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3 years ago

What is the answer to X+2y=6

1 answer:

3 0

$\text{Turn the equation into slope intercept form}\\\\\text{Slope intercept form: y = mx + b}\\\\\text{Solve:}\\\\x+2y=6\\\\\text{Subtract x from both sides}\\\\2y=-x+6\\\\\text{Divide both sides by 2}\\\\\boxed{y=-\frac{1}{2}x+3}$

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Consider the line integral Z C (sin x dx + cos y dy), where C consists of the top part of the circle x 2 + y 2 = 1 from (1, 0) t

pashok25 [27]

Direct computation:

Parameterize the top part of the circle $x^2+y^2=1$ by

$\vec r(t)=(x(t),y(t))=(\cos t,\sin t)$

with $0\le t\le\pi$ , and the line segment by

$\vec s(t)=(1-t)(-1,0)+t(2,-\pi)=(3t-1,-\pi t)$

with $0\le t\le1$ . Then

$\displaystyle\int_C(\sin x\,\mathrm dx+\cos y\,\mathrm dy)$

$=\displaystyle\int_0^\pi(-\sin t\sin(\cos t)+\cos t\cos(\sin t)\,\mathrm dt+\int_0^1(3\sin(3t-1)-\pi\cos(-\pi t))\,\mathrm dt$

$=0+(\cos1-\cos2)=\boxed{\cos1-\cos2}$

Using the fundamental theorem of calculus:

The integral can be written as

$\displaystyle\int_C(\sin x\,\mathrm dx+\cos y\,\mathrm dy)=\int_C\underbrace{(\sin x,\cos y)}_{\vec F}\cdot\underbrace{(\mathrm dx,\mathrm dy)}_{\vec r}$

If there happens to be a scalar function $f$ such that $\vec F=\nabla f$ , then $\vec F$ is conservative and the integral is path-independent, so we only need to worry about the value of $f$ at the path's endpoints.

This requires

$\dfrac{\partial f}{\partial x}=\sin x\implies f(x,y)=-\cos x+g(y)$

$\dfrac{\partial f}{\partial y}=\cos y=\dfrac{\mathrm dg}{\mathrm dy}\implies g(y)=\sin y+C$

So we have

$f(x,y)=-\cos x+\sin y+C$

which means $\vec F$ is indeed conservative. By the fundamental theorem, we have

$\displaystyle\int_C(\sin x\,\mathrm dx+\cos y\,\mathrm dy)=f(2,-\pi)-f(1,0)=-\cos2-(-\cos1)=\boxed{\cos1-\cos2}$

3 0

3 years ago

Select the expressions that are equivalent to 2(9r)

pashok25 [27]

Answer:

18r

Step-by-step explanation:

Multiply 9 by 2

5 0

3 years ago

Help pls haha also Merry Christmas

MArishka [77]

Answer:

x = √39

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Trigonometry

[Right Triangles Only] Pythagorean Theorem: a² + b² = c²

Step-by-step explanation:

Step 1: Identify

Leg a = x

Leg b = 5

Hypotenuse c = 8

Step 2: Solve for x

Substitute [PT]: x² + 5² = 8²
Isolate x term: x² = 8² - 5²
Exponents: x² = 64 - 25
Subtract: x² = 39
Isolate x: x = √39

3 0

3 years ago

Read 2 more answers

Find the volume of the region bounded above by the elliptical paraboloid zequals=9 minus 4 x squared minus 5 y squared9−4x2−5y2

Virty [35]

Answer:

$\int\limits^1_0 \int^1_0{z} \, dA$

Step-by-step explanation:

$\int\limits^1_0\int^1_0 {9-4x^2-5y^2dy} \, dx$

$\int\limits^1_0 {9y-4x^2y-\frac{5y^3}{3}|_0 ^1 } \, dx$

$\int\limits^1_0 {22/3 -4x^2} \, dx$

You finish the leftover.

7 0

3 years ago

in a circle, a 60° sector has an area of a 36π cm^2. find the radius of the circle. round your answer to the nearest whole centi

hammer [34]

Area of circle = $\frac{ \theta }{360^o} \times \pi r^2 \\ 36 \pi = \frac{60^o}{360^o} \times \pi r^2 \\ r^2=216 \\ r= \sqrt{216} =14.70 \ cm \\ r=15 \ cm \ to \ the \ nearest \ whole \ centimeter.$

3 0

3 years ago