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3 years ago

Write two expressions where the solution is 4

Mathematics

2 answers:

Luden [163]3 years ago

8 0

7x=28
What is x.

n+2=6

masya89 [10]3 years ago

8 0

8x+32-45=19 solve for x
or
(1000÷5+600)÷200

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Find the volume of the tetrahedron in the first octant bounded by the coordinate planes and the plane passing through (2 comma 0

SVETLANKA909090 [29]

Answer:

The volume of the tetrahedron is:

$\frac{50}{3}=16.667$

Step-by-step explanation:

The volume of the tetrahedron is given by the intersection of the planes x = 0, y = 0, z = 0 and the plane formed by the three points given.

The equation of the plane formed by the three points is:

Points: (2,0,0);(0,5,0);(0,0,4)

$\pi :\frac{x}{2} +\frac{y}{5} +\frac{z}{4} =1$

It can also be expressed as:

$10x + 4y+5z=20$

We have to calculate the triple integral, therefore we must define the domain:

The values of x are given by:

0≤x≤2

We will integrate the values of y between the y = 0 axis and the line formed when z = 0:

z=0 ⇒ 10x + 4y=2 ⇒ $y=\frac{20-10x}{4} =$

$0\leq y \leq 5-\frac{5}{2}x$

We will integrate the values of z between the plane z = 0 and the plane 10x + 4y+5z=20

10x + 4y+5z=20 ⇒ $z=\frac{20-10x-4y}{5} =4-2x-\frac{4}{5}y$

$0\leq z \leq 4-2x-\frac{4}{5}y$

The volume of the tetrahedron is:

$\int\limits^{2}_{0} \ \ \ \int\limits^{5-\frac{5}{2} x}_{0} \ \ \ \int\limits^{4-2x-\frac{4}{5}y }_{0} {z} \, dz\, dy \,dx$

$\int\limits^{2}_{0} \ \ \ \int\limits^{5-\frac{5}{2} x}_{0} \frac{z^2}{2}|^{4-2x-\frac{4}{5}y}_0\, dy \,dx$

$\frac{z^2}{2}|^{z=4-2x-\frac{4}{5}y}_{z=0}=\frac{5}{25}(5x+2(y-5))^2$

$\int\limits^{2}_{0} \ \ \ \int\limits^{5-\frac{5}{2} x}_{0} {\frac{5}{25}(5x+2(y-5))^2}\, dy \,dx$

$\int\limits^{2}_{0} {-\frac{25}{6}(x-2)^3} dx=-\frac{25}{24} (x-2)^4|^{2}_{0}=\frac{50}{3}$

6 0

4 years ago

Andrea is trying to determine the area of a tile for her bathroom with a side length of 8 inches. Draw a picture of the tile and

olasank [31]

Answer:

Step-by-step explanation:

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3 years ago

An illusionist needs up to 10 volunteers for a show. The illusionist needs no fewer than 4 female volunteers. Let x represent th

Tems11 [23]

Answer:

FIRST OPTION.

THIRD OPTION.

FIFTH OPTION.

Step-by-step explanation:

Let be "x" the number of of female volunteers and "y" the number of male volunteers.

You need to remember the meaning of the inequalities symbols:

: Less than.

$>$ : Greater than.

$\leq$ : Less than or equal to.

$\geq$ : Greater than or equal to.

In this case you know that the illusionist needs up to 10 volunteers, which indicates that the total number of volunteers can be less than or equal to 10 people. The inequality that represents this is:

$x+y\leq 10$

According to the exercise, the illusionist needs no fewer than 4 female volunteers. This means that number of female volunteer must be greater than or equal to 4:

$x\geq 4$