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2 years ago

Slope of (4,-1) (3,-2)

Mathematics

2 answers:

Alona [7]2 years ago

6 0

-1/2

lolollolololololololololololo

fgiga [73]2 years ago

3 0

Answer:

-1/2

Step-by-step explanation:

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What is 26/15 as a whole number?

Contact [7]

Answer:

1 11/15

Step-by-step explanation:

4 0

2 years ago

There are 40 mg of bacteria in the sample. The next day there are 50 mg of bacteria, and the following day there are 62.5 mg of

Yuliya22 [10]

Don’t take my
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2 years ago

Sarah wants to fence her garden, as shown below. Determine how much fencing to the nearst foot that

coldgirl [10]

Answer:

431.775 ft

Step-by-step explanation:

So basically we should first find the area of the rectangles which is 28 ft * 15 ft, which you get 420. Next for the semicircle, the diameter is 15 but we need the radius so you divide that by 2 to get 7.5 as the radius. Then u multiply 7.5 * π, or 3.14 to get 23.55. But since its a semicircle, or half a circle we divide 23.55 by 2 which is 11.775. Then we just add the results which is 420 ft and 11.755 ft to get a total area of 431.775 ft.

-Hope this helped!

4 0

3 years ago

I need help on problem 2 and 3.I want to know how to do it step by step.

Svetradugi [14.3K]

I think u have to multiply the radius and diameter. umm if i am correct the ans is 34396.95. or i think u have to divide. if u divide, the ans is 28.31. if i am incorrect let me know pls. and sry i cant help with no.3. thats difficult.
hope my ans is right. if ans is correct pls mark as brainliest ans.

3 0

2 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 function $A(d,h)$ is minimum at that point.

4 0

3 years ago

Slope of (4,-1) (3,-2)​

Slope of (4,-1) (3,-2)