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2 years ago

What angle (in radians) corresponds to 0.75 rotations around the unit circle?

Mathematics

1 answer:

polet [3.4K]2 years ago

6 0

3pi/2. The unit circle is 2pi

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Find the function of which is the solution of 36y"-48y'-48y=0 with initial conditions y1(0)=1. y1'(0)=0

lilavasa [31]

Answer:

$y=\frac{1}{4} e^{2x}+\frac{3}{4} e^{-\frac{2}{3}x }$

Step-by-step explanation:

Let, $D=\frac{d}{dx}$

Now, us simplify the given differential equation and write it in terms of D,

$36y''-48y'-48y=0$

or, $3y''-4y'-4y=0$

or, $(3D^2-4D-4)y=0$

We have our auxiliary equation:

$3D^2-4D-4=0$

or, $(3D+2)(D-2)=0$

or, $D=2, - \frac{2}{3}$

Therefore our solution is,

$y=Ae^{2x}+Be^{- \frac{2}{3}x}$

and, $y'=2Ae^{2x}-\frac{2}{3}Be^{\frac{2}{3}x }$

Applying the boundary conditions, we get,

$A+B=1$

$2A-\frac{2}{3}B=0$

Solving them gives us,

$A=\frac{1}{4} ,B=\frac{3}{4}$

Hence,

$y=\frac{1}{4} e^{2x}+\frac{3}{4} e^{-\frac{2}{3}x }$

4 0

3 years ago

A recipe calls for 3/4 cup of butter. Angie wants to triple the recipe, but she has only 1 5/8.

Lyrx [107]

Let's start out by tripling the original recipe to see how much butter Angie needs.

$\frac{3}{4} * 3 = total$
$\frac{3* 3}{4} = total$
$\frac{9}{4} = total$
$2 \frac{1}{4} = total$

So we need $2 \frac{1}{4}$ cups of butter, but Angie only has $1 \frac{5}{8}$ . Let's subtract what Angie has from the total to see how much more she needs.

$2 \frac{1}{4} - 1\frac{5}{8} = n$
$\frac{9}{4} - \frac{13}{8} = n$
we will need the least common denominator for both fractions
$\frac{2}{2} *(\frac{9}{4}) - \frac{13}{8} = n$
$\frac{18}{8} - \frac{13}{8} = n$
$\frac{5}{8} = n$

So Angie need $\frac{5}{8}$ cups more of butter for the recipe.

7 0

2 years ago

A measure that describes the typical value of a data set

jonny [76]

<u>e</u>

<u>measure of center</u>

as A measure that describes the typical value of a data set mean,median and mode.

6 0

2 years ago

-8xc = 1 solve for x

Nastasia [14]

Answer:

[-8c]⁻¹ = x

Step-by-step explanation:

-8xc = 1

____ ___

-8c -8c

$x = - \frac{1}{8c} \\ \\ or \\ \\ x = ({ -8c})^{-1}$

This, according to the Negative Exponential Rule [Reverse], is how you write this as a rational exponent. You bring the denominator to the numerator while ALTERING THE INTEGER SYMBOL FROM POSITIVE TO NEGATIVE:

b⁻ⁿ = 1\bⁿ

I am joyous to assist you anytime.

3 0

3 years ago

2 3/5 convert to decinal

Leokris [45]

So we know that 1/5=0.2

Then we take 5/5=1.0

Then we solve 2*1.0=2.0

Now we solve 1/5+1/5+1/5 or 1/5*3=0.6

So then the correct answer is 2.6

Hope this helps!!!

7 0

3 years ago