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3 years ago

Which logarithmic equations is equivalent to eight squared equals 64

Mathematics

1 answer:

yan [13]3 years ago

5 0

Hey jjizilt, thanks for submitting your question to Brainly!

The logarithm that equates to $8^{2}$ is $log_{8} 64$

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9a-18b+21c apply distributive property to factor out gcf of all three terms

horsena [70]

The GCF of the three terms (9a, -18b and 21c) is 3

Rewrite each of the terms so 3 is a factor
9a = 3*3a
-18b = -3*6b
21c = 3*7c

So we can say...
9a - 18b + 21c = 3*3a - 3*6b + 3*7c
9a - 18b + 21c = 3(3a - 6b + 7c)

Answer: 3(3a - 6b + 7c)

If you distribute outer 3 to each of the inner terms and multiply, you'll get the original expression again.

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3 years ago

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shopkeeper purchased a bicycle for rupees 5000 and marked its price a certain percent above the cost price then he sold it at 10

Gennadij [26K]

Lets say the final price of the bike is SP plus 13% VAT. So:

1.13 * SP = 6356.25

SP = 5625

Now SP was after 10% discount on Original Price, say MP. So:

0.9 * MP = 5625

MP = 6250

Therefore, the percent of Marked Price above Cost Price is:

(6250 - 5000) * 100/5000 = 25%

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3 years ago

Lindsay paid $90 for five hours of work how much is she paid per hour

kodGreya [7K]

Answer:

18$ you're welcome!

Step-by-step explanation:

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3 years ago

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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.

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3 years ago

Members of a junior high basketball team want to brag about how tall they are. First, they measured each player’s height in inch

stealth61 [152]

Answer: mean is 66 and the median height is 68.

Step-by-step explanation: uh I dont know what to put here....?

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3 years ago

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