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3 years ago

Find the area of ΔABC.

Mathematics

1 answer:

zysi [14]3 years ago

6 0

Answer:

Step-by-step explanation:

You know two sides of the triangle and the angle between them, so use the Law of Cosines to solve the triangle.

a² = √(b²+c² - 2bc·cosA)

= √(9²+7.8² - 2·9·7.8·cos(32°)

≅ 4.8

Then use Heron's formula to calculate the area.

semiperimeter s = 0.5×(a+b+c) ≅ 10.8

area = √(s-(s-a)(s-b)(s-c)) ≅ 18.6 square units

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Use the information to answer the following question.

svlad2 [7]

Since he starts with (10x+7) dollars and is buying two pairs of jeans that each cost (4x-5) dollars you should subtract the cost of the jeans from his starting amount.

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2 years ago

3. Ken solved the linear equation 2(5y - 1) = 18 using the following steps.

OlgaM077 [116]

Answer:

Step-by-step explanation:

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3 years ago

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Consider the differential equation: xy′(x2+7)y=cos(x)+e3xy. Put the differential equation into the form: y′+p(x)y=g(x), determin

icang [17]

Answer:

Linear and non-homogeneous.

Step-by-step explanation:

We are given that

$\frac{xy'}{(x^2+7)y}=cosx+\frac{e^{3x}}{y}$

We have to convert into y'+P(x)y=g(x) and determine P(x) and g(x).

We have also find type of differential equation.

$y'=\frac{(x^2+7)y}{x}(cosx+\frac{e^{3x}}{y}}$

$y'=\frac{(x^2+7)cosx}{x}y+\frac{(x^2+7)e^{3x}}{x}$

$y'-\frac{cosx(x^2+7)}{x}y=\frac{e^{3x}(x^2+7)}{x}$

It is linear differential equation because this equation is of the form

y'+P(x)y=g(x)

Compare it with first order first degree linear differential equation

$y'+P(x)y=g(x)$

$P(x)=-\frac{cosx (x^2+7)}{x},g(x)=\frac{e^{3x}(x^2+7)}{x}$

$\frac{dy}{dx}=\frac{(x^2+7)(ycosx+e^{3x})}{x}$

Homogeneous equation

$\frac{dy}{dx}=\frac{f(x,y)}{g(x,y)}$

Degree of f and g are same.

$f(x,y)=(x^2+7)(ycosx+e^{3x}),g(x,y)=x$

Degree of f and g are not same .

Therefore, it is non- homogeneous .

Linear and non-homogeneous.

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3 years ago

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