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2 years ago

What is the name of the relationship between ∠2 and ∠7?

Mathematics

2 answers:

baherus [9]2 years ago

8 0

Answer:

Alternate Exterior

Step-by-step explanation:

ive done this

kondaur [170]2 years ago

5 0

Answer:

Alternate Exterior

Step-by-step explanation:

They are opposite angles from each other on different lines

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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

2 years ago

Find the circumference of the larger circle if the area of one of the smaller circles is 48 pi in^2.

notsponge [240]

Answer:

C. 16√3π in.

Step-by-step explanation:

Circumference of a circle = 2πr where

r is the radius of the circle.

Given the area of one of the smaller circle to be 48π in², we can get the radius of one of the smaller circle.

If A = πr²

48π = πr²

r² = 48

r = √48 in

The radius of one of the smaller circle is √48.

To get the circumference of the larger circle, we need the radius of the larger circle. The radius R of the larger circle will be equivalent to the diameter (2r) of one of the smaller circle.

R = 2r

R = 2√48 inches

Since C = 2πR

C = 2π(2√48)

C = 4√48π in

C = 4(√16×3)π in

C = 4(4√3)π in

C = 16√3π in

Thw circumference of the larger circle is 16√3π in.

3 0

2 years ago

Read 2 more answers

Find the coordinates of point B along a directed line segment from A(3,4) and

andreev551 [17]

We have been given two points. $A(3,4)$ and $C(3,9)$ . We are asked to find the point B such that it divides line segment AC so that the ratio of AB to BC is 4:1.