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ikadub [295]
3 years ago
7

Find a cartesian equation for the curve and identify it. r = 10 tan(θ) sec(θ)

Mathematics
1 answer:
Vilka [71]3 years ago
3 0
For a cartesian equation
x=r\cos\theta \ and \ y=r\sin\theta \\  \\ \cos\theta=\frac{x}{r} \ and \ \sin\theta=\frac{y}{r} \\  \\ \tan\theta=\frac{\sin\theta}{\cos\theta}=\frac{y}{r}\cdot\frac{r}{x}=\frac{y}{x} \\  \\ \sec\theta=\frac{1}{\cos\theta}=\frac{r}{x}

Given r = <span>10 tan(θ) sec(θ)
r=10\tan\theta\sec\theta=10\cdot\frac{y}{x}\cdot\frac{r}{x} \\  \\ \Rightarrow10y=x^2 \\  \\ \Rightarrow y= \frac{1}{10} x^2

Therefore,</span>the curve is a parabola opening upward with vertex (0, 0).
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30 60 90 right triangle
leg = 6 so other leg = 6√3

A = (1/2)(6+6)( 6√3+ 6√3)
A = 6 (12√3)
A = 72√3

answer is D
72√3

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3 years ago
The human resources manager at a company records the length, in hours, of one shift at work, X. He creates the probability distr
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Step-by-step explanation: It passes the vibe check

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3 years ago
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Punctele O, A, B, C sunt coliniare în această ordine, iar segmentele OA, AB și BC au lungimile exprimate în cm, prin numere natu
julia-pushkina [17]

Răspuns:

a) OC = 18cm

b) MN = 6cm

Explicație pas cu pas:

Găsiți diagrama la întrebarea atașată.

a) Din diagramă se poate observa că OC = OA + AB + AC

OC = 2n + 2n + 2 + 2n + 4

OC = 6n + 6

Următorul este să obțineți valoarea lui n:

OM = OA + AM

Să obținem segmentul AM;

Deoarece M este segmentul mijlociu al AC, atunci;

AM = AC / 2

AM = AB + BC / 2

AM = 2n + 2 + 2n + 4/2

AM = 4n + 6/2

AM = 2n + 3

Din moment ce OM = OA + AM

OM = 2n + 2n + 3

OM = 4n + 3

Dat fiind OM = 11

11 = 4n + 3

4n = 11-3

4n = 8

n = 2

Următorul pas este să calculați OC;

OC = 6n + 6

OC = 6 (2) + 6

OC = 18

Prin urmare, lungimea segmentului OC este de 18 cm

b) Această întrebare ne cere să găsim segmentul de linie MN.

Din diagramă, MN = AM - AN

Deoarece AM = 2n + 3 din întrebarea 1;

AM = 2 (2) +3

AM = 4 + 3

AM = 7

Acum, să obținem AN:

Din diagramă, AN = ON-OA și ON = OB / 2

AN = OB / 2 - OA

AN = (2n + 2n + 2) / 2 - 2n

AN = 4n + 2/2 - 2n

AN = 2n + 1 - 2n

AN = 2n-2n + 1

AN = 1

De la MN = AM - AN

MN = 7 - 1

MN = 6cm

Prin urmare, distanța dintre N, mijlocul segmentului OB și punctul M este de 6cm

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3 years ago
For altitudes up to 36,000 feet, the relationship between ground temperature and atmospheric
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Answer:

a=16400 feet

Step-by-step explanation:

t = -0.0035 a +g

-17.40 = -0.0035 a+40

-17.40-40=-0.0035a+40-40

-57.40=-0.0035a

a = -57.40/-0.0035

a=16400 feet

7 0
3 years ago
I need help please and fast
patriot [66]

Answer:

20%

Step-by-step explanation:

The reason it is 20% is due to the fact that if you put it in a form showing 250/250 = 100/100 and put another proportional rate underneath it showing 200/250 = x/100, you would have to multiply the numerator of the fraction on the left by the denominator of the fraction on the right to get 20000. Now you divide 250 from 20000 and get x for 80, resulting in 80/100 or 80%. All you have to do now is subtract 100-80, which equals 20, resulting in 20%.

Hope that helps!! It's my first time in answering so, ya. ;D goodluck!

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3 years ago
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