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djyliett [7]
2 years ago
10

Write two expressions with the solution set of {5}, (make it simple)

Mathematics
1 answer:
Montano1993 [528]2 years ago
4 0
I have no idea ☠️ i just need to answer questions to be able to ask questions
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Find the slope of the tangent line to the given polar curve at the point specified by the value of θ
MariettaO [177]

The given curve has equation

<em>r(θ)</em> = 9 + 8 cos(<em>θ</em>)

and its derivative is

d<em>r</em>/d<em>θ</em> = -8 sin(<em>θ</em>)

When <em>θ</em> = <em>π</em>/3, we have <em>r</em> (<em>π</em>/3) = 13, and d<em>r</em>/d<em>θ</em> (<em>π</em>/3) = -4√3.

Differentiate these with respect to <em>θ</em> :

d<em>y</em>/d<em>θ</em> = d<em>r</em>/d<em>θ</em> sin(<em>θ</em>) + <em>r(θ)</em> cos(<em>θ</em>)

d<em>x</em>/d<em>θ</em> = d<em>r</em>/d<em>θ</em> cos(<em>θ</em>) - <em>r(θ</em>) sin(<em>θ</em>)

In polar coordinates, we have

<em>y(θ)</em> = <em>r(θ)</em> sin(<em>θ</em>)

<em>x(θ)</em> = <em>r(θ)</em> cos(<em>θ</em>)

and when <em>θ</em> = <em>π</em>/3, we have <em>y</em> (<em>π</em>/3) = 13√3/2 and <em>x</em> (<em>π</em>/3) = 13/2.

The slope of the tangent line to the curve is d<em>y</em>/d<em>x</em>. By the chain rule,

d<em>y</em>/d<em>x</em> = d<em>y</em>/d<em>θ</em> • d<em>θ</em>/d<em>x</em> = (d<em>y</em>/d<em>θ</em>) / (d<em>x</em>/d<em>θ</em>)

d<em>y</em>/d<em>x</em> = (d<em>r</em>/d<em>θ</em> sin(<em>θ</em>) + <em>r(θ)</em> cos(<em>θ</em>)) / (d<em>r</em>/d<em>θ</em> cos(<em>θ</em>) - <em>r(θ</em>) sin(<em>θ</em>))

When <em>θ</em> = <em>π</em>/3, the slope is

d<em>y</em>/d<em>x</em> = (-4√3 sin(<em>π</em>/3) + 13 cos(<em>π</em>/3)) / (-4√3 cos(<em>π</em>/3) - 13 sin(<em>π</em>/3))

d<em>y</em>/d<em>x</em> = (-4√3 (√3/2) + 13 (1/2)) / (-4√3 (1/2) - 13 (√3/2))

d<em>y</em>/d<em>x</em> = - 1/(17√3)

So, the tangent line has slope -1/(17√3) and passes through (13/2, 13√3/2). Using the point-slope formula, its equation is

<em>y</em> - 13√3/2 = -1/(17√3) (<em>x</em> - 13/2)

<em>y</em> = -(<em>x</em> - 338)/(17√3)

4 0
2 years ago
What do we get when we break apart 35+16 using place value?
geniusboy [140]

Answer:

35:

30 (tens) 5 (ones)

16:

10 (tens) 6 (ones)

Step-by-step explanation:

Add the tens:

30+10 =40

Add the ones:

5+6=11

Add the final answer for the tens and ones together:

40+11=51

I hope this helps! Lemme know in the comments if this made sense to you?

4 0
3 years ago
Read 2 more answers
If i = the square root of -1, what is the value of i³? A. -1 B. i C. 1 D.-i ?
mezya [45]
I=√-1
i^3=(√-1)^3

(√-1)^3=((√-1)^2)(√-1)=(-1)(√-1)=-√-1 or since i=√-1
-i is answer


<span>D is answer</span>
7 0
3 years ago
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Line a is a perpendicular bisector of line segment K M. It intersects line segment K M at point L. Line a also contains point N.
ASHA 777 [7]

Answer:

The value of segment LM is 9x + 5.

Step-by-step explanation:

Consider the image below.

A perpendicular bisector is a line segment that bisects another line segment into two equal parts and is perpendicular to this line segment.

So from the diagram below we know:

KL = LM

line <em>a</em> is ⊥ to KM

∠NLK = 90°

Since the angle measure of ∠NKL is not provided we cannot determine the value of <em>x</em>.

So, the value of segment LM is 9x + 5.

7 0
3 years ago
Read 2 more answers
Simplify square root of 64x squared
Delvig [45]

Answer:

8x

Step-by-step explanation:

The square root of 64 is 8 and the square root of x squared would just be x.

3 0
3 years ago
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