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2 years ago

1. Which monomial has the highest degree? A 18a5 B 12ab C 9ab D 6abaca

Mathematics

1 answer:

8_murik_8 [283]2 years ago

5 0

Question:Which monomial has the highest degree? Answer:

The sum of the exponents of the variables in the monomial. This must be positive and cannot be a fraction or decimal. i think <u><em>A 18a5 </em></u>is the answer please do tell me if i am wrong it took me a bit to get this answer have a nice weekend

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Match each vector operation with its resultant vector expressed as a linear combination of the unit vectors i and j.

Cloud [144]

Answer:

3u - 2v + w = 69i + 19j.

8u - 6v = 184i + 60j.

7v - 4w = -128i + 62j.

u - 5w = -9i + 37j.

Step-by-step explanation:

Note that there are multiple ways to denote a vector. For example, vector u can be written either in bold typeface "u" or with an arrow above it $\vec{u}$ . This explanation uses both representations.

$\displaystyle \vec{u} = \langle 11, 12\rangle =\left(\begin{array}{c}11 \\12\end{array}\right)$ .

$\displaystyle \vec{v} = \langle -16, 6\rangle= \left(\begin{array}{c}-16 \\6\end{array}\right)$ .

$\displaystyle \vec{w} = \langle 4, -5\rangle=\left(\begin{array}{c}4 \\-5\end{array}\right)$ .

There are two components in each of the three vectors. For example, in vector u, the first component is 11 and the second is 12. When multiplying a vector with a constant, multiply each component by the constant. For example,

$3\;\vec{v} = 3\;\left(\begin{array}{c}11 \\12\end{array}\right) = \left(\begin{array}{c}3\times 11 \\3 \times 12\end{array}\right) = \left(\begin{array}{c}33 \\36\end{array}\right)$ .

So is the case when the constant is negative:

$-2\;\vec{v} = (-2)\; \left(\begin{array}{c}-16 \\6\end{array}\right) =\left(\begin{array}{c}(-2) \times (-16) \\(-2)\times(-6)\end{array}\right) = \left(\begin{array}{c}32 \\12\end{array}\right)$ .

When adding two vectors, add the corresponding components (this phrase comes from Wolfram Mathworld) of each vector. In other words, add the number on the same row to each other. For example, when adding 3u to (-2)v,

$3\;\vec{u} + (-2)\;\vec{v} = \left(\begin{array}{c}33 \\36\end{array}\right) + \left(\begin{array}{c}32 \\12\end{array}\right) = \left(\begin{array}{c}33 + 32 \\36+12\end{array}\right) = \left(\begin{array}{c}65\\48\end{array}\right)$ .

Apply the two rules for the four vector operations.

$\displaystyle \begin{aligned}3\;\vec{u} - 2\;\vec{v} + \vec{w} &= 3\;\left(\begin{array}{c}11 \\12\end{array}\right) + (-2)\;\left(\begin{array}{c}-16 \\6\end{array}\right) + \left(\begin{array}{c}4 \\-5\end{array}\right)\\&= \left(\begin{array}{c}3\times 11 + (-2)\times (-16) + 4\\ 3\times 12 + (-2)\times 6 + (-5) \end{array}\right)\\&=\left(\begin{array}{c}69\\19\end{array}\right) = \langle 69, 19\rangle\end{aligned}$

Rewrite this vector as a linear combination of two unit vectors. The first component 69 will be the coefficient in front of the first unit vector, i. The second component 19 will be the coefficient in front of the second unit vector, j.

$\displaystyle \left(\begin{array}{c}69\\19\end{array}\right) = \langle 69, 19\rangle = 69\;\vec{i} + 19\;\vec{j}$ .

$\displaystyle \begin{aligned}8\;\vec{u} - 6\;\vec{v} &= 8\;\left(\begin{array}{c}11\\12\end{array}\right) + (-6) \;\left(\begin{array}{c}-16\\6\end{array}\right)\\&=\left(\begin{array}{c}88+96\\96 - 36\end{array}\right)\\&= \left(\begin{array}{c}184\\60\end{array}\right)= \langle 184, 60\rangle\\&=184\;\vec{i} + 60\;\vec{j} \end{aligned}$ .

$\displaystyle \begin{aligned}7\;\vec{v} - 4\;\vec{w} &= 7\;\left(\begin{array}{c}-16\\6\end{array}\right) + (-4) \;\left(\begin{array}{c}4\\-5\end{array}\right)\\&=\left(\begin{array}{c}-112 - 16\\42+20\end{array}\right)\\&= \left(\begin{array}{c}-128\\62\end{array}\right)= \langle -128, 62\rangle\\&=-128\;\vec{i} + 62\;\vec{j} \end{aligned}$ .

$\displaystyle \begin{aligned}\;\vec{u} - 5\;\vec{w} &= \left(\begin{array}{c}11\\12\end{array}\right) + (-5) \;\left(\begin{array}{c}4\\-5\end{array}\right)\\&=\left(\begin{array}{c}11-20\\12+25\end{array}\right)\\&= \left(\begin{array}{c}-9\\37\end{array}\right)= \langle -9, 37\rangle\\&=-9\;\vec{i} + 37\;\vec{j} \end{aligned}$ .

7 0

3 years ago

Estimate 17.5 times 8.4

aniked [119]

Answer:

147/150

Step-by-step explanation:

7 0

3 years ago

You have driving lessons every third day in swimming lessons every fifth day today you have both classes how many days will you

hjlf

To find the answer, you need to find the LCM of 3 and 5. It's 15, meaning that every 15 days, you will have both lessons on the same day. Have an awesome day! :)

8 0

2 years ago

20.) A=49.23 degrees, c=54.8Solve the right triangle. Express angles in decimal degrees.

vivado [14]

$\begin{gathered} a=41.50 \\ b=35.78 \\ B=40.76\text{ \degree} \\ \end{gathered}$

Explanation

Step 1

a) let

$\begin{gathered} A=49.23\text{ \degree} \\ c=54.8\text{ \degree} \end{gathered}$

b) b value

to find the measure of side b we can use cosine function

$\begin{gathered} cos\theta=\frac{adjacent\text{ side}}{hypotenuse} \\ replace \\ cos\text{ 49.23=}\frac{b}{54.8} \\ b=54.8*cos49.23 \\ b=35.78 \end{gathered}$

c) angle B

to find the measure of Angle B we can use sine function

$\begin{gathered} sin\theta=\frac{opposite\text{ side}}{hypotenuse} \\ replace \\ sin\text{ B=}\frac{35.78}{54.8} \\ sin\text{ B= 0.65}\Rightarrow inverse\text{ function to isolate B} \\ B=\sin^{-1}(0.65) \\ B=40.76 \end{gathered}$

d) side a

$\begin{gathered} sin\theta=\frac{opposite\text{ side}}{hypotenuse} \\ sin\text{ A=}\frac{a}{c}=\frac{\placeholder{⬚}}{\placeholder{⬚}} \\ sin\text{ 49.23=}\frac{a}{54.8} \\ multiply\text{ both sides by 54.8} \\ 54.8s\imaginaryI n\text{49.23=}\frac{a}{54.8}*54.8 \\ 41.50=a \end{gathered}$

so, the answer is

$\begin{gathered} a=41.50 \\ b=35.78 \\ B=40.76\text{ \degree} \\ \end{gathered}$

I hope this helps you

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11 months ago

Convert 2.4 hours into minutes?

Nikolay [14]

<h2>Answer:</h2><h2>C. 144 Minutes </h2><h2></h2><h2>Hope this helps!!</h2>

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3 years ago