All categories

3 years ago

Work out the value of angle x.

Mathematics

2 answers:

Thepotemich [5.8K]3 years ago

8 0

X=45

We already know that one angles is 90 degrees and that the full degrees inside a triangle is 180

So minus 90 from 180 and you get 90.

Since the other two angles are congruent that means they have the same measure so divide 90 by 2 to get the measure of both angles which is your answer

Anestetic [448]3 years ago

8 0

Answer:

The answer is 45 degree.

You might be interested in

Lynette has a metal doorstop with the dimensions shown.

Cerrena [4.2K]

Volume = 105in³

Mass = 871.5g

To find the volume of the metal we can find the area of a base, and multiply it by the prism's width.

The base is 30cm in area, and the width is 3.5cm, which makes the volume 105in³

The mass of the doorstop can be found by just multiplying the grams per cubic centimeter by the volume, which would be 871.5g

7 0

3 years ago

Apply the method of undetermined coefficients to find a particular solution to the following system.wing system.

jarptica [38.1K]

$y''-y'+y=\sin x$

The corresponding homogeneous ODE has characteristic equation $r^2-r+1=0$ with roots at $r=\dfrac{1\pm\sqrt3}2$ , thus admitting the characteristic solution

$y_c=C_1e^x\cos\dfrac{\sqrt3}2x+C_2e^x\sin\dfrac{\sqrt3}2x$

For the particular solution, assume one of the form

$y_p=a\sin x+b\cos x$

${y_p}'=a\cos x-b\sin x$

${y_p}''=-a\sin x-b\cos x$

Substituting into the ODE gives

$(-a\sin x-b\cos x)-(a\cos x-b\sin x)+(a\sin x+b\cos x)=\sin x$

$-b\cos x+a\sin x=\sin x$

$\implies a=1,b=0$

Then the general solution to this ODE is

$\boxed{y(x)=C_1e^x\cos\dfrac{\sqrt3}2x+C_2e^x\sin\dfrac{\sqrt3}2x+\sin x}$

$y''-3y'+2y=e^x\sin x$

$\implies r^2-3r+2=(r-1)(r-2)=0\implies r=1,r=2$

$\implies y_c=C_1e^x+C_2e^{2x}$

Assume a solution of the form

$y_p=e^x(a\sin x+b\cos x)$

${y_p}'=e^x((a+b)\cos x+(a-b)\sin x)$

${y_p}''=2e^x(a\cos x-b\sin x)$

Substituting into the ODE gives

$2e^x(a\cos x-b\sin x)-3e^x((a+b)\cos x+(a-b)\sin x)+2e^x(a\sin x+b\cos x)=e^x\sin x$

$-e^x((a+b)\cos x+(a-b)\sin x)=e^x\sin x$

$\implies\begin{cases}-a-b=0\\-a+b=1\end{cases}\implies a=-\dfrac12,b=\dfrac12$

so the solution is

$\boxed{y(x)=C_1e^x+C_2e^{2x}-\dfrac{e^x}2(\sin x-\cos x)}$

$y''+y=x\cos(2x)$

$r^2+1=0\implies r=\pm i$

$\implies y_c=C_1\cos x+C_2\sin x$

Assume a solution of the form

$y_p=(ax+b)\cos(2x)+(cx+d)\sin(2x)$

${y_p}''=-4(ax+b-c)\cos(2x)-4(cx+a+d)\sin(2x)$

Substituting into the ODE gives

$(-4(ax+b-c)\cos(2x)-4(cx+a+d)\sin(2x))+((ax+b)\cos(2x)+(cx+d)\sin(2x))=x\cos(2x)$

$-(3ax+3b-4c)\cos(2x)-(3cx+3d+4a)\sin(2x)=x\cos(2x)$

$\implies\begin{cases}-3a=1\\-3b+4c=0\\-3c=0\\-4a-3d=0\end{cases}\implies a=-\dfrac13,b=c=0,d=\dfrac49$

so the solution is

$\boxed{y(x)=C_1\cos x+C_2\sin x-\dfrac13x\cos(2x)+\dfrac49\sin(2x)}$

7 0

2 years ago

Help me out asap!!!!

attashe74 [19]

Answer:

anglePUM = 3° , PM = 5, UM = √75

Step-by-step explanation:

anglePUM = 180 - 60 - 90 = 30° (∠sum of Δ)

cos60 = PM/10

PM = 10cos60 = 5

sin60 = UM/10

UM = 10sin60 = √75

6 0

2 years ago

Explain how to solve linear equations.

muminat

Answer:

that means you need to find the surface area, but not the part that is touching the ground or the bottom.

3 0

3 years ago

Which expression equals a number that is NOT a rational number?

Leviafan [203]

Answer:

The correct answer would be 2π x 2²/5

Step-by-step explanation:

First, calculate the product, and evaluate the power which would be 2³π/5 and the solution is in an alternate form, therefore making it rational. :)

3 0

3 years ago

Read 2 more answers