-2-3(5x+7) May someone be able to help me with this equation

number between 1 and 10, inclusive, is randomly chosen. Events A and B are defined as follows. A: {The number is even} B: {The n

Rufina [12.5K]

Answer:

A U B = {1,2,3,4,5,6,8}

Step-by-step explanation:

Let's define the sets.

Let ¢ = universal set ( Contains all the elements in the set)

¢ = {1, 2, 3, 4, 5, 6, 7, 8, 9 , 10}

A= {2, 4, 6, 8}

B= {1,2,3,4,5,6}

Therefore: A U B (A union B):

A U B = {1, 2, 3, 4, 5, 6, 8}

6 0

4 years ago

Find the particular solution of the differential equation? /=5^3+9^2, when =1, =8

kipiarov [429]

Answer:

$\displaystyle s = \frac{5t^4}{4} + \frac{9}{t} - \frac{9}{4}$

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

Exponential Rule [Rewrite]: $\displaystyle b^{-m} = \frac{1}{b^m}$

Calculus

Derivatives

Derivative Notation

Solving Differentials - Integrals

Integration Constant C

Integration Rule [Reverse Power Rule]: $\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C$

Integration Property [Multiplied Constant]: $\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx$

Integration Property [Addition/Subtraction]: $\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx$

Step-by-step explanation:

*Note:

Ignore the Integration Constant C on the left hand side of the differential equation when integrating.

Step 1: Define

$\displaystyle \frac{ds}{dt} = 5t^3 + \frac{9}{t^2}$

t = 1

s = 8

Step 2: Integrate

[Derivative] Rewrite [Leibniz's Notation]: $\displaystyle ds = (5t^3 + \frac{9}{t^2})dt$
[Equality Property] Integrate both sides: $\displaystyle \int {} \, ds = \int {(5t^3 + \frac{9}{t^2})} \, dt$
[Left Integral] Reverse Power Rule: $\displaystyle s = \int {(5t^3 + \frac{9}{t^2})} \, dt$
[Right Integral] Rewrite [Integration Property - Addition]: $\displaystyle s = \int {5t^3} \, dt + \int {\frac{9}{t^2}} \, dt$
[Right Integrals] Rewrite [Integration Property - Multiplied Constant]: $\displaystyle s = 5\int {t^3} \, dt + 9\int {\frac{1}{t^2}} \, dt$
[Right Integrals] Rewrite [Exponential Rule - Rewrite]: $\displaystyle s = 5\int {t^3} \, dt + 9\int {t^{-2}} \, dt$
[Right Integrals] Reverse Power Rule: $\displaystyle s = 5(\frac{t^4}{4}) + 9(\frac{t^{-1}}{-1}) + C$
[Right Integrals] Rewrite [Exponential Rule - Rewrite]: $\displaystyle s = 5(\frac{t^4}{4}) + 9(\frac{1}{t}) + C$
Multiply: $\displaystyle s = \frac{5t^4}{4} + \frac{9}{t} + C$

Step 3: Solve

Substitute in variables: $\displaystyle 8 = \frac{5(1)^4}{4} + \frac{9}{1} + C$
Evaluate exponents: $\displaystyle 8 = \frac{5}{4} + \frac{9}{1} + C$
Divide: $\displaystyle 8 = \frac{5}{4} + 9 + C$
Add: $\displaystyle 8 = \frac{41}{4} + C$
[Subtraction Property of Equality] Isolate C: $\displaystyle \frac{-9}{4} = C$
Rewrite: $\displaystyle C = \frac{-9}{4}$

Particular Solution: $\displaystyle s = \frac{5t^4}{4} + \frac{9}{t} - \frac{9}{4}$

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

Unit: Differentials Equations and Slope Fields

Book: College Calculus 10e

3 0

3 years ago

The extended warranty on a garage door is $238. If the warranty costs 35% of the purchase price, how much does the garage door i

-BARSIC- [3]

Answer:

d. $680.

Step-by-step explanation:

Let x be the cost of garage door.

We have been given that the extended warranty on a garage door is $238 and the warranty costs 35% of the purchase price. This means 35% of x equals 238.

We can represent this information in an equation as:

$\frac{35}{100}x=238$

$0.35x=238$

$x=\frac{238}{0.35}$

$x=680$

Therefore, the cost of garage is $680 and option d is the correct choice.

4 0

3 years ago

Please help me literally need this to be answered in 2 hours P-L-E-A-S-E !!

Sonja [21]

Answer:

Yeah with that type of problem

Step-by-step explanation:

You aint getting answered for the next 4 hours <3

6 0

3 years ago

Help me please-math question

vlada-n [284]

Answer: Median = 50

Step by Step Explanation:

1. Sort the values from smallest to largest (Ascending order) - This step is already done for you in this data set.

2. Find the middle most number. If you're left with two numbers in the middle, find the average of those two numbers - Since this data set is pretty small, you can probably notice that the middle most number is 50.

I hope this helps! :D

8 0

3 years ago

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