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2 years ago

Use the identity below to complete the tasks:

Mathematics

1 answer:

pashok25 [27]2 years ago

4 0

Answer:

a = 5r² and b = r²s

Step-by-step explanation:

a3 - b3 = (a - b)(a + ab + b2)

Expressing 125q^6-r^6s^3 as a difference of 2 cubes

125q^6-r^6s^3

= 5³(r²)³ - (r³)²s³

= (5r²)³ - (r²s)³

Comparing with a³ - b³

a = 5r² and b = r²s

Hence the value of a is 5r² and b is r²s

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A disk with radius 3 units is inscribed in a regular hexagon. Find the approximate area of the inscribed disk using the regular

Oksi-84 [34.3K]

Answer:

The approximate are of the inscribed disk using the regular hexagon is $A=18\sqrt{3}\ units^2$

Step-by-step explanation:

we know that

we can divide the regular hexagon into 6 identical equilateral triangles

see the attached figure to better understand the problem

The approximate area of the circle is approximately the area of the six equilateral triangles

Remember that

In an equilateral triangle the interior measurement of each angle is 60 degrees

We take one triangle OAB, with O as the centre of the hexagon or circle, and AB as one side of the regular hexagon

Let

M ----> the mid-point of AB

OM ----> the perpendicular bisector of AB

x ----> the measure of angle AOM

$m\angle AOM =30^o$

In the right triangle OAM

$tan(30^o)=\frac{(a/2)}{r}=\frac{a}{2r}\\\\tan(30^o)=\frac{\sqrt{3}}{3}$

$\frac{a}{2r}=\frac{\sqrt{3}}{3}$

we have

$r=3\ units$

substitute

$\frac{a}{2(3)}=\frac{\sqrt{3}}{3}\\\\a=2\sqrt{3}\ units$

Find the area of six equilateral triangles

$A=6[\frac{1}{2}(r)(a)]$

simplify

$A=3(r)(a)$

we have

$r=3\ units\\a=2\sqrt{3}\ units$

substitute

$A=3(3)(2\sqrt{3})\\A=18\sqrt{3}\ units^2$

Therefore

The approximate are of the inscribed disk using the regular hexagon is $A=18\sqrt{3}\ units^2$

6 0

3 years ago

At oceanside middle school 110 students tried out for the football team only 80% of the students that tryout make the team how m

Olenka [21]

Step-by-step explanation:

answer is 22 students in the team

how do u get it? 

you know it is 80% of the students went for try out so you do 100% - 80% give you 20% students the number of students in the team already. so you do 20 / 100 x 110 students which already in the whole school over 1 which would give it 22

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2 years ago

Find value of x of question number F

a_sh-v [17]

Answer:

X=17

Step-by-step explanation:

AC^2=AB^2 +BC^2(PYTHAGOREAN THEORM)

100=64 +BC^2

36=BC^2

6CM=BC

AD^2=AB^2+BD^2(PYTHAGOREAN THEORM)

X^2 =64+225

X^2=289

X=17

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2 years ago

How to find a ratio for a repeating decimal

Marta_Voda [28]

Let x equal the repeating decimal you are trying to convert to a fraction.Examine the repeating decimal to find the repeating digit(s)Place the repeating digit(s) to the left of the decimal point.

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3 years ago

Which of the rectangles in the picture could be the image of rectangle A after a sequence of reflections, rotations and/or trans

zheka24 [161]

Answer:

Step-by-step explanation:

B. Rectangle 4

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3 years ago