The elephants at the Putnam Zoo are fed 9 1/2 barrels of corn each day. The buffalo are fed 1/2 as much corn as the elephants. How many barrels of corn are the buffalo fed each day?

z - 20x - 12y + 76 = 0 is the required equation of the plane that is tangent to the given surface at the point (5, 3, – 60).

Given the function is z=8-2x²-2y² and point is (5, 3, – 60).

We need to find the equation of the plane tangent to the given surface at the given point. The gradient vector of the function f(x, y, z) is given by(∂f/∂x)i + (∂f/∂y)j + (∂f/∂z)k∂f/∂x= -4x and ∂f/∂y= -4y

Therefore, the gradient vector is given by-4xi -4yj + k

Therefore, the equation of the tangent plane is given byz - z1=∇f(x1, y1) . (x - x1)i + ∇f(x1, y1) . (y - y1)j + (-1) [f(x1, y1, z1)]

where (x1, y1, z1) is the given pointWe have f(5, 3, – 60) = 8 – 2(5²) – 2(3²) = – 60

Therefore, the equation of the plane is given byz + 60= (-20i - 12j + k) . (x - 5) - (16i + 24j + k) . (y - 3)

Thus, z - 20x - 12y + 76 = 0 is the required equation of the plane that is tangent to the given surface at the point (5, 3, – 60).

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Answer:

Equation is a quadratic equation (polynomial ax+by+c with highest degree 2), so it has two solutions.

Answer:

B. is correct because it only can go 1 way.

Step-by-step explanation:

Answer:

solo multiplica los dos numeros 2x3= 6.

Answer:

aeaa axxd

Step-by-step explanation:

Answer:

the angles are supplementary

so, 5x + 140 = 180

5x = 180 - 140

5x = 40

X = 40

5

X = 8

Answer:

Surface area is the sum of the areas of all faces (or surfaces) on a 3D shape. A cuboid has 6 rectangular faces. To find the surface area of a cuboid, add the areas of all 6 faces. We can also label the length (l), width (w), and height (h) of the prism and use the formula, SA=2lw+2lh+2hw, to find the surface area.

Therefore, x^2 - x^2cosθ + C = 0 is the general solution of the given differential equation.

General solution of the given differential equation is x^2 - x^2cosθ + C = 0, where C is the constant of integration.

To solve the differential equation, we have to integrate the given equation. Here, x sinθ dθ + (x^3 - 2x^2cosθ) dx = 0.

Let's integrate it using separation of variables.

x sinθ dθ = - (x^3 - 2x^2cosθ) dx

Dividing both sides by x^2, we get

sinθ dθ/x - (x - 2cosθ) dx/x^2 = 0

Now, integrate the above equation.

∫sinθ dθ/x - ∫(x - 2cosθ) dx/x^2 = ln|C|

Simplifying the above equation, we get

- cosθ/x + 1/x - x^(-1) sinθ = ln|C|

Multiplying both sides by -x, we get

cosθ - x + x^2 sinθ = -x ln|C|

Rearranging the terms, we get

x^2 - x^2cosθ + ln|C| = 0

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The mean, variance, and standard deviation of the number of federal government employees who use e-mail can be calculated using the binomial distribution formula.

Given that 88% of federal government employees use e-mail, we can define the probability of success (p) as 0.88 and the number of trials (n) as 210.

The mean of a binomial distribution is given by μ = np, where μ is the mean and n is the number of trials. Therefore, the mean of the number of federal government employees who use e-mail is μ = 210 * 0.88 = 184.8.

The variance of a binomial distribution is given by [tex]\sigma^2 = np(1-p)[/tex], where [tex]\sigma^2[/tex] is the variance and n is the number of trials. Therefore, the variance of the number of federal government employees who use e-mail is σ^2 = 210 * 0.88 * (1-0.88) = 21.504.

The standard deviation of a binomial distribution is the square root of the variance. Therefore, the standard deviation of the number of federal government employees who use e-mail is σ = sqrt(21.504) ≈ 4.637.

In summary, the mean of the number of federal government employees who use e-mail is 184.8, the variance is 21.504, and the standard deviation is approximately 4.637. These values represent the average, spread, and deviation from the mean, respectively, for the number of federal government employees who use e-mail in a sample of 210 individuals.

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Answer:

y=2x+3

The coefficient attached to x is the slope and the number being added to it is the y intercept.

Please see the attached image

The sum numbers are 1, 2, 4, 5, 8, 10, 20, 40

Answer:

86.6

Step-by-step explanation:

Add them all up and divide by how many scores

Answer:

the solution to the system is (1,3)

Step-by-step explanation:

x = 1 , y = 3

Answer:

$800 in interest

Step-by-step explanation:

T = A(1 + rt)

T = 2,000(1 + .05(8))

T = 2,000(1.4)

T = 2800

2800 - 2000 = 800

Answer:

626

Step-by-step explanation

Answer:

numerator divided by denominator

Step-by-step explanation:

To determine if the function[tex]F(x) = -x1 + x1x2x2 - i1x2[/tex]is Lipschitz continuous, we need to examine its partial derivatives and check if they are bounded.

The function F(x) is defined on [tex]R^2,[/tex] so let's calculate its partial derivatives with respect to x1 and x2

∂F/∂x1 = [tex]-1 + x2^2[/tex]

∂F/∂x2 = [tex]x1x2 - i1[/tex]

Now, to determine Lipschitz continuity, we need to check if the partial derivatives are bounded on the given domain.

For ∂F/∂x1, we can see that it is not bounded because as x2 approaches positive or negative infinity, the value of ∂F/∂x1 also approaches positive or negative infinity, respectively. Therefore, ∂F/∂x1 is not bounded.

For ∂F/∂x2, we can also see that it is not bounded because as x1 approaches positive or negative infinity, the value of ∂F/∂x2 also approaches positive or negative infinity, respectively. Therefore, ∂F/∂x2 is not bounded.

Since both partial derivatives are not bounded, we can conclude that the function F(x) = -x1 + x1x2x2 - i1x2 is not Lipschitz continuous, neither locally nor globally, on the domain [tex]R^2.[/tex]

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The equation of the line is (y - 2) = 1.5(x - 4)

What is line ?

Euclid described a line as an "unextended length" that "stands equally with respect to its points"; he introduced the postulates as the main unprovable properties from which he constructed all of geometry, now called Euclidean geometry to avoid confusion with other geometries introduced from the late 19th century (such as non-Euclidean, projective and affine geometry).

In modern mathematics, given the multiplicity of geometries, the concept of line is closely related to the way geometry is described. For example, in analytic geometry, a plane line is often defined as a set of points whose coordinates correspond to a given linear equation, but in a more abstract setting, such as drop geometry, the line may be an object other than the set. of the points located on it.

When geometry is described by a set of axioms, the concept of line is usually left undefined (so-called primitive object). The properties of the lines are then determined by the axioms that refer to them. One of the advantages of this approach is the flexibility it gives users of the geometry. Thus, in differential geometry a line can be interpreted as a geodesic (shortest path between points), while in some projective geometries a line is a 2-dimensional vector space (all linear combinations of two independent vectors). This flexibility also extends beyond mathematics and allows physicists, for example, to think of the path of a light ray as a line.

Given, [tex]y = 1.5x - 6....(1)[/tex]

We are comparing equation (1) with y = mx+c and get m = 1.5

It is also given required equation passes through the point (4,2)

We know, if slope of a equation m and the equation passes through (a,b) then equation of the line (y-b) = m (x-a)

Here,

[tex]m = 1.5 \\ a = 4 \\ b = 2[/tex]

So, required equation of the line [tex](y - 2) = 1.5(x - 4)[/tex]

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Answer:

Step-by-step explanation:

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1

cecewiliams23

08/12/2016

Mathematics

High School

answered

How many solutions does the equation 5x + 3x − 4 = 10 have

2

SEE ANSWERS

Answer

4.0/5

28

MathGeek289

Ambitious

236 answers

69.7K people helped

This Must Only Have One Solution, Because The Right Side Of The Equation Is Just Plainly Ten. Lets Solve This:

5x + 3x - 4 = 10

Add Four To Both Sides To Begin Simplifying.

5x + 3x = 14

Now, Combine Like Terms.

8x = 14

Divide:

8x/8 = 1X = X

14/8

X = 14/8

14/8 = 1.75

X = 1.75

Check:

(5 * 1.75) + (3*1.75) - 4 = 10

8.75 + 5.25 - 4 = 10

14 - 4 = 10

10 = 10.

This Is True, So X Does Equal 1.75

Answer:

Vertex is (-4, -18)

Step-by-step explanation:

f(x) = [tex]ax^{2} +bx +c[/tex]

Let (h, k) be the vertex

An easy way to find h is to use the formula h = -b/2a

In your case where f(x) = [tex]x^{2} +8x - 2[/tex]   a = 2 and b = 8

So, h =  -8/2(1) = -8/2 = -4

Substitue -4 in for x to find k

k = ([tex]-4^{2}[/tex]) + 8(-4) - 2

  = (16) - 32 - 2

  = 16 - 32 - 2

  = -18

Vertex is (-4, -18)

Note:  Another way to find the vertex is to complete the square, but this can really be difficult in some cases

Answer:

Option D, (-4,-18)

Step-by-step explanation:

got it right on edge

Answer:

side a = Smallest = 9 inches

side b = 18 inches

side c = 17 inches

Step-by-step explanation:

The formula for the perimeter of a triangle = side a + side b + side c

side a = Smallest

The perimeter of a triangle is 44 inches.

The length of one side is twice the length of the shortest side

Hence:

b = 2a

The length of the other side is eight inches longer than the length of the shortest side.

Hence,

c = 8 + a

Hence, we substitute into the Intial formula

a + 2a + 8 + a = 44 inches

4a + 8 = 44

4a = 44 - 8

4a = 36

a = 36/4

a = 9 inches

Solving for b

b = 2a

b = 2 × 9 inches = 18 inches

Solving for c

c = a + 8

c = 9 inches + 8 = 17 inches

Answer:

Step-by-step explanation:

Let x be the number.

(x + 13)/2

Answer:

D

Step-by-step explanation:

because it is the answer that I think of

Answer:

Line segment PM = 4.2 length

ML = 6.2

ON = 3

NK = 2

Step-by-step explanation:

Just got it on plato your welcome:)

The segments formed by each transversals and the three parallel lines are

proportional according to the three parallel lines theorem.

The observations are;

Reasons:

The question is a four part question

Let the equations of the parallel lines be as follows;

Line, x; y = x

Line, y; y = x + 1

Line z; y = x + 2

The points at which transversal 1 intersect the lines x, y, and z, are;

A(0.4, 0.4), B(0.6, 1.6), and C(0.8, 2.8)

The length of segment [tex]\overline{AB}[/tex] = √((0.6 - 0.4)² + (1.6 - 0.4)²) = 0.2·√(37)

The length of segment [tex]\mathbf{\overline{CB}}[/tex] = √((0.8 - 0.6)² + (2.8 - 1.6)²) = 0.2·√(37)

The ratio of the lengths of the segment formed by transversal 1 is therefore;

[tex]\sqrt{x} \displaystyle Ratio \ of \ the \ length \ of \ the \ segments = \mathbf{\frac{\overline{CB}}{\overline{AB}}} =\frac{2 \cdot \sqrt{37} }{2 \cdot \sqrt{37} } = 1[/tex]

The points at which transversal 2 intersect the lines x, y, and z, are;

D(1.1, 3.1), E(1.3, 2.3), and F(1.5, 1.5)

The length of segment [tex]\overline{DE}[/tex] = √((1.3 - 1.1)² + (2.3 - 3.1)²) = 0.2·√(17)

The length of segment [tex]\overline{EF}[/tex] = √((1.5 - 1.3)² + (1.5 - 2.3)²) = 0.2·√(17)

[tex]\sqrt{x} \displaystyle Ratio \ of \ the \ length \ of \ the \ segments = \mathbf{\frac{\overline{EF}}{\overline{DE}}} =\frac{0.2 \cdot \sqrt{17} }{0.2 \cdot \sqrt{17} } = 1[/tex]

Therefore;

Which gives;

The the comparison can also be made with the triangle proportionality theorem.

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