All categories

3 years ago

Find the relative minimum of y = 2x 3 + 14x 2 - 10x - 46

Mathematics

2 answers:

nikitadnepr [17]3 years ago

7 0

Answer:

The minimum value is 47.704 when x = 1/3 correct to the nearest thousandth.

Step-by-step explanation:

y = 2x^3 + 14x^2 - 10x - 46

To find the turning point(s) on the curve we first differentiate:

dy/dx = 6x^2 + 28x - 10 This = zero for turning points:

6x^2 + 28x - 10 = 0

2(3x^2 + 14x - 5) = 0

(3x - 1 )(x + 5) = 0

x= 1/3, - 5.

We now determine the nature of the turning points:

The second derivative is 12x + 28

When x = 1/3 it's value is positive.

When x = -5 its value is -60 + 28 which is negative.

So x = 1/3 gives a relative minimum.

When x = 1/3, y = -47.704.

miss Akunina [59]3 years ago

3 0

The answer is x= 23/12 OR x=1 11/12 OR x=1.916

You might be interested in

A rectangular prism has a length of 3 1/2 in., a width of 3 1/2 in., and a height of 7 in. Danny has a storage container for the

marta [7]

The difference is 4.25in^3

6 0

3 years ago

The median of a data set 8, 21, 17, and 13 is 15. If 17 is changed to 18, what will be the new median? a. 15.5 c. 50 b. 17.5 d.

lubasha [3.4K]

Answer:

Option A) 15.5 is correct

The new median for the new data set is 15.5

Step-by-step explanation:

Given data set is 8,21,17,13

To find the median :

First order the given set of data into least to greatest

The ordered set is 8,13,17,21

Since the given set of data is even

We can take midvalues of data in the set

Median is the mean of two middle values in the data set

$Median=\frac{13+17}{2}$

$=\frac{30}{2}$

$=15$

Therefore Median=15 ( given )

Given that if 17 is changed to 18 then the given set of data 8,21,17,13 is changed into new set 8,21,18,13

To find the median :

First order the new set of data into least to greatest

The ordered set is 8,13,18,21

Since the given set of data is even

We can take two midvalues of new data in the set

Median is the mean of two middle values in the data set

$Median=\frac{13+18}{2}$

$=\frac{31}{2}$

$=15.5$

Therefore New Median=15.5

Therefore option A) 15.5 is correct

The new median for the new data set is 15.5

5 0

3 years ago

Ismael has a set of 5 solar panels and Ben has a set of 6 smaller solar panels. Each set of panels produce the same amount of en

eimsori [14]

9514 1404 393

Answer:

Ben's

Step-by-step explanation:

If E is the amount of energy that each full set of panels produces, then ...

3 of Ismael's 5 panels produce 3/5E

4 of Ben's 6 panels produce 4/6E

We can compare these fractions when they have a common denominator.

3/5E = 18/30E . . . . energy from Ismael's panels

4/6E = 20/30E . . . energy from Ben's panels

18/30 < 20/30 . . . . so Ben's panels are producing more energy

5 0

3 years ago

Please Help I Will Thank You And Give You 5 Stars

enyata [817]

Answer:

The first blank is m, the rest aren’t very clear

Step-by-step explanation:

6 0

3 years ago

julio is payed 1.4 times his normal hourly rate for each hour he works over 30 hours in a week last week he worked 35 hours and

Morgarella [4.7K]

Divide 30/1.4 and 436.60 should give uu how much he makes in his normal hourly rate multiply that by 5 and subtract that number from 436.60

7 0

3 years ago