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2 years ago

30 POINTS FOR THIS QUESTION

Mathematics

2 answers:

Tcecarenko [31]2 years ago

8 0

X+1 because the x intercept is -1

aalyn [17]2 years ago

3 0

×+1 because the x intercept is -1 :)

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The real numbers $x$ and $y$ are such that \begin{align*} x + y &= 4, \\ x^2 + y^2 &= 22, \\ x^4 &= y^4 - 176 \sqrt{

tamaranim1 [39]

You get everything you need from factoring the last expression:

$x^4-y^4=-176\sqrt7$

The left side is a difference of squares, and we get another difference of squares upon factoring. We end up with

$x^4-y^4=(x^2-y^2)(x^2+y^2)=(x-y)(x+y)(x^2+y^2)$

Plug in everything you know and solve for $x-y$ :

$-176\sqrt7=(x-y)\cdot4\cdot22\implies x-y=\boxed{-2\sqrt7}$

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3 years ago

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Find the directional derivative of f(x,y,z)=2z2x+y3f(x,y,z)=2z2x+y3 at the point (−1,4,3)(−1,4,3) in the direction of the vector

Feliz [49]

$f(x,y,z)=2z^2x+y^3$

$f$ has gradient

$\nabla f(x,y,z)=2z^2\,\vec\imath+3y^2\,\vec\jmath+4xz\,\vec k$

which at the point (-1, 4, 3) has a value of

$\nabla f(-1,4,3)=18\,\vec\imath+48\,\vec\jmath-12\,\vec k$

I'm not sure what the given direction vector is supposed to be, but my best guess is that it's intended to say $\vec u=15\,\vec\imath+25\,\vec\jmath$ , in which case we have

$\|\vec u\|=\sqrt{15^2+25^2}=5\sqrt{34}$

Then the derivative of $f$ at (-1, 4, 3) in the direction of $\vec u$ is

$D_{\vec u}f(-1,4,3)=\nabla f(-1,4,3)\cdot\dfrac{\vec u}{\|\vec u\|}=\boxed{\dfrac{294}{\sqrt{34}}}$

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3 years ago

What are the answers plz help me

Ghella [55]

Number 3 is 9 not negative 10

8 0

3 years ago

Hakim deposited $50 in a saving account earning 10% interest, compounded annually . To the nearest cent , how much interest will

Paraphin [41]

$\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$50\\ r=rate\to 10\%\to \frac{10}{100}\dotfill &0.10\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &2 \end{cases}$

$\bf A=50\left(1+\frac{0.10}{1}\right)^{1\cdot 2}\implies A=50(1.1)^2\implies A=60.5 \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \stackrel{\textit{earned interest}}{60.5 - 50\implies 10.5}~\hfill$

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3 years ago

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Which equation is true for the value x = 15?

boyakko [2]

The third one because 2(15+5)=2(20)=40

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3 years ago