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3 years ago

Is the relationship for Camille’s puppy’s weight in terms of time linear or nonlinear? Explain your response.

Mathematics

2 answers:

Irina18 [472]3 years ago

4 0

Answer:

It is a linear function, because the line has no curve, and the line is constant

Step-by-step explanation:

In a non linear function there would be a curve in the line, in this line there is no curve so therefore it is linear function.

Keith_Richards [23]3 years ago

3 0

Answer:

It is a linear function because

A linear relationship (or linear association) is term used to describe a straight-line between two variables. Linear relationships can be expressed either in a graphical format or as a mathematical equation of the form y = mx + b.

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Solve the following equations: (a) x^11=13 mod 35 (b) x^5=3 mod 64

tino4ka555 [31]

$x^{11}=13\pmod{35}\implies\begin{cases}x^{11}\equiv13\equiv3\pmod5\\x^{11}\equiv13\equiv6\pmod7\end{cases}$

By Fermat's little theorem, we have

$x^{11}\equiv (x^5)^2x\equiv x^3\equiv3\pmod5$

$x^{11}\equiv x^7x^4\equiv x^5\equiv6\pmod 7$

5 and 7 are both prime, so $\varphi(5)=4$ and $\varphi(7)=6$ . By Euler's theorem, we get

$x^4\equiv1\pmod5\implies x\equiv3^{-1}\equiv2\pmod5$

$x^6\equiv1\pmod7\impleis x\equiv6^{-1}\equiv6\pmod7$

Now we can use the Chinese remainder theorem to solve for $x$ . Start with

$x=2\cdot7+5\cdot6$

Taken mod 5, the second term vanishes and $14\equiv4\pmod5$ . Multiply by the inverse of 4 mod 5 (4), then by 2.

$x=2\cdot7\cdot4\cdot2+5\cdot6$

Taken mod 7, the first term vanishes and $30\equiv2\pmod7$ . Multiply by the inverse of 2 mod 7 (4), then by 6.

$x=2\cdot7\cdot4\cdot2+5\cdot6\cdot4\cdot6$

$\implies x\equiv832\pmod{5\cdot7}\implies\boxed{x\equiv27\pmod{35}}$

$x^5\equiv3\pmod{64}$

We have $\varphi(64)=32$ , so by Euler's theorem,

$x^{32}\equiv1\pmod{64}$

Now, raising both sides of the original congruence to the power of 6 gives

$x^{30}\equiv3^6\equiv729\equiv25\pmod{64}$

Then multiplying both sides by $x^2$ gives

$x^{32}\equiv25x^2\equiv1\pmod{64}$

so that $x^2$ is the inverse of 25 mod 64. To find this inverse, solve for $y$ in $25y\equiv1\pmod{64}$ . Using the Euclidean algorithm, we have

64 = 2*25 + 14

25 = 1*14 + 11

14 = 1*11 + 3

11 = 3*3 + 2

3 = 1*2 + 1

=> 1 = 9*64 - 23*25

so that $(-23)\cdot25\equiv1\pmod{64}\implies y=25^{-1}\equiv-23\equiv41\pmod{64}$ .

So we know

$25x^2\equiv1\pmod{64}\implies x^2\equiv41\pmod{64}$

Squaring both sides of this gives

$x^4\equiv1681\equiv17\pmod{64}$

and multiplying both sides by $x$ tells us

$x^5\equiv17x\equiv3\pmod{64}$

Use the Euclidean algorithm to solve for $x$ .

64 = 3*17 + 13

17 = 1*13 + 4

13 = 3*4 + 1

=> 1 = 4*64 - 15*17

so that $(-15)\cdot17\equiv1\pmod{64}\implies17^{-1}\equiv-15\equiv49\pmod{64}$ , and so $x\equiv147\pmod{64}\implies\boxed{x\equiv19\pmod{64}}$

5 0

3 years ago

Need help on this question for math

KATRIN_1 [288]

Answer:

y=-7

Step-by-step explanation:

hope that will help you

8 0

3 years ago

Please need help on this

Aleonysh [2.5K]

The answer is 1/3 is the answer.

4 0

3 years ago

Solve for H: A = L ⋅ W ⋅ H

Sergeu [11.5K]

Answer:

The answer would be

H = A over L times W

Step-by-step explanation:

This is because, when you multiply the L, W, and H you end up getting A. This means that A is the biggest number. We automatically can tell that H is what were looking for so putting those two things together we have this: H = A over ???

The ??? would have to be L times W because those are the only things left and they get multiplied together which in the end leaves us with

H = A over L times w

aka

H=A/LxW

6 0

3 years ago

If y varies directly as x and x=2 when y=−4, find y when x=−6.

kakasveta [241]

Answer:

Equation: x × -2 = y

Solution: y = 12

Step-by-step explanation:

if (x = 2) is (y = -4) then (x = 1) is (y = -2) so if (x = -6) is (y = 12) if we follow the equation [x × -2 = y] which was found using the first set of variables and dividing each by 2.

4 0

3 years ago