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elixir [45]
3 years ago
13

If y varies directly with x, and y = 18 when x = 4, what is the constant of proportionality?

Mathematics
1 answer:
GREYUIT [131]3 years ago
3 0
Y is directly proportional to x and therefore takes the form y=kx where k is the constant of proportionality.

Dividing both sides by x for the given values, k becomes 18/4 = 4.5
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An electric current, I, in amps, is given by I=cos(wt)+√8sin(wt), where w≠0 is a constant. What are the maximum and minimum valu
exis [7]
Take the derivative with respect to t
- w \sin(wt) + \sqrt{8} w cos(wt)
the maximum and minimum values occur when the tangent line is zero so we set the derivative to zero
0 = -w \sin(wt) + \sqrt{8} w cos(wt)
divide by w
0 =- \sin(wt) + \sqrt{8} cos(wt)
we add sin(wt) to both sides

\sin(wt)= \sqrt{8} cos(wt)
divide both sides by cos(wt)
\frac{sin(wt)}{cos(wt)}= \sqrt{8}   \\  \\ arctan(tan(wt))=arctan( \sqrt{8} ) \\  \\ wt=arctan(2 \sqrt{2)} OR\\ wt=arctan( { \frac{1}{ \sqrt{2} } )
(wt)=2(n*pi-arctan(2^0.5))
(wt)=2(n*pi+arctan(2^-0.5))
where n is an integer
the absolute max and min will be

I=cos(2n \pi -2arctan( \sqrt{2} ))
since 2npi is just the period of cos
cos(2arctan( \sqrt{2} ))= \frac{-1}{3} 

substituting our second soultion we get
I=cos(2n \pi +2arctan( \frac{1}{ \sqrt{2} } ))
since 2npi is the period
I=cos(2arctan( \frac{1}{ \sqrt{2}} ))= \frac{1}{3}
so the maximum value =\frac{1}{3}
minimum value =- \frac{1}{3}


4 0
3 years ago
Two cards are drawn at random without replacement from a deck of 52 playing cards. If the first card chosen is a King, what is t
gulaghasi [49]

Answer:

p=0.05882

Step-by-step explanation:

Probability is the likelihood of an event occurring.

-A standard deck of cards has 4 kings.

#After one card is removed, 51 remains of which 3 are kings:

P(king)=\frac{3}{51}\\\\=0.05882

Hence, the probability that the second card is king is 0.05882

3 0
2 years ago
Read 2 more answers
Suppose a shipment of 170 electronic components contains 3 defective components. to determine whether the shipment should be​ ac
lbvjy [14]
If nCk represents the number of ways k parts can be chosen from a pool of n, the probability of interest is the complement of the probability of selecting all good parts.
  1 - (167C3)/(170C3) = 42,085/804,440 ≈ 0.0523

_____
nCk = n!/(k!(n-k)!)
7 0
3 years ago
Name the geometric term(s) modeled by each object
anyanavicka [17]

A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The geometric term(s) modeled by each object are Hexagon, point, line, line, and plane, respectively.

<h3>What is a line?</h3>

A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. A line segment is also a line but the line with finite length and having fixed endpoints.

The geometric term(s) modeled by each object

9. Stop sign ⇒ Hexagon

10. Tip of pin ⇒ Point

11. Strings of a violin ⇒ Line

12. A car antenna ⇒ Line

13. A library card ⇒ Plane

Hence, The geometric term(s) modeled by each object are Hexagon, point, line, line, and plane, respectively.

Learn more about Line here:

brainly.com/question/21511618

#SPJ1

3 0
1 year ago
Which is the larger amount?<br> A) 5 cups<br> B) 500 milliliters
kvasek [131]

Answer:

a

Step-by-step explanation:

8 0
3 years ago
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