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3 years ago

Look at the image below

Mathematics

2 answers:

Nutka1998 [239]3 years ago

7 0

The answer should be 3619.1km³

xeze [42]3 years ago

3 0

Answer:

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Is this triangle a SSS, SAS, ASA, AAS, or HL?

Harman [31]

Answer:

sss

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

Someone plz help me plz

zheka24 [161]

Answer:

3(24+56)

Step-by-step explanation:

3 times sum of 24 and 56 so your adding 24 and 56 and multiplying it by 3

3(24+56)

8 0

3 years ago

Read 2 more answers

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 is the slope and y intercept of -2x +3y=-9

attashe74 [19]

Answer:

m = 2/3

b = -3

Step-by-step explanation:

Rearrange the equation to slope-intercept form (y = mx + b).

x and y are points on the graph.

m is the slope.

b is the y-intercept.

Isolate "y". This means separating it from the other numbers.

-2x +3y = -9

-2x + 2x +3y = -9 + 2x Add 2x to both sides

3y = 2x - 9

3y/3 = 2x/3 - 9/3 Divide both sides by 3

y = 2x/3 - 9/3 Simplify

y = (2/3)x - 3

Think about which numbers and "m" and "b" now that the equation is in y = mx + b. Include the plus and minus signs.

m = 2/3

b = -3

8 0

3 years ago

What is the equation of the midline of the function f(x) = 5.6sin (2.6x - 4.2) - 9.1?

Iteru [2.4K]

Answer:

$f(x) = -9.1$

Step-by-step explanation:

The midline is set on $f(x) = -9.1$ , when the sine function is equal to zero, eliminating the effect from amplitude. The midline is a horizontal line. Hence, the equation of the midline is:

$f(x) = -9.1$

5 0

3 years ago