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3 years ago

15 + 10² • [12 – (12 – 3 • 2)] + 6

Mathematics

2 answers:

IRINA_888 [86]3 years ago

7 0

[ Answer ]

$10458$

[ Explanation ]

Parenthesis

Exponents

Multiply

Divide

Add

Subtract

Parenthesis:

3 * 2 = 12

12 - 12 = 0

12 - 0 = 12

10^2 * 12

10 ^ 2 = 144

144 * 12 = 1728

1728 + 15 = 1743

1743 + 6 = 10458

nikklg [1K]3 years ago

7 0

Easy! Do you remember PEMDAS? This is the easiest way to solve this problem!

P: Parenthesis

E: Exponents

M: Multiplication

D: Division

A: Addition

S: Subtraction

All you have to do is out these steps in order and it would make you solve the problem correctly and quick!

Here we go!:

3 x 2 = 12

12 - 12 = 0

12 - 0 = 12

10^2 x 12

10 ^ 2 = 144

144 x 12 = 1728

1728 + 15 = 1743

1743 + 6 = 10458

The answer to this equation is : 10,458!

I hope this helped!

Yamauchi Wang

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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 $0\le t\le1$ .

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

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

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

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

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.