The volume of a rectangular prism is 12x^5-27x^3. What are the dimensions of the prism? Show all work.

The base of a solid oblique pyramid is an equilateral triangle with an edge length of s units. Which expression represents the h

aev [14]

Answer:

The height of the triangular base of the pyramid is s√3/2 units

Step-by-step explanation:

Here in this question, what we are concerned with is to calculate the height of the equilateral-triangle base of the oblique pyramid.

From the question, we are told that the equilateral triangle has a length of a units.

Let’s have a recall on some of the properties of equilateral triangles;

a. All sides are of equal lengths. Meaning side s is the length of all the sides in this case.

b. All angles are equal, meaning they are 60 degree each.

c. Dropping a perpendicular line from the top vertex to the base length will split the equilateral triangle into two right-angled triangles of angles 60 and 30 each.

So to find the height of this triangular base, we can use any of the two right angled triangles.

Kindly recall that the properties of each would be angles 30, 60 and side length s

so to calculate the height h, we can use trigonometric identities

Mathematically, the trigonometric identity we can use is the sine( side length s represents the hypotenuse, while the height h represents the opposite facing the angle 60 degrees)

Thus; we have

Sine of an angle = length of the opposite/length of hypotenuse

sin 60 = h/s

h = s sin 60

In surd form,

sin 60 = √3/2

Thus;

h = s * √3/2 = s√3/2 units

3 0

3 years ago

Lorelei filled her 5-gallon jug with water. How many times could she fill her 2-quart canteen with water from the jug?

Alina [70]

There are 4 quarts in each gallon.
It would take 2 fills of the canteen to make one gallon.
2x5=10

Also, this image may be helpful.

7 0

3 years ago

Read 2 more answers

Solve the following system of equations: x − 2y = 6 2x − 4y = 10

JulsSmile [24]

Answer:

x = -2

y = 1

Step-by-step explanation:

x−2y=6

Multiply both sides by 2

x-4y=12

Subtract x from both sides

-4y=12-x

2x−4y=10

Subtract 2x from both sides

-4y=10-2x

Put the 2 equations together:

12-x=10-2x

Add x to both sides

12=10-x

Subtract 10 from both sides

2= -x

Multiply both sides by -1

x= -2

x−2y=6

Multiply both sides by 2

2x-2y=12

Add 2y to both sides

2x=12+2y

2x−4y=10

Add 4y to both sides

2x=10+4y

x−2y=6

Multiply both sides by 2

2x-2y=12

Add 2y to both sides

2x=12+2y

2x−4y=10

Add 4y to both sides

2x=10+4y

Put the 2 equations together:

12+2y=10+4y

Subtract 10 from both sides

2+2y=4y

Subtract 2y from both sides

2=2y

y=1

7 0

3 years ago

Every natural number is an integer. True or false?

nexus9112 [7]

Answer:

yes every natural number is integer

because intezer is collection of positive and negative numbers....

7 0

4 years ago

Read 2 more answers

Find the domain of the function using interval notation. <img src="https://tex.z-dn.net/?f=f%28x%29%3D8%5Csqrt%7Bx-9%7D" id=

Irina18 [472]

Answer:

D_{f(x)} = [9, \infty)

Step-by-step explanation:

Here we have the square root of a function, in the following format:

$f(x) = \sqrt{g(x)}$

For the square root, and roots of even numbers(root of 4, 6, ...), we have the following condition in the domain

$g(x) \geq 0$

In this problem, we have that:

$f(x) = 8\sqrt{x-9}$

So

$x - 9 \geq 0$

$x \geq 9$

So the domain is

$D_{f(x)} = [9, \infty)$

3 0

3 years ago