This equation is an example of:

Mathematics

2 answers:

mariarad [96]3 years ago

4 0

Answer:

B. FOIL

Step-by-step explanation:

FOIL stands for Firsts, Outsides, Insides, and Lasts

This is a mnemonic to help you to remember how to multiply two binomials

From the image, we can see that the on the right side of the equals,

$(x)(-5x^2)$ is the product of the firsts of the binomials

$(x)(x)$ is the product of the outsides of the binomials

$(-2)(-5x^2)$ is the product of the insides of the binomials

$(-2)(x)$ is the product of the lasts of the binomials.

hoa [83]3 years ago

4 0

Answer:

B. FOIL

Step-by-step explanation:

"FOIL" is an acronym for First, Outer, Inner, Last. It refers to the relative positions of the terms in the multiplication of binomials.

The given equation shows the result of such a multiplication. It is an example of the application of FOIL.

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2 years ago

Find the distance traveled by a particle with position (x, y) as t varies in the given time interval. x = 5 sin2 t, y = 5 cos2 t

rodikova [14]

$\begin{cases}x(t)=5\sin2t\\y(t)=5\cos2t\end{cases}\implies\begin{cases}\frac{\mathrm dx}{\mathrm dt}=10\cos2t\\\frac{\mathrm dy}{\mathrm dt}=-10\sin2t\end{cases}$

The distance traveled by the particle is given by the definite integral

$\displaystyle\int_C\mathrm dS=\int_0^{3\pi}\sqrt{\left(\frac{\mathrm dx}{\mathrm dt}\right)^2+\left(\frac{\mathrm dy}{\mathrm dt}\right)^2}\,\mathrm dt$

where $C$ is the path of the particle. The distance is then

$\displaystyle\int_0^{3\pi}\sqrt{100\cos^22t+100\sin^22t}\,\mathrm dt=10\int_0^{3\pi}\mathrm dt=30\pi$