All categories

3 years ago

Two planes intersect in exactly one point

Mathematics

1 answer:

adell [148]3 years ago

7 0

Answer:

If two planes intersect, then their intersection is a line. A line contains at least two points. If two lines intersect, then exactly one plane contains both lines. If a point lies outside a line, then exactly one plane contains both the line and the point.

You might be interested in

What is the y-value when x equals 25? y= 650 - 15(x)

yarga [219]

Answer:

y= 275 when x is 25

5 0

3 years ago

If two of the four expressions x + y, x + 5y, x – y, and 5x – y are chosen at random, what is the probability that their product

storchak [24]

Answer:

1/6

Step-by-step explanation:

The product will only be of the required form if the two chosen factors are of the form (x +by) and (x -by).

For the factor (x+y), there is also a factor (x-y) on the list. For the factor (x+5y), there is no factor (x-5y) available.

So, of the (4·3)/2 = 6 possible ways to choose two expressions from the four given expressions, only one pair of the 6 will have a product of the required form.

The probability is 1/6.

8 0

3 years ago

Si una empresa obtiene un préstamo de S/3000 a seis años de plazo, con una tasa de interés compuesto del 15 % anual capitalizabl

Debora [2.8K]

Answer:

VF= $3.281,42

Interes= 3.281,42 - 3.000= $281.42

Step-by-step explanation:

Dada la siguiente información:

Prestamo (P)= $3.000

Tasa (i)= 0,015/2= 0,0075

Cantidad de periodos (n)= 6*2= 12 semestres

<u>Para calcular el valor final del prestamos, tenemos que usar la siguiente formula:</u>

VF= P*(1 + i)^n

VF= 3.000*1,0075^12

VF= $3.281,42

Interes= 3.281,42 - 3.000= $281.42

8 0

3 years ago

Having trouble with my functions homework plz can someone help

puteri [66]

Answer:

$g(x) = \frac{ - 19}{3} x \: + 2$

I hope that is right

4 0

3 years ago

Based on the graph given for f (x) construct the graph of f¹ (x). for f (x) find E, F and the formula of f (x) when it is known

Lostsunrise [7]

Answer:

To find an inverse function, reflect a graph of a function across the line y=x (and find the resulting equation)

To reflect a linear function in the line y=x, find points on f(x) and then swap their x and y coordinates.

Points on f(x): (0, -4) (2, 0) (5, 6)

Points reflected in line y=x: (-4, 0) (0, 2) (6, 5)

Plot points (-4, 0) (0, 2) (6, 5) and connect to form a straight line - this is the inverse of the function: $f^{-1}(x)$

To determine the equation of f(x):

Choose 2 points on f(x): (5, 6) and (0, -4)

Calculate the slope (gradient) by using:

$m=\dfrac{\triangle y}{\triangle x}=\dfrac{y_2-y_1}{x_2-x_1}=\frac{6--4}{5-0}=2$

Using the slope-intercept form: y = mx + b

(where m is the slope and b is in the y-intercept)

From inspection of the graph, we can see the line crosses the y-axis at -4,

⇒ f(x) = 2x - 4

As the line is actually a line segment (with endpoints (0, -4) and (5, 6), then

f(x) = 2x - 4, 0 ≤ x ≤ 5

To determine the equation of $f^{-1}(x)$ :

Rewrite f(x) as $y = 2x - 4$

Swap the x and y: $x = 2y - 4$

Rearrange to make y the subject: $y= \dfrac{1}{2}(x + 4)$

Replace y with $f^{-1}(x)$

So the equation of the inverse is: $f^{-1}(x)= \dfrac{1}{2}(x + 4)$

As the original function is a segment, then

$f^{-1}(x)= \dfrac{1}{2}(x + 4), \ \ \ -4\leq x\leq 6$

(shown in blue on the attached diagram)

** I can't see any points labelled E and F on the original function. If they are the endpoints of the line segment of f(x), then they are (0, -4) and (5, 6) **

4 0

2 years ago