] · [tex]r^{2}[/tex] · [tex]h[/tex]

v = [tex]\frac{1}{3}[/tex] · [tex]\pi[/tex] · [tex]10^{2}[/tex] · [tex]24[/tex] = [tex]800\pi[/tex] = [tex]2513.27412[/tex] = 2513

Answer:

a) Probability that a team will win the match given that it has won the first game = 0.66

b) Probability that a team will win the match given that it has won the first two games= 0.81

c) Probability that a team will win the match, given that it has won two out of the first three games = 0.69

Step-by-step explanation:

There are a total of seven games to be played. Therefore, W and L consists of 2⁷ equi-probable sample points

a) Since one game has already been won by the team, there are 2⁶ = 64 sample points left. If the team wins three or more matches, it has won.

Number of ways of winning the three or more matches left = [tex]6C3 + 6C4 + 6C5 + 6C6[/tex]

= 20 + 15 + 6 + 1 = 42

P( a team will win the match given that it has won the first game) = 42/64 = 0.66

b)  Since two games have already been won by the team, there are 2⁵ = 32 sample points left. If the team wins two or more matches, it has won.

Number of ways of winning the three or more matches left = [tex]5C2 + 5C3 + 5C4 + 5C5[/tex] = 10 + 10 + 5 +1 = 26

P( a team will win the match given that it has won the first two games) = 26/32 = 0.81

c) Probability that a team will win the match, given that it has won two out of the first three games

They have played 3 games out of 7, this means that there are 4 more games to play. The sample points remain 2⁴ = 16

They have won 2 games already, it means they have two or more games to win.

Number of ways of winning the three or more matches left = [tex]4C2 + 4C3 + 4C4[/tex] = 6 + 4 + 1 = 11

Probability that a team will win the match, given that it has won two out of the first three games = 11/16

Probability that a team will win the match, given that it has won two out of the first three games = 0.69

Answer:

c- the right triangle altitude theorem

Step-by-step explanation:

i did it on edge! ; )

The missing statement in Step 6 is ,c- The right triangle altitude theorem.

We have given that,

In △ABC, AD ⊥ BC

Prove: StartFraction sine (uppercase B) Over b EndFraction = StartFraction sine (uppercase C) Over c EndFraction.

Triangle A B C is shown.

The right triangle altitude theorem or geometric mean theorem is a result in elementary geometry that describes a relation between the altitude on the hypotenuse in a right triangle and the two-line segments it creates on the hypotenuse

Therefore we have,

A perpendicular bisector is drawn from point A to point D on side C B forming a right angle.

The length of A D is h, the length of C B is a, the length of C A is b, and the length of A B is c.

So the missing statement in Step 6

b = c

c=The right triangle altitude theorem.

To learn more about the right triangle altitude theorem visit:

https://brainly.com/question/723406

Answer:

$23.64

Step-by-step explanation:

12 * $1.97 = $23.64

Answer:

The sequence can be represented by the formula of its nth term:

[tex]a_n=\frac{(-1)^n}{n}[/tex]

Step-by-step explanation:

Notice that we are in the presence of an alternate sequence (the values alternate from negative to positive. Therefore we need to take into account that there should be a factor "-1" raised to the "n" value for the sequence. Also, given that the sequence looks in absolute value like the harmonic sequence, we conclude upon the following general form for the "nth" term of the sequence:

[tex]a_n=\frac{(-1)^n}{n}[/tex]

Answer:

50 to 60 seconds is the answer

Answer:

20gallons

Step-by-step explanation:

Answer:

Correct statement: "the number is divisible by 3".

Step-by-step explanation:

The statement provided is:

When a number is divisible by 9, the number is divisible by 3.

The general form of a conditional statement in if-then form is:

[tex]p\rightarrow q[/tex]

This implies that if p, then q.

The part after the "if" is known as the hypothesis and the part after the "then" is known as the conclusion.

The if-then form of the provided statement is:

If a number is divisible by 9, then the number is divisible by 3.

So, the conclusion is:

"the number is divisible by 3"

Answer:

a

Step-by-step explanation:

Answer:  Measure of angle T = 25 degrees and Measure of angle U = 45 degrees

Step-by-step explanation:

Measure of angle T = 25 degrees and TU = 12 is the pair of measurements would eliminate the possibility that the triangles are congruent.

" Triangles are said to be congruent if the corresponding sides and angles of the one triangle are equals to the other triangles."

According to the question,

In triangle KLM,

KM =27millimeters

LM = 20millimeters

KL = 12 millimeters

∠K= 45degrees

∠M= 25 degrees

∠L = 110degrees

From the given measurements of the triangle we have,

side with measure 27millimeters is opposite to angle 110° .

side with measure 12millimeters is opposite to angle 25° .

side with measure 20millimeters is opposite to angle 45°.

From the conditions in triangle TUV to be congruent to triangle KLM ,

Measure of angle T = 25 degrees and TU = 12  is against the given condition of congruent triangle.

As angle T and side TU are adjacent to each other, which is against the correspondence of the given triangle.

Hence, measure of angle T = 25 degrees and TU = 12 is the pair of measurements would eliminate the possibility that the triangles are congruent.

Learn more about congruent triangle here

https://brainly.com/question/12413243

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Answer:

You didn't state it but you need to find Angle A.

From the Pythagorean Theorem, we calculate side ac

side ac^2 = 5^2 - 3^2  =25 -9 = 16 Side AC = 4

arc tangent angle A = 3 / 4 = .75

angle A =  36.87 Degrees

Step-by-step explanation:

Answer:

Check below, please

Step-by-step explanation:

Hello!

1) In the Newton Method, we'll stop our approximations till the value gets repeated. Like this

[tex]x_{1}=2\\x_{2}=2-\frac{f(2)}{f'(2)}=2.5\\x_{3}=2.5-\frac{f(2.5)}{f'(2.5)}\approx 2.4166\\x_{4}=2.4166-\frac{f(2.4166)}{f'(2.4166)}\approx 2.41421\\x_{5}=2.41421-\frac{f(2.41421)}{f'(2.41421)}\approx \mathbf{2.41421}[/tex]

2)  Looking at the graph, let's pick -1.2 and 3.2 as our approximations since it is a quadratic function. Passing through theses points -1.2 and 3.2 there are tangent lines that can be traced, which are the starting point to get to the roots.

We can rewrite it as: [tex]x^2-2x-4=0[/tex]

[tex]x_{1}=-1.1\\x_{2}=-1.1-\frac{f(-1.1)}{f'(-1.1)}=-1.24047\\x_{3}=-1.24047-\frac{f(1.24047)}{f'(1.24047)}\approx -1.23607\\x_{4}=-1.23607-\frac{f(-1.23607)}{f'(-1.23607)}\approx -1.23606\\x_{5}=-1.23606-\frac{f(-1.23606)}{f'(-1.23606)}\approx \mathbf{-1.23606}[/tex]

As for

[tex]x_{1}=3.2\\x_{2}=3.2-\frac{f(3.2)}{f'(3.2)}=3.23636\\x_{3}=3.23636-\frac{f(3.23636)}{f'(3.23636)}\approx 3.23606\\x_{4}=3.23606-\frac{f(3.23606)}{f'(3.23606)}\approx \mathbf{3.23606}\\[/tex]

3) Rewriting and calculating its derivative. Remember to do it, in radians.

[tex]5\cos(x)-x-1=0 \:and f'(x)=-5\sin(x)-1[/tex]

[tex]x_{1}=1\\x_{2}=1-\frac{f(1)}{f'(1)}=1.13471\\x_{3}=1.13471-\frac{f(1.13471)}{f'(1.13471)}\approx 1.13060\\x_{4}=1.13060-\frac{f(1.13060)}{f'(1.13060)}\approx 1.13059\\x_{5}= 1.13059-\frac{f( 1.13059)}{f'( 1.13059)}\approx \mathbf{ 1.13059}[/tex]

For the second root, let's try -1.5

[tex]x_{1}=-1.5\\x_{2}=-1.5-\frac{f(-1.5)}{f'(-1.5)}=-1.71409\\x_{3}=-1.71409-\frac{f(-1.71409)}{f'(-1.71409)}\approx -1.71410\\x_{4}=-1.71410-\frac{f(-1.71410)}{f'(-1.71410)}\approx \mathbf{-1.71410}\\[/tex]

For x=-3.9, last root.

[tex]x_{1}=-3.9\\x_{2}=-3.9-\frac{f(-3.9)}{f'(-3.9)}=-4.06438\\x_{3}=-4.06438-\frac{f(-4.06438)}{f'(-4.06438)}\approx -4.05507\\x_{4}=-4.05507-\frac{f(-4.05507)}{f'(-4.05507)}\approx \mathbf{-4.05507}\\[/tex]

5) In this case, let's make a little adjustment on the Newton formula to find critical numbers. Remember their relation with 1st and 2nd derivatives.

[tex]x_{n+1}=x_{n}-\frac{f'(n)}{f''(n)}[/tex]

[tex]f(x)=x^6-x^4+3x^3-2x[/tex]

[tex]\mathbf{f'(x)=6x^5-4x^3+9x^2-2}[/tex]

[tex]\mathbf{f''(x)=30x^4-12x^2+18x}[/tex]

For -1.2

[tex]x_{1}=-1.2\\x_{2}=-1.2-\frac{f'(-1.2)}{f''(-1.2)}=-1.32611\\x_{3}=-1.32611-\frac{f'(-1.32611)}{f''(-1.32611)}\approx -1.29575\\x_{4}=-1.29575-\frac{f'(-1.29575)}{f''(-4.05507)}\approx -1.29325\\x_{5}= -1.29325-\frac{f'( -1.29325)}{f''( -1.29325)}\approx -1.29322\\x_{6}= -1.29322-\frac{f'( -1.29322)}{f''( -1.29322)}\approx \mathbf{-1.29322}\\[/tex]

For x=0.4

[tex]x_{1}=0.4\\x_{2}=0.4\frac{f'(0.4)}{f''(0.4)}=0.52476\\x_{3}=0.52476-\frac{f'(0.52476)}{f''(0.52476)}\approx 0.50823\\x_{4}=0.50823-\frac{f'(0.50823)}{f''(0.50823)}\approx 0.50785\\x_{5}= 0.50785-\frac{f'(0.50785)}{f''(0.50785)}\approx \mathbf{0.50785}\\[/tex]

and for x=-0.4

[tex]x_{1}=-0.4\\x_{2}=-0.4\frac{f'(-0.4)}{f''(-0.4)}=-0.44375\\x_{3}=-0.44375-\frac{f'(-0.44375)}{f''(-0.44375)}\approx -0.44173\\x_{4}=-0.44173-\frac{f'(-0.44173)}{f''(-0.44173)}\approx \mathbf{-0.44173}\\[/tex]

These roots (in bold) are the critical numbers

Answer:

800

Step-by-step explanation:

10,000 x 64 = 640,000

Square Root It Makes It

800

Answer:

6,400

Step-by-step explanation:

The square root of 10,000 times 64 is simplified to 6,400

Answer : The correct statements are,

AC = 5 cm

BA = 4 cm

The perimeter of triangle ABC is 12 cm.

Step-by-step explanation :

As we know that a, b, and c are midpoints of the sides of right triangle that means midpoint divide the side in equal parts.

Now we have to calculate the sides of triangle ABC by using Pythagoras theorem.

Using Pythagoras theorem in ΔACF :

[tex](AC)^2=(FA)^2+(CF)^2[/tex]

Now put all the values in the above expression, we get the value of side AC.

[tex](AC)^2=(3)^2+(4)^2[/tex]

[tex]AC=\sqrt{(9)^2+(16)^2}[/tex]

[tex]AC=5cm[/tex]

Using Pythagoras theorem in ΔDAB :

[tex](Hypotenuse)^2=(Perpendicular)^2+(Base)^2[/tex]

[tex](BD)^2=(AD)^2+(BA)^2[/tex]

Now put all the values in the above expression, we get the value of side BA.

[tex](5)^2=(3)^2+(BA)^2[/tex]

[tex]BA=\sqrt{(5)^2-(3)^2}[/tex]

[tex]BA=4cm[/tex]

Using Pythagoras theorem in ΔBEC :

[tex](Hypotenuse)^2=(Perpendicular)^2+(Base)^2[/tex]

[tex](BE)^2=(CE)^2+(CB)^2[/tex]

Now put all the values in the above expression, we get the value of side CB.

[tex](5)^2=(4)^2+(CB)^2[/tex]

[tex]CB=\sqrt{(5)^2-(4)^2}[/tex]

[tex]CB=3cm[/tex]

Now we have to calculate the perimeter of ΔABC.

Perimeter of ΔABC = Side AB + Side CB+ Side AC

Perimeter of ΔABC = 4 + 3 + 5

Perimeter of ΔABC = 12 cm

Now we have to calculate the area of ΔABC.

Area of ΔABC = [tex]\frac{1}{2}\times 4\times 3=6cm^2[/tex]

Now we have to calculate the area of ΔDEF.

Area of ΔDEF = [tex]\frac{1}{2}\times 8\times 6=24cm^2[/tex]

Area of ΔABC = [tex]\frac{6}{24}\times[/tex] Area of ΔDEF

Area of ΔABC = [tex]\frac{1}{4}[/tex] Area of ΔDEF

Answer:

Step-by-step explanation:

its B

Answer:

the answer is B

Step-by-step explanation:

Answer:

It may look simple to the owner because he is not the one losing a job. For the three machinists it represents a major event with major consequences

Answer:

Answer:

Option 2nd is correct.

=0.

Step-by-step explanation:

Given the function:

Solve:

First calculate:

f[g(x)]

Substitute the function g(x)

Replace x with x-8 in the function f(x) we get;

The distributive property says that:

Using distributive property:

⇒

Put x = 6 we get;

Therefore, the value of   is 0.

Step-by-step explanation:

Answer:

0

Step-by-step explanation:

f(x) = 6x + 12

g(x) = x − 8

f(g(6))=?

g(6)=6-8= -2

f(-2)= -2*6+12= -12+12=0

f(g(6))= f(-2)=0

Answer:

0.0013

Step-by-step explanation:

The probability of selling a property is 40%, so the probability of not selling it is 60%.

To find the probability of selling at least 11 properties, we can calculate the following cases:

Selling 11:

P(11) = C(13,11) * P(sell)^11 * P(not sell)^2

P(11) = (13! / (11! * 2!)) * 0.4^11 * 0.6^2

P(11) = 13*12/2 * 0.4^11 * 0.6^2 = 0.001178

Selling 12:

P(12) = C(13,12) * P(sell)^12 * P(not sell)^1

P(11) = (13! / (12! * 1!)) * 0.4^12 * 0.6^1

P(11) = 13 * 0.4^12 * 0.6 = 0.000131

Selling 13:

P(13) = C(13,13) * P(sell)^13 * P(not sell)^0

P(11) = 1 * 0.4^13 * 0.6^0

P(11) = 1 * 0.4^13 * 1 = 0.000007

Final probability:

P(at least 11) = P(11) + P(12) + P(13)

P(at least 11) = 0.001178 + 0.000131 + 0.000007 = 0.001316

P(at least 11) = 0.0013

Answer:

[tex]y = 10cos (7x) - \frac{4}{7}sin ( 7x )[/tex]

B.

B.

[tex]y = \frac{17}{8}e^4^x - \frac{1}{8}e^-^4^x[/tex]

Step-by-step explanation:

Question 1:

- We are given a homogeneous second order linear ODE as follows:

                                [tex]y'' + 49y = 0[/tex]

- A pair of independent functions are given as ( y1 ) and ( y2 ):

                               [tex]y_1 = cos ( 7x )\\\\y_2 = sin ( 7x )[/tex]

- The given ODE is subjected to following initial conditions as follows:

                               [tex]y ( 0 ) = 10\\\\y ' ( 0 ) = -4[/tex]

- We are to verify that the given independent functions ( y1 ) and ( y2 ) are indeed the solution to the given ODE. If the functions are solutions then find the complete solution of the homogeneous ODE of the form:

                               [tex]y = c_1y_1 + c_2y_2[/tex]

Solution:-

- To verify the functions are indeed the solution to the given ODE. We will plug the respective derivatives of each function [ y1 and y2 ] into the ODE and prove whether the equality holds true or not.

- Formulate the second derivatives of both functions y1 and y2 as follows:

                           [tex]y'_1 = -7sin(7x) , y''_1 = -49cos(7x)\\\\y'_2 = -7cos(7x) , y''_2 = -49sin(7x)\[/tex]

- Now plug the second derivatives of each function and the functions itself into the given ODE and verify whether the equality holds true or not.

                           [tex]y''_1 + 49y_1 = 0\\\\-49cos(7x) + 49cos ( 7x ) = 0\\0 = 0\\\\y''_2 + 49y_2 = 0\\\\-49sin(7x) + 49sin ( 7x ) = 0\\0 = 0\\\\[/tex]

- We see that both functions [ y1 and y2 ] holds true as the solution to the given homogeneous second order linear ODE. Hence, are the solution to given ODE.

- The complete solution to a homogeneous ODE is given in the form as follows:

                            [tex]y = c_1y_1 + c_2y_2\\\\y = c_1*cos(7x) + c_2*sin(7x)\\[/tex]

- To complete the above solution we need to determine the constants [ c1 and c2 ] using the initial conditions given. Therefore,

                           [tex]y (0) = c_1cos ( 0 ) + c_2sin ( 0 ) = 10\\\\y'(0) = -7c_1*sin(0) + 7c_2*cos(0) = -4\\\\c_1 ( 1 ) + c_2 ( 0 ) = 10, c_1 = 10\\\\-7c_1(0) + 7c_2( 1 ) = -4 , c_2 = -\frac{4}{7}[/tex]

- Now we can write the complete solution to the given homogeneous second order linear ODE as follows:

                           [tex]y = 10cos (7x) - \frac{4}{7}sin ( 7x )[/tex]    .... Answer

Question 2

- We are given a homogeneous second order linear ODE as follows:

                               [tex]y'' -16y =0[/tex]

- A pair of independent functions are given as ( y1 ) and ( y2 ):

                               [tex]y_1 = e^4^x\\\\y_2 = e^-^4^x[/tex]

- The given ODE is subjected to following initial conditions as follows:

                               [tex]y( 0 ) = 2\\y'( 0 ) = 9[/tex]

- We are to verify that the given independent functions ( y1 ) and ( y2 ) are indeed the solution to the given ODE. If the functions are solutions then find the complete solution of the homogeneous ODE of the form:

                               [tex]y = c_1y_1 + c_2y_2[/tex]

Solution:-

- To verify the functions are indeed the solution to the given ODE. We will plug the respective derivatives of each function [ y1 and y2 ] into the ODE and prove whether the equality holds true or not.

- Formulate the second derivatives of both functions y1 and y2 as follows:

                         [tex]y'_1 = 4e^4^x , y''_1 = 16e^4^x\\\\y'_2 = -4e^-^4^x , y''_2 = 16e^-^4^x[/tex]  

- Now substitute the second derivatives of each function and the functions itself into the given ODE and verify whether the equality holds true or not.

                           [tex]y''_1 - 16y_1 = 0\\\\16e^4^x - 16e^4^x = 0\\\\0 = 0\\\\y''_2 - 16y_2 = 0\\\\16e^-^4^x - 16e^-^4^x = 0\\\\0 = 0[/tex]

- We see that both functions [ y1 and y2 ] holds true as the solution to the given homogeneous second order linear ODE. Hence, are the solution to given ODE.

- The complete solution to a homogeneous ODE is given in the form as follows:

                            [tex]y = c_1y_1 + c_2y_2\\\\y = c_1*e^4^x + c_2*e^-^4^x[/tex]

- To complete the above solution we need to determine the constants [ c1 and c2 ] using the initial conditions given. Therefore,

                           [tex]y ( 0 ) = c_1 * e^0 + c_2 * e^0 = 2\\\\y' ( 0 ) = 4 c_1 * e^0 - 4c_2 * e^0 = 9\\\\c_1 + c_2 = 2 , 4c_1 - 4c_2 = 9\\\\c_1 = \frac{17}{8} , c_2 = -\frac{1}{8}[/tex]

- Now we can write the complete solution to the given homogeneous second order linear ODE as follows:

                           [tex]y = \frac{17}{8} e^4^x - \frac{1}{8}e^-^4^x[/tex]   .... Answer

Answer:

x = -2

y = -5

Step-by-step explanation:

We can solve this algebraically (substitution or elimination) or graphically. I will be using elimination:

Step 1: Add the 2 equations together

-8y = 40

y = -5

Step 2: Plug y into an original equation to find x

-3(-5) + 10x = -5

15 + 10x = -5

10x = -20

x = -2

And we have our final answers!

Answer:

[tex]\boxed{\sf \ \ \ x=-2 \ \ \ and \ \ \ y=-5 \ \ \ }[/tex]

Step-by-step explanation:

let s solve the following system

(1) -5y-10x=45

(2) -3y+10x=-5

let s do (1) + (2) it comes

-5y-10x-3y+10x=45-5=40

<=>

-8y=40

<=>

y = -40/8=-20/4=-5

so y = -5

let s replace y in (1)

25-10x=45

<=>

10x=25-45=-20

<=>

x = -20/10=-2

so x = -2

Answer:

34

Step-by-step explanation:

F(x) = 2x^3 - 7x + 1

Let x= 3

F(3) = 2* 3^3 - 7*3 + 1

      = 2 * 27 -21+1

      = 54 -21 + 1

      = 34

Answer: 34

Step-by-step explanation:

Answer:

C.6x³-33x² + 45x-6

Step-by-step explanation:

(3x-6)(2x^2-7x+1)

= 3x(2x² - 21x +1) -6(2x² - 7x+1)

= (6x³ - 21x² + 3x) - (12x² - 42x+6)

= 6x³ - 21x² + 3x -12x² + 42x -6

= 6x³-33x² + 45x-6

Answer/Step-by-step explanation:

==>Given:

=>Rectangular Pyramid:

L = 5mm

W = 3mm

H = 4mm

=>Rectangular prism:

L = 5mm

W = 3mm

H = 4mm

==>Required:

a. Volume of pyramid:

Formula for calculating volume of a rectangular pyramid us given as L*W*H

V = 5*3*4

V = 60 mm³

b. Volume of prism = ⅓*L*W*H

thus,

Volume of rectangular prism given = ⅓*5*3*4

= ⅓*60

= 20mm³

c. Volume of the prism = ⅓ x volume of the pyramid

Thus, 20 = ⅓ × 60

As we can observe from our calculation of the solid shapes given, the equation written above is true for all rectangular prism and rectangular pyramid of the same length, width and height.

Answer:

Step-by-step explanation:

1) divide equilateral tri from the middle you will get two 30-60-90 triangles

2) by using pythagorean law & trigimintory, you will get two unknowns (height and side length) and two functions