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3 years ago

What is the LCM of 13/16a^3b^3, 11/30a^5b

Mathematics

1 answer:

vichka [17]3 years ago

8 0

Answer:

The L.C.M of given numbers is $\frac{143}{240}a^5b^3$ .

Step-by-step explanation:

The given expressions are

$\frac{13}{16}a^3b^3$

$\frac{11}{30}a^5b$

The factors of given expressions are

$\frac{13}{16}a^3b^3=\frac{13}{8}\times \frac{1}{2}\times a\times a\times a\times b\times b\times b$

$\frac{11}{30}a^5b=\frac{11}{15}\times \frac{1}{2}\times a\times a\times a\times a\times a\times b$

$L.C.M.=\frac{13}{8}\times \frac{1}{2}\times a\times a\times a\times b\times b\times b\times \frac{11}{15}\times a\times a$

$L.C.M.=\frac{143}{240}\times a^5\times b^3$

$L.C.M.=\frac{143}{240}a^5b^3$

Therefore, the L.C.M of given numbers is $\frac{143}{240}a^5b^3$ .

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Answer:

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Step-by-step explanation:

Given the height reached by a dolphin expressed by the equation is h = -16t^2 + 80t. At maximum height, the velocity is zero, hence;

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2 years ago

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Answer:

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Step-by-step explanation:

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The applicable formulas are ...

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area of a rectangle:

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area of a trapezoid:

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Answer:

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Step-by-step explanation:

Given

Quadrilateral;

Vertices of (0,1), (3,4) (4,3) and (3,0)

$Perimeter = a\sqrt{2} + b\sqrt{10}$

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Let the vertices be represented with A,B,C,D such as

A = (0,1); B = (3,4); C = (4,3) and D = (3,0)

To calculate the actual perimeter, we need to first calculate the distance between the points;

Such that:

AB represents distance between point A and B

BC represents distance between point B and C

CD represents distance between point C and D

DA represents distance between point D and A

Calculating AB

Here, we consider A = (0,1); B = (3,4);

Distance is calculated as;

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

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Substitute these values in the formula above

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$AB = \sqrt{9+ 9}$

$AB = \sqrt{18}$

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$AB = \sqrt{9}*\sqrt{2}$

$AB = 3\sqrt{2}$

Calculating BC

Here, we consider B = (3,4); C = (4,3)

Here,

$(x_1,y_1) = B (3,4)$

$(x_2,y_2) = C(4,3)$

Substitute these values in the formula above

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

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Here, we consider C = (4,3); D = (3,0)

Here,

$(x_1,y_1) = C(4,3)$

$(x_2,y_2) = D (3,0)$

Substitute these values in the formula above

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Lastly;

Calculating DA

Here, we consider C = (4,3); D = (3,0)

Here,

$(x_1,y_1) = D (3,0)$

$(x_2,y_2) = A (0,1)$

Substitute these values in the formula above

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$DA = \sqrt{(3)^2 + (- 1)^2}$

$DA = \sqrt{9 + 1}$

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Divide both sides by $\sqrt{10}$

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