A rectangular prism has a volume of 66 ft³, a height of 2.2 ft, and a length of 5 ft. What is the width of the prism?

What is the base 5 representation of the number 465^8

Alika [10]

We need to convert given value 465^8 as the base 5 number.

Let us assume x is the exponent of 5 when we take base 5.

We can setup an equation now.

5^x=465^8

Taking ln on both sides, we get

$\ln \left(5^x\right)=\ln \left(465^8\right)$

$\mathrm{Apply\:log\:rule}:\quad \log _a\left(x^b\right)=b\cdot \log _a\left(x\right)$

$x\ln \left(5\right)=8\ln \left(465\right)$

$\mathrm{Divide\:both\:sides\:by\:}\ln \left(5\right)$

$\frac{x\ln \left(5\right)}{\ln \left(5\right)}=\frac{8\ln \left(465\right)}{\ln \left(5\right)}$

On simplifying, we get

$x=\frac{8\ln \left(465\right)}{\ln \left(5\right)}$

Therefore, $465^8 \ can \ be \ written \ as \ 5^{\frac{8\ln \left(465\right)}{\ln \left(5\right)}}.$ .

3 0

3 years ago

Read 2 more answers

Can you help me solve for slope

VMariaS [17]

Answer:

y = 4x - 7

Step-by-step explanation:

Hope it helps.

5 0

2 years ago

Read 2 more answers

Simplify 4(2x^3y^4)^4/2(2x^2y^6)^3. Show your work. Please help ASAP!!

vovikov84 [41]

Answer:

The simplified expression to the given expression is $\frac{4x^6}{y^2}$

Therefore $\frac{4(2x^3y^4)^4}{2(2x^2y^6)^3}=\frac{4x^6}{y^2}$

Step-by-step explanation:

Given fractional expression is $\frac{4(2x^3y^4)^4}{2(2x^2y^6)^3}$

To simplify the given expression as below :

$\frac{4(2x^3y^4)^4}{2(2x^2y^6)^3}$

$=\frac{2(2x^3y^4)^4}{(2x^2y^6)^3}$

$=\frac{2[(2)^4(x^3)^4(y^4)^4]}{(2)^3(x^2)^3(y^6)^3}$ ( using the property $(a^m)^n=a^{mn}$ )

$=\frac{2[(2)^4(x^{12})(y^{16})]}{(2)^3(x^6)(y^{18})}$

$=2[(2)^4(x^{12})(y^{16})](2)^{-3}(x^{-6})(y^{-18})$ ( ( using the property $a^m=\frac{1}{a^{-m}}$ )

$=2[2^{4-3}x^{12-6}y^{16-18}]$ ( using the property $a^m.a^n=a^{m+n}$ )

$=2[2^1x^6y^{-2}]$

$=\frac{4x^6}{y^2}$ ( using the property $a^m=\frac{1}{a^{-m}}$ )

Therefore the simplified expression is $\frac{4x^6}{y^2}$

Therefore $\frac{4(2x^3y^4)^4}{2(2x^2y^6)^3}=\frac{4x^6}{y^2}$

5 0

3 years ago

Question 1 (1 point)

grigory [225]

The answer is no solution

4 0

3 years ago

What is P(3 or divisor of 24)?

storchak [24]

Answer:

P

(

sum

>

3

and

divisor of

24

)

=

7

18

Explanation:

Possible target sums that meet the given requirements:

XXX

{

4

,

6

,

8

,

12

}

Consider the possible die rolls that can give these sums:

sum

−−−−

xxx

first roll

−−−−−−−

second roll

−−−−−−−−−

4

1

3

2

3

1

6

1

5

2

4

3

4

2

5

1

8

2

6

3

5

4

5

3

6

2

12

−−

6

−

6

−

Giving a total of

14

out of a possible

36

combinations that meet the given requirements.

Step-by-step explanation:

6 0

3 years ago