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3 years ago

The product of the slopes of perpendicular lines is always___

Mathematics

1 answer:

Mice21 [21]3 years ago

3 0

Answer:

-1

Step-by-step explanation:

The product of the slopes of perpendicular lines is always -1 .

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Assume that when adults with smartphones are randomly selected, 48% use them in meetings or classes. If 8 adult smartphone use

Lisa [10]

Answer:

The probability is 2.2%

Step-by-step explanation:

The probability that a randomly selected adult uses the telephone in classes is always equal to 0.48.

If x represents the number of adults selected from among the 8 that the telephone uses in classes, then x is a discrete random variable that follows a binomial distribution, with:

p = 0.48

q = 0.52

n = 8

We want to find the probability of x = 5

$P(x) = \frac{n!}{x!(n-x)!} *p ^ n *q ^{n-x}\\\\ P(x = 5) = \frac{8!}{5!(8-5)!} * 0.48 ^ 8 * 0.52 ^ 3\\\\ P(x = 5) = 0.02218$

The probability is 2.2%

6 0

3 years ago

The rectangular box shown in the figure has dimensions 9" × 5" × 3" (a = 9, b = 5, c = 3). Approximate the angle θ formed by a d

aliina [53]

The simplest method to do this is with the vector dot product. Let the vector A = <9i + 5j> with magnitude √106 be the base diagonal, and B = <5j + 3k> be the diagonal vector on the side, with magnitude √34. Then cos θ = (A dot B) divided by the product of the magnitudes. A dot B =30, so

cos θ = 30 / √(34 x 106)

= 0.4997 ==>

θ = 49.19° is the answer

4 0

3 years ago

Find the Jacobian ∂(x, y, z) ∂(u, v, w) for the indicated change of variables. If x = f(u, v, w), y = g(u, v, w), and z = h(u, v

jeyben [28]

Answer:

The Jacobian ∂(x, y, z) ∂(u, v, w) for the indicated change of variables

= -3072uv

Step-by-step explanation:

Step :-(i)

Given x = 1 6 (u + v) …(i)

Differentiating equation (i) partially with respective to 'u'

$\frac{∂x}{∂u} = 16(1)+16(0)=16$

Differentiating equation (i) partially with respective to 'v'

$\frac{∂x}{∂v} = 16(0)+16(1)=16$

Differentiating equation (i) partially with respective to 'w'

$\frac{∂x}{∂w} = 0$

Given y = 1 6 (u − v) …(ii)

Differentiating equation (ii) partially with respective to 'u'

$\frac{∂y}{∂u} = 16(1) - 16(0)=16$

Differentiating equation (ii) partially with respective to 'v'

$\frac{∂y}{∂v} = 16(0) - 16(1)= - 16$

Differentiating equation (ii) partially with respective to 'w'

$\frac{∂y}{∂w} = 0$

Given z = 6uvw ..(iii)

Differentiating equation (iii) partially with respective to 'u'

$\frac{∂z}{∂u} = 6vw$

Differentiating equation (iii) partially with respective to 'v'

$\frac{∂z}{∂v} =6 u (1)w=6uw$

Differentiating equation (iii) partially with respective to 'w'

$\frac{∂z}{∂w} =6 uv(1)=6uv$

Step :-(ii)

The Jacobian ∂(x, y, z)/ ∂(u, v, w) =

$\left|\begin{array}{ccc}16&16&0\\16&-16&0\\6vw&6uw&6uv\end{array}\right|$

Determinant 16(-16×6uv-0)-16(16×6uv)+0(0) = - 1536uv-1536uv

= -3072uv

Final answer:-

The Jacobian ∂(x, y, z)/ ∂(u, v, w) = -3072uv

6 0

3 years ago

The opposite corners of a quadrilateral are right angles. The quadrilateral is not a rhombus. What kind of quadrilateral is this

tatiyna

A rhombus is a 4 sided shape with equal lengths. Even though it has equal lengths, it has opposite sides that are parallel, and angles that are equal. It also has diaginols (dashed lines) meat in the middle

8 0

3 years ago

5.Write each algebraic expression in simplest form.

Hatshy [7]

Answer:

=12x+y

Step-by-step explanation:

Combine like terms

=5x+-3y+7x+4y

=(5x+7x)+(-3y+4y)

=12x+y

7 0

3 years ago

Read 2 more answers