The area of an 20-cm-wide rectangle is 460 cm². What is its length? The length is cm.

Mathematics

1 answer:

SVETLANKA909090 [29]2 years ago

7 0

460 divided by 20
= 23 cm

The length is 23cm

You might be interested in

10.) For the natural logarithm function, determine the point on the curve where its associated tangent line passes through the

Lunna [17]

f(x)=lnx

y=f(x)

dy/dx= 1/x

tangent at (x,y) has slope 1/x

eqn of tangent is y = mx + c

since the tangent passes through origin, c=0

substitute y = lnx and m= 1/x to above eqn

lnx = 1

x=e

y=lne=1

4 0

2 years ago

Solve the following initial-value problem, showing all work, including a clear general solution as well as the particular soluti

Vikki [24]

Answer:

General Solution is $y=x^{3}+cx^{2}$ and the particular solution is $y=x^{3}-\frac{1}{2}x^{2}$

Step-by-step explanation:

$x\frac{\mathrm{dy} }{\mathrm{d} x}=x^{3}+3y\\\\Rearranging \\\\x\frac{\mathrm{dy} }{\mathrm{d} x}-3y=x^{3}\\\\\frac{\mathrm{d} y}{\mathrm{d} x}-\frac{3y}{x}=x^{2}$

This is a linear diffrential equation of type

$\frac{\mathrm{d} y}{\mathrm{d} x}+p(x)y=q(x)$ ..................(i)

here $p(x)=\frac{-2}{x}$

$q(x)=x^{2}$

The solution of equation i is given by

$y\times e^{\int p(x)dx}=\int e^{\int p(x)dx}\times q(x)dx$

we have $e^{\int p(x)dx}=e^{\int \frac{-2}{x}dx}\\\\e^{\int \frac{-2}{x}dx}=e^{-2ln(x)}\\\\=e^{ln(x^{-2})}\\\\=\frac{1}{x^{2} } \\\\\because e^{ln(f(x))}=f(x)]\\\\Thus\\\\e^{\int p(x)dx}=\frac{1}{x^{2}}$