Ask question

Ask question

All categories

2 years ago

12

Marvin has 4 books to read for homework this week. If he reads 2/3 of a book each night, how many nights will it take all four b

ook?

1 answer:

stiks02 [169]2 years ago

3 0

3 nights___________________

You might be interested in

Find the solution of the initial value problem<br><br> dy/dx=(-2x+y)^2-7 ,y(0)=0

Leokris [45]

Substitute $v(x)=-2x+y(x)$ , so that $\dfrac{\mathrm dv}{\mathrm dx}=-2+\dfrac{\mathrm dy}{\mathrm dx}$ . Then the ODE is equivalent to

$\dfrac{\mathrm dv}{\mathrm dx}+2=v^2-7$

which is separable as

$\dfrac{\mathrm dv}{v^2-9}=\mathrm dx$

Split the left side into partial fractions,

$\dfrac1{v^2-9}=\dfrac16\left(\dfrac1{v-3}-\dfrac1{v+3}\right)$

so that integrating both sides is trivial and we get

$\dfrac{\ln|v-3|-\ln|v+3|}6=x+C$

$\ln\left|\dfrac{v-3}{v+3}\right|=6x+C$

$\dfrac{v-3}{v+3}=Ce^{6x}$

$\dfrac{v+3-6}{v+3}=1-\dfrac6{v+3}=Ce^{6x}$

$\dfrac6{v+3}=1-Ce^{6x}$

$v=\dfrac6{1-Ce^{6x}}-3$

$-2x+y=\dfrac6{1-Ce^{6x}}-3$

$y=2x+\dfrac6{1-Ce^{6x}}-3$

Given the initial condition $y(0)=0$ , we find

$0=\dfrac6{1-C}-3\implies C=-1$

so that the ODE has the particular solution,

$\boxed{y=2x+\dfrac6{1+e^{6x}}-3}$

5 0

3 years ago

The sum of four consecutive numbers is 42 what is the smallest number

vredina [299]

Let us take a number x
The four consecutive numbers will be
x+1, x+2, x+3

Thus our equation will be
x + x+1 + x+2 + x+3 = 42
4x + 6 = 42
4x = 36
x= 36/4
x= 9

Thus the four numbers are (substitute)
x=9
x+1=9+1=10
x+2=9+2=11
x+3=9+3=12

9,10,11,12

6 0

3 years ago

Read 2 more answers

What is the solution to this inequality -13x> - 39

s344n2d4d5 [400]

Answer:

Isolate the variable by dividing each side by factors that don't contain the variable.

Inequality Form: x < 3

Interval Notation:

( − ∞ , 3 )

3 0

3 years ago

Read 2 more answers

Rosena bought an 8 pack of donuts. The donuts cost $28.00 all together. What is the unit rate for the donuts in dollars?

san4es73 [151]

Answer:

$3.50

Step-by-step explanation:

I hope this helps!

3 0

2 years ago

Read 2 more answers

a number is multiplied by 3 and then 7 is added.The result is doubled ,giving the answer 80.Using n to represent the original nu

Darina [25.2K]

Answer:

2(n*3 + 7) = 80

Step-by-step explanation:

2(n*3 + 7) = 80

n*3 + 7 = 40

n*3 = 33

n = 11

5 0

3 years ago