Ask question

Ask question

All categories

3 years ago

8

Let a,b,c ∈ Z. Define the highest common factor hcf(a,b,c) to be the largest positive integer that divides a,b and c. Prove that

there are integers s,t,u such that hcf(a,b,c) = sa+tb+uc. Find such integers s,t,u when a = 91, b = 903, c = 1792

1 answer:

kakasveta [241]3 years ago

8 0

21 they have too be right next to each other and threy have too be right

You might be interested in

Suppose a change of coordinates T:R2→R2 from the uv-plane to the xy-plane is given by x=e−2ucos(5v), y=e−2usin(5v). Find the abs

anzhelika [568]

Complete Question

The complete question is shown on the first uploaded image

Answer:

The solution is $\frac{\delta (x,y)}{\delta (u, v)} | = 10e^{-4u}$

Step-by-step explanation:

From the question we are told that

$x = e^{-2a} cos (5v)$

and $y = e^{-2a} sin(5v)$

Generally the absolute value of the determinant of the Jacobian for this change of coordinates is mathematically evaluated as

$| \frac{\delta (x,y)}{\delta (u, v)} | = | \ det \left[\begin{array}{ccc}{\frac{\delta x}{\delta u} }&{\frac{\delta x}{\delta v} }\\\frac{\delta y}{\delta u}&\frac{\delta y}{\delta v}\end{array}\right] |$

$= |\ det\ \left[\begin{array}{ccc}{-2e^{-2u} cos(5v)}&{-5e^{-2u} sin(5v)}\\{-2e^{-2u} sin(5v)}&{-2e^{-2u} cos(5v)}\end{array}\right] |$

$Let \ a = -2e^{-2u} cos(5v), \\ b=-2e^{-2u} sin(5v),\\c =-2e^{-2u} sin(5v),\\d=-2e^{-2u} cos(5v)$

So

$\frac{\delta (x,y)}{\delta (u, v)} | = |det \left[\begin{array}{ccc}a&b\\c&d\\\end{array}\right] |$

=> $\frac{\delta (x,y)}{\delta (u, v)} | = | a * b - c* d |$

substituting for a, b, c,d

=> $\frac{\delta (x,y)}{\delta (u, v)} | = | -10 (e^{-2u})^2 cos^2 (5v) - 10 e^{-4u} sin^2(5v)|$

=> $\frac{\delta (x,y)}{\delta (u, v)} | = | -10 e^{-4u} (cos^2 (5v) + sin^2 (5v))|$

=> $\frac{\delta (x,y)}{\delta (u, v)} | = 10e^{-4u}$

7 0

3 years ago

Help like rn. Like rn please I will mark brainiest but pls help.

Naya [18.7K]

Answer:

90

and

20

i think so ye

Step-by-step explanation:

3 0

2 years ago

Read 2 more answers

Company A: A 2-column table with 5 rows. The first column is labeled hours with entries 5, 12, 20, 29, 42. The second column is

ryzh [129]

Answer:

The correct answer is C.

Step-by-step explanation:

I took the test

8 0

3 years ago

Read 2 more answers

Work out the area of a triangle base 7.5m and height 6cm

navik [9.2K]

First convert 7.5 meters to 750cm, then use your formula A=1/2bh and pop it in your calculator: (1/2)(750)(6) and be sure to include cm as the unit of measurement in your final answer.

5 0

3 years ago

Which expression is equivalent to x + 0.2x<br><br>1.2x<br>0.2x squared <br>0.2x <br>1.02x

Aleks04 [339]

The answer to this expression would be 1.2x

4 0

3 years ago