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3 years ago

Which ordered pair is the solution to the system

Mathematics

1 answer:

svetoff [14.1K]3 years ago

6 0

Answer:

2 ordered pairs are solutions:

(1, -11) and (3, -9)

Step-by-step explanation:

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Austin is 69 years younger than Jamie. 3 years ago, Jamie's age was 4 times Austin's age. How old is Austin now?

matrenka [14]

Answer: 26 years old

Step-by-step explanation:

Create an equation with Austin as x and Jamie as x+69 (I just like workin with addition signs more)= 4(x-3)= x+69-3
Simplify the equations --> 4x-12=x+66
Solve the equation: 3x-12=66 --> 3x=78 --> x=26

This is the same as other age problems, just with the extra step of distributing the multiplication.

4 0

3 years ago

What is the square of 7

kkurt [141]

2.64575131106 I don’t know if you need to round the answer or not

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3 years ago

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Which equation can be used to find the volume of the cylinder?

sergejj [24]

Answer:

V = π × 4² × 16

Step-by-step explanation:

The formula for the volume of a cylinder is

V = πr²h

Data:

r = 4 in

h = 16 in

Calculation:

V = πr²h = π × 4² × 16

4 0

3 years ago

Find the derivative of ln(cosx²).

RoseWind [281]

Answer:

$\displaystyle \frac{dy}{dx} = -2x \tan (x^2)$

General Formulas and Concepts:

Calculus

Differentiation

Derivatives
Derivative Notation

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

$\displaystyle y = \ln (\cos x^2)$

Step 2: Differentiate

Logarithmic Differentiation [Derivative Rule - Chain Rule]: $\displaystyle y' = \frac{(\cos x^2)'}{\cos x^2}$
Trigonometric Differentiation [Derivative Rule - Chain Rule]: $\displaystyle y' = \frac{-\sin x^2 (x^2)'}{\cos x^2}$
Basic Power Rule: $\displaystyle y' = \frac{-2x \sin x^2}{\cos x^2}$
Rewrite [Trigonometric Identities]: $\displaystyle y' = -2x \tan (x^2)$