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3 years ago

The difference of twice a number and 10 is less than 22

Mathematics

2 answers:

valentinak56 [21]3 years ago

5 0

2(n-10)≤ 28 or n ≤ 24

Igoryamba3 years ago

5 0

Answer:

2x-10≤22

Step-by-step explanation:

2x≤22+10=32

x≤16

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If f(1)=3 and f(n)=-2f(n-1)+1,then f(5)=

Drupady [299]

F(5) = - 2f(4) + 1
f(4) = -2f(3) + 1
f(3) = -2f(2) + 1
f(2) = -2f(1) + 1
Therefore:
f(2) = -2(3) + 1 = -5
f(3) = -2(-5) + 1 = 11
f(4) = -2(11) + 1 = -21
Therefore f(5) = -2(-21) + 1 = 43

5 0

3 years ago

If the gradient of the tangent to

Marizza181 [45]

Answer:

Point A(9, 3)

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

Identify

$\displaystyle y = \sqrt{x}$

$\displaystyle y' = \frac{1}{6}$

Step 2: Differentiate

[Function] Rewrite [Exponential Rule - Root Rewrite]: $\displaystyle y = x^{\frac{1}{2}}$
Basic Power Rule: $\displaystyle y' = \frac{1}{2}x^{\frac{1}{2} - 1}$
Simplify: $\displaystyle y' = \frac{1}{2}x^{-\frac{1}{2}}$
[Derivative] Rewrite [Exponential Rule - Rewrite]: $\displaystyle y' = \frac{1}{2x^{\frac{1}{2}}}$
[Derivative] Rewrite [Exponential Rule - Root Rewrite]: $\displaystyle y' = \frac{1}{2\sqrt{x}}$

Step 3: Solve

Find coordinates of A.

x-coordinate

Substitute in y' [Derivative]: $\displaystyle \frac{1}{6} = \frac{1}{2\sqrt{x}}$
[Multiplication Property of Equality] Multiply 2 on both sides: $\displaystyle \frac{1}{3} = \frac{1}{\sqrt{x}}$
[Multiplication Property of Equality] Cross-multiply: $\displaystyle \sqrt{x} = 3$
[Equality Property] Square both sides: $\displaystyle x = 9$

y-coordinate

Substitute in x [Function]: $\displaystyle y = \sqrt{9}$
[√Radical] Evaluate: $\displaystyle y = 3$

∴ Coordinates of A is (9, 3).

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

Unit: Derivatives

Book: College Calculus 10e

7 0

3 years ago

I need help on 2,5 10-12,29 please anyone !!

AfilCa [17]

Answer:

2:1/2

5:16/24

10:Movie B

11:Movie D

12:2/3

I can't see 29. If you show it, then i will solve it.

Step-by-step explanation:

3 0

3 years ago

Sorting Quadratic Function Discriminants

nataly862011 [7]

The number of zeros of the quadratic functions, considering their discriminant, is given as follows:

discriminant = 0: 1 Real number solution.

discriminant = -36: 0 Real number solutions.

discriminant = 3: 2 Real number solutions.

discriminant = 2: 2 Real number solutions.

discriminant = 100: 2 Real number solutions.

discriminant = -4: 0 Real number solutions.

<h3>What is the discriminant of a quadratic equation and how does it influence the solutions?</h3>

A quadratic equation is modeled by:

$y = ax^2 + bx + c$

The discriminant is:

$\Delta = b^2 - 4ac$

The solutions are as follows:

If $\mathbf{\Delta > 0}$ , it has 2 real solutions.

If $\mathbf{\Delta = 0}$ , it has 1 real solutions.

If $\mathbf{\Delta < 0}$ , it has 0 real solutions.

Hence, for the given values of the discriminant, we have that:

discriminant = 0: 1 Real number solution.

discriminant = -36: 0 Real number solutions.

discriminant = 3: 2 Real number solutions.

discriminant = 2: 2 Real number solutions.

discriminant = 100: 2 Real number solutions.

discriminant = -4: 0 Real number solutions.

More can be learned about quadratic functions at brainly.com/question/24737967

#SPJ1

5 0

1 year ago

What is the value of x? A. 4 B. 4√3 C. 8 D. 8√3

SashulF [63]

Answer:

B. 4√3

Step-by-step explanation:

$\sin \: 60 \degree = \frac{x}{8} \\ \\ \therefore \: \frac{ \sqrt{3} }{2} = \frac{x}{8} \\ \\ \therefore \: x = \frac{8 \times \sqrt{3} }{2} \\ \\ \therefore \: x = 4 \times \sqrt{3}\\ \\ \huge \purple{ \boxed{ \therefore \: x = 4 \sqrt{3} }}\\$

4 0

3 years ago