Find the constant of variation if x and y vary directly and x = 6 when y= -2/3 ?

djyliett [7]

Answer:

See below

Step-by-step explanation:

$\tan A+\tan B + \tan A.\tan B = 1\\\\ \implies \: \tan A + \tan B = 1 - \tan A.\tan B \\ \\ \implies \: \frac{\tan A + \tan B}{ 1 - \tan A.\tan B } = 1\\ \\ \implies \: \tan (A + B) = 1 \\ \\ \implies \: \tan (A + B) =\tan 45 \degree \\ \\ \implies \: A + B = 45 \degree \\ \\ thus \: proved$

8 0

2 years ago

Points F(3, 3), K(6, 5), J(8, 2) and L(5, 0) lie in a coordinate plane. Which lines are perpendicular?

Romashka-Z-Leto [24]

To determine if a line is perpendicular to another, you must first determine the slope...
m = y1-y2/x1-x2
m of FK = 3-5/3-6 = -2/-3 = 2/3
m of FJ = 3-2/3-8 = 1/-5
m of FL = 3-0/3-5 = 3/-2
m of KJ = 5-2/6-8 = 3/-2
m of KL = 5-0/6-5 = 5
m of JL = 2-0/ 8-5 = 2/3

In order for two lines to be perpendicular, their slopes must be opposite reciprocals...
FK is perpendicular to FL
FK is perpendicular to KJ
JL is perpendicular to FL
JL is perpendicular to KJ
FJ is perpendicular to KL

8 0

3 years ago

How long will it take for 2 g of a sample of iodine-131, which has a half-life of about 8 days, to decay to 0.04 g?

Zigmanuir [339]

We know that

<span>This problem can be represented through the following equation
</span>
A = A₀(1/2)^t/h
where
A-----------> is the amount of substance left after time t
A₀ ----------> is the original amount---------> 2 g
h-------------> is the half-life-----------> 8 days

for A=0.04 g
t=?
0.04 = 2(1/2)^t/8
0.02 = (1/2)^t/8
Take ln on both sides:
ln(0.02) = ln [(1/2)^t/8]
ln(0.02) = (t/8)(ln 1/2)
t = 8*ln(0.02)/ln(1/2)
t = 45.15 days

the answer is 45.15 days

6 0

2 years ago

Please help me i really need it please

tatiyna

Answer:

1. 12 outcomes 2. 24 outcomes

Step-by-step explanation:

6 0

2 years ago

A downtown parking lot charges $5 per hour for the first 2 hours, then $2.50 per hour after that. which equation(s) describes th

Natasha_Volkova [10]

The required function is $y=\$ 5 \times 2 \ for \ x\leq 2\\y=\$ 10+\$ 2.50 \times (x-2) \ for \ x > 2$ .

<h3>What is piece wise function used for?</h3>

We use piece wise functions to describe situations in which a rule or relationship changes as the input value crosses certain “boundaries.” For example, we often encounter situations in business for which the cost per piece of a certain item is discounted once the number ordered exceeds a certain value.

We know that, the parking lot charges $5 per hour for the first two hours, and then $2.50 per hour after that.

So the function behaves differently in different intervals of its domain, this will be a piece wise function. To write it, we just need to clarify how the function behaves in each part of the domain.

So the function is

$y=\$ 5 \times 2 \ for \ x\leq 2\\y=\$ 10+\$ 2.50 \times (x-2) \ for \ x > 2$

So for the first two hours (x is the number of hours), the cost is $5, then for any hour after that, the cost will be the $10 for the first two hours plus $2.50 for each hour after that.

To learn more about piece wise function from the given link:

brainly.com/question/26681300

#SPJ4

5 0

1 year ago