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ozzi
3 years ago
10

Which equation represents the graph below? A. y=3x-2 B.y=-2x+3 C.y=3x-2 D.2x+3

Mathematics
1 answer:
KatRina [158]3 years ago
5 0

Answer:

d

Step-by-step explanation:

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Need to find the constant
evablogger [386]

time, t = 50

rate, r = 40

number of words, w

t = w/r

=》 50 = w/ 40

=》 w = 50 × 40 = 2000words

4 0
3 years ago
All of these ODEs model a system with a spring, mass and dashpot.
Wewaii [24]

Answer:

− 3 y ' ' − 3 y ' + 3 y = 0 : over-damped

− 2 y ' ' − 4 y ' + 1 y = 0 : over-damped

1 y ' ' + 7 y ' + 5 y = 0: over-damped

Step-by-step explanation:

Using the characteristic equation you can express a differential equation of order n as an algebraic equation of degree n:

a_ny^n+a_n_-_1y^{n-1}+...+a_1y'+a_oy=0

This differential equation will have a characteristic equation of the form:

a_nr^n+a_n_-_1r^{n-1}+...+a_1r+a_o=0

Now, you can classify the solution for a differential equation using a simple method. In order to do it, you just need to use the discriminant.

  • If the discriminant is greater than zero, the solution is over-damped

  • If the discriminant is less than zero, the solution is under-damped

  • If the discriminant is equal to zero, the solution is critically damped

So, given the differential equation:

-3y''-3y+3y=0

Which has characteristic equation of the form:

-3r^2-3r+3=0

The quadratic polynomial of the form:

ar^2+br+c=0

Has discriminant:

Disc=b^2-4ac

In this case:

a=-3\\b=-3\\c=3

So:

Disc=(-3)^2-4(-3)(3)=9-(-36)=45

In this case:

Disc=45>0

Therefore the solution is over-damped.

Now, given the differential equation:

-2y''-4y'+1y=0

Which has characteristic equation of the form:

-2r^2-4r+1=0

The quadratic polynomial of the form:

ar^2+br+c=0

Has discriminant:

Disc=b^2-4ac

In this case:

a=-2\\b=-4\\c=1

So:

Disc=(-4)^2-4(-2)(1)=16+8=24

In this case:

Disc=24>0

Therefore the solution is over-damped.

Finally, given the differential equation:

1y''+7y'+5y=0

Which has characteristic equation of the form:

1r^2+7r+5=0

The quadratic polynomial of the form:

ar^2+br+c=0

Has discriminant:

Disc=b^2-4ac

In this case:

a=1\\b=7\\c=5

So:

Disc=(7)^2-4(1)(5)=49-20=29

In this case:

Disc=29>0

Therefore the solution is over-damped.

6 0
3 years ago
Students in a world geography class want to determine the distances between cities in Europe. The map gives all
galina1969 [7]

Using a proportional relationship, we have that:

  • a) The constant of proportionality is of 0.625, hence the equation is: y = 0.625x.
  • b) The distance of two cities that are 5 miles apart is of 8 kilometers.
  • c) When they are 200 kilometers apart, we have that the distance in miles is of y = 0.625(200) = 125.

<h3>What is a proportional relationship?</h3>
  • A <em>proportional relationship</em> is a function in which the <u>output variable is given by the input variable multiplied by a constant of proportionality</u>, that is:.

y = kx

  • In which k is the constant of proportionality.

Item a:

From the graph, when x = 8, y = 5, hence:

y = kx

5 = 8k

k = \frac{5}{8}

k = 0.625

The constant of proportionality is of 0.625, hence the equation is: y = 0.625x.

Item b:

From the graph, when y = 5, x = 8, hence:

  • The distance of two cities that are 5 miles apart is of 8 kilometers.

Item c:

When they are 200 kilometers apart, we have that the distance in miles is of y = 0.625(200) = 125.

You can learn more about proportional relationship at brainly.com/question/13550871

4 0
2 years ago
2. Which of the following is a composite number? A. 139 B. 91 C. 13 D. 29
love history [14]
7 x 13 = 91.......so 91 is not a prime, it is a composite
8 0
3 years ago
Read 2 more answers
Factor the expression using the GCF. The expression 21m−49n factored using the GCF is...
Roman55 [17]

Answer:  7(3m - 7n)

<u>Step-by-step explanation:</u>

Factor each term then see what value(s) they have in common:

          21m         -          49n

            ∧                        ∧

          3 · 7 · m              7 · 7 · n

Both terms have a 7 in common.  What is left over after removing the 7?

21m: 7(3m)

49n: 7(7n)

GCF: 7           Leftovers: 3m <em>and</em>  7n

Factored form of expression is: 7(3m - 7n)

6 0
3 years ago
Read 2 more answers
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