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3 years ago

Solve the double inequality 16<5x-6<29

Mathematics

2 answers:

butalik [34]3 years ago

4 0

Answer:

22/5<x<7

Step-by-step explanation:

16<5x−6<29

16+6<5x−6+6<29+6(Add 6 to all parts)

22<5x<35

22/5<5x/5<35/5

22/5<x<7

ozzi3 years ago

3 0

Answer:

Step-by-step explanation:

16 < 5x-6 < 29

add 6

22 < 5x < 35

divide by 5

4.4 < x < 7

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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

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3 years ago

How many four-digit positive integers are there with thousands digit $2?$.

VARVARA [1.3K]

Answer:

There are one thousand. Starting at 2000 and going to 2999

Step-by-step explanation:

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3 years ago

30 POINTS! Use the graph of f to estimate the local maximum and local minimum.

nadya68 [22]

$y_{min}=-1\ for\ x=(2k+1)\pi\ for\ k\in\mathbb{Z^-}\cup\{0\}\ \vee\ x=\dfrac{3\pi}{2}+2k\pi\ for\ k\in\mathbb{Z^+}\cup\{0\}$

$y_{max}=1\ for\ x=2k\pi\ for\ k\in\mathbb{Z^-}\cup\{0\}\ \vee\ x=\dfrac{5\pi}{2}+2k\pi\ for\ k\in\mathbb{Z^+}\cup\{0\}$

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3 years ago

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aniked [119]

Answer:

Step-by-step explanation:

Blue is 1 and a quarter.

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3 years ago

In a bag are eight red marbles and 2 blue marbles what chance does garcia have drawing a blue marble

Ierofanga [76]

Total number of balls = 8+2 = 10.

Chance of drawing a blue marble = total number of blue ball in bag
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total number of balls in bag

= 2
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10

= 1
---------
5

Hope this helps!

6 0

3 years ago