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Delicious77 [7]

2 years ago

9

Directions: Follow the instructions for the following inequalities. 1. 4<7 Multiply both sides by 7 , then by 6, then by 3, t

hen by 10 2. 11>-2 Add 5 to both sides, then add 3, then add (-4) 3. -4<-2 Subtract 6 from both sides, then 8, and then 2 4. -8<8 Divide both sides by -4, then by -2 5. Write a short explanation of the effects of the above operations. Did this affect the inequality sign? Was it still true? Why or why not?

1 answer:

worty [1.4K]2 years ago

4 0

In the given question, we have to perform this experiment and test if the inequality is true or not.

Adding the same value to both sides of the inequality will not change the inequality sign

<h3>Inequality</h3>

data;

4 < 7
11 > - 2
-4 < - 2
-8 < 8

In the first case, we would do follow the process

$6 * 7 * 4 < 7 * 7 * 6\\168 < 294$

In the second case;

$11 > - 2\\\\5 + 11 > -2 + 5\\3 + 16 > 3 + 3\\4+ 19 > 6 + 4\\23 > 10$

In all the scenarios, the operations did not affect the inequality sign because we are doing it equally to all side and at the end of the day nullifies each other.

Learn more on inequality here;

brainly.com/question/24372553

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I need the answer please and can u answer my recent to.

ale4655 [162]

Answer:

30 hours.

Step-by-step explanation:

Richard can build 15 snowballs in 1 hour

But 2 snowballs melt every 15 minutes

In 1 hour, the number of snowballs that will have melted is:

$\frac{60}{15}$ × 2 = 8

The number of snowballs that will have remained = 15 - 8 = 7

So 7 snowballs will have remained in 1 hour

For 210 snowballs to have remained, it will take:

$\frac{210}{7}$ × 1 = 30 hours.

3 0

3 years ago

Write the standard form of the line that has a slope - 3/4 intercept of -2Include your work in your final answer Type your answe

lukranit [14]

Y = -3/4x - 2
Add 2 and subtract y
-3/4x - y = 2
No fractions or negative
Multiply all by 4
-3x - 4y = 8
Now multiply all by (-)
Solution: 3x + 4y = -8

3 0

3 years ago

Find the product of the complex number and it's conjugate. <br><br> 9-5i

Dennis_Churaev [7]

Conjugate of 9-5i is 9+5i
product of those two: (9-5i)*(9+5i) = $9^{2} - (5i)^{2} =81-25* i^{2} =81-25*(-1)=81+25=106$

3 0

3 years ago

Question in pictures

yan [13]

The derivatives of the functions are listed below:

(a) $f'(x) = -7\cdot x^{-\frac{9}{2} }- 2\cdot x + 4 - \frac{1}{5} - 5\cdot x^{-2}$

(b) $f'(x) = \frac{1}{3}\cdot (x + 3)^{-\frac{2}{3} }\cdot (x+ 5)^{\frac{1}{3} } + \frac{1}{3} \cdot (x + 5)^{-\frac{2}{3} } \cdot (x + 3)^{\frac{1}{3} }$

(c) f'(x) = [(cos x + sin x) · (x² - 1) - (sin x - cos x) · (2 · x)] / (x² - 1)²

(d) f'(x) = (5ˣ · ㏑ 5) · ㏒₅ x + 5ˣ · [1 / (x · ㏑ 5)]

(e) f'(x) = 45 · (x⁻⁵ + √3)⁻⁸ · x⁻⁶

(f) $f'(x) = (\ln x + 1)\cdot [7^{x\cdot \ln x \cdot \ln 7}+7\cdot (x\cdot \ln x)^{6}]$

(g) $f'(x) = -2\cdot \arccos x \cdot \left(\frac{1}{\sqrt{1 - x^{2}}} \right) - \left(\frac{1}{1 + x} \right) \cdot \left(\frac{1}{2} \cdot x^{-\frac{1}{2} }\right)$

(h) f'(x) = cot x + cos (㏑ x) · (1 / x)

<h3>How to find the first derivative of a group of functions</h3>

In this question we must obtain the <em>first</em> derivatives of each expression by applying <em>differentiation</em> rules:

(a) $f(x) = 2 \cdot x^{-\frac{7}{2} } - x^{2} + 4 \cdot x - \frac{x}{5} + \frac{5}{x} - \sqrt[11]{2022}$

$f(x) = 2 \cdot x^{-\frac{7}{2} } - x^{2} + 4 \cdot x - \frac{x}{5} + \frac{5}{x} - \sqrt[11]{2022}$ Given
$f(x) = 2 \cdot x^{-\frac{7}{2} } - x^{2} + 4\cdot x - \frac{x}{5} + 5 \cdot x^{-1} - \sqrt[11]{2022}$ Definition of power
$f'(x) = -7\cdot x^{-\frac{9}{2} }- 2\cdot x + 4 - \frac{1}{5} - 5\cdot x^{-2}$ Derivative of constant and power functions / Derivative of an addition of functions / Result

(b) $f(x) = \sqrt[3]{x + 3} \cdot \sqrt[3]{x + 5}$

$f(x) = \sqrt[3]{x + 3} \cdot \sqrt[3]{x + 5}$ Given
$f(x) = (x + 3)^{\frac{1}{3} }\cdot (x + 5)^{\frac{1}{3} }$ Definition of power
$f'(x) = \frac{1}{3}\cdot (x + 3)^{-\frac{2}{3} }\cdot (x+ 5)^{\frac{1}{3} } + \frac{1}{3} \cdot (x + 5)^{-\frac{2}{3} } \cdot (x + 3)^{\frac{1}{3} }$ Derivative of a product of functions / Derivative of power function / Rule of chain / Result

(c) f(x) = (sin x - cos x) / (x² - 1)

f(x) = (sin x - cos x) / (x² - 1) Given
f'(x) = [(cos x + sin x) · (x² - 1) - (sin x - cos x) · (2 · x)] / (x² - 1)² Derivative of cosine / Derivative of sine / Derivative of power function / Derivative of a constant / Derivative of a division of functions / Result

(d) f(x) = 5ˣ · ㏒₅ x

f(x) = 5ˣ · ㏒₅ x Given
f'(x) = (5ˣ · ㏑ 5) · ㏒₅ x + 5ˣ · [1 / (x · ㏑ 5)] Derivative of an exponential function / Derivative of a logarithmic function / Derivative of a product of functions / Result

(e) f(x) = (x⁻⁵ + √3)⁻⁹

f(x) = (x⁻⁵ + √3)⁻⁹ Given
f'(x) = - 9 · (x⁻⁵ + √3)⁻⁸ · (- 5) · x⁻⁶ Rule of chain / Derivative of sum of functions / Derivative of power function / Derivative of constant function
f'(x) = 45 · (x⁻⁵ + √3)⁻⁸ · x⁻⁶ Associative and commutative properties / Definition of multiplication / Result

(f) $f(x) = 7^{x\cdot \ln x} + (x \cdot \ln x)^{7}$

$f(x) = 7^{x\cdot \ln x} + (x \cdot \ln x)^{7}$ Given
$f'(x) = 7^{x\cdot\ln x} \cdot \ln 7 \cdot (\ln x + 1) + 7\cdot (x\cdot \ln x)^{6}\cdot (\ln x + 1)$ Rule of chain / Derivative of sum of functions / Derivative of multiplication of functions / Derivative of logarithmic functions / Derivative of potential functions
$f'(x) = (\ln x + 1)\cdot [7^{x\cdot \ln x \cdot \ln 7}+7\cdot (x\cdot \ln x)^{6}]$ Distributive property / Result

(g) $f(x) = \arccos^{2} x - \arctan (\sqrt{x})$

$f(x) = \arccos^{2} x - \arctan (\sqrt{x})$ Given
$f'(x) = -2\cdot \arccos x \cdot \left(\frac{1}{\sqrt{1 - x^{2}}} \right) - \left(\frac{1}{1 + x} \right) \cdot \left(\frac{1}{2} \cdot x^{-\frac{1}{2} }\right)$ Derivative of the subtraction of functions / Derivative of arccosine / Derivative of arctangent / Rule of chain / Derivative of power functions / Result

(h) f(x) = ㏑ (sin x) + sin (㏑ x)

f(x) = ㏑ (sin x) + sin (㏑ x) Given
f'(x) = (1 / sin x) · cos x + cos (㏑ x) · (1 / x) Rule of chain / Derivative of sine / Derivative of natural logarithm /Derivative of addition of functions
f'(x) = cot x + cos (㏑ x) · (1 / x) cot x = cos x / sin x / Result

To learn more on derivatives: brainly.com/question/23847661

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7 0

2 years ago

In a circle with a radius of 6 ft, an arc is intercepted by a central angle of 270 degrees.

aliya0001 [1]

Answer: 28.26 ft

Step-by-step explanation:

The formula to calculate the length of arc $l$ is:

$l=r \theta$

Where:

$r=6 ft$ is the radius of the circle

$\theta=270\° \frac{\pi}{180\°}=\frac{3}{2} \pi=4.71 rad$ is the angle in radians

$l=(6 ft)(4.71 rad)$

$l=28.26 ft$ This is the length of the arc

3 0

3 years ago