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eduard
3 years ago
11

Two less than 3/2 of a number (x) is more than 5 1/2

Mathematics
1 answer:
garik1379 [7]3 years ago
3 0

Answer:

3/2x-2>5 1/2

Step-by-step explanation:

Two less than a number means we are subtracting 2, so we can write it into the equation as -2.

Since we dont know the value of x, we can just write 3/2 of x by multiplying 3/2 by x. So 3/2x. Also, since we are subtracting two from 3/2x, -2 comes after 3/2x.

Now, since it says that it is more than 5 1/2, we could use the greater than sign (>), to express that. So >5  1/2

Our final expression is 3/2x-2>5 1/2.

Hope this helps!

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1.) The island shown has a population of 12,175 people. Find the population
miv72 [106K]

Answer:

Population density = 148.22\ \text{people per square kilometer}

Step-by-step explanation:

The attached figure shows the dimension of an island.

Population density is equal to total population per unit land area.

Firstly we will find the area of the triangle using Pythagoras theorem as follows :

H^2=B^2+P^2

H is Hypotenuse, B is base and P is perpendicular

B=\sqrt{H^2-P^2} \\\\B=\sqrt{(18.5)^2-(11.1)^2} \\\\B=14.8\ km

Area of triangle is given by :

A=\dfrac{1}{2}\times b\times P\\\\A=\dfrac{1}{2}\times 14.8\times 11.1\\\\A=82.14\ km^2

\text{Population density}=\dfrac{\text{Total population}}{\text{land area}}\\\\=\dfrac{12175 }{82.14}\\\\=148.22\ \text{people per square kilometer}

Hence, the population density is 148.22\ \text{people per square kilometer}.

7 0
3 years ago
(a)5%)Let fx, y) = x^4 + y^4 - 4xy + 1. and classify each critical point Find all critical points of fx,y) as a local minimum, l
lara31 [8.8K]

f(x,y)=x^4+y^4-4xy+1

has critical points wherever the partial derivatives vanish:

f_x=4x^3-4y=0\implies x^3=y

f_y=4y^3-4x=0\implies y^3=x

Then

x^3=y\implies x^9=x\implies x(x^8-1)=0\implies x=0\text{ or }x=\pm1

  • If x=0, then y=0; critical point at (0, 0)
  • If x=1, then y=1; critical point at (1, 1)
  • If x=-1, then y=-1; critical point at (-1, -1)

f(x,y) has Hessian matrix

H(x,y)=\begin{bmatrix}12x^2&-4\\-4&12y^2\end{bmatrix}

with determinant

\det H(x,y)=144x^2y^2-16

  • At (0, 0), the Hessian determinant is -16, which indicates a saddle point.
  • At (1, 1), the determinant is 128, and f_{xx}(1,1)=12, which indicates a local minimum.
  • At (-1, -1), the determinant is again 128, and f_{xx}(-1,-1)=12, which indicates another local minimum.
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3 years ago
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Answer:

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Step-by-step explanation:

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evablogger [386]
Answer:
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Explanation:
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Fun Fact:
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I hope this help and have a nice day :)
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Whats the expression
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