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Vesna [10]
2 years ago
6

Can i please get help now

Mathematics
1 answer:
Inga [223]2 years ago
7 0

Answer:

Terms=7a,3 Variables=a Coi=7 Constants=3

Step-by-step explanation:

Terms are the things you use in the equation.

Terms=7a, 3

Variables are the letters next to numbers

Variables= a

Coificents are numbers next to the variable.

Coi=7

Constants are numbers by themselves

Constants=3

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Find the intervals on which​ f(x) is​ increasing, the intervals on which​ f(x) is​ decreasing, and the local extrema. f (x )equa
Kaylis [27]

Answer:

f(x) is increasing in the intervals (-∞,-4) and (9,∞)

f(x) is decreasing in the ingercal (-4,9)

The local extrema is:

local max at (-4,496)

and local min at (9,-1701)

Step-by-step explanation:

In order to solve this problem we must start by finding the derivative of the provided function, which we can find by using the power rule.

if f(x)=ax^{n} then f'(x)=anx^{n-1}

so we get:

f(x)=2x^{3}-15x^{2}-216x

f'(x)=6x^{2}-30x-216

in order to find the critical points we mus set the derivative equal to zero, since the local max an min will happen when the slope of the tangent line to the given point is zero, so we get:

6x^{2}-30x-216=0

we can solve this by factoring, so let's factor that equation:

6(x+4)(x-9)=0

we can now set each of the factors equal to zero so we get:

x+4=0 and x-9=0

when solving each for x we get that:

x=-4 and x=9

These are our critical points, now we can build the possible intervals we are going to use to determine where the function will be increasing and where it will be decreasing:

(-∞,-4), (-4,9) and (9,∞)

so now we need to test these intervals in the derivative to see if the graph will be increasing or decreasing in the given intervals. So let's pick x=-5 for the first one, x=0 for the second one and x=10 for the third one.

When evaluating them into the first derivative we get that:

f'(-5)=84, this is a positive answer so it means that the function is increasing in the interval (-∞,--4)

f'(0)=-216, this is a negative anser so it means that the function is decreasing in the interval (-4,9)

f'(10)=84, this is a positive answer so it means that the function is increasing in the interval (9,∞)

Now, for the local extrema, we can see that at x=-4, the function it's increasing on the left of this point while it's decreasing to the right, which means that there will be a local maximum at x=-4, so the local max is the point (-4,496)

We can see that at x=9, the function it's decreasing on the left of this point while it's increasing to the right, which means that there will be a local minimum at x=-9, so the local min is the point (9,-1701)

7 0
3 years ago
Complete the equation. Round to the nearest hundredth where necessary.
Alexandra [31]

Answer:

D

Step-by-step explanation:

There are 1.61 km in 1 mi.

10 mi × (1.61 km/mi) = 16.1 km

7 0
3 years ago
Which of the following is an equation for the plane through the point (1, 1, −1) and parallel
Bas_tet [7]

The given plane, x-y+z=3, has normal vector \vec n = \langle1,-1,1\rangle. Any plane parallel to this one has the same normal vector.

Let (x,y,z) be any point in the plane we want. The plane contains the point (1, 1, -1), so an arbitrary vector in this plane is

\langle x,y,z\rangle - \langle 1,1,-1\rangle = \langle x-1, y-1, z+1 \rangle

and this is perpendicular to \vec n.

So the equation of the plane is

\langle x-1, y-1, z+1 \rangle \cdot \vec n = 0 \implies (x-1) - (y-1) + (z+1) = 0 \implies \boxed{x - y + z = -1}

or equivalently,

\boxed{-x + y - z = 1}

6 0
2 years ago
You invest $2000 in an account that pays 2.7% interest compunded annually. If you make no payments into the account, what will t
vaieri [72.5K]

Answer:

Annually: 2,610.56

Monthly: 2,619.13

Step-by-step explanation:

3 0
3 years ago
6k^3+10k^2−56k and 5(7k−3)(3k−7)share a common binomial factor. What binomial factor do they share?
goldenfox [79]

Answer:

Step-by-step explanation:

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common factor is 3k-7

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