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love history [14]

3 years ago

10

An angle measures 90º more than the measure of its supplementary angle. What is the measure of each angle?

2 answers:

masha68 [24]3 years ago

8 0

Answer:

theyre both 90 degrees because supplementary angles always add up to 180

lord [1]3 years ago

6 0

Is the a shape. I assume the 90 degree angle is a right angle and the others are also 90

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How do I solve both questions?

diamong [38]

1. divide 8.75 by 3.5 and divide 9.75 by 3.75
2. do 2.5 ×2 plus 1.25

5 0

3 years ago

Solve y ' ' + 4 y = 0 , y ( 0 ) = 2 , y ' ( 0 ) = 2 The resulting oscillation will have Amplitude: Period: If your solution is A

Vlad [161]

Answer:

$y(x)=sin(2x)+2cos(2x)$

Step-by-step explanation:

$y''+4y=0$

This is a homogeneous linear equation. So, assume a solution will be proportional to:

$e^{\lambda x} \\\\for\hspace{3}some\hspace{3}constant\hspace{3}\lambda$

Now, substitute $y(x)=e^{\lambda x}$ into the differential equation:

$\frac{d^2}{dx^2} (e^{\lambda x} ) +4e^{\lambda x} =0$

Using the characteristic equation:

$\lambda ^2 e^{\lambda x} + 4e^{\lambda x} =0$

Factor out $e^{\lambda x}$

$e^{\lambda x}(\lambda ^2 +4) =0$

Where:

$e^{\lambda x} \neq 0\\\\for\hspace{3}any\hspace{3}\lambda$

Therefore the zeros must come from the polynomial:

$\lambda^2+4 =0$

Solving for $\lambda$ :

$\lambda =\pm2i$

These roots give the next solutions:

$y_1(x)=c_1 e^{2ix} \\\\and\\\\y_2(x)=c_2 e^{-2ix}$

Where $c_1$ and $c_2$ are arbitrary constants. Now, the general solution is the sum of the previous solutions:

$y(x)=c_1 e^{2ix} +c_2 e^{-2ix}$

Using Euler's identity:

$e^{\alpha +i\beta} =e^{\alpha} cos(\beta)+ie^{\alpha} sin(\beta)$

$y(x)=c_1 (cos(2x)+isin(2x))+c_2(cos(2x)-isin(2x))\\\\Regroup\\\\y(x)=(c_1+c_2)cos(2x) +i(c_1-c_2)sin(2x)\\$

Redefine:

$i(c_1-c_2)=c_1\\\\c_1+c_2=c_2$

Since these are arbitrary constants

$y(x)=c_1sin(2x)+c_2cos(2x)$

Now, let's find its derivative in order to find $c_1$ and $c_2$

$y'(x)=2c_1 cos(2x)-2c_2sin(2x)$

Evaluating $y(0)=2$ :

$y(0)=2=c_1sin(0)+c_2cos(0)\\\\2=c_2$

Evaluating $y'(0)=2$ :

$y'(0)=2=2c_1cos(0)-2c_2sin(0)\\\\2=2c_1\\\\c_1=1$

Finally, the solution is given by:

$y(x)=sin(2x)+2cos(2x)$

5 0

3 years ago

Hello please help will give brainliest! Thank you

Andreas93 [3]

Answer:

C

Step-by-step explanation:

thats my opinion

I hope it helps

7 0

3 years ago

What is -5.8+ (2.5) Evaluate expression

sweet [91]

-5.8 + (-2.5)

is just 5.8 - 2.5

Which is -8.3

8 0

3 years ago

Henry can make 8 cupcakes (the y value) with one cup of flour (the x value). How many cup cakes can he make with 7 cups of flour

Yuki888 [10]

Answer:

56

Step-by-step explanation:

8 cupcakes per 1 cup of flower

56 cupcakes per 7 cups of flower

times both by 7

5 0

3 years ago