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2 years ago

Draw the next pattern in sequence:1;3;10...

Mathematics

1 answer:

polet [3.4K]2 years ago

3 0

Answer:

1, 3, 10, 34....

Step-by-step explanation:

3x each number and add the previous numbers:

(1 x 3) + 0= 3

(3 x 3) + 1 = 10

(3 x 10) +3 + 1 = 34

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The curve

kherson [118]

Answer:

Point N(4, 1)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Multiplication Property of Equality
Division Property of Equality
Addition Property of Equality
Subtraction Property of Equality

Algebra I

Coordinates (x, y)
Functions
Function Notation
Terms/Coefficients
Anything to the 0th power is 1
Exponential Rule [Rewrite]: $\displaystyle b^{-m} = \frac{1}{b^m}$
Exponential Rule [Root Rewrite]: $\displaystyle \sqrt[n]{x} = x^{\frac{1}{n}}$

Calculus

Derivatives

Derivative Notation

Derivative of a constant is 0

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Derivative Rule [Chain Rule]: $\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)$

Step-by-step explanation:

Step 1: Define

$\displaystyle y = \sqrt{x - 3}$

$\displaystyle y' = \frac{1}{2}$

Step 2: Differentiate

[Function] Rewrite [Exponential Rule - Root Rewrite]: $\displaystyle y = (x - 3)^{\frac{1}{2}}$
Chain Rule: $\displaystyle y' = \frac{d}{dx}[(x - 3)^{\frac{1}{2}}] \cdot \frac{d}{dx}[x - 3]$
Basic Power Rule: $\displaystyle y' = \frac{1}{2}(x - 3)^{\frac{1}{2} - 1} \cdot (1 \cdot x^{1 - 1} - 0)$
Simplify: $\displaystyle y' = \frac{1}{2}(x - 3)^{-\frac{1}{2}} \cdot 1$
Multiply: $\displaystyle y' = \frac{1}{2}(x - 3)^{-\frac{1}{2}}$
[Derivative] Rewrite [Exponential Rule - Rewrite]: $\displaystyle y' = \frac{1}{2(x - 3)^{\frac{1}{2}}}$
[Derivative] Rewrite [Exponential Rule - Root Rewrite]: $\displaystyle y' = \frac{1}{2\sqrt{x - 3}}$

Step 3: Solve

Find coordinates

x-coordinate

Substitute in y' [Derivative]: $\displaystyle \frac{1}{2} = \frac{1}{2\sqrt{x - 3}}$
[Multiplication Property of Equality] Multiply 2 on both sides: $\displaystyle 1 = \frac{1}{\sqrt{x - 3}}$
[Multiplication Property of Equality] Multiply √(x - 3) on both sides: $\displaystyle \sqrt{x - 3} = 1$
[Equality Property] Square both sides: $\displaystyle x - 3 = 1$
[Addition Property of Equality] Add 3 on both sides: $\displaystyle x = 4$

y-coordinate

Substitute in x [Function]: $\displaystyle y = \sqrt{4 - 3}$
[√Radical] Subtract: $\displaystyle y = \sqrt{1}$
[√Radical] Evaluate: $\displaystyle y = 1$

∴ Coordinates of Point N is (4, 1).

Topic: AP Calculus AB/BC (Calculus I/II)

Unit: Derivatives

Book: College Calculus 10e

4 0

3 years ago

What weight of dry substance is in 150g of a 3% substance solution? What weight of an 8% solution can we have with the same weig

Pavlova-9 [17]

The answers are: 4.5 g and 56.25 g respectively.

Since the first type of measurement in this question is weight or mass, I'll suppose that the percentage concentration is % mass/mass. For that type of concentration measurement, just multiply the percentage by the total mass to get the mass of the wanted material.
So 150 g * 3% = 150 g * 0.03 = 4.5g

For the 8% solution with the same amount of dry substance, use the ratio of percentages, multiplied by the mass of the first solution to get the wanted amount of new solution:
3/8 * 150 g = 56.35 g

5 0

3 years ago

PLEASE HELP! I have a deadline tonight ,I have to get this done! thank you!! Two questions (:

Viktor [21]

Both of your answers are correct. In the first equation, if you were to substitute 3 for x, because you have to do exponents first, you have 3^2, which is 9, and 9*6 =54. If you were to substitute -3 for x again you would have to do the exponents first which would be -3^2 which is 9, and 9*6 = 54.

For the second question, if I substitute 0.75 for t, I get -9 + 18 + 7. This is equal to 16, and therefore the answer would be D. Hope this helps! :D. Let me know if you have questions about my explanation, and feel free to post more questions.

3 0

3 years ago

Find the midpoint of the following

zloy xaker [14]

Measure the distance between the two end points, and divide the result by 2. This distance from either end is the midpoint of that line. Alternatively, add the two x coordinates of the endpoints and divide by 2. Do the same for the y coordinates.

6 0

3 years ago

Read 2 more answers

Plz help me get the right answer for these I hate math -.-

spin [16.1K]

Answer:

C. y = 60x + 120

Step-by-step explanation:

The cost increases by $60 for every hour you rent, so '60x' represents this part of the equation. Since it increases $60 for each hour, there is a flat rate of $120 to rent the limo since at the first hour, the cost is $180. $180 - $60 = $120

7 0

3 years ago

Draw the next pattern in sequence:1;3;10...​

Draw the next pattern in sequence:1;3;10...