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3 years ago

Cynthia is mowing lawns for extra money. The amount of money she made after putting gas in the lawnmower is shown below.

Mathematics

2 answers:

Katarina [22]3 years ago

7 0

Answer:

Step-by-step explanation:

The amount of money Cynthia made is the product of the number of lawns she mowed and 20 minus 3.

Nimfa-mama [501]3 years ago

5 0

Answer:

Step-by-step explanation:

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Which graph represents a function

Oduvanchick [21]

Answer:

Step-by-step explanation:

Linear as said in it's name is a function that creates (visualy) a straight line.

FROM all the graphs A shows a straight line therefore, the answer.

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3 years ago

A container holds 5L of fluid. Does it hold more than or less than 500mL of fluid

Yuri [45]

There are 1000 mL in one liter, so there are 5000 Ml in the 5 L container. thus, it holds more than the 500 mL container.

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3 years ago

A music store is having a sale where you can buy 2 new-release CDs for $15. How much will 7 CDs cost? Use at least 2 ways to sho

Pavlova-9 [17]

Answer: $52.50

Step-by-step explanation:

1 way : 15 divided by 2 then multipy your answer by 7

2nd way : 15x7. Once you get that answer divide it by 2 to get $52.50

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2 years ago

Read 2 more answers

Fine the equation, in standard form, of the line passing through the points (3,-4) and (5,1)

Talja [164]

The point-slope form:

$y-y_1=m(x-x_1)\\\\m=\dfrac{y_2-y_1}{x_2-x_1}$

We have the points (3, -4) and (5, 1). Substitute:

$m=\dfrac{1-(-4)}{5-3}=\dfrac{5}{2}\\\\y-(-4)=\dfrac{5}{2}(x-3)$

The standard form: $Ax+By=C$

$y+4=\dfrac{5}{2}(x-3)$ <em>multiply both sides by 2</em>

$2y+8=5(x+3)$ <em>use distributive property</em>

$2y+8=5x+15$ <em>subtract 2y from both sides</em>

$8=5x-2y+15$ <em>subtract 15 from both sides</em>

$-7=5x-2y$

<h3>Answer: 5x - 2y = -7</h3>

5 0

3 years ago

Evaluate the surface integral S F · dS for the given vector field F and the oriented surface S.

sweet-ann [11.9K]

Answer:

2.794

Step-by-step explanation:

Recall that if G(x,y) is a parametrization of the surface S and F and G are smooth enough then

$\bf \displaystyle\iint_{S}FdS=\displaystyle\iint_{R}F(G(x,y))\cdot(\displaystyle\frac{\partial G}{\partial x}\times\displaystyle\frac{\partial G}{\partial y})dxdy$

F can be written as

F(x,y,z) = (xy, yz, zx)

and S has a straightforward parametrization as

$\bf G(x,y) = (x, y, 3-x^2-y^2)$

with 0≤ x≤1 and 0≤ y≤1

$\bf \displaystyle\frac{\partial G}{\partial x}= (1,0,-2x)\\\\\displaystyle\frac{\partial G}{\partial y}= (0,1,-2y)\\\\\displaystyle\frac{\partial G}{\partial x}\times\displaystyle\frac{\partial G}{\partial y}=(2x,2y,1)$

we also have

$\bf F(G(x,y))=F(x, y, 3-x^2-y^2)=(xy,y(3-x^2-y^2),x(3-x^2-y^2))=\\\\=(xy,3y-x^2y-y^3,3x-x^3-xy^2)$

and so

$\bf F(G(x,y))\cdot(\displaystyle\frac{\partial G}{\partial x}\times\displaystyle\frac{\partial G}{\partial y})=(xy,3y-x^2y-y^3,3x-x^3-xy^2)\cdot(2x,2y,1)=\\\\=2x^2y+6y^2-2x^2y^2-2y^4+3x-x^3-xy^2$

we just have then to compute a double integral of a polynomial on the unit square 0≤ x≤1 and 0≤ y≤1

$\bf \displaystyle\int_{0}^{1}\displaystyle\int_{0}^{1}(2x^2y+6y^2-2x^2y^2-2y^4+3x-x^3-xy^2)dxdy=\\\\=2\displaystyle\int_{0}^{1}x^2dx\displaystyle\int_{0}^{1}ydy+6\displaystyle\int_{0}^{1}dx\displaystyle\int_{0}^{1}y^2dy-2\displaystyle\int_{0}^{1}x^2dx\displaystyle\int_{0}^{1}y^2dy-2\displaystyle\int_{0}^{1}dx\displaystyle\int_{0}^{1}y^4dy+\\\\+3\displaystyle\int_{0}^{1}xdx\displaystyle\int_{0}^{1}dy-\displaystyle\int_{0}^{1}x^3dx\displaystyle\int_{0}^{1}dy-\displaystyle\int_{0}^{1}xdx\displaystyle\int_{0}^{1}y^2dy$

=1/3+2-2/9-2/5+3/2-1/4-1/6 = 2.794

5 0

2 years ago