Ask question

Ask question

All categories

2 years ago

15

What is the solution set of {x | x < -3} ∩ {x | x > 5}?

1 answer:

valentinak56 [21]2 years ago

7 0

Answer:

the empty set {∅}

Step-by-step explanation:

{x | x < -3} ∩ {x | x > 5} is giving us

(-∞, -3) intersecting (5, ∞).

Since those two intervals do not intersect the solution is the empty set

You might be interested in

Determine the angles of rotation. (CHOOSE ALL ANSWERS THAT APPLY)

NeTakaya

Answer:

a.

Step-by-step explanation:

6 0

3 years ago

The area of a rhombus is given by the formula A=1/2xy,where x and y are the lengths of the diagonals. If the diagonals of a rhom

Ivahew [28]

The area of the triangle would be 100 cm

3 0

3 years ago

A card is drawn from a well shuffled deck of 52 cards what is the probability of drawing an ace or a six

Allisa [31]

Answer:

8/52

Step-by-step explanation:

The first thing to do is write it out;

How many aces are in a deck and how many sixes?

There are 4 of each so, 4+4 = 8 therefore our beginning ratio will be;

8/52 cards are going to be an ace or a six.

6 0

3 years ago

Find, correct to four decimal places, the length of the curve of intersection of the cylinder 16x2 + y2 = 16 and the plane x + y

lubasha [3.4K]

First find a parameterization for the curve of intersection.

Given the equation of a cylinder, a natural choice for a parameterization would be one utilizing cylindrical coordinates. Here,

$16x^2+y^2=16\implies x^2+\left(\dfrac y4\right)^2=1$

which suggests we could use

$\begin{cases}x(t)=\cos t\\y(t)=4\sin t\\z(t)\end{cases}$

with $0\le t\le2\pi$ , and we get $z(t)$ from the equation of the plane,

$x+y+z=12\implies z(t)=12-x(t)-y(t)=12-\cos t-4\sin t$

Now use the arc length formula:

$\displaystyle\ell=\int_0^{2\pi}\sqrt{\left(\dfrac{\mathrm dx}{\mathrm dt}\right)^2+\left(\dfrac{\mathrm dy}{\mathrm dt}\right)^2+\left(\dfrac{\mathrm dz}{\mathrm dt}\right)^2}\,\mathrm dt$

$\displaystyle\ell=\int_0^{2\pi}\sqrt{\sin^2t+16\cos^2t+(\sin t-4\cos t)^2}\,\mathrm dt$

$\displaystyle\ell=\sqrt2\int_0^{2\pi}\sqrt{\sin^2t-4\cos t\sin t+16\cos^2t}\,\mathrm dt\approx\boxed{24.0878}$

4 0

4 years ago

Solve using the quadratic formula x2 - 6x - 40=0 Question options: x = 10 or x = -4 x = 4 or x = -10 x = -7 or x = 7 x = -4 - √7

Crazy boy [7]

Answer:

$x=-10$ or $x=4$

Step-by-step explanation:

$ax^2+bx+c=0$

$x^2-6x-40=0$

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

$x=\frac{-6\pm\sqrt{6^2-4(1)(-40)}}{2(1)}$

$x=\frac{-6\pm\sqrt{36+160}}{2}$

$x=\frac{-6\pm\sqrt{196}}{2}$

$x=\frac{-6\pm14}{2}$

$x=-3\pm7$

$x=-10$ or $x=4$

6 0

3 years ago

Read 2 more answers