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4 years ago

What is the radius of a sphere with a volume of

Mathematics

1 answer:

Nataly [62]4 years ago

8 0

Answer:

Radius, r = 10.64 m

Step-by-step explanation:

The formula of a spherical shaped object is given by :

$V=\dfrac{4}{3}\pi r^3$

r is radius of a sphere

$r=(\dfrac{3V}{4\pi })^{1/3} \\\\r=(\dfrac{3\times 5044}{4\times 3.14 })^{1/3} \\\\r=10.64\ m$

So, the radius of a sphere is 10.64 m.

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Soloha48 [4]

2 gallons because 4 ounces are in one gallon in gas

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4 years ago

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I don't understand this. please help me, much appreciated !!

nevsk [136]

Apparently, the calculator at the link in your lesson is fully capable of giving you the necessary numbers. My own TI-84 work-alike gives me the account balances, but the rest of the numbers need to be figured.

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3 years ago

show all work to multiply 3 plus the square root of negative 16 times 6 minus the square root of negative 64

Aloiza [94]

Answer:

$\Huge \boxed{3+16i}$

$\rule[225]{225}{2}$

Step-by-step explanation:

$3+\sqrt{-16} * 6-\sqrt{-64}$

Using imaginary number rule : $\sqrt{-n} =\sqrt{n} *i$

Where $n$ is a positive integer.

$3+\sqrt{16} *i* 6-\sqrt{64}*i$

$3+4i* 6-8i$

Multiplying.

$3+24i-8i$

Combining like terms.

$3+16i$

$\rule[225]{225}{2}$

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4 years ago

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In The Figure Below, What is the reflection of point D across line x=0?

nignag [31]

X=0 is actually the y axis, so the y coordinate of the reflection doesn't change, while the x coordinate changes from a negative to a positive or from a positive to a negative.
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3 years ago

Find the solution of the differential equation f' (t) = t^4+91-3/t

Lynna [10]

Answer:

$\displaystyle f(t) = \frac{t^5}{5} + 91t - 3ln|t| - \frac{1819}{20}$

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

Functions
Function Notation

Calculus

Derivatives

Derivative Notation

Antiderivatives - Integrals

Integration Constant C

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

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

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

Step-by-step explanation:

Step 1: Define

Identify

$\displaystyle f'(t) = t^4 + 91 - \frac{3}{t}$

$\displaystyle f(1) = \frac{1}{4}$

Step 2: Integration

Integrate the derivative to find function.

[Derivative] Integrate: $\displaystyle \int {f'(t)} \, dt = \int {t^4 + 91 - \frac{3}{t}} \, dt$
Simplify: $\displaystyle f(t) = \int {t^4 + 91 - \frac{3}{t}} \, dt$
Rewrite [Integration Property - Addition/Subtraction]: $\displaystyle f(t) = \int {t^4} \, dt + \int {91} \, dt - \int {\frac{3}{t}} \, dt$
[1st Integral] Integrate [Integral Rule - Reverse Power Rule]: $\displaystyle f(t) = \frac{t^5}{5} + \int {91} \, dt - \int {\frac{3}{t}} \, dt$
[2nd Integral] Integrate [Integral Rule - Reverse Power Rule]: $\displaystyle f(t) = \frac{t^5}{5} + 91t - \int {\frac{3}{t}} \, dt$
[3rd Integral] Rewrite [Integral Property - Multiplied Constant]: $\displaystyle f(t) = \frac{t^5}{5} + 91t - 3\int {\frac{1}{t}} \, dt$
[3rd Integral] Integrate: $\displaystyle f(t) = \frac{t^5}{5} + 91t - 3ln|t| + C$

Our general solution is $\displaystyle f(t) = \frac{t^5}{5} + 91t - 3ln|t| + C$ .

Step 3: Find Particular Solution

Find Integration Constant C for function using given condition.

Substitute in condition [Function]: $\displaystyle f(1) = \frac{1^5}{5} + 91(1) - 3ln|1| + C$
Substitute in function value: $\displaystyle \frac{1}{4} = \frac{1^5}{5} + 91(1) - 3ln|1| + C$
Evaluate exponents: $\displaystyle \frac{1}{4} = \frac{1}{5} + 91(1) - 3ln|1| + C$
Evaluate natural log: $\displaystyle \frac{1}{4} = \frac{1}{5} + 91(1) - 3(0) + C$
Multiply: $\displaystyle \frac{1}{4} = \frac{1}{5} + 91 - 0 + C$
Add: $\displaystyle \frac{1}{4} = \frac{456}{5} - 0 + C$
Simplify: $\displaystyle \frac{1}{4} = \frac{456}{5} + C$
[Subtraction Property of Equality] Isolate C: $\displaystyle -\frac{1819}{20} = C$
Rewrite: $\displaystyle C = -\frac{1819}{20}$
Substitute in C [Function]: $\displaystyle f(t) = \frac{t^5}{5} + 91t - 3ln|t| - \frac{1819}{20}$