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3 years ago

Find the solution to the system of equations.

Mathematics

1 answer:

Tanya [424]3 years ago

7 0

Answer:

x = - 4, y = 7

Step-by-step explanation:

Given the 2 equations

- 7x - 2y = 14 → (1)

6x + 6y = 18 → (2)

Multiplying (1) by 3 and adding to (2) will eliminate the y- term

- 21x - 6y = 42 → (3)

Add (2) and (3) term by term to eliminate y

- 15x = 60 ( divide both sides by 15 )

x = - 4

Substitute x = - 4 into either of the 2 equations and evaluate for y

Substituting into (2)

6(- 4) + 6y = 18

- 24 + 6y = 18 ( add 24 to both sides )

6y = 42 ( divide both sides by 6 )

y = 7

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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

HELP.

Viefleur [7K]

Answer:

The number of cases in the year 2010 is 266.

Step-by-step explanation:

An exponential function is one that the independent variable x appears in the exponent and has a constant a as its base. Its expression is:

f(x)=aˣ

being a positive real, a> 0, and different from 1, a ≠ 1.

In this case:

$r(t) = 207*e^{0.005*t}$

where t is the number of years since 1960 and e is an irrational number of which it is not possible to know its exact value because it has infinite decimal places. The first figures are 2,7182818284590452353602874713527 and is often called the Euler's number. e is the base of natural logarithms.

In this case, you want to know the number of cases r (t) in 2010. So, to know t you must know how many years have passed since 1960. For that, you can simply do the following subtraction: 2010-1960 and you get as a result : 50.

Replacing in the exponential expression r (t):

$r(t) = 207*e^{0.005*50}$