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lara31 [8.8K]
3 years ago
10

What is the value of x in this equation [x+17]=20x

Mathematics
1 answer:
Digiron [165]3 years ago
3 0

Answer:

0.90=X or 0.89=X

If it's not right, then i'm sorry :)

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What is the period of the graph of the equation y = a sin bx?
steposvetlana [31]

T=2π/|b|. The period of an equation of the form y = a sin bx is T=2π/|b|.

In mathematics the curve that graphically represents the sine function and also that function itself is called sinusoid or sinusoid. It is a curve that describes a repetitive and smooth oscillation. It can be represented as y(x) = a sin (ωx+φ) where a is the amplitude, ω is the angular velocity with ω=2πf, (ωx+φ) is the oscillation phase, and φ the initial phase.

The period T of the sin function is T=1/f, from the equation ω=2πf we can clear f and substitute in T=1/f.

f=ω/2π

Substituting in T=1/f:

T=1/ω/2π -------> T = 2π/ω

For the example y = a sin bx, we have that a is the amplitude, b is ω and the initial phase φ = 0. So, we have that the period T of the function a sin bx is:

T=2π/|b|

7 0
3 years ago
A light bulb of 200W emits 1.5μm.How many photons are emmited per second.​
Vinvika [58]

Answer:

Step-by-step explanation:

An incandescent light bulb filament is approximated by a black body radiator, and in the case of a 60W bulb the filament temperature is around 2500˚C which is 2870˚K.

There are a couple of standard black body results that we can use. Firstly the total irradiance emitted per unit area of black body is equal to:

Ed=σT4

where σ=5.67×10−8 Wm−2K−4 is the Stephan-Boltzmann constant. For our bulb we get:

Ed=5.67×10−8⋅28704=3.85×106 Wm−2

As this is a 60W bulb then it has a total irradiance of 60W. Therefore the equivalent black body surface area is:

603.85×106=1.56×10−5 m2

which is 15.6mm2 of filament area.

Secondly we have that the total number of photons emitted per second per unit area of black body is equal to:[1]

Qd=σQT3

where σQ=1.52×1015 photons.sec−1m−2K−3. For our bulb this is:

Qd=1.52×1015⋅28703=3.59×1025 photons.sec−1m−2

Multiplying by the bulb’s equivalent black body surface area gives the result we require:

3.59×1025⋅1.56×10−5=5.6×1020 photons/sec

As a sanity check we know that these photons have a total energy of 60 joules per second, so the average energy per photon is:

605.6×1020=1.1×10−19 joules

A photon of wavelength λ has energy E=hcλ, and so the average energy corresponds with a photon of wavelength:

λ=hc1.1×10−19=1.9μm

Here’s a chart of the power distribution by wavelength, with the average photon wavelength shown as the dashed line, and visible wavelengths highlighted:

emember that there are a higher proportion of photons for the longer, lower energy wavelengths, so the average is weighted to the right.

We can also see from the original calculation that the general case is:

QdWEd=σQT3WσT4=2.68×1022WT photons/sec

for a bulb of wattage W watts and filament temperature T ˚K. So the photon emission rate is inversely proportional to the filament temperature. As a somewhat counter-intuitive example, a 60W halogen bulb with 3200˚K filament only emits photons at 90% of the rate of the standard 60W bulb, despite being visibly brighter.

The reason is that as the temperature increases then an increased proportion of shorter wavelength photos are emitted and therefore the average energy per photon increases, decreasing the number emitted per second. However at the same time an increased proportion of the photons are visible rather than infra-red, making the bulb appear brighter. Here’s the power distribution chart with the 60W halogen curve added for comparison:

3 0
3 years ago
If m(x)=x+5/x-1 and n(x) = x – 3, which function has the same domain as (m.n)(x)
meriva

Answer:

The domain of function (m.n)x is same as domain of function m(x).

Step-by-step explanation:

Domain: Any set of input values for which the function is defined and valid.

m(x)=x+5/x-1

Domain of m(x) is x>1 or x<1, x≠1, because if x=1 the function will be undefined.

n(x) = x – 3

Domain of x -3 is -∞<x<∞ i.e all real numbers

(m.n)x = (x+5/x-1)(x-3)

          = (x+5)(x-3)/x-1

The Domain of (m.n)x is x<1 or x>1 or x≠1 because the function is undefined for x=1

So, the domain of function (m.n)x is same as domain of function m(x).

8 0
3 years ago
Matrix A has dimensions 2x3. Matrix B has dimensions 3x6. These two matrices can be multiplied
alexdok [17]
If you mean A*B, then yes since,

number of columns in matrix A = number of rows in matrix B

ie the inner dimensions both match up (both are 3)

However, B*A is not defined
8 0
3 years ago
2 pipes running together can fill a cistern in 3 1÷3 min.if one pipe takes 3 min more than the other to fill it,find the time in
charle [14.2K]
It takes one pipe x minutes, the other pipe x+3 minutes
the portion filled per minute is by one pipe is 1/x, by the second pipe 1/(x+3)

when two pipes running together:
3&1/3[1/x+1/(x+3)] =1, 1 means the whole cistern
solve for x: 3&1/3(x+3) +3 1/3(x)=x(x+3)
6 &2/3 x +10 =x^2+3x
x^2- (3&2/3) x-10=0
3x^2-11x-30=0

this cannot be factored, so use the quadratic equation: 
x is about 5.5
x+3=8.5
8 0
3 years ago
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