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3 years ago

5

In the town zoo 3/28 of the animals are birds of the birds for 4/15 are birds of prey what fraction of the animals at the zoo ar

e birds of prey

2 answers:

KIM [24]3 years ago

7 0

4/15 of 3/28....." of " means multiply

4/15 * 3/28 = 12/420 reduces to 1/35 <== birds of prey

Rudiy273 years ago

5 0

Answer:

$\frac{1}{35}$

Step-by-step explanation:

In this problem we have to multiply the fractions, because it says that $\frac{3}{28}$ of the animals are birds, and from that fraction $\frac{4}{15}$ are birds of prey. In other words, $\frac{4}{15}$ of $\frac{3}{28}$ are birds of the prey. One strategy to solve this quickly is remembering that "of" is translated into math language as multiplication, so:

$\frac{3}{28} \frac{4}{15} = \frac{12}{420} =\frac{1}{35}$

Therefore, $\frac{1}{35}$ of the total birds, are birds of the prey.

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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:

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

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

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

- 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:

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

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

6 0

2 years ago

35 POINTS PLS HELP I HAVE UNTIL 12 TO FINISH

evablogger [386]

Answer: The first one is = 27.5

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4 0

3 years ago

A camp counselor starts from home and drives to a campground. The expression 130−60t represents the distance, in miles, the coun

telo118 [61]

Answer:

<em>The value 60 represents the speed of the vehicle the counselor is driving.</em>

Step-by-step explanation:

<u>Linear Function</u>

The linear relationship between two variables d and t can be written in the form

$d=mt+b$

Where m is the slope (or rate of change of d with respect to t) and b is the y-intercept or the point where the graph of the line crosses the y-axis

The function provided in our problem is

$d=130-60t$

Where d is the distance in miles the counselor still needs to drive after t hours. Rearranging the expression:

$d=-60t+130$

Comparing with the general form of the line we can say m=-60, b=130. The value of -60 is the slope or the rate of change of d with respect to t. Since we are dealing with d as a function of time, that value represents the speed of the vehicle the counselor is driving. It's negative because the distance left to drive decreases as the time increases

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2 years ago

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I am Lyosha [343]

Answer:

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or look at it this way:

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Step-by-step explanation:

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2 years ago

Please help me this looks easy but I don’t understand it tho

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2 years ago