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2 years ago

13

What are the zeros of f(x) = x(x-7)?

1 answer:

den301095 [7]2 years ago

3 0

Answer:

c. 0 and 7

Step-by-step explanation:

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Find the smallest positive $n$ such that \begin{align*} n &\equiv 3 \pmod{4}, \\ n &\equiv 2 \pmod{5}, \\ n &\equiv

Alex777 [14]

4, 5, and 7 are mutually coprime, so you can use the Chinese remainder theorem right away.

We construct a number $x$ such that taking it mod 4, 5, and 7 leaves the desired remainders:

$x=3\cdot5\cdot7+4\cdot2\cdot7+4\cdot5\cdot6$

Taken mod 4, the last two terms vanish and we have

$x\equiv3\cdot5\cdot7\equiv105\equiv1\pmod4$

so we multiply the first term by 3.

Taken mod 5, the first and last terms vanish and we have

$x\equiv4\cdot2\cdot7\equiv51\equiv1\pmod5$

so we multiply the second term by 2.

Taken mod 7, the first two terms vanish and we have

$x\equiv4\cdot5\cdot6\equiv120\equiv1\pmod7$

so we multiply the last term by 7.

Now,

$x=3^2\cdot5\cdot7+4\cdot2^2\cdot7+4\cdot5\cdot6^2=1147$

By the CRT, the system of congruences has a general solution

$n\equiv1147\pmod{4\cdot5\cdot7}\implies\boxed{n\equiv27\pmod{140}}$

or all integers $27+140k$ , $k\in\mathbb Z$ , the least (and positive) of which is 27.

3 0

2 years ago

Please help!!!!!<br> One third of a number x is no more than 15.

Nitella [24]

Answer:

1/3x is less than or equal to 15

Step-by-step explanation:

assuming you want an equation?

1/3x is less than or equal to 15

its this sign < with line under (srry i don't have the symbol)

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2 years ago

Jane has a bag of candy. She gives pieces to her friend. Then Jane's grandmother buys Jane 5 more pieces of candy than she had o

sammy [17]

Answer: She would have 32 pieces of cand in her bag

Step-by-step explanation: 27+5=32

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3 years ago

Read 2 more answers

Find a potential function for F or determine that F is not conservative. (If F is not conservative, enter NOT CONSERVATIVE.) F =

xxMikexx [17]

For $F$ to be conservative, we need to have

$\dfrac{\partial f}{\partial x}=\cos z$

$\dfrac{\partial f}{\partial y}=10y$

$\dfrac{\partial f}{\partial z}=-x\sin z$

Integrate the first PDE with respect to $x$ :

$\displaystyle\int\frac{\partial f}{\partial x}\,\mathrm dx+\int\cos z\,\mathrm dx\implies f(x,y,z)=x\cos z+g(y,z)$

Differentiate with respect to $y$ :

$\dfrac{\partial f}{\partial y}=10y=\dfrac{\partial g}{\partial y}\implies g(y,z)=5y^2+h(z)$

Now differentiate $f$ with respect to $z$ :

$\dfrac{\partial f}{\partial z}=-x\sin z=-x\sin z+\dfrac{\mathrm dh}{\mathrm dz}\implies\dfrac{\mathrm dh}{\mathrm dz}=0\implies h(z)=C$

So we have

$f(x,y,z)=x\cos z+5y^2+C$

so $F$ is indeed conservative.

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3 years ago

lydia and cliff bought a lot with the intention of building a house on it. they needed to determine how much it would to build t

grin007 [14]

Okay... but what is your question?

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2 years ago