If y varies directly as x, and y = 25 when x = 5, find y when x = 25.

Solve 2cos x+2cos 2x=0 on the interval [0,2pi)

rjkz [21]

$2cosx+2cos2x=0 \\ -2sin^2x+2cos^2x+2cosx=0 \\ -2(1-cos^2x)+2cos^2x+2cosx=0 \\ -2+2cos^2x+2cos^2x+2cosx=0 \\ 4cos^2x+2cosx-2=0 \\ t=cos x \\ 4t^2+2t-2=0 \\ \Delta=4+32=36 \\ t_1= \frac{-2-6}{8}=-1 \\ t_2= \frac{-2+6}{8}= \frac{1}{2} \\ cos x=-1 \lor cos x= \frac{1}{2} \\ x=-\pi \lor x= \frac{5\pi}{3}$

6 0

2 years ago

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Dorothy types 120 words per minute. How many words does Dorothy type in 1.75 minutes?

nirvana33 [79]

As you are looking for 1.75 minutes (or 105 seconds), the best thing to do is to find how many words she can type in 0.25 minutes (this is a quarter, and you can divide 1.75 by this). To find a quarter, you have to divide by 4, 120/4= 30. Therefore, every 15 seconds, Dorothy can type 30 words. As you've got 105 seconds, divide this by 15, and this gives you 7. Then multiply 30 by 7, and this gives you 210.
Dorothy can type 210 words in 1.75 minutes
Hope this helps :)

8 0

3 years ago

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8.4 divided by 10 = ?

ASHA 777 [7]

Answer:

0.84

If you're looking for a percentage it'd be 84%

Step-by-step explanation:

7 0

3 years ago

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Deidre is planting tulips in her garden, and she has 44 red bulbs and 44 purple bulbs to plant in one row. What is the probabili

Mekhanik [1.2K]

Answer:

$P=7.62*10^{-26}$

Step-by-step explanation:

From the question we are told that:

Available plants:

44 red bulbs

44 purple bulbs

Generally the equation for Total possible arrangement is mathematically given by

$n= 88!/(44!*44!)$

$n=2.6*10^{25}$

Since

Its either

All 44 red bulbs and All 44 purple bulbs next to each other in one row

OR

All 44 purple bulbs and All 44 Red bulbs next to each other in one row

Therefore

Probability is

$P=\frac{2}{2.6*10^{25}}$

$P=7.62*10^{-26}$

8 0

2 years ago

5. Select ALL of the following expressions that are linear functions (they do not need to be in slope-intercept form).

Anon25 [30]

Answer:

The following are the LINEAR functions.

$2x\:+\:4\:=\:3x\:-\:8$

$y = 3x - 2$

$1$

$3x\:+\:-y\:=\:24$

Step-by-step explanation:

We know that linear functions are the equations with a straight line graph in an XY plane.

Also, a linear function is a function of the form

$f(x)=mx+b$

where m is the slope and b is the y-intercept. The only power of the variable is 1.

So, from the given expressions we can determine that:

1) $y^2=\:5x\:+2$

$y^2=\:5x\:+2$ is NOT a linear function because the power of y is 2, hence the graph won't be a straight line. Therefore, it is not a linear function

2) $2x\:+\:4\:=\:3x\:-\:8$

$2x\:+\:4\:=\:3x\:-\:8$

$x=12$

This is a linear equation is an equation of a straight line, written in one variable. The only power of the variable is 1

3) $y = 3x - 2$

$y = 3x - 2$ is a linear function because it is of the form $f(x)=mx+b$ and the power of its x and y variables is 1. Hence, the function has a straight line graph.

4) $y\:+\:x^2\:=\:12$

$y\:+\:x^2\:=\:12$ is NOT a linear function because the power of x is 2, hence the graph won't be a straight line. Therefore, it is not a linear function.

5) $y\:=\:x^2\:+\:2x$

$y\:=\:x^2\:+\:2x$ is NOT a linear function because the power of x is 2, hence the graph won't be a straight line. Therefore, it is not a linear function.

6) $1$

$1$ is a constant function and a constant function is also considered linear in this context, as it is a polynomial of degree $0$ or is the $0$ polynomial.

7) $3x\:+\:-y\:=\:24$

$3x\:+\:-y\:=\:24$ is a linear function as the power of its x and y variables is 1. Hence, the function has a straight line graph. Therefore, it is a linear function.

In a summary, the following are the LINEAR functions.

$2x\:+\:4\:=\:3x\:-\:8$

$y = 3x - 2$

$1$

$3x\:+\:-y\:=\:24$

7 0

2 years ago