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3 years ago

PLS HELP ASAP!!!! Determine whether each relation is a function. Explain your reasoning.

Mathematics

1 answer:

V125BC [204]3 years ago

6 0

Each domain needs to have one range every x can only have 1 y they can be the same y value so...

Yes it is a function

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What is the period of y=3cot(4x−3π)

Stells [14]

Hello!

hint: we can rewrite your function as below:

3/tan(4x−3π) = 3(1+tan4xtan3π)/tan4x−tan3π =

=3/tan(4x) = 3cot(4x)

now, since the period P of cotangent function is pi, then the period of cot(4x), which is the period of our original function, is such that:

"4P=π"

Hope this Helps! Have A Wonderful Day! :)

4 0

3 years ago

A tank contains 9,000 L of brine with 18 kg of dissolved salt. Pure water enters the tank at a rate of 90 L/min. The solution is

aev [14]

Let x(t) denote the amount of salt (in kg) in the tank at time t. The tank starts with 18 kg of salt, so x (0) = 18.

The solution is drained from the tank at a rate of 90 L/min, so that the amount of salt in the tank changes according to the differential equation

dx(t)/dt = - (x(t) kg)/(9000 L) × (90 L/min) = -1/100 x(t) kg/min

or, more succintly,

x' = -1/100 x

This equation is separable as

dx/x = -1/100 dt

Integrating both sides gives

∫ dx/x = -1/100 ∫ dt

ln|x| = -1/100 t + C

x = exp(-1/100 t + C )

x = C exp(-t/100)

(a) Using the initial condition x (0) = 18, we find

18 = C exp(0) ==> C = 18

so that

x(t) = 18 exp(-t/100)

(b) After 20 minutes, we have

x (20) = 18 exp(-20/100) = 18 exp(-1/5) ≈ 14.74

so the tank contains approximately 14.74 kg of salt after this time.

7 0

3 years ago

How do you add vectors? Add the vector <3,4> to the vector that goes 7 units at an angle of 2π/3.

telo118 [61]

The sum of two vectors is (- 0.5, 10.1)

Explanation:

To add two vectors, add the corresponding components.

Let u =⟨u1,u2⟩ and v =⟨v1,v2⟩ be two vectors.

Then, the sum of u and v is the vector

u +v =⟨u1+v1, u2+v2⟩

(b)

Two vectors = ( 3, 4 )

angle 2π/3 = 120°

In x axis, the vector is = 7 cos 120°

$= 7 X -\frac{1}{2} \\\\=- \frac{7}{2}$

In y axis, the vector is = 7 sin 120°

= 7 X 0.866

= 6.062

The second vectors are ( -3.5, 6.062)

Sum of two vectors = [( 3 + (-3.5) ), (4 + 6.062)]

= (- 0.5, 10.1)

8 0

3 years ago

total number of boys and girls in a class is 42. if the number of girls is 10 more than the boys find the number of boys?? answe

dsp73

Answer:

$\boxed{\sf Total \ number \ of \ boys = 16}$

Given:

Total number of boys and girls in class = 42

Total number of girls = 10 more than the boys

To Find:

Total number of boys

Step-by-step explanation:

Let total number of boys be 'x'

$\sf So, \\ \sf Total \: number \ of \ girls = x + 10 \\ \\ \therefore \\ \sf \implies Total \: number \: of \: boys \: and \: girls \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: = Total \: number \: of \: boys + Total \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: number \: of \: girls \\ \\ \sf \implies 42 = x + (x + 10) \\ \\ \sf 42 = x + (x + 10) \: is \: equivalent \: to \: x + (x + 10) = 42 : \\ \sf \implies x + (x + 10 )= 42 \\ \sf \implies x + x + 10 = 42 \\ \\ \sf x + x = 2x : \\ \sf \implies \boxed{ \sf 2x} + 10 = 42$

$\sf Substrate \: 10 \: from \: both \: sides : \\ \sf \implies 2x + (10 - \boxed{ \sf 10}) = 42 - \boxed{ \sf 10} \\ \\ \sf 10 - 10 = 0 : \\ \sf \implies 2x = 42 - 10 \\ \\ \sf 42 - 10 = 32 : \\ \sf \implies 2x = \boxed{ \sf 32} \\ \\ \sf Divide \: both \ sides \: by \: 2 : \\ \sf \implies \frac{2x}{ \boxed{ \sf 2}} = \frac{32}{ \boxed{ \sf 2}} \\ \\ \sf \frac{2x}{2} = \frac{ \cancel{2}}{ \cancel{2}} \times (x) = x : \\ \sf \implies x = \frac{32}{2} \\ \\ \sf \frac{32}{2} = \frac{16 \times \cancel{2}}{ \cancel{2}} = 16 : \\ \sf \implies x = 16$

So,

Total number of boys = x = 16

6 0

4 years ago

9- pls help!!!! math -

Andre45 [30]

Answer:

Step-by-step explanation:

7 cuz I did this on my notebook

I hope it helps :)

have a greatday

4 0

3 years ago