WILL NAME BRAINLIST PLEASE

For which value(s) of the constant k is the circle x² + (y − k)² = 16 tangent to the line y = 3?

STALIN [3.7K]

Answer:

Step-by-step explanation:Let us find points of intersection of line

3

x

+

4

y

−

k

=

0

and circle

x

2

+

y

2

=

16

. We can do this by putting value of

y

from first equation i.e.

y

=

k

−

3

x

4

and we get

x

2

+

(

k

−

3

x

)

2

16

=

16

or

16

x

2

+

k

2

+

9

x

2

−

6

k

x

=

256

i.e.

25

x

2

−

6

k

x

+

k

2

−

256

=

0

This would give two values of

x

and corresponding two values of

y

i.e. two points. But tangent cuts the circle in only at one point. This will be so when discriminant is zero i.e.

(

−

6

k

)

2

−

4

⋅

25

⋅

(

k

2

−

256

)

=

0

or

−

64

k

2

+

25600

=

0

or

k

=

±

20

graph{(x^2+y^2-16)(3x+4y-20)(3x+4y+20)=0 [-10, 10, -5, 5]}

5 0

4 years ago

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I NEED HELP! simplify this expression

ioda

Answer:

25

Step-by-step explanation:

36-1*16+5 (PEMDAS, exponents first)

36-16+5 (PEMDAS, multiplication)

20+5 (PEMDAS, add and subtract left to right)

25 (PEMDAS, add and subtract left to right)

7 0

3 years ago

A company can produce as many as 50 mountain bikes and as many as 60 road bikes per day. It takes 4 hours of labor to produce a

-BARSIC- [3]

4x + 5y ≤ 300

Good luck!

8 0

3 years ago

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The Center for Medicare and Medical Services reported that there were 295,000 appeals for hospitalization and other Part A Medic

Ymorist [56]

Answer:

(a) 0.00605

(b) 0.0403

(c) 0.9536

(d) 0.98809

Step-by-step explanation:

We are given that 40% of first-round appeals were successful (The Wall Street Journal, October 22, 2012) and suppose ten first-round appeals have just been received by a Medicare appeals office.

This situation can be represented through Binomial distribution as;

$P(X=r)= \binom{n}{r}p^{r}(1-p)^{n-r} ; x = 0,1,2,3,....$

where, n = number of trials (samples) taken = 10

r = number of success

p = probability of success which in our question is % of first-round

appeals that were successful, i.e.; 40%

So, here X ~ $Binom(n=10,p=0.40)$

(a) Probability that none of the appeals will be successful = P(X = 0)

P(X = 0) = $\binom{10}{0}0.40^{0}(1-0.40)^{10-0}$

= $1*0.6^{10}$ = 0.00605

(b) Probability that exactly one of the appeals will be successful = P(X = 1)

P(X = 1) = $\binom{10}{1}0.40^{1}(1-0.40)^{10-1}$

= $10*0.4^{1} *0.6^{10-1}$ = 0.0403

(c) Probability that at least two of the appeals will be successful = P(X>=2)

P(X >= 2) = 1 - P(X = 0) - P(X = 1)

= 1 - $\binom{10}{0}0.40^{0}(1-0.40)^{10-0} - \binom{10}{1}0.40^{1}(1-0.40)^{10-1}$

= 1 - 0.00605 - 0.0403 = 0.9536

(d) Probability that more than half of the appeals will be successful = P(X > 0.5)

For this probability we will convert our distribution into normal such that;

X ~ N( $\mu = n*p=4,\sigma^{2}= n*p*q = 2.4$ )

and standard normal z has distribution as;

Z = $\frac{X-\mu}{\sigma}$ ~ N(0,1)

P(X > 0.5) = P( $\frac{X-\mu}{\sigma}$ > $\frac{0.5-4}{\sqrt{2.4} }$ ) = P(Z > -2.26) = P(Z < 2.26) = 0.98809

3 0

3 years ago

quick my girl just sent me a photo of a girl and shes asking me if shes cute, ik this trick but should i tell her the truth? or

mr_godi [17]

If my man asked me if I thought another girl was cute I personally would probably be jealous but that’s just me. Maybe reassure her that she’s pretty and that’s she’s the only person you want to be with

4 0

3 years ago

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