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2 years ago

What is the measure of angle b°?

Mathematics

2 answers:

Tasya [4]2 years ago

7 0

Answer:

b = 110°

Step-by-step explanation:

The sum of angles in a trapezoid is 360°

Summing the angles we get:

65°+55°+130°=250°

Then subtracting this value from 360° we get:

360°-250°=110°

Final answer of 110°

Sergio [31]2 years ago

3 0

Answer:

b=110°

Step-by-step explanation:

if you add up the other angles and subtract that from 360 you get that angle

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A 24,000 gallon pool is being filled at a rate of 40 gallons per minute. At this rate how many minutes will it take to fill this

hammer [34]

450 minutes for 18,000 gallons of water.

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3 years ago

Find a particular solution to the nonhomogeneous differential equation y??+4y?+5y=?10x+e^(?x).

Firdavs [7]

Answer:

A) Particular solution:

$2x+\frac{1}{2}e^{-x}-\frac{8}{5}$

B) Homogeneous solution:

$y_{h}=e^{-2x}(c_{1}cos(x)+c_{2}sin(x))$

C) The most general solution is

$y=e^{-2x}(c_{1}cos(x)+c_{2}sin(x))+2x+\frac{1}{2}e^{-x}-\frac{8}{5}$

Step-by-step explanation:

Given non homogeneous ODE is

$y''+4y'+5y=10x+e^{-x}---(1)$

To find homogeneous solution:

$D^{2}+4D+5=0\\D^{2}+4D+4-4+5=0\\\\(D+2)^{2}=-1\\D+2=\pm iD=-2 \pm i\\y_{h}=e^{-2x}(c_{1}cos(x)+c_{2}sin(x))---(2)$

To find particular solution:

$y_{p}=Ax+B+Ce^{-x}\\\\y'_{p}=A-Ce^{-x}\\y''_{p}=Ce^{-x}\\$

Substituting $y_{p},y'_{p},y''_{p}$ in (1)

$y''_{p}+4y'_{p}+5y_{p}=10x+e^{-x}\\Ce^{-x}+4(A-Ce^{-x})+5(Ax+B+Ce^{-x})=10x+e^{-x}\\$

Equating the coefficients

$5Ax+2Ce^{-x}+4A+5B=10x+e^{-x}\\5A=10\\A=2\\4A+5B=0\\B=-\frac{4A}{5}B=-\frac{8}{5}2C=1\\C=\frac{1}{2}\\So,\\y_{p}=2x+\frac{1}{2}e^{-x}-\frac{8}{5}---(3)\\$

The general solution is

$y=y_{h}+y_{p}$

from (2) ad (3)

$y=e^{-2x}(c_{1}cos(x)+c_{2}sin(x))+2x+\frac{1}{2}e^{-x}-\frac{8}{5}$

6 0

2 years ago

The square of a number plus three times the number is 70. find the numbers.

Harrizon [31]

Answer:

Step-by-step explanation:

The equation for that is

$x^2+3x=70$

If we subtract over the 70, we have a quadratic that we can factor to solve for the values of x that will make that equation true.

$x^2+3x-70=0$

Now we need the factors of 70 that will either add or subtract to give us the linear term of 3. The factors of 70 that will work are 10 and 7. 10 times 7 is 70, and 10 - 7 = 3:

$x^2+10x-7x-70=0$ and now we will factor by grouping: