All categories

3 years ago

A method for determining whether a critical point is a minimum. True or false?

Mathematics

1 answer:

natita [175]3 years ago

7 0

Answer:

We can find if a critical point is a local minimum or maximum by looking at the second derivatives.

Step-by-step explanation:

If you take the first derivative, you will find the slope at the given point, which if it is a minimum or a maximum will be 0.

Then we take the second derivative. If that number is a positive number, then we have a local minimum. If it is a negative number, then it is a local maximum.

You might be interested in

A cone with volume 1350 m³ is dilated by a scale factor of 1/3.

ki77a [65]

Answer:

450

Step-by-step explanation:

You basically do 1350 * 1/3 or 1350/3

6 0

3 years ago

Read 2 more answers

Naval intelligence reports that 4 enemy vessels in a fleet of 17 are carrying nuclear weapons. If 9 vessels are randomly targete

icang [17]

Answer:

0.7588 = 75.88% probability that more than 1 vessel transporting nuclear weapons was destroyed

Step-by-step explanation:

The vessels are destroyed without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x successes is given by the following formula:

$P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}$

In which:

x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

In this question:

Fleet of 17 means that $N = 17$

4 are carrying nucleas weapons, which means that $k = 4$

9 are destroyed, which means that $n = 9$

What is the probability that more than 1 vessel transporting nuclear weapons was destroyed?

This is:

$P(X > 1) = 1 - P(X \leq 1)$

In which

$P(X \leq 1) = P(X = 0) + P(X = 1)$

$P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}$

$P(X = 0) = h(0,17,9,4) = \frac{C_{4,0}*C_{13,9}}{C_{17,9}} = 0.0294$

$P(X = 1) = h(1,17,9,4) = \frac{C_{4,1}*C_{13,8}}{C_{17,9}} = 0.2118$

Then

$P(X \leq 1) = P(X = 0) + P(X = 1) = 0.0294 + 0.2118 = 0.2412$

$P(X > 1) = 1 - P(X \leq 1) = 1 - 0.2412 = 0.7588$

0.7588 = 75.88% probability that more than 1 vessel transporting nuclear weapons was destroyed

8 0

3 years ago

Enlarge the triangle by scale factor -1/3 with centre (-1,2)

Scorpion4ik [409]

Answer:

All the sides of the triangle X'Y'Z' are twice as long as the sides of the original triangle XYZ. The triangle XYZ has been enlarged by a scale factor of 2.

All the sides of the triangle X'Y'Z' are twice as long as the sides of the original triangle XYZ. The triangle XYZ has been enlarged by a scale factor of 2.Enlargement is an example of a transformation. A transformation is a way of changing the size or position of a shape.To enlarge a shape, a centre of enlargement is required. When a shape is enlarged from a centre of enlargement, the distances from the centre to each point are multiplied by the scale factor.

5 0

3 years ago

Find the slope of the line that passes through (-20, -51) and (31, -75).

lilavasa [31]

Answer:

-8/17

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(-75-(-51))/(31-(-20))

m=(-75+51)/(31+20)

m=-24/51

m=-8/17

7 0

3 years ago

URGENT WILL GIVE YOU 100 POINTS PLEASE ANSWER CORRECTLY

wariber [46]

Answer:

1. x = 18.4

2. x = -1.25

3. x = $\frac{5}{12}$

4. x = 12.3

5. x = 6.4

6. z = 5.8

7. x = $\frac{1}{12}$

8. x = - $\frac{1}{4}$

9. x = $\frac{1}{3}$

10. x = -9

11. z = 18

12. x = 7

13. x = -9

14. x = -36

15. x = -7

16. x = 8

17. z = -1.5

18. x = - $\frac{45}{7}$

19. x = 16

20. x = -12

21. x = $\frac{8}{3}$

22. x = -1.6

23. x = 1.8

24. x = -8.2

Step-by-step explanation:

1. x - 3.5 = 14.9 (add 3.5 to each side)

x = 18.4

2. x + 2.25 = 1 (subtract 2.25 from each side)

x = -1.25

3. - $\frac{1}{3}$ = x - $\frac{3}{4}$ (add $\frac{3}{4}$ to each side)

$\frac{3}{4}$ - $\frac{1}{3}$ = x (multiply $\frac{3}{4}$ by $\frac{3}{3}$ and $\frac{1}{3}$ by $\frac{4}{4}$ to get a common denominator)

$\frac{9}{12}$ - $\frac{4}{12}$ = x

$\frac{5}{12}$ = x

4. x - 2.8 = 9.5 (add 2.8 to each side)

x = 12.3

5. x - 8.5 = -2.1 (add 8.5 to each side)

x = 6.4

6. z - 9.4 = -3.6 (add 9.4 to each side)

z = 5.8

7. x + $\frac{5}{6}$ = $\frac{11}{12}$ (subtract $\frac{5}{6}$ from each side)

x = $\frac{11}{12}$ - $\frac{5}{6}$ (multiply $\frac{5}{6}$ by $\frac{2}{2}$ to get a common denominator)

x = $\frac{11}{12}$ - $\frac{10}{12}$

x = $\frac{1}{12}$

8. - $\frac{5}{6}$ + x = - $\frac{13}{12}$ (add $\frac{5}{6}$ to each side)

x = $\frac{5}{6}$ - $\frac{13}{12}$ (multiply $\frac{5}{6}$ by $\frac{2}{2}$ to get a common denominator)

x = $\frac{10}{12}$ - $\frac{13}{12}$

x = - $\frac{3}{12}$ = - $\frac{1}{4}$

9. x - $\frac{1}{9}$ = $\frac{5}{18}$ (add $\frac{1}{9}$ to each side)

x = $\frac{1}{9}$ + $\frac{5}{18}$ (multiply $\frac{1}{9}$ by $\frac{2}{2}$ to get a common denominator)

x = $\frac{2}{18}$ + $\frac{5}{18}$

x = $\frac{6}{18}$ = $\frac{3}{9}$ = $\frac{1}{3}$

10. x + 6 = -3 (subtract 6 from each side)

x = -9

11. z - 7 = 11 (add 7 to each side)

z = 18

12. -1 = x - 8 (add 8 to each side)

7 = x

13. -4x = 36 (divide each side by -4)

x = -9

14. - $\frac{x}{3}$ = 12 (multiply each side by -3)

x = -36

15. 63 = -9x (divide each side by -9)

-7 = x

16. 6.4 = 0.8x (divide each side by 0.8)

8 = x

17. -2.8z = 4.2 (divide each side by -2.8)

z = -1.5

18. - $\frac{7}{9}$ x = 5 (divide each side by - $\frac{7}{9}$ )

x = $\frac{5}{1}$ ÷ - $\frac{7}{9}$

x = $\frac{5}{1}$ (times) - $\frac{9}{7}$

x = - $\frac{45}{7}$

19. $\frac{1}{2}$ x = 8 (divide each side by $\frac{1}{2}$ )

x = 16

20. - $\frac{3}{4}$ x = 9 (divide each side by - $\frac{3}{4}$ )

x = -12

21. - $\frac{7}{8}$ x = - $\frac{21}{64}$ (divide each side by - $\frac{7}{8}$ )

x = - $\frac{7}{8}$ ÷ - $\frac{21}{64}$

x = - $\frac{7}{8}$ (times) - $\frac{64}{21}$

x = $\frac{448}{168}$ = $\frac{56}{21}$ = $\frac{8}{3}$

22. 1.6x = -3.2 (divide each side by 1.6)

x = -1.6

23. - $\frac{1}{2}$ = - $\frac{5}{18}$ x (divide each side by - $\frac{5}{18}$ )

1.8 = x

24. -2.5x = 20.5 (divide each side by -2.5)

x = -8.2

3 0

2 years ago

Read 2 more answers