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3 years ago

Need help figuring this out!

Mathematics

1 answer:

Ulleksa [173]3 years ago

6 0

For this case, we have that by definition, the area of a triangle is given by:

$A = \frac {b * h} {2}$

where:

b: It's the base

h: It's the height

In this case we have:

$b = 21 \ ft\\h = 6 \ ft$

Substituting:

$A = \frac {21 * 6} {2}\\A = 63 \ ft ^ 2$

Answer:

$63 \ ft ^ 2$

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Consider the following differential equation. x^2y' + xy = 3 (a) Show that every member of the family of functions y = (3ln(x) +

Veronika [31]

Answer:

Verified

$y(x) = \frac{3Ln(x) + 3}{x}$

$y(x) = \frac{3Ln(x) + 3 - 3Ln(3)}{x}$

Step-by-step explanation:

Question:-

- We are given the following non-homogeneous ODE as follows:

$x^2y' +xy = 3$

- A general solution to the above ODE is also given as:

$y = \frac{3Ln(x) + C }{x}$

- We are to prove that every member of the family of curves defined by the above given function ( y ) is indeed a solution to the given ODE.

Solution:-

- To determine the validity of the solution we will first compute the first derivative of the given function ( y ) as follows. Apply the quotient rule.

$y' = \frac{\frac{d}{dx}( 3Ln(x) + C ) . x - ( 3Ln(x) + C ) . \frac{d}{dx} (x) }{x^2} \\\\y' = \frac{\frac{3}{x}.x - ( 3Ln(x) + C ).(1)}{x^2} \\\\y' = - \frac{3Ln(x) + C - 3}{x^2}$

- Now we will plug in the evaluated first derivative ( y' ) and function ( y ) into the given ODE and prove that right hand side is equal to the left hand side of the equality as follows:

$-\frac{3Ln(x) + C - 3}{x^2}.x^2 + \frac{3Ln(x) + C}{x}.x = 3\\\\-3Ln(x) - C + 3 + 3Ln(x) + C= 3\\\\3 = 3$

- The equality holds true for all values of " C "; hence, the function ( y ) is the general solution to the given ODE.

- To determine the complete solution subjected to the initial conditions y (1) = 3. We would need the evaluate the value of constant ( C ) such that the solution ( y ) is satisfied as follows:

$y( 1 ) = \frac{3Ln(1) + C }{1} = 3\\\\0 + C = 3, C = 3$

- Therefore, the complete solution to the given ODE can be expressed as:

$y ( x ) = \frac{3Ln(x) + 3 }{x}$

- To determine the complete solution subjected to the initial conditions y (3) = 1. We would need the evaluate the value of constant ( C ) such that the solution ( y ) is satisfied as follows:

$y(3) = \frac{3Ln(3) + C}{3} = 1\\\\y(3) = 3Ln(3) + C = 3\\\\C = 3 - 3Ln(3)$

- Therefore, the complete solution to the given ODE can be expressed as:

$y(x) = \frac{3Ln(x) + 3 - 3Ln(3)}{y}$

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6 0

3 years ago

Help me with this,i really forgot how to do these type of questions

Montano1993 [528]

Work=speed times time (my equation to help me figure it out)

ok, 10 men take 84 days to complete a job
therefor, each man completes 1/10 of the job in 84 days
each man does 1/840 of the job per 1 day

so, if we had 5 more, or 15 men

15 times 1/840 times xdays=1 job complete
15/840 times xdays=1job
times both sides by 840/15
xdays=840/15
xdays=56
56 days it would take

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3 years ago

Question 26 teresa runs 3 miles in 28 minutes. at the same rate, how many miles would she run in 42 minutes?

Leya [2.2K]

The answer is 4.5 miles. Hope it helps!

8 0

3 years ago

13. The table represents some points of a linear function.

RUDIKE [14]

Answer:

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Step-by-step explanation:

To find the slope of the function, you need two points in order, the first point having its x and y coordinates labeled as x1 and y1, and the second point having its coordinates labeled as x2 and y2. then, use the equation for slope, which is m=(y2-y1)/(x2-x1), and plug in the numbers. You should get m=(-10+2)/(-2+4)= -8/2= -4.

Then, use the slope and a point on the graph, and plug it into point slope form, which is y-y1=m(x-x1). No matter what point you use, you should get the same thing. I used the point (-2, -4). Using this point, the steps to arrange the equation in slope intercept form is: y+2=-4(x+4)=> y+2=-4x-16 => y=-4x-18.

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3 years ago

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kolezko [41]

Step-by-step explanation:

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3 years ago

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