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sasho [114]
3 years ago
9

Simplify: (d - 3)(d + 9)

Mathematics
1 answer:
podryga [215]3 years ago
8 0
<span>Simplify: (d - 3)(d + 9)


A) d^2 + 6
B) d^2 - 27
C) d^2 - 12d - 27
D) d^2 + 6d - 27</span>
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4 tens and 10 ones is 410
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3 years ago
Simplify [2 (cos 210 + i sin 210)]^3
Dennis_Churaev [7]
After simplifying the real and imaginary parts you'd get -8i

3 0
3 years ago
A company wishes to manufacture some boxes out of card. The boxes will have 6 sides (i.e. they covered at the top). They wish th
Serhud [2]

Answer:

The dimensions are, base b=\sqrt[3]{200}, depth d=\sqrt[3]{200} and height h=\sqrt[3]{200}.

Step-by-step explanation:

First we have to understand the problem, we have a box of unknown dimensions (base b, depth d and height h), and we want to optimize the used material in the box. We know the volume V we want, how we want to optimize the card used in the box we need to minimize the Area A of the box.

The equations are then, for Volume

V=200cm^3 = b.h.d

For Area

A=2.b.h+2.d.h+2.b.d

From the Volume equation we clear the variable b to get,

b=\frac{200}{d.h}

And we replace this value into the Area equation to get,

A=2.(\frac{200}{d.h} ).h+2.d.h+2.(\frac{200}{d.h} ).d

A=2.(\frac{200}{d} )+2.d.h+2.(\frac{200}{h} )

So, we have our function f(x,y)=A(d,h), which we have to minimize. We apply the first partial derivative and equalize to zero to know the optimum point of the function, getting

\frac{\partial A}{\partial d} =-\frac{400}{d^2}+2h=0

\frac{\partial A}{\partial h} =-\frac{400}{h^2}+2d=0

After solving the system of equations, we get that the optimum point value is d=\sqrt[3]{200} and  h=\sqrt[3]{200}, replacing this values into the equation of variable b we get b=\sqrt[3]{200}.

Now, we have to check with the hessian matrix if the value is a minimum,

The hessian matrix is defined as,

H=\left[\begin{array}{ccc}\frac{\partial^2 A}{\partial d^2} &\frac{\partial^2 A}{\partial d \partial h}\\\frac{\partial^2 A}{\partial h \partial d}&\frac{\partial^2 A}{\partial p^2}\end{array}\right]

we know that,

\frac{\partial^2 A}{\partial d^2}=\frac{\partial}{\partial d}(-\frac{400}{d^2}+2h )=\frac{800}{d^3}

\frac{\partial^2 A}{\partial h^2}=\frac{\partial}{\partial h}(-\frac{400}{h^2}+2d )=\frac{800}{h^3}

\frac{\partial^2 A}{\partial d \partial h}=\frac{\partial^2 A}{\partial h \partial d}=\frac{\partial}{\partial h}(-\frac{400}{d^2}+2h )=2

Then, our matrix is

H=\left[\begin{array}{ccc}4&2\\2&4\end{array}\right]

Now, we found the eigenvalues of the matrix as follow

det(H-\lambda I)=det(\left[\begin{array}{ccc}4-\lambda&2\\2&4-\lambda\end{array}\right] )=(4-\lambda)^2-4=0

Solving for\lambda, we get that the eigenvalues are:  \lambda_1=2 and \lambda_2=6, how both are positive the Hessian matrix is positive definite which means that the functionA(d,h) is minimum at that point.

4 0
3 years ago
Is -5 a solution to the equation 6x +5 = 5x + 8 + 2x? Explain.
MrRa [10]

Answer:

No -5 is not the solution, But x =-3 is the solution.

Step-by-step explanation:

Given:

6x+5= 5x+8+2x

We need to find the solution for above equation we get;

Solution:

Now when we put the value of x =-5 we get

6x+5 =5x+8+2x\\\\6\times-5+5 = 5\times-5+8+2\times-5\\\\-30+5 = -25+8-10\\\\-25\neq -27

hence -5 is not the Solution for given equation.

On Solving the above equation we get;

6x+5 =7x+8

Now Combining the like terms we get;

7x-6x =5-8

Now Using Subtraction property we get;

x = -3

Hence The solution to equation is -3.

6 0
3 years ago
The digit in which number represents a value of 9 hundredths
Artyom0805 [142]

Answer : 1.29

Reason : Any number in the second decimal place represents a value of 9 hundredths

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