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3 years ago

Find the rectangular coordinates of the point (sqrt3,pi/6)

Mathematics

1 answer:

madreJ [45]3 years ago

5 0

Answer:

$(x, y) = \left(\frac{3}{2}, \frac{\sqrt{3}}{2}\right)$

Step-by-step explanation:

The rectangular coordinates of the point are:

$(x,y) = \left(\sqrt{3}\cdot \cos\frac{\pi}{6}, \sqrt{3}\cdot \sin\frac{\pi}{6}\right)$

$(x, y) = \left(\frac{3}{2}, \frac{\sqrt{3}}{2}\right)$

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I NEED HELP PLEASE, THANKS! :)

Alenkasestr [34]

Answer:

Option A

Step-by-step explanation:

This is a great question!

The first thing we want to do here is to graph the system of " inequalities " -

$\begin{bmatrix}2x+9y\le \:100\\ 9x+y\le \:54\end{bmatrix}$

As x is ≥ 0, respectively y ≥ 0, it makes things a lot simpler, as it kind of restricts us to quadrant 1, but not entirely.

First change each inequality to " slope - intercept " form, as such -

$2x + 10y \leq 100,\\10y \leq 100 - 2x,\\y \leq - 1 / 5x + 10\\----------\\9x + y \leq 54,\\y \leq - 9x + 54$

The graphed solutions would be in the attachment. I have colored the region with which the two intersect, and the fact that we are limited to quadrant 1. In this colored region there are 3 major points, ( 5, 9 ), ( 0, 10 ), and ( 6, 0 ). We have to determine which of these are are maximum points, as the minimum are the same. Substitute these values ( ( 5, 9 ), ( 0, 10 ), and ( 6, 0 ) ) into the equation f( x, y ) = 10x + 4y,

$f ( x, y ) = 10( 5 ) + 4( 9 ),\\f ( x, y ) = 86 -\\f ( x, y ) = 10( 0 ) + 4( 10 ),\\f ( x, y ) = 40 -\\f ( x, y ) = 10( 6 ) + 4( 0 ),\\f ( x, y ) = 60$

( 5, 9 ) resulted in the greatest amount, 86. That would make it our maximum point -

<u><em>Solution = Option A</em></u>

3 0

3 years ago

your family is driving from cincinnati to st louis. the graph relates your distance from st.louis d in miles and travel time h (

rewona [7]

The solution is about a distance-time graph. The interpretation of the graph is that it took the family 6 hours to travel a distance of 360 miles. Note that the distance is plotted on y-axis and time on the x-axis.

<h3>What is a distance-time graph?</h3>

A distance time graph is a simple graph that shows the relationship between the time travelled the distance covered while doing do.

The slope-intercept form is

y= mx+b−⋯(1)

The y-intercept is 360

⇒b = 360; and m = −60

Substituting the value of m = −60

and b = 360

in (1) above,

⇒y = −60x +360

The x-intercept is

y = 0,

⇒0= −60x+360

hence, x=6

The y-intercept is

x=0

⇒y=−60(0)+360

⇒y=360

In conclusion, the x - intercept is the time in hours between Cincinnati and St. Loui: and

The y - intercept is the distance between Cincinnati and St. Louis.

Learn more about distance-time graphs at:
brainly.com/question/13877898
#SPJ1

6 0

2 years ago

Mr. Cresta spends $6.00 for every $3.00 he saves. Write a ratio equivalent to Mr. Cresta's spending

Andrei [34K]

Answer:

12:6 or $12 for every $6 he saves

Step-by-step explanation:

If he spends $6.00 for every $3.00, he would save $6 if he spends $12. In this case you could multiple or divide 6 by any number, and do the same to 3 to get an equivalent ratio. Ex. Multiple 6 times 2 to get $12 and 3 times 2 to get $6.

8 0

3 years ago

Makovka662 [10]

Answer:

Option A ( -3/2 , $\frac{-3\sqrt{3} }{2}$ )

Step-by-step explanation:

According to Question, The Spinner Rotate 600* Thus after Completing 360* it Comes Exactly Where It Started . Now again rotate It 180* .

Now We Are on ( -X axis ) & Completed 360*+180*=540* Rotation

Now After Rotate It 60* More we come in Third Quadrant & Here In Third Quadrant Only Tangent & Cotangent Is Positive .(Sine & Cosine is Negative)

(For Diagram, Please Find in attachment)

Now In Triangle OAB

Cos60* = OA / OB

1/2 = -X / 3 Thus X= -3/2

Sin60* = AB / OB

$\sqrt{3}$ /2 = -Y / 3 Thus Y = - $\sqrt{3}$ * 3 /2

6 0

3 years ago

Complete the equation of the graphed linear function. Write the slope in decimal form.

Leno4ka [110]

Y=mx+b
m=slope
b=y intercept, aka where the line crosses the y axis or where x=0

we can find the y axis by looking
it crosses the y axis at 4 units up
so
b=4
y=mx+4
we also se another point
(-5,0)
when x=-5, y=0
0=m(-5)+4
solve for m
0=m(-5)+4
subtract 4
-4=m(-5)
divide both sides by -5
-4/-5=4/5=m

equaiton is
y=4/5x+4
y=0.8x+4

8 0

3 years ago