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3 years ago

Find a101 of the sequence 5,8,11,

Mathematics

1 answer:

guajiro [1.7K]3 years ago

3 0

Answer:

305

Step-by-step explanation:

This sequence es the sum of 3

5+3 =8

8+3 = 11

then

101 = 100 + 1

the fisrt date is 5

the another 100:

100*3 = 300

300 + 5 = 305

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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

Need help quick, please?

My name is Ann [436]

Remember that the general formula for a circle is 
(x – h)² + (y – k)² = r², where (h,k) is the coordinate of the center.
We already know that (h,k) = (5,-4), since we know the center's coordinates. We need to find r, the radius, using the distance between the center and the point (-3,2).
To do this, we can either use the distance formula, or plug in the points in our circle equation and solve for r.
Let's do the second one, plugging in and solving for r.
We can use the point (-3,2) for (x,y):
(x – h)² + (y – k)² = r²
(-3 - 5)² + (2 - -4)² = r²
(-8)² +(6)² = r²
64 + 36 = r²
100 = r²
r = 10
We know that r=10, and that r² = 100
Using h, k, and r, we can now solve for the equation of the circle in standard form.
The equation of the circle is:
(x – 5)² + (y + 4)² = 100

8 0

2 years ago

Which equation is graphed along with the parent

snow_lady [41]

Answer:

$g(x) = \sqrt[3]{x - 3 } + 4$

5 0

2 years ago

Read 2 more answers

A machine takes 2.8 hours to make 9 parts at that rate,how many parts can machine make in 28.0

BigorU [14]

The answer is 90.
28/2.8 = 10
10 x 9 = 90

4 0

2 years ago

Find the equation of the line given the slope and the y-intercept

GREYUIT [131]

Answer:

y = $\frac{1}{2}x + 3$

Step-by-step explanation:

The equation for a linear graph is usually written in the following format...

y = mx + b

Where m would be the slope, usually referring to rise over run and b would be the y-intercept (where the line crosses the y-axis). From the graph, we can see that the line crosses the y-axis at point 3 so b would be 3. The graph also shows us that for every 1 value that the line rises it moves to the right 2 values. Therefore, the slope would be 1/2. Using these values we can create the following equation...

y = $\frac{1}{2}x + 3$

7 0

2 years ago