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2 years ago

In Tim's garden, the flowers are only red, white, yellow and blue

Mathematics

2 answers:

goldenfox [79]2 years ago

7 0

What question goes with this?

Damm [24]2 years ago

4 0

Are you looking for probability?

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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

The sides of a triangle are 3x+ 2, 6x, and 5x. Find the expression to represent the perimeter. To find the perimeter, we ADD the

frosja888 [35]

Answer:

14x + 2

Step-by-step explanation:

Perimeter = sum of the measures of each side

If a triangle has side lengths of 3x+ 2, 6x, and 5x then the perimeter of that triangle is equal to 3x + 2 + 6x + 5x

Notice that the expression 3x + 2 + 6x + 5x has similar terms so to get the simplist version of the perimeter we would simply combine like terms

3x + 6x + 5x = 14x

The perimeter would = 14x + 2

7 0

3 years ago

Read 2 more answers

Company XYZ has 34 employees in the Finance Department, 45 technicians, and 32 in the Engineering Department. The HR Department

Crank

Answer:

66.7%

Step-by-step explanation:

The total number of complaints were:

5 + 3 + 7 = 15

The percent that came from either technicians or the Finance Department is:

(5 + 3) / 15 × 100% = 66.7%

7 0

3 years ago

Plz help asappppp I’ll give brainliest

Elena L [17]

Answer: c I think

Step-by-step explanation:

7 0

3 years ago

Jina and her husband are each starting a saving plan. Jina will initially set aside $650 and then add $135 every month to the sa

Basile [38]

Step-by-step explanation:

If A=650+135N; and B=585N,

then A+B= 650+135N+585N=650+620N

T=720N+650

4 0

3 years ago