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marysya [2.9K]
3 years ago
5

Solve for x 3 x − 8 ≤ 23 AND − 4 x + 26 ≥ 6 Please help thank you!!

Mathematics
1 answer:
MAXImum [283]3 years ago
8 0

To solve for x, you need to isolate/get the variable "x" by itself in the inequality:

3x - 8 ≤ 23       Add 8 on both sides

3x - 8 + 8 ≤ 23 + 8

3x ≤ 31         Divide 3 on both sides to get "x" by itself

\frac{3x}{3} \leq \frac{31}{3}

x\leq \frac{31}{3}     (x is any number less than or equal to 31/3)

-4x + 26 ≥ 6          Subtract 26 on both sides

-4x ≥ -20      Divide -4 on both sides [When you multiply/divide by a negative number to both sides of an inequality, you flip the sign </>]

\frac{-4x}{-4} \geq \frac{-20}{-4}   (two negative signs cancel each other out and become positive)

x ≤ 5     (x is any number less than or equal to 5)

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The given parameters:

  • <em>Number of revolution of the electron, N = 1.4 x 10⁶ rev per sec</em>
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  • <em>Mass of electron, m = 9.11 x 10⁻³¹ kg</em>

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The angular speed of the electron is calculated as follows;

\omega = 2\pi N\\\\\omega = 2\pi \ \frac{rad}{1 \ rev} \times 1.4 \times 10^6 \ rev/s\\\\\omega = 8.798 \times 10^6 \ rad/s

The charge of the electrons is calculated as follows;

F_c= m\omega ^2 r\\\\F_{B}= qvB = q\omega r B \\\\F_c = F_B\\\\m\omega ^2 r =  q\omega r B \\\\q = \frac{m\omega ^2 r}{\omega r B} \\\\q = \frac{m \omega }{B} \\\\q = \frac{9.11 \times 10^{-31} \times 8.798 \times 10^6}{10^{-5}} \\\\q = 8.02 \times 10^{-19} \ C

The charge of the electrons is 8.02 \times 10^{-19} \ C.

The complete question here:

Electrons execute 1.4*10^6 revolutions per sec in a magnetic field of flux density 10⁻⁵ T. What will be the value of charge of the electron?

Learn more about magnetic force of electrons here: brainly.com/question/3990732

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7. The area of a square piece of cardboard is 70 cm2. What is the
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Answer:

8.3 cm

Step-by-step explanation:

<h2>so area of a square= side×side</h2><h2>since all sides are equal in a square</h2><h2>so= s×s=70cm²</h2><h2>√s²=√70</h2><h2>s=8.3 cm</h2>
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2 years ago
Set up and evaluate the optimization problems. (Enter your answers as comma-separated lists.) Find two positive integers such th
alexira [117]

Answer and Step-by-step explanation:

Let x and y be two positive integers and their sum is 14:

X + y = 14

And the sum of square of this number is:

f = x2 + y2

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Differentiate with respect to x, we get:

F’(x) = [ x2 + (14 – x)2]’ = 0

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Hence, y = 14 – x = 14 -7 = 7

Now taking second derivative test:

F”(x) > 0

For x = y = 7,f reaches its maximum value:

(7)2 + (7)2 = 49 + 49

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F at endpoints x Є [ 0, 14]

F(0) = 02 + (14 – 0)2

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Hence the sum of squares of these numbers is minimum when x = y = 7

And maximum when numbers are 0 and 14.

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2 years ago
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