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3 years ago

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Mr. McGregor has discovered that a large dog can destroy his entire garden in 2 hours and that a small boy can do the same job i

n 1 hour. How long would it take the large dog and the small boy working together to destroy Mr McGregor's garden?

1 answer:

mash [69]3 years ago

6 0

Answer: -1

Step-by-step explanation:

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Find the value of x

Novay_Z [31]

Answer:

<em>x=3</em>

Step-by-step explanation:

<u>Angles and Lines</u>

We must recall:

The sum of the internal angles of a triangle is 180°
Two linear angles add up to 180°

The image shows a triangle and the extension of its base to form two linear angles.

Note from the triangle, angle R is what it takes to get to 180°:

$m\angle R=180-25x-(57+x)$

From the line SQ, angle R what it takes to get to 180°. Thus:

$m\angle R=180-45x$

Equating:

$180-25x-(57+x)=180-45x$

Subtracting 180 and simplifying:

$-25x-57-x=-45x$

$19x=57$

Dividing by 19:

x=3

4 0

2 years ago

Evaluate the spherical coordinate integral

expeople1 [14]

Rewrite the equations of the given boundary lines:

<em>y</em> = -<em>x</em> + 1 ==> <em>x</em> + <em>y</em> = 1

<em>y</em> = -<em>x</em> + 4 ==> <em>x</em> + <em>y</em> = 4

<em>y</em> = 2<em>x</em> + 2 ==> -2<em>x</em> + <em>y</em> = 2

<em>y</em> = 2<em>x</em> + 5 ==> -2<em>x</em> + <em>y</em> = 5

This tells us the parallelogram in the <em>x</em>-<em>y</em> plane corresponds to the rectangle in the <em>u</em>-<em>v</em> plane with 1 ≤ <em>u</em> ≤ 4 and 2 ≤ <em>v</em> ≤ 5.

Compute the Jacobian determinant for this change of coordinates:

$J=\begin{bmatrix}\frac{\partial u}{\partial x}&\frac{\partial u}{\partial y}\\\frac{\partial v}{\partial x}&\frac{\partial v}{\partial y}\end{bmatrix}=\begin{bmatrix}1&1\\-2&1\end{bmatrix}\implies|\det J|=3$

Rewrite the integrand:

$-3x+4y=-3\cdot\dfrac{u-v}3+4\cdot\dfrac{2u+v}3=\dfrac{5u+7v}3$

The integral is then

$\displaystyle\iint_R(-3x+4y)\,\mathrm dx\,\mathrm dy=3\iint_{R'}\frac{5u+7v}3\,\mathrm du\,\mathrm dv=\int_2^5\int_1^45u+7v\,\mathrm du\,\mathrm dv=\boxed{333}$

5 0

3 years ago

What is the equation of the following line? Be sure to scroll down first to see all answer options. (0,3) (3,0) A. y = -x + 3 B.

qaws [65]

The correct answer is Choice A.

If you plot the points on a graph, you will see that there is a slope of -1 and the y-intercept is (0, 3).

This matches the equation of y = -x + 3 in Choice A.

4 0

4 years ago

At a toy factory, toy cars are produced on an assembly line. It takes 8.216 seconds to attach the wheels. It takes 3.652 seconds

AlexFokin [52]

From what I think;

8.216secs - 1 wheel; 3.652- 1 hood
for I toy car with a wheel and hood the total time is 8.216+ 3.652 = 11.868secs
let x secs be the total time taken to put a wheel and hood for 42 cars
x secs = 42 cars × the total time for one car
x secs = 42× 11.868
x secs= 498.456 secs

8 0

3 years ago

Find the midpoint of the line segment joining the points (−2,−1) and (−8,4).

Temka [501]

Answer:

(-5, 1.5)

Step-by-step explanation:

(-2 ,-1) ; (-8 , 4)

Midpoint = $(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})\\\\$

$=(\frac{-2-8}{2}, \frac{-1+4}{2})\\\\=(\frac{-10}{2},\frac{3}{2})\\\\=(-5 , 1.5)$

8 0

3 years ago