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2 years ago

(5a^3-2)(5a^3+2) expand and combine like terms

Mathematics

1 answer:

joja [24]2 years ago

4 0

Step-by-step explanation:

(5a³-2)(5a³+2)

5a³×5a³+ 5a³×2 - 2× 5a³+ 5a³×2
5a³+10a³- 10a³ + 10a³
5a³+10a³ + 10a³-10a³
15a³ Answer

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Point: (-3, 7); Slope: 4

GaryK [48]

Answer:

y - 7 = 4(x + 3)

Step-by-step explanation:

Write the equation of a line using the point slope formula. Substitute m = 4 and the point (-3,7) in the formula.

$y - y_1 = m(x-x_1)\\y - 7 = 4(x--3)\\y - 7 = 4(x+3)$

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3 years ago

Lim x-1 x2 - 1/ sin(x-2)

balu736 [363]

Answer:

$\lim_{x \to 1}\frac{x^2-1}{sin(x-2)}=0$

Explanation:

Assuming the correct expression is to find the following limit:

$\lim_{x \to 1}\frac{x^2-1}{sin(x-2)}$

Use the property the limit of the quotient is the quotient of the limits:

$\lim_{x \to 1}\frac{x^2-1}{sin(x-2)}=\frac{\lim_{x \to 1}x^2-1}{\lim_{x \to 1}sin(x-2)}$

Evaluate the numerator:

$\frac{\lim_{x \to 1}x^2-1}{\lim_{x \to 1}sin(x-2)}=\frac{1^2-1}{\lim_{x \to1}sin(x-2)}=\frac{0}{\lim_{x \to 1}sin(x-2}$

Evaluate the denominator:

Since $\lim_{x \to1}sin(x-2)\neq 0$

$\frac{0}{\lim_{x \to1}sin(x-2)}=0$

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3 years ago

A hockey puck travels at a constant speed of 20 m/s what is the speed in miles per hour

Aleksandr [31]

YAY FREE POINTS THANKS SO MUCH!!!

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3 years ago

3x-4(2+3x)=82

enyata [817]

Answer:

x=-10

Step-by-step explanation:

3x-4(2+3x)=82

3x-(4*2)+(4*3x)=82

3x-8-12x=82

-9x-8=82

-9x-8+8=82+8

-9x=90

-9x/-9=x

90/-9=-10

x=-10

8 0

3 years ago

Read 2 more answers

A certain semiconductor device requires a tunneling probability of T = 10-5 for an electron tunneling through a rectangular barr

Goryan [66]

Answer:

Generally the barrier width is $a = 1.9322 *10^{-9} \ m$

Step-by-step explanation:

From the question we are told that

The tunneling probability required is $T = 1 * 10^{-5}$

The barrier height is $V_o = 0.4 eV$

The electron energy is $E = 0.08eV$

Generally the wave number is mathematically represented as

$k = \sqrt{ \frac{2 * m [V_o - E]}{\= h^2} }$

Here m is the mass of the electron with the value $m = 9.11 *10^{-31} \ kg$

h is is know as h-bar and the value is $\= h = 1.054*10^{-34} \ J \cdot s$

$k = \sqrt{ \frac{2 * 9.11 *10^{-31 } [0.4 - 0.04] * 1.6*10^{-19}}{[1.054*10^{-34}^2]} }$

=> $k = 3.073582 *10^{9} \ m^{-1}$

Generally the tunneling probability is mathematically represented as

$T = 16 * \frac{E}{V_o } * [1 - \frac{E}{V_o} ] * e^{-2 * k * a}$

$1.0 *10^{-5} = 16 * \frac{0.04}{0.4 } * [1 - \frac{0.04}{0.4} ] * e^{-2 * 3.0736 *10^{9} * a}$

=> $6.944*10^{-6}= e^{-2 * 3.0736 *10^{9} * a}$

Taking natural log of both sides

$ln[6.944*10^{-6}] = -2 * 3.0736 *10^{9} * a}$

=> $-11.8776 = -2 * 3.0736 *10^{9} * a}$

=> $a = 1.9322 *10^{-9} \ m$

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3 years ago