For what side length(s) is the area of an equilateral triangle equal to 30 cm?? Only enter the number, in centimeters, rounded to two decimal places. A cm ►

Answers

Answer 1

Answer:

Answer: The sides length are 8.32 cm

Step-by-step explanation:

An equilateral triangle has all his sides of the same lenght, so we assume that the triangle has an L lenght in his sides.

The area of a triangle is $Area = (base * height)/(2)$ where the base is L, the Area is 30 and an unknown height.

To determine the height, we cut the triangle in half and take one side. By simetry, one side has a base of $(L)/(2)$ , a hypotenuse of L and a the unknown height.

Then we apply the Pythagoras theorem, this states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides, or, $hypotenuse = \sqrt{c^(2) + c^(2) }$ Where one c is $(L)/(2)$ and the other is the height.

Then we find one of the c of the equation wich will be the height.

$height = \sqrt{hypotenuse^(2)-base^(2) }$

$height = \sqrt{ L^(2) -(L)/(4) ^(2)}\nheight = \sqrt{( 3L^(2))/(4) } \n\nheight = (√(3)L )/(2)$

Finally, we use the triangle area mentioned before an find the value of L.

$30 = (L*(√(3)L )/(2) )/(2) \n\nL = \sqrt{(120)/(√(3) ) } \n\nL = 8.32 cm$

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The rectangular prism shown is formed by six intersecting planes.Where do the planes ABFE and EFGH intersect

Answers

The planes ABFE and EFGH intersected by line EF.

What is Prism?

A prism is a polyhedron in geometry made up of an n-sidedpolygon basis, a second base that is a rigidly translated copy of the first base, and n additional faces that must all be parallelograms and connect the corresponding sides of the two bases.

We have cuboidal prism which have faces ABFE and EFGH.

To find the point for intersecting we have to find a point or line which is common in both planes.

Here the point E and F are common.

But the plane EF is also common

Thus, the intersecting line is line EF.

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Answer:

Line EF

Step-by-step explanation:

Planes intersect at lines

If a new truck costs $43,750 and it depreciates 18% per year, what will the truck be worth in 5 years? 1 SEE ANSWER

Answers

if it depreciates by 18%, then as each year passes, its worth is reduced to 82% of its value
So, after 5 years, it is worth 43750

Mr. Ruiz drove 205 miles in 5 hours on Saturday and 180 miles in 4 hours on Sunday. What was his average speed, in miles per hour, for the two days

Answers

Answer:

In miles per hour was 34 mph

Step-by-step explanation:

205/5 = 41

180/4 = 27

to find the average you add both speeds then divide by how many there are.

41 + 27 = 68

68/2 = 34

A cube-shaped water tank having 6 ft side lengths is being filled with water. The bottom is solid metal but the sides of the tank are thin glass which can only withstand a maximum force of 200 lb. How high (in ft) can the water reach before the sides shatter?(Assume a density of water rho = 62.4 lb/ft3.
Round your answer to two decimal places.)

Answers

The distance the in which the water will reach before it shatters will be 1.03ft

Data;

Let the integral run from surface (y = 0) to maximum depth (y = d)ft
Let the differential depth = dydt
The area of each depth = 6dy ft^2

The Force Acting at any Depth

Using integration, the force at any depth y is 62.4y lb/ft^3

$200 = \int\limits^d_0 {62.4y} \, 6dy\n 200 = \int\limits^d_0 {374.4y} \, dy\n 200 = \int\limits^6_0 {374.4y} \, dy\n 200 = [374.4/2 y^2]_0^d\n200 = 187.2(d^2 - 0)\n200 = 187.2d^2\nd^2 = 200/187.2\nd = 1.03ft$

From the calculations above, the distance in which the water will reach before it shatters is 1.03ft

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What is the sum of 18 23/30+ 2/3

Answers

Answer:

See image

Step-by-step explanation:

You know only the given information aboutthe measures of the angles of a triangle. Find the probability that the triangle is equiangular.
39. Each is a multiple of 12.

Answers

Since they are multiples if 12

The possibilities are

12, 12, 156

12,24,144

12,36,132

12,48,120

12,60,108

12,72,96

12,84,84

24,24,132

24,36,120

24,48,108

24,60,96

24,72,84

36,36,108

36,48,96

36,60,84

36,72,72

48,48,84

48,60,72

60,60,60

Hence the probability is 1/19 or 0.0526

Final answer:

An equiangular triangle has all angles equal to 60 degrees. A triangle with angles that are multiples of 12 can be equiangular triangle only if each angle is 60 degrees. The probability of this is low due to multiple possibilities of multiple of 12.

Explanation:

In mathematics, a triangle is defined as equiangular if all its angles are equal. For a triangle to be equiangular, each angle must measure 60 degrees because the sum of all angles in a triangle is always 180 degrees.

Note, if each angle of a triangle is a multiple of 12, the only way it can be an equiangular triangle is if each angle measures 60 degrees (which is indeed a multiple of 12). Therefore, for a triangle with angles that are multiples of 12 to be an equiangular triangle, each angle must be 60 degrees.

However, multiple possibilities exist for angles of a triangle that are a multiple of 12, for instance, 12, 72, 96 or 24, 36, 120 etc. Therefore the probability that randomly picked triangle with the given condition is equiangular is relatively very low.

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