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3 years ago

Determine the intervals on which the function is increasing, decreasing, and constant

Mathematics

2 answers:

aleksley [76]3 years ago

4 0

Answer:

Continuously increasing

Step-by-step explanation:

Given is a graph of the function which shows a curve passing through 0, passing only in I and III quadrants.

It starts from bottom for low values of x, and slowly raise upto 0 and then again start raising.

This implies that gradient or slope of the function is positive and never negative or zero.

THis in turn implies that the curve is strictly increasing throughout its domain.

max2010maxim [7]3 years ago

3 0

I believe it's increasing on all fronts, because if you start from the right, you see that the y values always increase, hence they are increasing. They do it for when x<0 and when x>0. So, it should be increasing on all real numbers

You might be interested in

Find a homogeneous linear differential equation with constant coefficients whose general solution is given. y = c1 cos(x) + c2 s

Anton [14]

Answer:

The homogeneous differential equation is

d^4y/dx^4 + 37d²y/dx² + 36 = 0

y^(iv) + 37y'' + 36 = 0

Step-by-step explanation:

We want to find a homogeneous linear differential equation with constant coefficients whose general solution is given as

y = c1 cos(x) + c2 sin(x) + c3 cos(6x) + c4 sin(6x)

This, we are working in reverse. Instead of having a differential equation, and writing and solving it's characteristic equation, before writing it's general solution, we are already given the general solution, so, we work in reverse.

Given

y = c1 cos(x) + c2 sin(x) + c3 cos(6x) + c4 sin(6x)

By observation, we have

(1) Homogeneous differential equation of the fourth order, because of the number of constants

(2) Two pairs of complex roots, that's why we have cosines, and sines.

Knowing that if

m = a ± ib

The general solution is

y = (e^ax)(c1 cos bx + c2 sin bx)

We can now write for

y = [c1 cos(x) + c2 sin(x)] + [c3 cos(6x) + c4 sin(6x)]

m = 0 ± i

and

m = 0 ± 6i

So that we have

m = √(-1)

m = √(-36)

m² = -1

m² = -36

m² + 1 = 0

m² + 36 = 0

The auxiliary equation is therefore

(m² + 1)(m² + 36) = 0

m^4 + 36m² + m² + 36 = 0

m^4 + 37m² + 36 = 0

Finally, the homogeneous differential equation is

d^4y/dx^4 + 37d²y/dx² + 36 = 0

y^(iv) + 37y'' + 36 = 0

5 0

3 years ago

A machine used to regulate the amount of a certain chemical dispensed in the production of a particular type of cough syrup can

olchik [2.2K]

Answer:

The mean value of the chemical to be added to every bottle of syrup so that the bottle wont be rejected would be = 1.41750 ml

Step-by-step explanation:

Standard deviation ( σ )= 0.250 ml

assume the required amount of chemical to be deposited in each syrup bottle to be X

Hence the distribution of X in each bottle can be represented as :

X Г N ( u , 0.250 )

for a bottle not to be rejected : P ( X ≤ 2 )

To determine the setting so that no more than 1% of the bottles of cough syrup prepared by this machine will be rejected we have to standardize the variable X

at X = 2 ml

$\frac{x - u }{std} = \frac{2 - u}{std}$

z = $\frac{2-u}{0.250}$ = z ----------- ( 1 )

probability for a bottle to be rejected : P( x >2 ) = 1 - P ( x ≤ 2 )

= 0.01

attached below is a normal distribution curve showing probability values

from the curve

p( 0 < Z < z ) = 0.5 - 0.01 = 0.49

Area = 0.49 hence from the Normal table where area = 0.49 the value of z = 2.33

Referring back to equation 1 above: z = $\frac{2-u}{0.250}$ = 2.33 --------- (2)

u = mean value that should be added so that the bottle will not be rejected

make u subject of the equation : u = 2 - ( 2.33 * 0.250 )

u = 1.41750

The mean value of the chemical to be added to every bottle of syrup so that the bottle wont be rejected would be = 1.41750 ml

6 0

4 years ago

Chloe drew a triangle with side lengths of 30 centimeters, 24 centimeters, and 18 centimeters. Juan drew a triangle with side le

vlada-n [284]

Answer:

A and B

Step-by-step explanation:

Each side in Chloe's triangle is 1.5 times the length of each side in Juan's triangle. Thus, they are 'similar' by the math definition of that word, by the SSS Rule for Similar Triangles.

That means they are different only in size. So, their angle measures are the same and they are the same shape.

A and B are true.

C is never true, because the sum of all 3 angles in a triangle is always 180°.

D is not true, because they are similar.

5 0

3 years ago

Find the solutions of the system: y = 2(5)-x and x + y = 2

bixtya [17]

The two equations in y-intercept form are:
y=-x+2 and y=-x+10

You have to graph them to find the solution, which is the point they intercept each other.

Both lines have the same slope so they will never intercept which means they have no solution.

So, the answer is no solution.

I hope that helps!

7 0

3 years ago

Jett has a large empty container, as shown below.

Marrrta [24]

Answer:

120 cubic inches

Step-by-step explanation:

12*4*5=240

240/2=120

6 0

3 years ago

Read 2 more answers