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3 years ago

A pile of 55 coins consisting of nickels and dimes is $3.90. Find the number of each.

Mathematics

1 answer:

Dovator [93]3 years ago

7 0

Answer:

Step-by-step explanation:

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Find a homogeneous linear differential equation with constant coefficients whose general solution is given by

frez [133]

Answer:

$y" + 2y' + 2y = 0$

Step-by-step explanation:

Given

$y=c_1e^{-x}cosx+c_2e^{-x}sinx$

Required

Determine a homogeneous linear differential equation

Rewrite the expression as:

$y=c_1e^{\alpha x}cos(\beta x)+c_2e^{\alpha x}sin(\beta x)$

Where

$\alpha = -1$ and $\beta = 1$

For a homogeneous linear differential equation, the repeated value m is given as:

$m = \alpha \± \beta i$

Substitute values for $\alpha$ and $\beta$

$m = -1 \± 1*i$

$m = -1 \± i$

Add 1 to both sides

$m +1= 1 -1 \± i$

$m +1= \± i$

Square both sides

$(m +1)^2= (\± i)^2$

$m^2 + m + m + 1 = i^2$

$m^2 + 2m + 1 = i^2$

In complex numbers:

$i^2 = -1$

So, the expression becomes:

$m^2 + 2m + 1 = -1$

Add 1 to both sides

$m^2 + 2m + 1 +1= -1+1$

$m^2 + 2m + 2= 0$

This corresponds to the homogeneous linear differential equation

$y" + 2y' + 2y = 0$

6 0

3 years ago

A line goes through the points (4, 5) and (2, -6). Write the equation of the line in slope-intercept form.

myrzilka [38]

3/4 & 1/-3 would be the answer

7 0

3 years ago

What is the simplified form of √144x^36

Nadusha1986 [10]

Answer:

The simplified form of $\sqrt{144x^{36}}$ is $12x^{18}$

Step-by-step explanation:

Given : $\sqrt{144x^{36}}$

We have to write the simplified form of $\sqrt{144x^{36}}$

Consider the given expression $\sqrt{144x^{36}}$

We know $\sqrt{144}=12$

and $\sqrt{x^{36}}=\sqrt{x^{18}\cdot x^{18}}$

Thus,

$\sqrt{144x^{36}}=\sqrt{12^2\cdot (x^{18})^2}$

Simplify, we have,

$=\sqrt{12^2\cdot (x^{18})^2}=12x^{18}$

Thus, The simplified form of $\sqrt{144x^{36}}$ is $12x^{18}$

6 0

3 years ago

Read 2 more answers

Sherry is driving 390 miles to visit The gateway arch in St. Louis. She drives at an average rate of 65 miles per hour. Explain

grandymaker [24]

Answer:

t = 6 s

Step-by-step explanation:

Given that,

Sherry is driving 390 miles to visit The gateway arch in St. Louis.

She drives at an average rate of 65 miles per hour.

We need to find the amount of time it will take Sherry to get to the arch. Let the time is t.

Speed = distance/time

$t=\dfrac{d}{v}\\\\t=\dfrac{390}{65}\\\\t=6\ h$

Hence, it will take 6 hours to get to the arch.

8 0

3 years ago

Okay i need some help fast

Troyanec [42]

Answer:

Dimensions : 1 by 1 by 2 feet,

Volume ⇒ 2 ft^3

Step-by-step explanation:

Here, I can only assume that this rectangular prism is assigned to have dimensions 1 foot by 1 foot by 2 feet;

I can tell that these types of boxes have height and width as the same lengths, so given that;

Dimensions : 1 by 1 by 2 feet,

Volume ⇒ 1 * 1 * 2 ( by definition ) ⇒ 2 ft^3

In other words, Volume ⇒ 2 ft^3

6 0

3 years ago