<img src="https://tex.z-dn.net/?f=s%20-%20a%20%3D%20%20%20%5Csqrt%7Bab%20%2B%20t%20%7B%20%5C%5C%20t%7D%5E%7B2%7D%20%7D%20" id="T

All categories

3 years ago

exFormula1" title="s - a = \sqrt{ab + t { \\ t}^{2} } " alt="s - a = \sqrt{ab + t { \\ t}^{2} } " align="absmiddle" class="latex-formula">

Mathematics

1 answer:

murzikaleks [220]3 years ago

7 0

Step-by-step explanation:

ehehehehehehehhehehehe

You might be interested in

The vector (a) is a multiple of the vector (2i +3j) and (b) is a multiple of (2i+5j) The sum (a+b) is a multiple of the vector (

kow [346]

Answer:

$\|a\| = 5\sqrt{13}$ .

$\|b\| = 3\sqrt{29}$ .

Step-by-step explanation:

Let $m$ , $n$ , and $k$ be scalars such that:

$\displaystyle a = m\, (2\, \vec{i} + 3\, \vec{j}) = m\, \begin{bmatrix}2 \\ 3\end{bmatrix}$ .

$\displaystyle b = n\, (2\, \vec{i} + 5\, \vec{j}) = n\, \begin{bmatrix}2 \\ 5\end{bmatrix}$ .

$\displaystyle (a + b) = k\, (8\, \vec{i} + 15\, \vec{j}) = k\, \begin{bmatrix}8 \\ 15\end{bmatrix}$ .

The question states that $\| a + b \| = 34$ . In other words:

$k\, \sqrt{8^{2} + 15^{2}} = 34$ .

$k^{2} \, (8^{2} + 15^{2}) = 34^{2}$ .

$289\, k^{2} = 34^{2}$ .

Make use of the fact that $289 = 17^{2}$ whereas $34 = 2 \times 17$ .

$\begin{aligned}17^{2}\, k^{2} &= 34^{2}\\ &= (2 \times 17)^{2} \\ &= 2^{2} \times 17^{2} \end{aligned}$ .

$k^{2} = 2^{2}$ .

The question also states that the scalar multiple here is positive. Hence, $k = 2$ .

Therefore:

$\begin{aligned} (a + b) &= k\, (8\, \vec{i} + 15\, \vec{j}) \\ &= 2\, (8\, \vec{i} + 15\, \vec{j}) \\ &= 16\, \vec{i} + 30\, \vec{j}\\ &= \begin{bmatrix}16 \\ 30 \end{bmatrix}\end{aligned}$ .

$(a + b)$ could also be expressed in terms of $m$ and $n$ :

$\begin{aligned} a + b &= m\, (2\, \vec{i} + 3\, \vec{j}) + n\, (2\, \vec{i} + 5\, \vec{j}) \\ &= (2\, m + 2\, n) \, \vec{i} + (3\, m + 5\, n) \, \vec{j} \end{aligned}$ .

$\begin{aligned} a + b &= m\, \begin{bmatrix}2\\ 3 \end{bmatrix} + n\, \begin{bmatrix} 2\\ 5 \end{bmatrix} \\ &= \begin{bmatrix}2\, m + 2\, n \\ 3\, m + 5\, n\end{bmatrix}\end{aligned}$ .

Equate the two expressions and solve for $m$ and $n$ :

$\begin{cases}2\, m + 2\, n = 16 \\ 3\, m + 5\, n = 30\end{cases}$ .

$\begin{cases}m = 5 \\ n = 3\end{cases}$ .

Hence:

$\begin{aligned} \| a \| &= \| m\, (2\, \vec{i} + 3\, \vec{j})\| \\ &= m\, \| (2\, \vec{i} + 3\, \vec{j}) \| \\ &= 5\, \sqrt{2^{2} + 3^{2}} = 5 \sqrt{13}\end{aligned}$ .

$\begin{aligned} \| b \| &= \| n\, (2\, \vec{i} + 5\, \vec{j})\| \\ &= n\, \| (2\, \vec{i} + 5\, \vec{j}) \| \\ &= 3\, \sqrt{2^{2} + 5^{2}} = 3 \sqrt{29}\end{aligned}$ .

6 0

3 years ago

What are linear equations? Explain In full depth please

jasenka [17]

Answer:

, a linear equation is an equation that may be put in the form where are the variables, and are the coefficients, which are often real numbers. The coefficients may be considered as parameters of the equation, and may be arbitrary expressions, provided they do not contain any of the variables.

Step-by-step explanation:

y= 2x+1 is a linear equation

4 0

3 years ago

Hcf 16 and 24 find ???

grin007 [14]

Answer:

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

Identify the terms of the expression 9a+4b-18

madreJ [45]

Hey there!

We may ask. What exactly is a term anyways.

Well, a term is a single number, a variable, or a number and a variable that would have to be multiply together. This is what a term would be.

Therefore, as we look above, we see the following equation.

9a+4b-18

18 is a term

4b is a term

9a is a term

This whole thing, would be called an expression, as this is expression something. Perhaps the amount of students who ate ice-cream at a football game, or something similar.

I hope you found this helpful! :)

6 0

3 years ago

Write and solve a proportion to answer the question.

Reptile [31]

Answer:

Step-by-step explanation:

p/100×25=12

p/4=12

(p/4)×4=12×4

p=48

I hope this makes sense

8 0

3 years ago