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3 years ago

The seventh root of x divided by eighth root of x

Mathematics

2 answers:

Solnce55 [7]3 years ago

8 0

1.573173141822894. I think this is the answer but not 100% sure. Good luck!

kogti [31]3 years ago

4 0

(Seventh root x) / eighth root x)
You can't use the radical rules because indexes are different. Change to rational form.
x^(1/7) / x^(1/8)
x ^ ((1/7)-(1/8))
x ^ ((8/56)-(7/56))
x ^ (1/56)

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Nu is designing a rectangular sandbox.The bottomm is 16 square feet.Which dimensions require the least amount of materail for th

zzz [600]

Given Information:

Area of rectangle = 16 square feet

Required Information:

Least amount of material = ?

Answer:

x = 4 ft and y = 4 ft

Step-by-step explanation:

We know that a rectangle has area = xy and perimeter = 2x + 2y

We want to use least amount of material to design the sandbox which means we want to minimize the perimeter which can be done by taking the derivative of perimeter and then setting it equal to 0.

So we have

xy = 16

y = 16/x

p = 2x + 2y

put the value of y into the equation of perimeter

p = 2x + 2(16/x)

p = 2x + 32/x

Take derivative with respect to x

d/dt (2x + 32/x)

2 - 32/x²

set the derivative equal to zero to minimize the perimeter

2 - 32/x² = 0

32/x² = 2

x² = 32/2

x² = 16

x = $\sqrt{16} = 4$ ft

put the value of x into equation xy = 16

(4)y = 16

y = 16/4

y = 4 ft

So the dimensions are x = 4 ft and y = 4 ft in order to use least amount of material.

Verification:

xy = 16

4*4 = 16

16 = 16 (satisfied)

7 0

3 years ago

Explain how to get that answer!!

ra1l [238]

We need to simplify $\frac{ \sqrt{14x^3} }{ \sqrt{18x} }$

First lets factor $\sqrt{14x^3}$

$\sqrt{14x^3}$ = $\sqrt{14} \sqrt{x^3}$
$\sqrt{14} = \sqrt{2} \sqrt{7}$ by applying the radical rule $\sqrt[n]{ab} = \sqrt[n]{a} \sqrt[n]{b}$
$\sqrt{x^3} = x^{3/2}$ By applying the radical rule $\sqrt[n]{x^m} = x^{m/n}$

So
$\sqrt{14x^3}$ = $\sqrt{14} \sqrt{x^3}$ = $\sqrt{2} \sqrt{7}x^{3/2}$

Now let's factor $\sqrt{18x}$
By applying the radical rule $\sqrt[n]{ab} = \sqrt[n]{a} \sqrt[n]{b}$ ,
$\sqrt{18x} = \sqrt{18} \sqrt{x}$
$\sqrt{18} = \sqrt{2} * 3$

So $\sqrt{18x}$ = $\sqrt{2}*3 \sqrt{x}$

So $\frac{ \sqrt{14x^3} }{ \sqrt{18x} }$ = $\frac{ \sqrt{2} \sqrt{7} x^{3/2} }{ \sqrt{2}*3 \sqrt{x} }$

We know that $\sqrt[n]{x} = x^{1/n}$ so $\sqrt{x} = x^{1/2}$

We now have $\frac{ \sqrt{2} \sqrt{7} x^{3/2} }{ \sqrt{2}*3 \sqrt{x}} = \frac{ \sqrt{2} \sqrt{7} x^{3/2} }{ \sqrt{2}*3x^{1/2}}$

We know that $\frac{x^a}{x^b} = x^{a-b}$
So $\frac{x^{3/2}}{x^{1/2}} = x^{3/2 - 1/2} = x$

We now got $\frac{ \sqrt{2} \sqrt{7} x^{3/2} }{ \sqrt{2}*3x^{1/2}} = \frac{ \sqrt{2} \sqrt{7} x }{ \sqrt{2}*3}
$

We can notice that the numerator and the denominator both got √2 in a multiplication, so we can simplify them, and we get:
$\frac{ \sqrt{2} \sqrt{7} x }{ \sqrt{2}*3} = \frac{ \sqrt{7}x }{3}$

All in All, we get $\frac{ \sqrt{14x^3} }{ \sqrt{18x} }$ = $\frac{ \sqrt{7}x }{3}$

Hope this helps! :D

6 0

3 years ago

Use the future value formula to find the indicated value. FV = $ 5330 n=24; i=0.08; PMT=? PMT=$ (round to the nearest cent)

spin [16.1K]

Hi there
The future value formula is
Fv=pmt [(1+r)^(n)-1)÷r]
Solve the formula for PMT
PMT=Fv÷[(1+r)^(n)-1)÷r]
So
PMT=5,330÷(((1+0.08)^(24)−1)÷(0.08))
PMT=79.83

Good luck!

4 0

3 years ago

A student wanted to know what is 16% 75

natulia [17]

First you turn 16 to 0.16 then multiply 0.16 x 75 and you should get 12
I hope this helps you and your welcome : )

3 0

3 years ago

Bens score in a game is x points and Olives score is three times that of ben. Their combined point total is -48 points.

andrew-mc [135]

B. The equation is 4x = -48. Ben’s point total is -12.

6 0

3 years ago