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3 years ago

If 3 cot theta= 2, find the value of 2sin theta -3cos theta /2sin theta +3cos theta

Mathematics

1 answer:

sergeinik [125]3 years ago

5 0

Answer:

Step-by-step explanation:

Using the trigonometric identity

cotx = $\frac{cosx}{sinx}$

Given

3cotθ = 2 , then

3 $\frac{coso}{sino}$ = 2 ( multiply both sides by sinθ )

3cosθ = 2sinθ ( subtract 3cosθ from both sides )

2sinθ - 3cosθ = 0

Thus

$\frac{2sin0-3cos0}{2sin0+3cos0}$

= $\frac{0}{2sin0+3cos0}$

= 0

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A ball is thrown vertically in the air with a velocity of 90ft/s. Use the projectile formula h=−16t2+v0t to determine at what ti

Debora [2.8K]

Answer:

$t=1.7 \ sec\ , t=4.0\ sec$

Step-by-step explanation:

Vertical Throw

It refers to a situation where an object is thrown verticaly upwards with some inicial speed v_o and let in free air (no friction) until it completes its movement up and finally returns to the very same point of lauch. The only acting force is gravity

The projectile formula is given as

$h=-16t^2+v_0t$

where t is time in seconds, h is the height in feet and v is the speed in ft/sec

We are required to find the time t where h=120 ft, knowing $v_o=90\ ft/sec$

$-16t^2+90t=120$

Rearranging

$-16t^2+90t-120=0$

This is a second-degree equation which will be solved with the formula

$\displaystyle x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$\displaystyle x=\frac{-90\pm \sqrt{90^2-4(-16)(-120)}}{2(-16)}$

$\displaystyle x=\frac{-90\pm \sqrt{1380}}{-32}$

Two solutions are obtained

$\boxed{t=1.7 \ sec\ , t= 4.\ sec}$

Both solutions are possible because the ball actually is at 120 ft in its way up and then when going down

6 0

3 years ago

Read 2 more answers

How many square feet of out door carpet will we need for this hole

Vadim26 [7]

Hey! Let me help you on this one.

As you can see, this is a very complex shape, and this might confuse you at first. Don't fear, there is a very easy and fun way to solve it.

Take a closer look at the problem. Do you notice anything? It consists of few different shapes that might be much easier for you to find area of.

For example, as you can see on the image I have sent you, these are the shapes present in the figure.

On this image, only two types of figures are present - triangle and a rectangle. Both shapes have a very easy area formula.

Triangle - $S= \frac{a*b}{2}$

Rectangle - $S=a*b$

Using these formulas, let's find the area of this complex figure by solving for each individual shape, and then, adding everything together.

Triangle at the bottom has a side of 4 feet, and an unknown second side. We can find it by getting the difference of 12 feet and 8 feet.

Why you might ask? Well, if you look at it closer, the difference is exactly the length of the side we need.

$12-8=4$

Neat! It's four as well. Let's start solving for its area.

$S= \frac{4*4}{2}$
$S=8$

Area of the first triangle is 8 feet squared. Let's get into the second triangle. It's right above this one!

Length of its right side is 3 feet, and the length of the bottom side is the same as the one we found few steps back - four feet.

$S= \frac{4*3}{2}$
$S= 6$

Awesome! Area of the second triangle is 6 feet squared. Let's take a closer look at the last figure - rectangle.

$S=8*3$
$S=24$

Area of the rectangle is 24 feet squared. Done, we have all the areas of individual shapes. Let's add them together.

$24+6+8=38$

Answer: The area of this figure is 38 feet squared

5 0

4 years ago

Yes,I need help with another one of these , the number that got cut off is 24 btw.

V125BC [204]

Since, PS and QR are parallel, we know that <QRP is equal to <RPS. Therefore, we can solve for y by setting the two equations equal to each other.

5y+14=8y-13

*Subtract 5y from both sides to isolate the variable*

14=3y-13

*Add 13 to both sides*

27=3y

*Divide both sides by 3*

9=y

Now, plug in 9 for y in the equation 8y-13 to find the measure of that angle.

8(9)-13

<RPS=59

Now, the sum of the angles in any triangle is equal to 180 degrees. We can use this knowledge to set up an equation to solve for x.

3x+2x+1+59=180

*Combine like terms*

5x+60=180

*Subtract 60 from both sides*

5x=120

*Divide both sides by 5*

x=24

Now, we can find <RSP by pluggin 24 in for x.

2(24)+1

48+1

<RSP=49 degrees

Hope this helps!!

3 0

3 years ago

A small tree was planted at a height of 5 feet. The tree has been planted for 14 months, and is now 41.4 feet tall. Which equati

zlopas [31]

5 times 14 divided by 41-4

5 0

4 years ago

Which sum or difference is modeled by the algebra tiles?

Andrew [12]

Answer:

Step-by-step explanation:

Blue is postive and Red is Negative so you would just write them down as seen and because x^2 is negative in the second equation there will be a subtraction sign to represent it.

3 0

3 years ago