(28 POINTS) write the next three terms in the sequence.

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)

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

Hence, we have:

$(3,4,5)=\dfrac{11}{5}(1,2,3)+\dfrac{2}{15}(2,-3,-4)+\dfrac{8}{15}(1,0,-2)\\\\i.e.\\\\(3,4,5)=\dfrac{11}{5}u+\dfrac{2}{15}v+\dfrac{8}{15}w$

5 0

4 years ago

What is 2x-6+7=4x+4-2 equal to?

Hatshy [7]

Answer:

x=(-2)

Step-by-step explanation:

subtract 4x from 2x

-6+7=1 4-2=2 subtract 1 from 2

-2x=1 x=-2

5 0

3 years ago

Which expression represents the area of the base of the cone? A cone with diameter 12 inches, height 8 inches, and slant height

Wewaii [24]

Answer: (pi) (6 squared)

Step-by-step explanation:

Hi, the base area of a cone is a circle, so, to answer this question we have to apply the next formula:

Area of a circle: (pi) radius^2

The diameter (d) of a circle is equal to: 2 radius

So:

D = 2r

Replacing with the value given:

12 =2r

12/2=r

radius= 6 inches

Back with the Area formula:

A = (pi) 6^2

Feel free to ask for more if needed or if you did not understand something.

8 0

4 years ago

Briefly discuss the three combinations of variable types that can form bivariate data.

netineya [11]

Answer:

Step-by-step explanation:

from the word Bi "meaning two"

Bivariate data are two different variables obtained from the same population element. Bivariate data are used if the sampled data cannot be graphically displayed using a single variable.

To form a bivariate data, there are three combinations of variable

1. Both variables are qualitative i.e attribute in nature

2. Both variables are quantitative i.e numerical

3. One of them is qualitative whilee the other is quantitative

Qualitative data are data that are measure of type which could represent a name, colour,symbol. traits or characteristics

Quantitative data are data that can be counted, measured and expressed using numbers/

7 0

3 years ago

!!!! Will give brainlist !!!!

denis23 [38]

The correct answer is he would be at 80 ft

6 0

4 years ago

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