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Levart [38]
3 years ago
11

Determine whether the given function is a solution to the given differential equation.

Mathematics
1 answer:
lesantik [10]3 years ago
8 0

Given :

A function , x = 2cos t -3sin t               .....equation 1.

A differential equation , x'' + x = 0      .....equation 2.

To Find :

Whether the given function is a solution to the given differential equation.

Solution :

First derivative of x :

x'=\dfrac{d(2cos t - 3sin t)}{dt}\\\\x'=\dfrac{d(2cost)}{dt}-\dfrac{(3sint)}{dt}\\\\x'=-2sint-3cost

Now , second derivative :

x''=\dfrac{d(-2sint-3cost)}{dt}\\\\x''=-\dfrac{d(2sint)}{dt}-\dfrac{d(3cost)}{dt}\\\\x''=-2cost+3sint

( Note : derivative of sin t is cos t and cos t is -sin t )

Putting value of x'' and x in equation 2 , we get :

=(-2cos t + 3sin t ) + ( 2cos t -3sin t )

= 0

So , x'' and x satisfy equation 2.

Therefore , x function is a solution of given differential equation .

Hence , this is the required solution .

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Austen needs to buy a bathroom mirror that is 2 feet wide and 3 feet long. If the mirror
PtichkaEL [24]
<h2><u>Question :-</u></h2>

Austen needs to buy a bathroom mirror that is 2 feet wide and 3 feet long. If the mirror sells for $5.00 per square foot, what will the total cost of the mirror be?

<h3>____________________</h3>

<h2><u>Solution :-</u></h2>

<h3><u>Given Information :-</u></h3>

  • <u>Length of the mirror Austen needs to buy ➢</u> 3 ft
  • <u>Width of the mirror Austen needs to buy ➢</u> 2 ft
  • <u>Cost of mirror per square foot ➢</u> $5.00

<h3><u>To Find :-</u></h3>

  • Total cost of the mirror Austen needs to buy.

<h3><u>Formula Used :-</u></h3>

  1. Area of Mirror = Length × Width
  2. Total cost of mirror = Area of mirror × Cost of mirror per square foot

<h3><u>Calculation :-</u></h3>

  • <u>Area of mirror :-</u>

<em><u>Substituting the values given in the 1st formula, We get, </u></em>

⇒ Area of mirror = ( 3 × 2 ) ft²

⇒ Area of mirror = 6 ft²

  • <u>Now finding the total cost of mirror,</u>

<em><u>Substituting the values calculated above in the 2nd formula, We get </u></em>

⇒ Total Cost of mirror = $ ( 6 × 5.00 )

⇒ Total Cost of mirror = $30

<h3>___________________</h3>

<h2><u>Final Answer :-</u></h2>

  • Total cost of the mirror Austen needs to buy will be $30

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7 0
3 years ago
a bag contains 60 marbles, some blue and some green. the ratio of blue marbles to green ones is 1:5. how many blue marbles are t
olga55 [171]
Hello!

For every 1 blue marble there are 5 greens

You add the numbers in the ratio

1 + 5 = 6

Divide this number from the amount of marbles

60 / 6 = 10

Multiply the ratio by this

1 * 10 = 10

5 * 10 = 50

There are 10 blue marbles and 50 green ones

The answer is 10

Hope this helps!
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Find the probability of selecting none of the correct six integers in a lottery, where the order in which these integers are sel
Andre45 [30]

Answer:

Step-by-step explanation:

Given

there are six integers to win a lottery

case-1 Integer not exceeding 40

no of ways to choose 6 incorrect numbers

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Case-2 no of ways to choose 6 incorrect numbers out of 48 integers

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Case-3 no of ways to choose 6 incorrect numbers out of 56 integers

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=0.489

Cae-4 no of ways to choose 6 incorrect numbers out of 64 integers

\dfrac{^{58}C_{6}}{^{64}C_{6}}

=0.54

6 0
3 years ago
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