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3 years ago

13

Simplify the expression √((49x^4)/y^5 ). Show your work.

2 answers:

lesantik [10]3 years ago

7 0

Answer:

Step-by-step explanation:

$\sqrt{\frac{49x^{4}}{y^{5}}}=\sqrt{\frac{7*7*x*x*x*x}{y*y*y*y*y}}\\\\=\frac{7*x*x}{y*y}\sqrt{\frac{1}{y}}\\\\=\frac{7x^{2}}{y^{2}}\sqrt{\frac{1}{y}}$

Slav-nsk [51]3 years ago

5 0

Answer:7x^2 $\sqrt{y}$ /y^3

Step-by-step explanation:

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First-order linear differential equations

kkurt [141]

Answer:

$(1)\ logy\ =\ -sint\ +\ c$

$(2)\ log(y+\dfrac{1}{2})\ =\ t^2\ +\ c$

Step-by-step explanation:

1. Given differential equation is

$\dfrac{dy}{dt}+ycost = 0$

$=>\ \dfrac{dy}{dt}\ =\ -ycost$

$=>\ \dfrac{dy}{y}\ =\ -cost dt$

On integrating both sides, we will have

$\int{\dfrac{dy}{y}}\ =\ \int{-cost\ dt}$

$=>\ logy\ =\ -sint\ +\ c$

Hence, the solution of given differential equation can be given by

$logy\ =\ -sint\ +\ c.$

2. Given differential equation,

$\dfrac{dy}{dt}\ -\ 2ty\ =\ t$

$=>\ \dfrac{dy}{dt}\ =\ t\ +\ 2ty$

$=>\ \dfrac{dy}{dt}\ =\ 2t(y+\dfrac{1}{2})$

$=>\ \dfrac{dy}{(y+\dfrac{1}{2})}\ =\ 2t dt$

On integrating both sides, we will have

$\int{\dfrac{dy}{(y+\dfrac{1}{2})}}\ =\ \int{2t dt}$

$=>\ log(y+\dfrac{1}{2})\ =\ 2.\dfrac{t^2}{2}\ + c$

$=>\ log(y+\dfrac{1}{2})\ =\ t^2\ +\ c$

Hence, the solution of given differential equation is

$log(y+\dfrac{1}{2})\ =\ t^2\ +\ c$

8 0

3 years ago

Evan invested $800 in an account that pays 3.25% interest compounded annually.

Aleksandr [31]

Answer:

Evans would have $852.8

Step-by-step explanation:

Given

$PV = \$800$

$r = 3.25\%$

$t = 2$

$n = 1$ --- annually'

Required

The future value

This is calculated using:

$FV = PV*(1 + \frac{r}{n})^{nt$

So, we have:

$FV = 800 * (1 + 3.25\%/1)^{2*1}$

$FV = 800 * (1 + 3.25\%)^{2}$

$FV = 800 * (1 + 0.0325)^{2}$

$FV = 800 * (1 .0325)^2$

$FV = 852.845$

$FV = 852.8$

FV =

8 0

3 years ago

A person can pay $8 for a membership to the science museum and then go to the museum for just $1 per visit. What is the maximum

laila [671]

The maximum number of visits for a member of science museum is 36.

Step-by-step explanation:

Given,

Membership fee = $8

Per visit fee = $1

Total cost = $44

Let,

x be the number of visits

y be the total cost

Total cost = per visit fee*number of visits + membership fee

y = x+8

$44=x+8\\44-8=x\\36=x\\x=36$

The maximum number of visits for a member of science museum is 36.

Keywords: variable, addition

Learn more about variables at:

#LearnwithBrainly

5 0

3 years ago

What is the fractional notation of 2.4%

Vanyuwa [196]

2.4% = 2.4/100 or as a decimal fraction 0.024.

8 0

3 years ago

2. Diamond has $350 in her bank account. She

lorasvet [3.4K]

Answer:

$173.70 will be the balance

Step-by-step explanation:

350 - (4*18.45) - (2*51.25)

350 - 73.80 - 102.50= 173.70

7 0

3 years ago