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2 years ago

Please help me. please please please

Mathematics

1 answer:

Anastasy [175]2 years ago

8 0

Answer:

$\frac{27}{8}$

Step-by-step explanation:

$\left(\frac{16}{81}\right)^{\frac{-3}{4}}=\frac{16^{\frac{-3}{4}}}{81^{\frac{-3}{4}}}$

$=\frac{2^{-3} }{3^{-3} }$

$=\frac{\frac{1}{8}}{\frac{1}{27}}$

$=\frac{1*27}{8*1}$

$=\frac{27}{8}$

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Two trains leave a town at the same time heading in opposite directions. One train is traveling 12 mph faster than the other. Af

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Two trains leave a town at the same time heading in opposite directions. One train is traveling 12 mph faster than the other. After two hours, they are 232 miles apart. What is the average speed of each train?

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3 years ago

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Susie is paying $555.26 every month for her $150,000 mortgage. If this is a 30 year mortgage, how much interest will she pay ove

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$49,893.6

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2 years ago

Determine the salary per pay period. Law Clerk: $48,950; weekly. Round to the nearest Hundredth.

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2 years ago

Calculate the area of the triangle with the following vertices (3, -7), (6, 4), (-2, -3)

Monica [59]

Answer:

$\boxed{\mathsf{A} \triangle = \red{\dfrac{67}{2}u.a}}$

Step-by-step explanation:

Let's follow up with the solution. Considering a triangle with the vertices $\mathsf{A(x_A, y_A)}$ , $\mathsf{B(x_B, y_B)}$ and $\mathsf{C(x_C, y_C)}$ , have a look at the representation in the cartesian plan.

From this representation we can say that the area (A) of a triangle through the knowledge of <u>analytical geometry</u> is given by the determinant of the vertices divided by two, mathematically,

$\mathsf{A} \triangle = \dfrac{\left| \begin{array}{ccc} \mathsf{x_A} & \mathsf{y_A }& 1 \\ \mathsf{x_B} & \mathsf{ y_B} & 1 \\ \mathsf{ x_C} & \mathsf{ y_C} & 1 \end{array} \right|}{2}$

So, applying this knowledge we're going to have,

$\mathsf{A} \triangle = \dfrac{\left| \begin{array}{ccc} 3 & -7 & 1 \\ 6 & 4 & 1 \\ -2 & -3 & 1 \end{array} \right|}{2}$

$\mathsf{A} \triangle = \dfrac{1}{2}\left[ \left.\begin{array}{ccc} 3 & -7 & 1 \\ 6 & 4 & 1 \\ -2& -3 & 1 \end{array} \right| \begin{array}{cc} 3 & -7 \\ 6 & 4 \\ -2 & -3 \end{array} \right]$

$\mathsf{A} \triangle = \dfrac{12 + 14 - 18 - (-8 - 9 - 42)}{2}$

$\red{\mathsf{A} \triangle = \dfrac{67}{2} = 33,5u.a}$

Hope you enjoy it, see ya!)

$\green{\mathsf{FROM}}:$ Mozambique, Maputo – Matola City – T-3

DavidJunior17

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3 years ago

Find the multiplicative inverse of 6 + 2i

Marina CMI [18]

If you're using the app, try seeing this answer through your browser: brainly.com/question/2774989

________________

Find the multiplicative inverse of

$\mathsf{z=6+2i}$

________

The inverse multiplicative of $\mathsf{z=a+bi}$ is

$\mathsf{\dfrac{1}{z}}\\\\\\
=\mathsf{\dfrac{1}{a+bi}\qquad\quad(a\ne 0~~and~~b\ne 0)}\\\\\\
=\mathsf{\dfrac{1}{a+bi}\cdot \dfrac{a-bi}{a-bi}}\\\\\\
=\mathsf{\dfrac{1\cdot (a-bi)}{(a+bi)\cdot (a-bi)}}\\\\\\
=\mathsf{\dfrac{a-bi}{a^2-\,\diagup\hspace{-10}abi+\,\diagup\hspace{-10}abi-(bi)^2}}$

$=\mathsf{\dfrac{a-bi}{a^2-b^2\cdot i^2}}\\\\\\
=\mathsf{\dfrac{a-bi}{a^2-b^2\cdot (-1)}}\\\\\\
=\mathsf{\dfrac{a-bi}{a^2+b^2}}\\\\\\\\
\therefore~~\mathsf{\dfrac{1}{a+bi}=\dfrac{a}{a^2+b^2}-\dfrac{b}{a^2+b^2}\,i\qquad\quad\checkmark}$

________

For this question,

$\mathsf{z=6+2i}$

So,

$\mathsf{\dfrac{1}{z}}\\\\\\
=\mathsf{\dfrac{1}{6+2i}}\\\\\\
=\mathsf{\dfrac{6}{6^2+2^2}-\dfrac{2}{6^2+2^2}\,i}\\\\\\
=\mathsf{\dfrac{6}{36+4}-\dfrac{2}{36+4}\,i}\\\\\\
=\mathsf{\dfrac{6}{40}-\dfrac{2}{40}\,i}$

$\therefore~~\mathsf{\dfrac{1}{z}=\dfrac{3}{20}-\dfrac{1}{20}\,i}\quad\longleftarrow\quad\textsf{this is the answer.}$

I hope this helps. =)

6 0

3 years ago

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Please help me. please please please​

Please help me. please please please