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3 years ago

11

One angle of a triangle is three times larger as another. the measure of the third angle is 50 degrees more than that of the sma

llest angle. Find the measure of each angle.

1 answer:

vodka [1.7K]3 years ago

5 0

Answer:

Smallest angle of triangle=26 degrees

Second angle of triangle =78 degrees

Third angle of triangle =76 degrees

Step-by-step explanation:

Let x be the smallest angle of triangle

Second angle of triangle=3x

Third angle of triangle=x+50

We know that

Sum of angles of triangle=180 degrees

Using the property

$x+3x+x+50=180$

$5x=180-50$

$5x=130$

$x=\frac{130}{5}$

$x=26$ degree

Smallest angle of triangle=26 degrees

Second angle of triangle =3(26)=78 degrees

Third angle of triangle =26+50=76 degrees

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Find a particular solution to the nonhomogeneous differential equation y'' + 4 y = cos(2x) + sin(2x).

alukav5142 [94]

The characteristic solution follows from solving the characteristic equation,

$r^2+4=0\implies r=\pm2i$

so that

$y_c=C_1\cos2x+C_2\sin2x$

A guess for the particular solution may be $a\cos2x+b\sin2x$ , but this is already contained within the characteristic solution. We require a set of linearly independent solutions, so we can look to

$y_p=ax\cos2x+bx\sin2x$

which has second derivative

${y_p}''=(-4ax+4b)\cos2x+(-4bx-4a)\sin2x$

Substituting into the ODE, you have

$y''+4y=\cos2x+\sin2x$
$\implies4b\cos2x-4a\sin2x=\cos2x+\sin2x$
$\implies\begin{cases}4b=1\\-4a=1\end{cases}\implies a=-\dfrac14,b=\dfrac14$

Therefore the particular solution is

$y_p=-\dfrac14x\cos2x+\dfrac14x\sin2x$

Note that you could have made a more precise guess of

$y_p=(a_1x+a_0)\cos2x+(b_1x+b_0)\sin2x$

but, of course, any solution of the form $a_0\cos2x+b_0\sin2x$ is already accounted for within $y_c$ .

6 0

3 years ago

Given: △ABC, m∠C=90° m∠ABC=30°, AL ∠ bisector CL=6 ft. Find: LB

vlada-n [284]

For a better understanding of the solution given here please go through the diagram in the file attached.

To solve this question we will make use of the "Triangle Angle Bisector Theorem", which states that, "An angle bisector of an angle of a triangle divides the opposite side in two segments that are proportional to the other two sides of the triangle."

Thus, in our question, we will have:

$\frac{LB}{CL}= \frac{AB}{AC}$

The above equation can be rearranged as:

$LB=CL\times \frac{AB}{AC}=\frac{CL}{(\frac{AC}{AB})}$ ...(Equation 1)

If we have a proper look at the denominator which is $\frac{AC}{AB}$ , we note that in $\Delta ABC$ , $\frac{AC}{AB}=Sin(\angle ABC)=Sin(30^\circ)$

Thus, (Equation 1) wil give us:

$LB=\frac{CL}{Sin(30^\circ)} =\frac{6}{0.5}=12$

<u>Therefore, LB= 12 feet</u>

3 0

3 years ago

nikklg [1K]

Answer:

E

Step-by-step explanation:

19) Amount of oil in = amount of oil in final product

.025(x) + .09(40-x) = .055(40) (x = 2.5% amt 40 - x = 9% amt)

x = 21.54 L of 2.5 % then 9% = 18.46 L

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2 years ago

3/4= 5/10= 4/9= 2/6= 2/8= 4/6=

mylen [45]

3/4=0.75
5/10=0.5
4/9≈0.44
2/6≈0.33
2/8=0.25
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7 0

3 years ago

Bobs burgers bam has a special deal of 4 hamburgers for $6. At that rate, how much should it cost to buy 3 hamburgers?

Natasha_Volkova [10]

Answer:

$4.50

Step-by-step explanation:

6/4=1.5

1.5x3=4.5

7 0

4 years ago