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2 years ago

Find the magnitude and direction (in degrees) of the vector. (Assume 0° ≤ < 360°.)

1 answer:

3 0

$6i~~ + ~~2\sqrt{3}j\implies < \stackrel{a}{6}~~,~~\stackrel{b}{2\sqrt{3}} > \\\\[-0.35em] ~\dotfill\\\\ \stackrel{magnitude}{\sqrt{a^2+b^2}}\implies \sqrt{6^2+(2\sqrt{3})^2}\implies \sqrt{36+(2^2\cdot 3)}\implies \sqrt{36+12}\implies \sqrt{48} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{direction}{tan^{-1}\left( \cfrac{b}{a}\right)}\implies tan^{-1}\left( \cfrac{2\sqrt{3}}{6} \right)\implies tan^{-1}\left( \cfrac{\sqrt{3}}{3} \right) \\\\\\ tan^{-1}\left( \cfrac{1}{\sqrt{3}} \right)\implies 30^o$

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Gabriela Mistral was a poet, diplomat, teacher and humanitarian. Each week she worked a certain amount of days as a poet diploma

Ipatiy [6.2K]

Answer:

Gabriela Mistral works as a humanitarian for $8$ days.

Step-by-step explanation:

Gabriela Mistral was a poet, diplomat, teacher and humanitarian such that each week she worked a certain amount of days as a poet diplomat teacher and humanitarian.

Ratio is $1:1:3:2$

Let $x$ denotes total number of days Gabriela Mistral work.

As she works 12 days as a teacher,

$\frac{3}{7}x=12\\ x=\frac{7}{3}(12)\\ x=28$

Total number of days $=x=28$

So,

she works as a humanitarian for $\frac{2}{7}x=\frac{2}{7}(28)=8$ days.

6 0

3 years ago

3The frequency (in Hz) of a vibrating violin string is given by f = 1 2L s T rho where L is the length of the string (in meters)

bagirrra123 [75]

Answer:

(i) $\dfrac{df}{dL}=-\dfrac{1}{2L^2}\sqrt{\dfrac{T}{\rho}}$

(ii) $\dfrac{df}{dT}=\dfrac{1}{4L\sqrt{T\rho}}$

(iii) $\dfrac{df}{d\rho}=-\dfrac{\sqrt{T}}{4L\rho^{-\frac{3}{2}}}}$

Step-by-step explanation:

Let as consider the frequency (in Hz) of a vibrating violin string is given by

$f=\dfrac{1}{2L}\sqrt{\dfrac{T}{\rho}}$

(i)

Differentiate f with respect L (assuming T and rho are constants).

$\dfrac{df}{dL}=\dfrac{d}{dL}\dfrac{1}{2L}\sqrt{\dfrac{T}{\rho}}$

Taking out constant terms.

$\dfrac{df}{dL}=\dfrac{1}{2}\sqrt{\dfrac{T}{\rho}}\dfrac{d}{dL}\dfrac{1}{L}$

$\dfrac{df}{dL}=\dfrac{1}{2}\sqrt{\dfrac{T}{\rho}}(-\dfrac{1}{L^2})$

$\dfrac{df}{dL}=-\dfrac{1}{2L^2}\sqrt{\dfrac{T}{\rho}}$

(ii)

Differentiate f with respect T (assuming L and rho are constants).

$\dfrac{df}{dT}=\dfrac{d}{dT}\dfrac{1}{2L}\sqrt{\dfrac{T}{\rho}}$

Taking out constant terms.

$\dfrac{df}{dT}=\dfrac{1}{2L}\sqrt{\dfrac{1}{\rho}}\dfrac{d}{dT}\sqrt{T}}$

$\dfrac{df}{dT}=\dfrac{1}{2L}\sqrt{\dfrac{1}{\rho}}(\dfrac{1}{2\sqrt{T}})$

$\dfrac{df}{dT}=\dfrac{1}{4L\sqrt{T\rho}}$

(iii)

Differentiate f with respect rho (assuming L and T are constants).

$\dfrac{df}{d\rho}=\dfrac{d}{d\rho}\dfrac{1}{2L}\sqrt{\dfrac{T}{\rho}}$

Taking out constant terms.

$\dfrac{df}{d\rho}=\dfrac{\sqrt{T}}{2L}\dfrac{d}{d\rho}(\rho)^{-\frac{1}{2}}}$

$\dfrac{df}{d\rho}=\dfrac{\sqrt{T}}{2L}(-\dfrac{1}{2}(\rho)^{-\frac{3}{2}}})$

$\dfrac{df}{d\rho}=-\dfrac{\sqrt{T}}{4L\rho^{-\frac{3}{2}}}}$

4 0

3 years ago

What is the number 21 a prime or composite

Marrrta [24]

$21|3 \\ 7|7 \\ 1 \\ \\ 21=3*7 \\ \\ D_{21}= \{1;3;7;21\} \\ \\ it \ means \ that \ 21 \ is \ composite \ number$

7 0

3 years ago

Solve for z : 4z-6/4=3z+1

ruslelena [56]

Note the equal sign, what you do to one side, you do to the other side. Isolate the variable z.

First, subtract 3z and add 6/4 to both sides

4z (-3z) - 6/4 (+6/4) = 3z (-3z) + 1 (+6/4)

4z - 3z = 1 + 6/4

Simplify. Note that 1 = 4/4.

z = 4/4 + 6/4

Simplify. Combine like terms

z = 10/4

Simplify. Change the improper fraction into mixed fraction and simplify.

z = 10/4 = 2 2/4 = 2 1/2

7 0

3 years ago

Please help me quick

Stolb23 [73]

Answer:

I belive it has no x intercepts

6 0

3 years ago

Read 2 more answers