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3 years ago

What is a negative 3 cubed written as a fraction

Mathematics

2 answers:

Advocard [28]3 years ago

8 0

When you have an exponent that is negative, it means to take reciprocal of the fraction then take it the power.

Some examples:

5^-2 = 1/5^2 = 1/25
10^-3 = 1/10^-3 = 1/1000

If this answer wasn't clear enough, just comment below or DM me a message!

Elan Coil [88]3 years ago

6 0

The answer will be 1/a^3. Hope it help!

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3 years ago

1. If m varies directly as v2 and m = 3, when v =2, calculate the value of m when v =9. (3marks)

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3 years ago

An equilateral triangle has a side length of 6. What is the height of the triangle?

vlabodo [156]

Since the height of an equilateral triangle in terms of its side s is s√3/2, the height of the triangle is 6√3/2 = 3√3 and so the area is (1/2)(6)(3√3) = 9√3.

If we draw a horizontal line a height of h from the base of the triangle, the region is split into two regions: the lower region consisting of a trapezoid of height h and the upper region consisting of a triangle of height 3√3 - h. 

Since the upper triangle and the triangle itself are similar triangles, the base and height are proportional. If we let x denote the base of the length of the upper triangle, we have: 

(S. of small triangle)/(S. of big triangle) = (Ht. of small triangle)/(Ht. of big triangle) 
==> x/6 = (3√3 - h)/(3√3) 
==> x = (6√3 - 2h)/√3 

Thus, the area of the upper triangle is: 

A = (1/2)[(6√3 - 2h)/√3](3√3 - h) = [(6√3 - 2h)(3√3 - h)]/(2√3). 
(Made a dumb mistake about the height here for some reason) 

Since we require that the area of this triangle is to be half of the total area (9√3/2), we need to solve: 

[(6√3 - 2h)(3√3 - h)]/(2√3) = 9√3/2 
==> (6√3 - 2h)(3√3 - h) = 27 
==> 54 - 6h√3 - 6h√3 + 2h^2 = 27 
==> 2h^2 - 12h√3 + 27 = 0. 

Solving with the Quadratic Formula gives: 

h = (6√3 + 3√6)/2 ≈ 8.87 units and h = (6√3 - 3√6)/2 ≈ 1.52 units. 

Since h = (6√3 + 3√6)/2 would place the line outside of the triangle, we pick h = (6√3 - 3√6)/2. 

Therefore, the line should be ==> (6√3 - 3√6)/2 units from the base. 

I hope this helps! ^^ Brainliest Please?

5 0

3 years ago

Read 2 more answers

If D is midpoint of side BC of triangle ABC. P and Q are points lying respectively on side AB and AC such that DP is parallel to

LUCKY_DIMON [66]

See proof below

Step-by-step explanation:

Assume triangle ABC to have vertices at;

A(2,-1), B(2,-7) and C(6,-7)

D is midpoint of BC, thus D is at (4,-7)

The P and Q, are lying on side AB and AC, hence assume P is at (2,-4) and Q is at (4,-4) such at DP is parallel to QA

Plot the points on a graph tool and join the points to view the sketch.

To prove area of triangle CPQ is 1/4 area of ABC will be;

Find area ABC and CPQ then compare the areas.

Apply the distance formula to find the length of sides of the triangles then find the areas.

The distance formula is;

$d=\sqrt{x_2-x_1)^2+(y_2-y_1)^2}$

Length of side AB from the sketch is;

$AB=\sqrt{(2-2)^2+(-7--1)^2} =\sqrt{-6^2} =\sqrt{36} =6units$

Length of side BC will be;

$BC=\sqrt{(-7--7)^2+(6-2)^2} =\sqrt{4^2} =\sqrt{16} =4units$

Thus area of triangle ABC will be;

1/2 *base length*height ------because it is a right-triangle

1/2*4*6=12 square units

Find the lengths of all sides of triangle CPQ

Length of side PQ is half that of side BC thus PQ=2 units

Length of side PC is;

$PC=\sqrt{(6-2)^2+(-7--4)^2} =\sqrt{4^2+-3^2} =\sqrt{16+9} =\sqrt{25} =5units$

Length of side QC will be;

$QC=\sqrt{(6-4)^2+(-7--4)^2} =\sqrt{2^2+-3^3} =\sqrt{4+9} =\sqrt{13}$

QC= √13 = 3.6 units

Find area of triangle CPQ given all sides by applying the Heron's formula for area of triangle which is;

A=√s(s-a)(s-b)(s-c) where;

A=area of the triangle

s= half the perimeter of the triangle

a=side PQ = 2 units

b=side PC = 5 units

c= side QC = 3.6 units

Finding the perimeter of triangle CPQ will be;

P=sum of all sides

P=2+5+3.6 =10.6 units

s=10.6/2 = 5.3

Area of the triangle CPQ will be;

$A=\sqrt{5.3(5.3-2)(5.3-5)(5.3-3.6)} \\A=\sqrt{5.3(3.3)(0.3)(1.7)} \\A=\sqrt{8.9} =2.98$

A=3.0 (1 decimal place)

Compare the areas;

Area of triangle ABC=12 square units

Area of triangle CPQ = 3 square units

Area of triangle CPQ / Area of triangle ABC = 3/12 =1/4

Thus you have proved that area of triangle CPQ is 1/4 th area of triangle ABC because 1/4 *12 =3

Learn More

Area of a triangle ;brainly.com/question/14869984

The Heron's formula : brainly.com/question/10713495

Keywords: midpoint, triangle, sides, parallel, prove , area, equal

#LearnwithBrainly

6 0

3 years ago

There is a bag filled with 5 blue, 6 red and 2 green marbles.

nadya68 [22]

Answer:

5/11

Step-by-step explanation:

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3 years ago