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Trava [24]
3 years ago
8

Find the points on the curve y = 2x3 + 3x2 − 12x + 6 where the tangent line is horizontal.

Mathematics
1 answer:
Orlov [11]3 years ago
3 0
N.b., this is copied from an answer I wrote for someone else.

Thinking about the graph of y, the rate of change is zero whenever there is an extremum.

First, differentiate y.

y'=6x^2+6x-12

Next, find the zeros of y' by factoring.

6(x^2+x-2)=0 \\ x = -2, x = 1

Now, we substitute these x-values into the original equation to find the coordinates. 

(-2,21), (1,-6)
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17. The answer should be 17
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Family Video charges $10 for
Irina18 [472]

Answer:

4 movies, $20

Step-by-step explanation:

Given data

Family Video

charges $10 for a monthly membership and

$2.50 per movie

let the number of movies be x

and the charge for x movies be y

y= 10+2.5x----------1

Babe's  Movies

charges a $12

membership and $2 per

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let the number of movies be x

and the charge for x movies be y

y= 12+2x----------2

equate 1 and 2

10+2.5x= 12+2x

collect like terms

12-10= 2.5x-2x

2= 0.5x

x= 2/0.5

x= 4 movies

put x= 4 in equation 1 or 2

y= 12+2x----------2

y= 12+2*4

y= 12+8

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4 0
3 years ago
Given klmn is a trapezoid, kl = mn, m<1 = m<2, lm/kn = 8/9, pklmn = 132. Find: the length of the legs
Ilia_Sergeevich [38]

Answer:

The length of legs lm, mn, and lk is 32 while that of kn is 36.

Step-by-step explanation:

The diagram is attached in the answer.

As both the angles are equal thus the two forms isosceles triangles. This is true because the converse of base angle theorem is applicable here. The theorem clearly states that when a trapezoid is divided by the diagonal, it forms two set of angles where m<1=m<2 and m<lmk=m<nmk

This leads the two set of legs such as

\dfrac{lm}{kn}=\dfrac{8}{9}

Or this could be written as

lm=8x\\kn=9x

Now the remaining two sides are given as

lk=lm as this form an isosceles triangle so

lk=8x

Similarly

mn=lm\\

Or

mn=8x

Now the perimeter is given as

\text{perimeter}=lm+mn+kn+lk\\

Here perimeter is given as 132 so this gives:

\text{perimeter}=lm+mn+kn+lk\\132=8x+8x+8x+9x\\132=33x\\x=\dfrac{132}{33}\\x=4

So the four legs are of length as given below:

lm=8x=8\times 4=32\\mn=8x=8\times 4=32\\lk=8x=8\times 4=32\\kn=9x=9\times4=36

So the length of legs lm, mn, and lk is 32 while that of kn is 36.

6 0
2 years ago
Find the area of a parallelogram with base b and height h.
Gre4nikov [31]
To find an area of a parallelogram is by multiplying the b and h to get 1095.2
7 0
3 years ago
What is this fraction in simplest form 12/75 please help me this homework is so hard my teacher said just try your best
garri49 [273]

Answer:

4/25

Step-by-step explanation:

12 divided by 3

72 divided by 3

Greatest Common Divisor:

3

So 12/72 simplifed would be 4/25 and the GCD would be 3.

8 0
2 years ago
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