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3 years ago

What do diffraction and refraction have

Mathematics

1 answer:

nignag [31]3 years ago

4 0

Answer:

They are both due to the wave nature of light.

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How many ways can 5 apple trees, 4 pear trees, and 3 cherry trees be arranged along a fence line?

Tems11 [23]

Answer:

Step-by-step explanation:

5 x 4 x 3=60

3 0

3 years ago

Read 2 more answers

6) A geologist collects rocks. He has three types, sedimentary, metamorphic and

rodikova [14]

Answer:

3:5

Step-by-step explanation:

s:m = 2:3

m:i = 9:10

convert m to same number so they are comparable

s:m = 6:9 (multiple so the ratio is still the same as 2:3)

m:i = 9:10 (the same thing as before)

s:i = 6:10

s:i = 3:5 (simplify)

7 0

2 years ago

How to differentiate ?

Bas_tet [7]

Use the power, product, and chain rules:

$y = x^2 (3x-1)^3$

• product rule

$\dfrac{\mathrm dy}{\mathrm dx} = \dfrac{\mathrm d(x^2)}{\mathrm dx}\times(3x-1)^3 + x^2\times\dfrac{\mathrm d(3x-1)^3}{\mathrm dx}$

• power rule for the first term, and power/chain rules for the second term:

$\dfrac{\mathrm dy}{\mathrm dx} = 2x\times(3x-1)^3 + x^2\times3(x-1)^2\times\dfrac{\mathrm d(3x-1)}{\mathrm dx}$

• power rule

$\dfrac{\mathrm dy}{\mathrm dx} = 2x\times(3x-1)^3 + x^2\times3(3x-1)^2\times3$

Now simplify.

$\dfrac{\mathrm dy}{\mathrm dx} = 2x(3x-1)^3 + 9x^2(3x-1)^2 \\\\ \dfrac{\mathrm dy}{\mathrm dx} = x(3x-1)^2 \times (2(3x-1) + 9x) \\\\ \boxed{\dfrac{\mathrm dy}{\mathrm dx} = x(3x-1)^2(15x-2)}$

You could also use logarithmic differentiation, which involves taking logarithms of both sides and differentiating with the chain rule.

On the right side, the logarithm of a product can be expanded as a sum of logarithms. Then use other properties of logarithms to simplify

$\ln(y) = \ln\left(x^2(3x-1)^3\right) \\\\ \ln(y) = \ln\left(x^2\right) + \ln\left((3x-1)^3\right) \\\\ \ln(y) = 2\ln(x) + 3\ln(3x-1)$

Differentiate both sides and you end up with the same derivative:

$\dfrac1y\dfrac{\mathrm dy}{\mathrm dx} = \dfrac2x + \dfrac9{3x-1} \\\\ \dfrac1y\dfrac{\mathrm dy}{\mathrm dx} = \dfrac{15x-2}{x(3x-1)} \\\\ \dfrac{\mathrm dy}{\mathrm dx} = \dfrac{15x-2}{x(3x-1)} \times x^2(3x-1)^3 \\\\ \dfrac{\mathrm dy}{\mathrm dx} = x(15x-2)(3x-1)^2$

7 0

2 years ago

A taxi charges $1.25 per mile and a flat fee of $2.75. How much would Maria pay for a 5 mile ride?

Olegator [25]

Answer:

Step-by-step explanation:

so you write the expression 2.75+1.25x= ?

If we subsitute the X for 5(miles) the we'll have the expression 2.75+1.25(5)= ?

and if you simplify that you will get 9.

7 0

3 years ago

How do you write 6,007,200 in two other forms

miskamm [114]

Six million and seventy two hundred. 6.0072 x 10*

*=6

3 0

3 years ago