a) The hypotenuse of a right angled triangle is 15 cm. Taking the
perpendicular sides as x , y write the relation connecting the sides ?
b) If the area is 30 cm² find the length of its perpendicular sides ?

An obvious substitution would be to take u = x - y and v = x + 2y, so that 0 < u < 1 (which follows from y = x   ==>   x - y = 0 and y = x - 1   ==>   x - y = 1), and 0 < v < 1.

Solve for x and y in terms of u and v :

u - v = (x - y) - (x + 2y) = -3y   ==>   y = (v - u)/3

2u + v = 2 (x - y) + (x + 2y) = 3x   ==>   x = (2u + v)/3

Compute the Jacobian and its determinant:

[tex]J=\begin{bmatrix}D_ux&D_vx\\D_uy&D_vy\end{bmatrix}=\begin{bmatrix}\dfrac23&\dfrac13\\\\-\dfrac13&\dfrac13\end{bmatrix} \implies |\det(J)|=\dfrac13[/tex]

Now in the integral, we have

[tex]\displaystyle\iint_R\frac{x+2y}{\cos(x-y)}\,\mathrm dx\,\mathrm dy = \frac13\int_0^1\int_0^1\frac{v}{\cos(u)}\,\mathrm du\,\mathrm dv \\\\ \displaystyle= \frac13\left(\int_0^1v\,\mathrm dv\right)\left(\int_0^1\sec(u)\,\mathrm du\right) \\\\ \displaystyle= \frac13\bigg(\frac{v^2}2\bigg)\bigg|_0^1\bigg(\ln|\sec(u)+\tan(u)|\bigg)\bigg|_0^1 \\\\ \displaystyle= \boxed{\frac16\ln(\sec(1)+\tan(1))}[/tex]

Answer:

Negative. The answer gives - 5

Answer:

Negative

Step-by-step explanation:

-40/8 is equivalent to -5. Since -5 or "negative five" is negative (as it states), the equation is negative.

Answer:

t = 0.77930

t = 1.2832

Step-by-step explanation:

Parameterize the path by

r (x) = (x, x + 2)

with 0 ≤ x ≤ 2. Then

r' (x) = (1, 1)   ==>   ||r' (x)|| = √(1² + 1²) = √2

and the line integral is

[tex]\displaystyle\int_Lxy\,\mathrm ds=\sqrt2\int_0^2x(x+2)\,\mathrm dx=\boxed{\frac{20\sqrt2}3}[/tex]

Answer:

Step-by-step explanation:

There are not rotational symmetry.

Answer:

200

Step-by-step explanation:

You were right to divide 55 by 163. The problem, however, asks for the answer to be rounded to the nearest tenth.

Therefore, 55 / 163 = 0.3374 = 33.7%

Hope this helps!

Answer:

Please say in English

Step-by-step explanation:

I don't understand, Sorry

Answer:

6/6=1

Step-by-step explanation:

There are six sides on a die and you have six total outcomes. Hope this helps! :)

Answer:

3 divided by 7 and x=-1.5*x

Step-by-step explanation:

Answer:

It discusses the role of the God in influencing our decisions

Answer:

I believe it is choice D

Step-by-step explanation:

in the excerpt it talks about how sight gives us the ability to observe and experience. it also states "we prefer sight to almost everything else." hope I'm right! ☺️

Answer:

Step-by-step explanation:

1.

[tex]-\frac{5 \pi }{6} +2\pi =\frac{-5\pi +12 \pi }{6} =\frac{7\pi }{6}[/tex]

2.

405-360=45°

a.

Answer:

1170cm^3

Step-by-step explanation:

Break it into two prisms. 5 x 9 x 15 and 11 x 3 x 15. Find the volume of each and add.

(5 x 9 x 15) + (11 x 3 x 15)

675 + 495

1170cm^3

b.

Answer:

846cm^2

Step-by-step explanation:

Add each side's area together.

(9x15) + (5x15) + (6x15) + (3x15) + (12x15) + (11x15) + (5x9) + (5x9) + (11x3) + (11x3)

135 + 75 + 90 + 45 + 180 + 165 + 45 + 45 + 33 + 33

846 cm^2

Answer:

(a)1170 cm^3

(b)846 cm^2

Step-by-step explanation:

(a) Rectangle #1= 11 x 3 = 33 cm^2

Rectangle #2 = 5 x 9 = 45 cm^2

Volume = 45 + 33 = 78 x 15 = 1170 cm^3

(b) First find the surface are of all 8 faces in the prism and then add them all.

1st face = (11 x 3) + (5 x 9 ) = 33 + 45 = 78 cm^2

2nd face = (11 x 3) + (5 x 9 ) = 33 + 45 = 78 cm^2

3rd face = 15 x 3 = 45 cm^2

4th face = 15 x 6 = 90 cm^2

5th face = 15 x 9 = 135 cm^2

6th face = 15 x 5 = 75 cm^2

7th face = 15 x 12 = 180 cm^2

8th face = 15 x 11 = 165 cm^2

1st + 2nd + 3rd +4th + 5th+ 6th + 7th + 8th = 846 cm^2

Hope this helps!

Answer:

E = 427 votes

Step-by-step explanation:

Translating the word problem into an algebraic expression, we have;

E = D + 95

E = C + 186

Equating the two equations, we have;

D + 95 = C + 186

D = C + 186 - 95

D = C + 91

Also, the sum of all the votes is equal to 1000.

E + D + C = 1000

Substituting the value of "D" we have;

E + (C + 91) + C = 1000

E + C + 91 + C = 1000

E + 2C + 91 = 1000

E + 2C = 1000 - 91

E + 2C = 909

But, E = C + 186

Substituting the value of "E" we have;

(C + 186) + 2C = 909

C + 186 + 2C = 909

3C + 186 = 909

3C = 909 - 186

3C = 723

C = 723/3

C = 241 votes

Next, we would find Elaine's vote;

E = C + 186

E = 241 + 186

E = 427 votes

Lastly, we would find Dean's vote;

E = D + 95

427 = D + 95

D = 427 - 95

D = 332 votes

Check:

E + D + C = 1000

427 + 332 + 241 = 1000

1000 = 1000

Answer:

mug = 4

plate = 7

Step-by-step explanation:

10 x + 2y =54

8x + 2y = 46

2x = 8

x = 4

2y = 14

y = 7

-4/3

For your question: Suppose cos(x) =1/(sqrt(5)) and sin(x) >0. What is the value of tan(2x)?

The value of tan(2x) is equal to -4/3

Answer:

B: A systematic random sample

Step-by-step explanation:

Systematic sampling is a type of probability sampling in which members of a larger population are chosen at random from a larger population but at a fixed, periodic interval. This interval, also known as the sampling interval, is calculated by dividing the population size by the sample size desired. Despite the fact that the sample population is chosen in advance, systematic sampling is still considered random if the periodic interval is set in advance and the starting point is chosen at random.

Hope this helps and if it does, don't be afraid to give my answer a "Thanks" and maybe a Brainliest if it's correct?  

Step-by-step explanation:

everything can be found in the picture

Answer:

Hello There!!

Step-by-step explanation:

Museums are regarded as information resources because there are historical things and artifacts there.

hope this helps,have a great day!!

~Pinky~

Answer:

B, 4x6x7 and 1x3x3.

Step-by-step explanation:

First, remember the formula: V=LWH (Volume equals length times width times height). Lastly, find the equations that match that formula, therefor B, 4x6x7 and 1x3x3 matches the formula, so B  is your correct answer.

Answer:

this probability is 0.68

Step-by-step explanation:

the probability she buys fruit but not a CD is

0.6 × (1 - 0.2) = 0.48

the probability she buys a CD by not fruit is

0.2 × (1 - 0.6) = 0.08

the probability that she buys both is

0.6 × 0.2 = 0.12

the probability that she buys fruit or a CD or both is adding all 3 probabilities :

0.48 + 0.08 + 0.12 = 0.68

Grapefruit=108

Orange=100

Apple=90

a) (108-90)/90*100 = 18/90*100=20%

b) (108-90)/108= 18/108*100=16 2/3%

Answer:

The grapefruit is 20% heavier than the orange:)

Step-by-step explanation:

Let the weight of orange be x.

This means that the weight of grapefruit is:

       1.08x

( Since grapefruit is: 8% heavier than orange )

Also, the weight of apple is 10% lighter than apple.

This means that the weight of apple is: 0.90 x

Answer:

The best point estimate for the mean amount of money spent for textbooks for all students at the College is of $121.60.

Step-by-step explanation:

Best point estimate:

The best point estimate of a population mean is the sample mean.

In this question:

The sample mean amount of money spent for textbooks was $121.60, which means that the best point estimate for the mean amount of money spent for textbooks for all students at the College is of $121.60.

Answer:

Step-by-step explanation:

Wage = rate / hr * the number of hours worked.

Wage = ?

rate = 15.45

time = 29.25 hours

Wage = 15.45 * 29.25

Wage = 451.91

Answer:

Step-by-step explanation:

11.04 = 10(1.02)^n

1.104 = 1.02^n

ln 1.104 = ln 1.02^n

ln 1.104 = n ln 1.02

n = ln 1.104/ ln 1.02

n = 4.99630409516

4.99 can be rounded to 5.

So a reasonable domain would be 0 ≤ x < 5

PART B)

f(0) = 10(1.02)^0

f(0) = 10(1)

f(0) = 10

The y-intercept represents the height of the plant when they began the experiment.

f(1) = 10(1.02)^1

f(1) = 10(1.02)

f(1) = 10.2

(1, 10.2)

f(5) = 10(1.02)^5

f(5) = 10(1.1040808)

f(5) = 11.040808

f(1)=10(1.02)^1

f(1)=10.2

Average rate= (fn2-fn1)/(n2-n1)

                     =11.04-10.2/(5-1)

                    =0.22

the average rate of change of the function f(n) from n = 1 to n = 5 is 0.22.  

Answer:

5/6 + 11/6 = 16/ 6

Step-by-step explanation:

Distance between any Teo labeled tick marks =

(1 - 2/3) / 2 = 1/3 ÷ 2 = 1/3 * 1/2 = 1/6

From the left :

2/3 + 1/6 = 5/6

5/3 + 1/6 = 11/6

5/6 + 11/6 = (5 + 11) / 6 = 16/6

5/6 + 11/6 = 16/ 6

Answer:

7

Step-by-step explanation:

5 x 7 = 35 or 35/5 = 7 [ correct me if i'm wrong ]

Answer:

I. m = 2401

II. ((n+1) ∆ y)/n = 1/n[(n – y + 2)(n – y) + 1]

Step-by-step explanation:

I. Determination of m

x ∆ y = x² − 2xy + y²

2 ∆ − 5 = √m

2² − 2(2 × –5) + (–5)² = √m

4 – 2(–10) + 25 = √m

4 + 20 + 25 = √m

49 = √m

Take the square of both side

49² = m

2401 = m

m = 2401

II. Simplify ((n+1) ∆ y)/n

We'll begin by obtaining (n+1) ∆ y. This can be obtained as follow:

x ∆ y = x² − 2xy + y²

(n+1) ∆ y = (n+1)² – 2(n+1)y + y²

(n+1) ∆ y = n² + 2n + 1 – 2ny – 2y + y²

(n+1) ∆ y = n² + 2n – 2ny – 2y + y² + 1

(n+1) ∆ y = n² – 2ny + y² + 2n – 2y + 1

(n+1) ∆ y = n² – ny – ny + y² + 2n – 2y + 1

(n+1) ∆ y = n(n – y) – y(n – y) + 2(n – y) + 1

(n+1) ∆ y = (n – y + 2)(n – y) + 1

((n+1) ∆ y)/n = [(n – y + 2)(n – y) + 1] / n

((n+1) ∆ y)/n = 1/n[(n – y + 2)(n – y) + 1]

Answer:

You need to ask yourself what times 20  gives you 600.  Then ask yourself what times 20 gives you 160.  Then that will give you your answer.

Step-by-step explanation:

Answer:

anu po yan salamat po sa point

Answer:

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