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3 years ago

Which of the following shows the graph of the eniquality y>x+3 PLEASE include image

Mathematics

1 answer:

7nadin3 [17]3 years ago

5 0

in plain and short, to graph an inequality, we first graph its EQUALITY graph, and then we do the shading.

so to graph y > x + 3, we first graph y = x + 3, which is just a line, and then do a true/false check on a point to see which side we shade.

let's hmmm check the point say (0,2), x = 0, y = 2.

y > x + 3

2 > 0 + 3

2 > 3 <--- is that true? is 2 really larger than 3? nope, so is false.

that simply means that the point (0, 2) is on the false area, so that's the area we do NOT shade, so <u>we shade the other side</u>.

y > x + 3, means "y" is greater than or larger than that line, but not equals, larger not equal, meaning the values on the borderline are not included, so the line is a dashed line.

check the picture below.

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3 years ago

The lengths of three line segments are 4 centimeters, 5 centimeters, and 9 centimeters. Using this information, triangles can be

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Anybody who looks at it would think it's just a straight line segment, 9 cm long.

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3 years ago

What type of triangle is given by the points D(1,1), E(3,8) and F(5,1).

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2 years ago

when measuring ,100degrees Fahrenheit squat to 37.7777 degrees celsius. Round to the nearest thousandth

Gre4nikov [31]

Answer: 37.778 degrees

Step-by-step explanation:

The third digit to the right of the decimal is thousandths. If the next digit to the right of that is 5 or more, add one to the thousandths. Otherwise leave it as is. Just drop everything to the right of the place you rounded to.

7 is greater than 5, so add 1 to the 7 in the thousandths place and get

37.778

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3 years ago

The base of an aquarium with given volume V is made of slate and the sides are made of glass. If the slate costs seven times as

Olin [163]

Answer:

x = ∛(2V/7)

y = ∛(2V/7)

z = 3.5 [∛(2V/7)]

{x,y,z} = { ∛(2V/7), ∛(2V/7), 3.5[∛(2V/7)] }

Step-by-step explanation:

The aquarium is a cuboid open at the top.

Let the dimensions of the base of the aquarium be x and y.

The height of the aquarium is then z.

The volume of the aquarium is then

V = xyz

Area of the base of the aquarium = xy

Area of the other faces = 2xz + 2yz

The problem is to now minimize the value of the cost function.

The cost of the area of the base per area is seven times the cost of any other face per area.

With the right assumption that the cost of the other faces per area is 1 currency units, then, the cost of the base of the aquarium per area would then be 7 currency units.

Cost of the base of the aquarium = 7xy

cost of the other faces = 2xz + 2yz

Total cost function = 7xy + 2xz + 2yz

C(x,y,z) = 7xy + 2xz + 2yz

We're to minimize this function subject to the constraint that

xyz = V

The constraint can be rewritten as

xyz - V = 0

Using Lagrange multiplier, we then write the equation in Lagrange form

Lagrange function = Function - λ(constraint)

where λ = Lagrange factor, which can be a function of x, y and z

L(x,y,z) = 7xy + 2xz + 2yz - λ(xyz - V)

We then take the partial derivatives of the Lagrange function with respect to x, y, z and λ. Because these are turning points and at the turning point, each of the partial derivatives is equal to 0.

(∂L/∂x) = 7y + 2z - λyz = 0

λ = (7y + 2z)/yz = (7/z) + (2/y) (eqn 1)

(∂L/∂y) = 7x + 2z - λxz = 0

λ = (7x + 2z)/xz = (7/z) + (2/x) (eqn 2)

(∂L/∂z) = 2x + 2y - λxy = 0

λ = (2x + 2y)/xy = (2/y) + (2/x) (eqn 3)

(∂L/∂λ) = xyz - V = 0

We can then equate the values of λ from the first 3 partial derivatives and solve for the values of x, y and z

(eqn 1) = (eqn 2)

(7/z) + (2/y) = (7/z) + (2/x)

(2/y) = (2/x)

y = x

Also,

(eqn 1) = (eqn 3)

(7/z) + (2/x) = (2/y) + (2/x)

(7/z) = (2/y)

z = (7y/2)

Hence, at the point where the box has minimal area,

y = x,

z = (7y/2) = (7x/2)

We can then substitute those into the constraint equation for y and z

xyz = V

x(x)(7x/2) = V

(7x³/2) = V

x³ = (2V/7)

x = ∛(2V/7)

y = x = ∛(2V/7)

z = (7x/2) = 3.5 [∛(2V/7)]

The values of x, y and z in terms of the volume that minimizes the cost function are

{x,y,z} = {∛(2V/7), ∛(2V/7), 3.5[∛(2V/7)]}

Hope this Helps!!!

7 0

3 years ago