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4 years ago

A dog groomer could clean four dogs in an hour how many could they clean in 5/6 of an hour

Mathematics

1 answer:

Alex Ar [27]4 years ago

7 0

Answer:

3,333...

Step-by-step explanation: U can do a rule of three

4 ---- 1

x ---- 5/6

4 x 5/6 = 20/6

20/6 = 3,33...

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Solve the equation for all real values of x.<br> cosxtanx - 2 cos x=-1

IceJOKER [234]

Solution to equation $cosxtanx - 2 cos^2 x=-1$ for all real values of x is $x=2k\pi + \frac{\pi}{6} , x=2k\pi + \frac{5\pi}{6}$ .

<u>Step-by-step explanation:</u>

Here we have , $cosxtanx - 2 cos^2 x=-1$ . Let's solve :

⇒ $cosxtanx - 2 cos^2 x=-1$

⇒ $cosx(\frac{sinx}{cosx}) - 2 cos^2 x=-1$

⇒ $sinx = 2 cos^2 x-1$

⇒ $sinx = 2 (1-sin^2x)-1$

⇒ $sinx = 1-2sin^2x$

⇒ $2sin^2x+sinx-1=0$

By quadratic formula :

⇒ $sinx = \frac{-b \pm \sqrt{b^2-4ac} }{2a}$

⇒ $sinx = \frac{-1 \pm \sqrt{1^2-4(2)(-1)} }{2(2)}$

⇒ $sinx = \frac{-1 \pm3}{4}$

⇒ $sinx = \frac{1}{2} , sinx =-1$

⇒ $sinx = sin\frac{\pi}{6} , sinx = sin\frac{3\pi}{2}$

⇒ $x=\frac{\pi}{6} , x=\frac{3\pi}{2}$

But at $x=\frac{3\pi}{2}$ we have equation undefined as $cos\frac{3\pi}{2}=0$ . Hence only solution is :

⇒ $x=\frac{\pi}{6}$

Since , $sin(\pi -x)=sinx$

⇒ $x=\pi -\frac{\pi}{6} = \frac{5\pi}{6}$

Now , General Solution is given by :

⇒ $x=2k\pi + \frac{\pi}{6} , x=2k\pi + \frac{5\pi}{6}$

Therefore , Solution to equation $cosxtanx - 2 cos^2 x=-1$ for all real values of x is $x=2k\pi + \frac{\pi}{6} , x=2k\pi + \frac{5\pi}{6}$ .

3 0

3 years ago

Sam needs 7 1/2 cups of orange juice to make punch for a group of her friends. She only has 5 1/3 cups. Write and solve an equat

Solnce55 [7]

Answer:

Equation is $x+\frac{16}{3}=\frac{15}{2}$ where $x$ denotes number of cups of orange juice needed by Sam.

$x=\frac{13}{6}$

Step-by-step explanation:

Let $x$ denotes number of cups of orange juice needed by Sam.

Number of cups needed to make punch $=7\frac{1}{2} =\frac{15}{2}$

Number of cups with Sam $=5\frac{1}{3}=\frac{16}{3}$

Therefore,

$x+\frac{16}{3}=\frac{15}{2}\\\\x= \frac{15}{2}-\frac{16}{3}\\\\x=\frac{45-32}{6}\\\\x=\frac{13}{6}$

4 0

3 years ago

Consider the function below. f(x) = ln(x4 + 27) (a) Find the interval of increase. (Enter your answer using interval notation.)

andrezito [222]

Answer:

a) The function is constantly increasing and is never decreasing

b) There is no local maximum or local minimum.

Step-by-step explanation:

To find the intervals of increasing and decreasing, we can start by finding the answers to part b, which is to find the local maximums and minimums. We do this by taking the derivatives of the equation.

f(x) = ln(x^4 + 27)

f'(x) = 1/(x^2 + 27)

Now we take the derivative and solve for zero to find the local max and mins.

f'(x) = 1/(x^2 + 27)

0 = 1/(x^2 + 27)

Since this function can never be equal to one, we know that there are no local maximums or minimums. This also lets us know that this function will constantly be increasing.

6 0

3 years ago

Which statement BEST explains the role of DNA in the growth and specialization of an organisms?

prisoha [69]

A. DNA stores genetic information
DNA is located inside the nucleus of a cell which holds a person's genetic information

7 0

3 years ago

Some help me please help me please help me please help me please help me please help me please help me please help me please

Svetllana [295]

Answer:

2mph

Step-by-step explanation: