The product of two positive numbers is . what is the minimum value of their sum?

FACTORIZE AND Split the middle term: 72 + b - b^2

seraphim [82]

Answer:

- (b - 9)(b + 8)

Step-by-step explanation:

72 + b - b² ← factor out - 1 from each term and rearrange into standard form

= - (b² - b - 72) ← factor the quadratic

Consider the factors of the constant term (- 72) which sum to give the coefficient of the b- term (- 1)

The factors are - 9 and + 8

Use these factors to split the b- term

b² - 9b + 8b - 72 ( factor the first/second and third/fourth terms )

b(b - 9) + 8(b - 9) ← factor out (b - 9) from each term

(b - 9)(b + 8)

Then

72 + b - b² = - (b - 9)(b + 8)

7 0

2 years ago

Or

Neporo4naja [7]

The probability that a single can will contain 11.6 ounces or less of soda is 0.2843

<h3>Probability that a can contains 11.6 ounces or less</h3>

The given parameters are:

x = 11.6

Mean = 12

Standard deviation = 0.7

Calculate the z value using:

$z = \frac{x - \bar x}{\sigma}$

This gives

$z = \frac{11.6-12}{0.7}$

z = -0.57

The probability is then calculated as:

P(x ≤ 11.6) = P(z ≤ -0.57)

Using the z table of probabilities, we have:

P(x ≤ 11.6) = 0.2843

<h3>Probability that a pack contains 11.6 ounces or less</h3>

In (a), the probability that a can contains 11.6 ounces or less is 0.2843

The probability that all cans in a pack contains 11.6 ounces or less is

P(6) = 0.2843^6

P(6) = 0.00053

<h3>Probability that a case contains 11.6 ounces or less</h3>

In (a), the probability that a can contains 11.6 ounces or less is 0.2843

The probability that all cans in a case contains 11.6 ounces or less is

P(36) = 0.2843^36

P(36) ≈ 0

<h3>Draw three normal distributions</h3>

See attachment for the normal distributions

<h3>The happening on the graph</h3>

The summary of the graph is that, as the sample size increases the probability decreases

Read more about probability at:

brainly.com/question/11234923

#SPJ1

8 0

2 years ago

Can you help me with this

Karo-lina-s [1.5K]

Answer

38°

Step-by-step explanation:

52+90+x=180

180-52-90=x

x=38

3 0

2 years ago

Read 2 more answers

If f(x, y, z) = x sin(yz), (a) find the gradient of f and (b) find the directional derivative of f at (2, 4, 0) in the direction

valentina_108 [34]

Answer:

a) $\nabla f(x,y,z) = \sin{yz}\mathbf{i} + xz\cos{yz}\mathbf{j} + xy \cos{yz}\mathbf{k}$ .

b) $Du_{f}(2,4,0) = -\frac{8}{\sqrt{11}}$

Step-by-step explanation:

Given a function $f(x,y,z)$ , this function has the following gradient:

$\nabla f(x,y,z) = f_{x}(x,y,z)\mathbf{i} + f_{y}(x,y,z)\mathbf{j} + f_{z}(x,y,z)\mathbf{k}$ .

(a) find the gradient of f

We have that $f(x,y,z) = x\sin{yz}$ . So

$f_{x}(x,y,z) = \sin{yz}$

$f_{y}(x,y,z) = xz\cos{yz}$

$f_{z}(x,y,z) = xy \cos{yz}$ .

$\nabla f(x,y,z) = f_{x}(x,y,z)\mathbf{i} + f_{y}(x,y,z)\mathbf{j} + f_{z}(x,y,z)\mathbf{k}$ .

$\nabla f(x,y,z) = \sin{yz}\mathbf{i} + xz\cos{yz}\mathbf{j} + xy \cos{yz}\mathbf{k}$

(b) find the directional derivative of f at (2, 4, 0) in the direction of v = i + 3j − k.

The directional derivate is the scalar product between the gradient at (2,4,0) and the unit vector of v.

We have that:

$\nabla f(x,y,z) = \sin{yz}\mathbf{i} + xz\cos{yz}\mathbf{j} + xy \cos{yz}\mathbf{k}$

$\nabla f(2,4,0) = \sin{0}\mathbf{i} + 0\cos{0}\mathbf{j} + 8 \cos{0}\mathbf{k}$ .

$\nabla f(2,4,0) = 0i+0j+8k=(0,0,8)$

The vector is $v = i + 3j - k = (1,3,-1)$

To use v as an unitary vector, we divide each component of v by the norm of v.

$|v| = \sqrt{1^{2} + 3^{2} + (-1)^{2}} = \sqrt{11}$

So

$v_{u} = (\frac{1}{\sqrt{11}}, \frac{3}{\sqrt{11}}, \frac{-1}{\sqrt{11}})$

Now, we can calculate the scalar product that is the directional derivative.

$Du_{f}(2,4,0) = (0,0,8).(\frac{1}{\sqrt{11}}, \frac{3}{\sqrt{11}}, \frac{-1}{\sqrt{11}}) = -\frac{8}{\sqrt{11}}$

6 0

3 years ago

How to use the Pythagorean theorem to provee if a triangle with the side lengths 7,14,28 is a right triangle. Plz help

Lapatulllka [165]

Answer: find the answer in the explanation.

Step-by-step explanation:

To use the Pythagorean theorem to prove if a triangle with the side lengths 7,14,28 is a right triangle, you will square 7 and add it to the square of 14. The square root of the sum will be equal to 28 if it is a right angle triangle. Otherwise, it is not.

(7^2 + 14^2) = 49 + 196

245

Find the square root of 245

Square root = 15.65

Since it is not 24, the triangle is not a right angle triangle.

8 0

3 years ago