Solve each equation by factoring ⁉️NEED THIS ASAP⁉️ #10

Lily visits 100 patients in a month and records the age of each patient. The pie chart below shows the number of patients she ha

iogann1982 [59]

Answer:

15

Step-by-step explanation:

5 0

3 years ago

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ratelena [41]

For the first interval (-1, 2), f(-1) = f(2), which means that the average rate of change on that interval is zero, so the correct option is A.

<h3>Over which interval the rate of change is zero?</h3>

For a function f(x) we define the average rate of change over the interval (a, b) is defined as:

R = (f(b) - f(a))/(b - a)

Here the function is:

f(x) = x^2 - x -1

And the rate of change will be zero on an interval (a, b) if and only if:

f(b) = f(a).

Notice that the first interval is (-1, 2)

f(-1) = (-1)^2 - (-1) - 1 = 1 + 1 - 1 = 1

f(2) = 2^2 - 2 - 1 = 4 - 2 - 1 =1

Then f(-1) = f(2), which means that the average rate of change on that interval is zero, so the correct option is A.

If you want to learn more about average rate of change:

brainly.com/question/23483858

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4 0

2 years ago

a small Computing Center has found that the number of jobs submitted per day to its computers has a mean of 65 jobs and a standa

jek_recluse [69]

Check the attached file for the solution.

6 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

Can someone explain major and minor arcs in relation to circles.

Lelechka [254]

A Major Arc within a circle is something that that is more than half of the circle, and therefore, larger than the minor arc. The way in which this could be used in an example is; Tony has a pizza with 8 slices, 6 of these slices are pepperoni and 2 are chilli beef. In this case, the pepperoni slices are the major arc and the chilli beef slices are the minor arc.
The Major Arc will always be bigger than the minor arc- whether this is 181 degrees to 179, or whether this is 350 degrees to 10 degrees.
The Minor Arc is always the smallest arc, and this can be explained by; Benedict has an apple pie that has 10 slices, between him and his friends, they have eaten four slices. In this case, they have eaten the 'minor arc'
There is a picture attached, and this is the examples of a major and a minor arc.
Hope this has been able to help you :)

3 0

4 years ago