Can you help this plz

Mathematics

1 answer:

Angelina_Jolie [31]2 years ago

5 0

#1.) shade 4 boxes
#2.) its too dark to read # two

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Use the given transformation to evaluate the integral. 9 x − 3y 2x − y dA, R where R is the parallelogram enclosed by the lines

hichkok12 [17]

$\displaystyle\iint_R(9x-3y)(2x-y)\,\mathrm dA$

$\begin{cases}u=x-3y\\v=2x-y\end{cases}\implies\begin{cases}x=\frac{3v-u}5\\y=\frac{v-2u}5\end{cases}\implies\mathrm dA=|\det J|\,\mathrm du\,\mathrm dv$

where $J$ is the Jacobian matrix for the transformation,

$J=\begin{bmatrix}u_x&u_y\\v_x&v_y\end{bmatrix}=\begin{bmatrix}-\dfrac15&\dfrac35\\\\-\dfrac25&\dfrac15\end{bmatrix}\implies|\det J|=\dfrac15$

We have

$9x-3y=8x+x-3y=\dfrac85(3v-u)+u=\dfrac{24v-3u}5$

so that the integral is

$\displaystyle\frac1{25}\int_9^{10}\int_0^{10}(24v-3u)v\,\mathrm du\,\mathrm dv=\boxed{\frac{4051}5}$

5 0

3 years ago

Will mark brainliest if correct’

mixer [17]

Answer:

-1280

Step-by-step explanation:

Given a₁ = -10, n = 8, r =2

Required to find nᵗʰ term.

From the general formula: aₙ= a₁ (r)ⁿ⁻¹

Therefore nᵗʰ = -10(2)⁸⁻¹

= -10(2)⁷

= - 10(128)

= - 1280

7 0

2 years ago

Let's simplify

Zielflug [23.3K]

Step-by-step explanation:

Given

$= \frac{1.5 \times {10}^{4} \times 4.5 \times {10}^{3} }{2.5 \times 10 ^{2} } \\ = \frac{6.75 \times {10}^{4 + 3} }{2.5 \times {10}^{2} } \\ = \frac{6.75 \times {10}^{7} }{2.5 \times {10}^{2} } \\ = 2.7 \times {10}^{7 - 2} \\ = 2.7 \times {10}^{5}$