Which shows the list of numbers from least to greatest |-3|,

The base of a solid right pyramid is a regular hexagon with a radius of 2x units and an apothem of units. A solid right pyramid

Xelga [282]

Answer:

$6 x^2*\sqrt{3}$

Step-by-step explanation:

The base of the pyramid we need to study is a hexagon.

Let's look at the attached image of an hexagon to understand how we are going to find the area of this figure.

Notice that an hexagon is the combination of 6 exactly equal equilateral triangles in our case of size "2x" (notice that the "radius" of the hexagon is given as "2x")

Therefore the area of the hexagon is going to be 6 times the area of one of those equilateral triangles.

We know the area of a triangle is the product of its base times its height, divided by 2: $\frac{base*height}{2} = \frac{2x*height}{2}$

We notice that the triangle's height is exactly what is called the "apothem" of the hexagon (depicted in green in our figure) which measures $x\sqrt{3}$ , so replacing this value in the formula above for the area of one of the triangles:

$\frac{2x*height}{2}= \frac{2x*x\sqrt{3} }{2}=x^2\sqrt{3}$

Then we multiply this area times 6 to get the total area of the hexagon (6 of these triangles):

Area of hexagon = $6x^2\sqrt{3}$

which is the last option given in the list.

5 0

3 years ago

Read 2 more answers

Use four rectangles to estimate the area between the graph of the function f(x) = V3x + 5 and the x-axis on the interval[0, 4] u

yuradex [85]

Answer:

12.123

Step-by-step explanation:

You want the area under the curve f(x) = √(3x+5) on the interval [0, 4] estimated using the left sum and four subintervals.

<h3>Riemann sum</h3>

When the interval [0, 4] is divided into four equal parts, each has unit width. That means the area of the rectangle defined by the curve and the interval width will be equal to the value of the curve at the left end of the interval.

The area we want is the sum ...

f(0) +f(1) +f(2) +f(3)

As the attachment shows, that sum is ...

area ≈ 12.123 . . . square units

__

<em>Additional comment</em>

The table values in the attachment are rounded to 7 decimal places. Trailing zeros are not shown. Actual values used have 12 significant digits, as the total shows.

Such a sum is called a Riemann sum, named for a German mathematician. Four such sums are commonly used, and further refinements are possible. Those are the left sum (as here), the right sum, the midpoint sum, and a sum using a trapezoidal approximation of the rectangle area.

For left, right, and midpoint sums, n function values are required for n subintervals. When the trapezoidal approximation is used, n+1 function values are required.

7 0

1 year ago

After a special medicine is introduced into a petri dish full of bacteria, the number of bacteria remaining in the dish decrease

Digiron [165]

Answer:

the answer is 5.5

5 0

3 years ago

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The Campbell family has a disposable income of $60,000 annually. Assume that their marginal propensity to consume is 0.8 (the Ca

posledela

<span>Given the Keynesian equation C=A+MD, we find 10000 + (0.8 x 60000) = $58000. M is the Marginal propensity to consume, the A is the Autonomous consumption, and D is disposable income, giving Annual consumer spending as C.</span>

7 0

3 years ago

you wish to purchase dog food foe your kennel. you find 2 equal brands. bowser dog food comes in 50lb. bags for 32.50 per bag .

evablogger [386]

Answer:

Woof Woof dog food is a better deal. It costs $1.48 per pound.

Bowser dog food costs $1.54 per pound.

6 0

3 years ago

Which shows the list of numbers from least to greatest |-3|, | 3/2|, |-2|, |3.5|, -1?