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3 years ago

If y is directly proportional to x and y = 17.5 when x = 21.

Mathematics

1 answer:

Vinvika [58]3 years ago

7 0

Then what’s the question?

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A sequence is a function whose is the set of natural numbers. Answer here Need help!!!!

Harrizon [31]

Or a subset of the natural numbers.

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3 years ago

During a Middle School basketball season, Antonio made 17 of his free throws out of 20. What percent of his free throws did he m

hram777 [196]

I see a fraction. Don't you. Here it is 17/20. Now, let's divide 17 by 20 to get a decimal number, which is 0.85. Next, we multiply 0.85 by 100 to get the percent because that is what the question desires for us to express our answer. As a result, we get 85%, and Antonio made 85% of his free throws. By the way, I hope my response helps you.

8 0

3 years ago

Read 2 more answers

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

Maria must choose a number between 61 and 107 that is a multiple of 5, 6, and 10. Write all the numbers that she could choose. I

RSB [31]

Multiples of 5 : 65,70,75,80,85,90,95,100,105
multiples of 6 : 66,72,78,84,90,96,102
multiples of 10 : 70,80,90,100

she could choose : 90...and thats it

4 0

3 years ago

Two middle school classes take a vote on the destination for a class trip. Class A has 25 students, 56% of whom voted to go to S

Kryger [21]

Answer:

The value of n is 15.

Step-by-step explanation:

The combined proportion is computed using the formula:

$P=\frac{n_{A}\cdot p_{A}+n_{B}\cdot p_{B}}{n_{A}+n_{B}}$