Find the general solution of the given second-order differential equation. 25y'' − 15y' − 4y = 0

Clint is in study hall reading the hunger games after 20 minutes he is on page 151 after 45 minutes he's on page 181 how many pa

Mademuasel [1]

After 20 minutes Clint is on page = 151

After 45 minutes Clint is on page = 181

Time slot = $45-20=25$ minutes

Difference in pages in 25 minutes = $181-151=30$ pages.

Lets suppose Clint is reading each page at same pace.

So , In 25 minutes, he can read = 30 pages

In 1 minute he can read = $\frac{30}{25}=1.2$ pages

Initial time is 20 minutes, so he can read the number of pages in 20 minutes = $20\times1.2=24$

So, number of pages Clint read prior to study hall were =

$151-24=127$ pages.

6 0

2 years ago

A thin sheet of ice is in the form of a circle. If the ice is melting in such a way that the area of the sheet is decreasing at

elena-14-01-66 [18.8K]

Answer:

dx/dt = 0,04 m/sec

Step-by-step explanation:

Area of the circle is:

A(c) =π*x² where x is a radius of the circle

Applying differentiation in relation to time we get:

dA(c)/dt = π*2*x* dx/dt

In this equation we know:

dA(c)/dt = 0,5 m²/sec

And are looking for dx/dt then

0,5 = 2*π*x*dx/dt when the area of the sheet is 12 m² (1)

When A(c) = 12 m² x = ??

A(c) = 12 = π*x² ⇒ 12 = 3.14* x² ⇒ 12/3.14 = x²

x² = 3,82 ⇒ x = √3,82 ⇒ x = 1,954 m

Finally plugging ths value in equation (1)

0,5 = 6,28*1,954*dx/dt

dx/dt = 0,5 /12.28

dx/dt = 0,04 m/sec

7 0

1 year ago

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Zayed is helping his classmates get ready for their math test by making them identical packages of pencils and calculators. He h

oee [108]

So 72 pencils and 24 calculators
so greates number of identical calculators

this means
what is the biggest number that we can divide 72 and 24 by and get a whole number
this is called the GCM or greatest common multipule

to find the GCM, you factor 72 and group the like ones
72=2 times 2 times 2 times 3 times 3
24=2 times 2 times 2 times 3
so the common group is 2 times 2 times 2 times 3 or 24
so the greates number of packs is 24

so pencils
72 divided by 24=72/24=3
3 pencils per pack

24 divided by 24=24/24=1
1 calulator per pack

answer is 3 pencils and 1 calculator per pack

6 0

2 years ago

Read 2 more answers

Here is a typical statement made by the media: "Based on a recent study, pennies weigh an average of 2.5 grams with a margin of

Damm [24]

The answer is A I think

8 0

2 years ago

Read 2 more answers

Please help!! I need to get this done! Im begging you, brainliest and points!

Viefleur [7K]

Answer:

Solution; ( 1, 0 ), and ( - 3, 4 )

Step-by-step explanation:

See procedure below;

First let us make these two functions ( y = -x + 1 , y = x^2 + x - 2 ) equivalent;

- x + 1 = x^2 + x - 2,

-x - x + 1 + 2 - x^2 = 0,

- 2x + 3 - x^2 = 0,

x^2 + 2x - 3 = 0,

Now factor the simplified equation;

x^2 + 2x - 3 = 0,

( x^2 - x ) + ( 3x - 3 ) = 0,

x ( x - 1 ) + 3 ( x - 1 ) = 0,

( x - 1 )( x + 3 ) = 0,

And solve for x;

x - 1 = 0, and x + 3 = 0,

x = 1, and x = - 3

Now substitute this value of x into the two functions as to receive the y values for each x - value;

y = - ( 1 ) + 1, y = 0 for x = 1,

y = ( - 3 )^2 - 3 - 2, y = 9 - 3 - 2, y = 4 for x = - 3,

Solution; ( 1, 0 ), and ( - 3, 4 )

8 0

1 year ago