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4 years ago

Suppose the measure of an angle is 67 degrees what is the measure of its complementary angle

1 answer:

3 0

Complementary angles are angles whose sum is 90 degrees.

90 - 67 = 23

23 degrees is the measure of its complementary angle.

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Consider the system of differential equations dxdt=−4ydydt=−4x. Convert this system to a second order differential equation in y

koban [17]

$\dfrac{\mathrm dy}{\mathrm dt}=-4x\implies x=-\dfrac14\dfrac{\mathrm dy}{\mathrm dt}\implies\dfrac{\mathrm dx}{\mathrm dt}=-\dfrac14\dfrac{\mathrm d^2y}{\mathrm dt^2}$

Substituting this into the other ODE gives

$-\dfrac14\dfrac{\mathrm d^2y}{\mathrm dt^2}=-4y\implies y''-16y=0$

Since $x(t)=-\dfrac14y'(t)$ , it follows that $x(0)=-\dfrac14y'(0)=4\implies y'(0)=-16$ . The ODE in $y$ has characteristic equation

$r^2-16=0$

with roots $r=\pm4$ , admitting the characteristic solution

$y_c=C_1e^{4t}+C_2e^{-4t}$

From the initial conditions we get

$y(0)=5\implies 5=C_1+C_2$

$y'(0)=16\implies-16=4C_1-4C_2$

$\implies C_1=\dfrac12,C_2=\dfrac92$

So we have

$\boxed{y(t)=\dfrac12e^{4t}+\dfrac92e^{-4t}}$

Take the derivative and multiply it by -1/4 to get the solution for $x(t)$ :

$-\dfrac14y'(t)=\boxed{x(t)=-\dfrac12e^{4t}+\dfrac92e^{-4t}}$

7 0

3 years ago

What 2+2 pleas help emergeacny

saveliy_v [14]

Answer:4

Step-by-step explanation:

i think?

maybe 5

5 0

3 years ago

Read 2 more answers

In the middle of a thing :

gavmur [86]

Answer:

Not gonna lie I don't know and this is old but plz give me brainliest.

Step-by-step explanation:

6 0

3 years ago

What is the product in distributive property for 7x63

Sauron [17]

Distributive property is
a(b+c)=ab+ac

we can make it easier by splitting up 63 into 60+3

so
7(63)=7(60+3)=7*60+7*3=420+21=441

7 0

3 years ago

Read 2 more answers

Angle JKL is an equilateral triangle jk=13x+5 KL=17x-19 and JL=8x+35

Goshia [24]

The value of x is 6, then the value of JK is 83, KL is 83 and JL is 83.

<h3>What is a triangle?</h3>

A triangle is a polygon that has three sides and three vertices. It is one of the basic figures in geometry.

An equilateral triangle is a shape with three sides that have an equal measure of side length.

The 3 sides of triangle JKL are equal to each other, therefore we can equate any of the two sides together to find the unknown variable called x.

So, JK = KL

JK = 13x + 5

KL + 17x - 19

13x + 5 = 17x - 19

Collect like terms;

17x - 13x = 19 + 5

4x = 24

x = 24/4

x = 6

We can now proceed to find the sides;

JK = 13x + 5

13 x 6 + 5

= 78 + 5

= 83

JK = 83

KL = 17x - 19

= 17 x 6 - 19

= 102 - 19

= 83

KL = 83

JL= 8x + 35

= 8 x 6 + 35

= 48 + 35

= 83

JL = 83

Hence, The value of x is 6, then the value of JK is 83, KL is 83 and JL is 83.

Learn more about the triangles;

brainly.com/question/2773823

#SPJ1

7 0

1 year ago