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2 years ago

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Name the property that justifies each statement. The measure of an angle is 52 more than its complement. What is the measure of

the complements.
Ik what the measurement is but what is the property used thx

1 answer:

emmainna [20.7K]2 years ago

8 0

It is complementary angles. That's what you can write for the property. That means the complements are 19 and 71.

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Set up but do not solve for the appropriate particular solution yp for the differential equation y′′+4y=5xcos(2x) using the Meth

taurus [48]

Answer:

So, solution of the differential equation is

$y(t)=-\frac{5x^2}{4}\cot 2x\cdot \cos 2x+c_1e^{-2it}+c_2e^{2it}\\$

Step-by-step explanation:

We have the given differential equation: y′′+4y=5xcos(2x)

We use the Method of Undetermined Coefficients.

We first solve the homogeneous differential equation y′′+4y=0.

$y''+4y=0\\\\r^2+4=0\\\\r=\pm2i\\\\$

It is a homogeneous solution:

$y_h(t)=c_1e^{-2i t}+c_2e^{2i t}$

Now, we finding a particular solution.

$y_p(t)=A5x\cos 2x\\\\y'_p(t)=A5\cos 2x-A10x\sin 2x\\\\y''_p(t)=-A20\sin 2x-A20x\cos 2x\\\\\\\implies y''+4y=5x\cos 2x\\\\-A20\sin 2x-A20x\cos 2x+4\cdot A5x\cos 2x=5x\cos 2x\\\\-A20\sin 2x=5x\cos 2x\\\\A=-\frac{x}{4} \cot 2x\\$

we get

$y_p(t)=A5\cos 2x\\\\y_p(t)=-\frac{5x^2}{4}\cot 2x\cdot \cos 2x\\\\\\y(t)=y_p(t)+y_h(t)\\\\y(t)=-\frac{5x^2}{4}\cot 2x\cdot \cos 2x+c_1e^{-2it}+c_2e^{2it}\\$

So, solution of the differential equation is

$y(t)=-\frac{5x^2}{4}\cot 2x\cdot \cos 2x+c_1e^{-2it}+c_2e^{2it}\\$

7 0

3 years ago

X2 − 2x − 2 into the form a(x − h)2 + k.

Sedbober [7]

Answer:

x² - 2x - 2

By Completing the Square....

x² - 2x + 1² - 2 - 1²

(x - 1)² - 3 .....

Hope it helps.

3 0

2 years ago

Suppose that, for a set of data, the range is x and the interquartile range is y. Which statement MUST be true? A) x = y B) x ≤

Vitek1552 [10]

c i suppose the answer

3 0

3 years ago

Read 2 more answers

Which statement about the following equation is true?

spayn [35]

The given expression is

$3x^2 -8x +5 = 5x^2$

We have to find the discriminant first . And for that, first we need to move whole terms of the left side to right side, that is

$5x^2 -3x^2 +8x -5=0$

$2x^2+ 8x -5 =0$

The formula of discriminant is

$D =b^2 -4ac$

Substituting the values of a,b and c, we will get

$D = 8^2 -4(2)(-5)=64+40 = 104$

And since the discriminant is greater than 0, or it is positive so we have two real roots.

Therefore the correct option is B .

7 0

3 years ago

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A triangle has side lengths of 15 10 and 7 is it a right triangle

lions [1.4K]

Answer:

No, it is not a right triangle.

Step-by-step explanation:

Given:

The sides of the triangle = 15 10 and 7

To Find:

Whether the triangle is a right triangle = ?

Solution:

According to Pythagorean theorem , In an right triangle the the sum of the squares of the two smaller sides must equal to the square of the larger side

$a^2 +b^2 =c^2\\$

where

a and b are the smaller sides

c is the larger side

Now from the given data, lets assume

a = 10 and b =7 and c =15

Substituting in the above equation we get,

$(10)^2 +(7)^2 = (15)^2$

100 + 49 = 225

149 = 225

$149 \neq 225$

So, the given triangle is not a right triangle.

7 0

3 years ago