Sin (5/6) show work for circle

Find the least common multiple (LCM) of 8y^6+ 144y^5+ 640y^4 and 2y^4 + 40y^3 + 200y^2.

Mice21 [21]

Answer:

LCM = $8y^{4}(y+ 10)^{2}(y + 8)$

Step-by-step explanation:

Making factors of $8y^{6}+ 144y^{5}+ 640y^{4}$

Taking $8y^{4}$ common:

$\Rightarrow 8y^{4} (y^{2}+ 18y+ 80)$

Using factorization method:

$\Rightarrow 8y^{4} (y^{2}+ 10y + 8y + 80)\\\Rightarrow 8y^{4} (y (y+ 10) + 8(y + 10))\\\Rightarrow 8y^{4} (y+ 10)(y + 8))\\\Rightarrow \underline{2y^{2}} \times 4y^{2} \underline{(y+ 10)}(y + 8)) ..... (1)$

Now, Making factors of $2y^{4} + 40y^{3} + 200y^{2}$

Taking $2y^{2}$ common:

$\Rightarrow 2y^{2} (y^{2}+ 20y+ 100)$

Using factorization method:

$\Rightarrow 2y^{2} (y^{2}+ 10y+ 10y+ 100)\\\Rightarrow 2y^{2} (y (y+ 10) + 10(y + 10))\\\Rightarrow \underline {2y^{2} (y+ 10)}(y + 10) ............ (2)$

The underlined parts show the Highest Common Factor(HCF).

i.e. HCF is $2y^{2} (y+ 10)$ .

We know the relation between LCM, HCF of the two numbers 'p' , 'q' and the numbers themselves as:

$HCF \times LCM = p \times q$

Using equations (1) and (2): $\Rightarrow 2y^{2} (y+ 10) \times LCM = 2y^{2} \times 4y^{2}(y+ 10)(y + 8) \times 2y^{2} (y+ 10)(y + 10)\\\Rightarrow LCM = 2y^{2} \times 4y^{2}(y+ 10)(y + 8) \times (y + 10)\\\Rightarrow LCM = 8y^{4}(y+ 10)^{2}(y + 8)$

Hence, LCM = $8y^{4}(y+ 10)^{2}(y + 8)$

5 0

2 years ago

3 pieces of wood have a total length of 32 m. The second piece is twice the size of the first and the third piece is 2 more mete

andreev551 [17]

Answer:

X + Y + Z = 32

X2 = Y

X3 + 2 = Z

X + X2 + X3 + 2 = 32

Make X alone

There is a 2 so we subtract 2 from both sides

X + X2 + X3 = 30

Add the X's up

X + X2 + X3 = X6

X6 = 30

Divide by 6

30 / 6 = 5

You are left with X=5

The first piece of wood has a length of 5

5 x 2 = 10

The second piece has a value of 10

5 x 3 + 2 = 17

The third piece is 17

Hope this helps. If you have any questions you may ask.

Step-by-step explanation:

5 0

3 years ago

Which polynomial function has a leading coefficient of 1 and roots /7 and - /3 with multiplicity 1?

VladimirAG [237]

Answer:

A. f(x) = (x - √2)(x + √3)

Step-by-step explanation:

Leading coefficient is 1, multiplicity is 1, roots are √2 and -√3. It means the function is the product of two binomials.

The function with the roots of a and b is:

f(x) = (x - a)(x - b)

Substitute and and b:

f(x) = (x - √2)(x - (-√3)) ⇒
f(x) = (x - √2)(x + √3)

Correct choice is A

4 0

2 years ago

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A bicycle wheel has a radius of 13 inches. What is the distance the bicycle will travel after 30 revolutions of the wheel? Use 3

SpyIntel [72]

Radius = 13 inches

Circumference of wheel = 1 revolution
2πr = 2 x 3.14 x 13 = 81.64 inches

1 revolution = 81.64 inches
30 revolutions = 2449.2inches

7 0

2 years ago

Help please will mark brainliest

Andrew [12]

Answer:

i thinks its -9

Step-by-step explanation:

4 0

2 years ago

Read 2 more answers