3

Mathematics

1 answer:

il63 [147K]3 years ago

5 0

Answer:

Step-by-step explanation:

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Kalon and his friend Marna own a chimney sweep service company. Working together, they can clean a chimney in 1 5/7 hours. If it

QveST [7]

The amount of work done by Kalon in an hour is equal to 1/4. This is based on his time to finish the job. Letting x be the number of hours Marna can finish the job alone will let her finish 1/x of the job in an hour. If their rates are added together and multiplied by the number of hours they worked together, the product should be one whole job.
(1/4 + 1/x)(1 5/7) = 1
The value of x is 3. Therefore, it will take 3 hours for Marna to clean the chimney alone.

6 0

2 years ago

Read 2 more answers

Find all solutions to the equation (sinx-cosx)^2=1

svetoff [14.1K]

Answer:

$x=\dfrac{\pi k}{2},\ k\in Z.$

Step-by-step explanation:

Simplify the equation $(\sin x-\cos x)^2=1:$

$\sin^2 x-2\sin x\cos x+\cos ^2x=1,\\ \\ (\sin^2x+\cos^2x)-2\sin x\cos x=1.\\$

Since

$\sin^2 x+\cos^2 x=1$

and

$2\sin x\cos x=\sin 2x,$

we have

$1-\sin 2x=1,\\ \\\sin 2x=0,\\ \\2x=\pi k,\ k\in Z,\\ \\x=\dfrac{\pi k}{2},\ k\in Z.$

8 0

3 years ago

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Write the equation of a line perpendicular to 9xplus7yequals6 that passes through the point (9,negative 7).

andrew11 [14]

$k:\ y=m_1x+b_1\\\\l:\ y=m_2x+b_2\\\\k\ ||\ l\iff m_1=m_2\\\\k\ \perp\ l\iff m_1m_2=-1$

We have:

$k:\ 9x+7y=6\ \ \ |-9x\\\\7y=-9x+6\ \ \ \ |:7\\\\y=-\dfrac{9}{7}x+\dfrac{6}{9}\to m_1=-\dfrac{9}{7}\\\\l:\ y=m_2x+b\\\\l\ \perp\ k\iff-\dfrac{9}{7}m_2=-1\ \ \ \ |\cdot\left(-\dfrac{7}{9}\right)\\\\m_2=\dfrac{7}{9}\to\ l:\ y=\dfrac{7}{9}x+b$