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3 years ago

If a storm window is 315 square inches, what are the dimensions if the window is 6 inches higher than it is wide

1 answer:

3 0

$\bf \textit{area of a rectangle}\\\\ A=Lw~~ \begin{cases} L=length\\ w=width\\[-0.5em] \hrulefill\\ L=\stackrel{\textit{6 more than \underline{w}}}{w+6}\\ A=315 \end{cases}\implies 315=(w+6)(w) \\\\\\ 315=w^2+6w\implies 0=w^2+6w-315 \\\\\\ (w+21)(w-15)=0\implies w= \begin{cases} -21\\ \boxed{15} \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill w=15\qquad \stackrel{w+6}{L=21}~\hfill$

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How do i add and subtract polynomials?<br>(4v-6v)-(v-5v^3)+(5v^3+4)

Ksenya-84 [330]

Distribute and add like terms and you are good

alirghty

we can make it easier by simplifying what we can

(4v-6v)=-2v so

(-2v)-1(v-5v³)+(5v³+3)=
-2v-v+5v³+5v³+3=
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3 years ago

F⃗ (x,y)=−yi⃗ +xj⃗ f→(x,y)=−yi→+xj→ and cc is the line segment from point p=(5,0)p=(5,0) to q=(0,2)q=(0,2). (a) find a vector pa

DerKrebs [107]

a. Parameterize $C$ by

$\vec r(t)=(1-t)(5\,\vec\imath)+t(2\,\vec\jmath)=(5-5t)\,\vec\imath+2t\,\vec\jmath$

with $0\le t\le1$ .

b/c. The line integral of $\vec F(x,y)=-y\,\vec\imath+x\,\vec\jmath$ over $C$ is

$\displaystyle\int_C\vec F(x,y)\cdot\mathrm d\vec r=\int_0^1\vec F(x(t),y(t))\cdot\frac{\mathrm d\vec r(t)}{\mathrm dt}\,\mathrm dt$

$=\displaystyle\int_0^1(-2t\,\vec\imath+(5-5t)\,\vec\jmath)\cdot(-5\,\vec\imath+2\,\vec\jmath)\,\mathrm dt$

$=\displaystyle\int_0^1(10t+(10-10t))\,\mathrm dt$

$=\displaystyle10\int_0^1\mathrm dt=\boxed{10}$

d. Notice that we can write the line integral as

$\displaystyle\int_C\vecF\cdot\mathrm d\vec r=\int_C(-y\,\mathrm dx+x\,\mathrm dy)$

By Green's theorem, the line integral is equivalent to

$\displaystyle\iint_D\left(\frac{\partial x}{\partial x}-\frac{\partial(-y)}{\partial y}\right)\,\mathrm dx\,\mathrm dy=2\iint_D\mathrm dx\,\mathrm dy$

where $D$ is the triangle bounded by $C$ , and this integral is simply twice the area of $D$ . $D$ is a right triangle with legs 2 and 5, so its area is 5 and the integral's value is 10.

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3 years ago

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Fudgin [204]

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Step-by-step explanation:

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HELP PLEASE, WILL MARK BRANLIEST!!!

zhannawk [14.2K]

Answer:

144

Step-by-step explanation:

angle A + angle B = 180 (supplementary angle)

A = 4B

4b+b=180

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Divide 5 on both sides to get b=36

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