All categories

2 years ago

Evaluate the equation. H divided by 3 = 69 2/3

Mathematics

1 answer:

Strike441 [17]2 years ago

7 0

Answer:

138

Step-by-step explanation:

Do the inverse. 69 2/3 multiplied by 3 is 138.

You might be interested in

Which is greater 139/8 or 135/7

Keith_Richards [23]

139/8 = 17.375
135/7 = 19.285

135/7 is greater

8 0

4 years ago

Read 2 more answers

What is the perimeter and area

Arisa [49]

Is there a diagram or something to look at for this ...?

7 0

3 years ago

Read 2 more answers

Suppose u = (1,2,3), v = (2, -3, -4), and w = (1,0,-2). (a) Find u-2v + 3w. (b) Write the vector (3,4,5) as a linear combination

marishachu [46]

<h2>Answer with explanation:</h2>

We are given vectors u,v and w as follows:

$u=(1,2,3)\,\ v=(2,-3,-4),\ and\ w=(1,0,-2)$

(a)

Now we are asked to find the value of:

$u-2v+3w$

The value is calculated as follows:

$u-2v+3w=(1,2,3)-2(2,-3,-4)+3(1,0,-2)\\\\i.e.\\\\u-2v+3w=(1,2,3)+(-2\times 2,-2\times -3,-2\times -4)+(3\times 1,3\times 0,3\times -2)\\\\i.e.\\\\u-2v+3w=(1,2,3)+(-4,6,8)+(3,0,-6)\\\\i.e.\\\\u-2v+3w=(1-4+3,2+6+0,3+8-6)\\\\i.e.\\\\u-2v+3w=(0,8,5)$

Hence,

$u-2v+3w=(0,8,5)$

(b)

We are asked to represent (3,4,5) as a linear combination of u, v, and w.

Let:

$(3,4,5)=au+bv+cw$

$(3,4,5)=a(1,2,3)+b(2,-3,-4)+c(1,0,-2)$

i.e.

$(3,4,5)=(a,2a,3a)+(2b,-3b,-4b)+(c,0,-2c)\\\\i.e.\\\\(3,4,5)=(a+2b+c,2a-3b,3a-4b-2c)\\\\i.e.\\\\a+2b+c=3----------(1)$

$2a-3b=4-------------(2)$

$3a-4b-2c=5------------(3)$

on multiplying equation(1) by 2 an then adding equation (1) to equation (3)

$5a=11\\\\i.e.\\\\a=\dfrac{11}{5}$

on putting the value of a in equation (2) we get:

$2\times \dfrac{11}{5}-3b=4\\\\i.e.\\\\\dfrac{22}{5}-3b=4\\\\i.e.\\\\3b=\dfrac{22}{5}-4\\\\i.e.\\\\3b=\dfrac{2}{5}\\\\i.e.\\\\b=\dfrac{2}{15}$

Now on putting the value of a and b in equation (1)

$\dfrac{11}{5}+2\times \dfrac{2}{15}+c=3\\\\i.e.\\\\\dfrac{11}{5}+\dfrac{4}{15}+c=3\\\\i.e.\\\\c=3-\dfrac{11}{5}-\dfrac{4}{15}\\\\i.e.\\\\c=\dfrac{3\times 15-11\times 3-4}{15}\\\\i.e.\\\\c=\dfrac{45-33-4}{15}\\\\i.e.\\\\c=\dfrac{8}{15}$