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2 years ago

Line v has a slope of –8/7. Line W is perpendicular to V. What is the slope of line w?

Mathematics

1 answer:

blondinia [14]2 years ago

7 0

Answer:

$\frac{7}{8}$

Step-by-step explanation:

The slope of a perpendicular line is opposite and reciprocal to the original slope. Flip the fraction and change the sign, and you're all set!

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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

Find the area of the figure. Round to the nearest hundredth when necessary.

Delvig [45]

Answer:

215.20 ft^2

Step-by-step explanation:

The figure has 2 semi-circles.

First we find the area of each circle using the formula $\pi r^{2}$ because that is the area formula for a circle.

The semi-circle to the left gives the diameter which is 22 feet. The radius would be half the diameter thus r=11 for semi-circle one.

Then we are to find the diameter of the second semi-circle. Given the entire length to be 30 feet, 30-22 leaves us with 8 feet as its diameter thus r=4.

Left: r=11

Right: r=4

Then, plugging both into the formula for area of a circle, we get

Left: 380.1327

Right: 50.26548

We must divide each by two because we are only looking for semi-circle which is exactly half the area of a full circle.

Then,

Left: 190.066

Right: 25.1327

190.066+ 25.1327= 215.199 = 215.2ft^2

8 0

3 years ago

The average time a subscriber spends reading The Wall Street Journal is 49 minutes (The Wall Street Journal Subscriber Study). A

erica [24]

Answer:

$P(X>60)=P(\frac{X-\mu}{\sigma}>\frac{60-\mu}{\sigma})=P(Z>\frac{60-49}{16})=P(z>0.6875)$

And we can find the probability with the complement rule and the normal standard distirbution and we got:

$P(z>0.6875)=1-P(z$

Step-by-step explanation:

Let X the random variable that represent the time spent reading of a population, and for this case we know the distribution for X is given by:

$X \sim N(49,16)$

Where $\mu=49$ and $\sigma=16$

We are interested on this probability

$P(X>60)$

And we can use the z score formula given by:

$z=\frac{x-\mu}{\sigma}$

Using this formula we got:

$P(X>60)=P(\frac{X-\mu}{\sigma}>\frac{60-\mu}{\sigma})=P(Z>\frac{60-49}{16})=P(z>0.6875)$

And we can find the probability with the complement rule and the normal standard distirbution and we got:

$P(z>0.6875)=1-P(z$

5 0

3 years ago

Find the midpoint of A and B where A has coordinates (8,5)<br> and B has coordinates (3, 7).

Mama L [17]

Answer:

Step-by-step explanation:

Average of x-coordinates = (8+3)/2 = 5.5

Average of y-coordinates = (5+7)/2 = 6

Midpoint at (5.5,6)

5 0

3 years ago

HELP PLEASE ILL MAKE YOU THE BRAINIEST What is the area of the regular polygon?

Fed [463]

Based on the calculations, the area of this regular polygon (hexagon) is equal to 24 m².

<h3>How to calculate the area of a regular polygon?</h3>

Mathematically, the area of a regular polygon can be calculated by using this formula:

Area = (n × s × a)/2

<u>Where:</u>

n is the number of sides.

s is the side length.

a is the apothem.

<u>Note:</u> The apothem of a regular polygon is half the length of one side.

Therefore, Length = 2 × 2 = 4 meter.

Substituting the parameters into the formula, we have;

Area = (6 × 4 × 2)/2

Area = 48/2

Area = 24 m².

Read more on polygon here: brainly.com/question/16691874

#SPJ1

4 0

2 years ago