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3 years ago

Find the volume of the composite solid. Round your answer to the nearest tenth

Mathematics

1 answer:

WITCHER [35]3 years ago

7 0

Answer:

1130.4 cubic meters

Step-by-step explanation:

I think your question is missed of key information, allow me to add in and hope it will fit the original one. Please have a look at the attached photo.

My answer:

The composite solid has two cones:

The height of the big cone is: 12 m
The height of the small cone is: 18
The radius of the common base of the two cones is: 6 m

=> the volume of the big cone is:

V = (1/3)π $r^{2}$ ·h = (1/3)*3.14* $6^{2}$ *18 = 678.24 cubic meters

=> the volume of the small cone is:

V = (1/3)π $r^{2}$ ·h = (1/3)*3.14* $6^{2}$ *12 = 452.16 cubic meters

=> the volume of the composite solid :

= 678.24 + 452.16

=1130.4 cubic meters

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Find the minimum value of the function for the polygonal convex set determined by the given system of inequalities.

lutik1710 [3]

Answer:

Option b (4,1)

Step-by-step explanation:

The region given by the system of inequalities is shown in the graph. We must look within this region for the point that minimizes the objective function $f(x, y) = 8x + 8y$

The minimum points are found in the lower vertices of the region.

These vertices are found by equating the equations of the lines::

$3x+2y=14\\-5x +5y=10$

-------------------

$x = 2\\y = 4$

$-8x + 3y = -29\\3x + 2y = 14$

---------------------

$x = 4\\y = 1$

The lower vertices are:

(4, 1) (2, 4)

Now we substitute both points in the objective function to see which of them we get the lowest value of $f(x, y)$

$f(4, 1) = 8(4) +8(1) = 40\\f(2, 4) = 8(2) + 8(4) = 48$

Then the value that minimizes f(x, y) is (4,1).

Option b

5 0

3 years ago

the figure below is a square . Find the length of side x in simplest radical form with a rational denominator.

wel

Answer:

$\sqrt{14}$

Step-by-step explanation:

In any square with side length $s$ , the diagonal of the square is equal to $s\sqrt{2}$ . Since the side length of this square is $\sqrt{7}$ , the diagonal is equal to $\sqrt{7}\cdot \sqrt{2}=\boxed{\sqrt{14}}$ .

Alternatively, you can form two 45-45-90 triangles with the diagonal of the square. The diagonal acts as the hypotenuse for the both these triangles, and the legs of both triangles are equal to the side length of the square. To find the length of the diagonal, use the Pythagorean Theorem, which states $a^2+b^2=c^2$ , where $c$ is the hypotenuse of the triangle, and $a$ and $b$ are the two legs of the triangle.