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3 years ago

If TU = x + 5, UV = 20, and TV = 10x − 11, what is TV?

Mathematics

1 answer:

Aleksandr-060686 [28]3 years ago

3 0

Answer:

TV = 29

Step-by-step explanation:

TU + UV = TV

x + 5 + 20 = 10x - 11

5 + 20 + 11 = 10x - x

36 = 9x

36/9 = x

x = 4

TV = 10x − 11 = 10 * 4 - 11 = 40 - 11 = 29

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<h3>Normal Probability Distribution</h3>

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Beads are dropped to create a conical pile such that the ratio of its radius to the height of the pile is constant at 2:3 and th

pav-90 [236]

Answer:

$\displaystyle \frac{dh}{dt} = \frac{1}{20 \pi} \ cm/s$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Algebra I

Equality Properties

Geometry

Volume of a Cone: $\displaystyle V = \frac{1}{3} \pi r^2h$

Calculus

Derivatives

Derivative Notation

Differentiating with respect to time

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Step-by-step explanation:

Step 1: Define

$\displaystyle \frac{r}{h} = \frac{2}{3} \\\frac{dV}{dt} = 5 \ cm^3/s\\h = 15 \ cm$

Step 2: Rewrite Cone Volume Formula

Find the volume of the cone with respect to height.

Define ratio: $\displaystyle \frac{r}{h} = \frac{2}{3}$
Isolate r: $\displaystyle r = \frac{2}{3} h$
Substitute in r [VC]: $\displaystyle V = \frac{1}{3} \pi (\frac{2}{3}h)^2h$
Exponents: $\displaystyle V = \frac{1}{3} \pi (\frac{4}{9}h^2)h$
Multiply: $\displaystyle V = \frac{4}{27} \pi h^3$

Step 3: Differentiate

Basic Power Rule: $\displaystyle \frac{dV}{dt} = \frac{4}{27} \pi \cdot 3 \cdot h^{3-1} \cdot \frac{dh}{dt}$
Simplify: $\displaystyle \frac{dV}{dt} = \frac{4}{9} \pi h^{2} \frac{dh}{dt}$

Step 4: Find Height Rate

Find dh/dt.

Substitute in known variables: $\displaystyle 5 \ cm^3/s = \frac{4}{9} \pi (15 \ cm)^{2} \frac{dh}{dt}$
Isolate dh/dt: $\displaystyle \frac{5 \ cm^3/s}{\frac{4}{9} \pi (15 \ cm)^{2} } = \frac{dh}{dt}$
Rewrite: $\displaystyle \frac{dh}{dt} = \frac{5 \ cm^3/s}{\frac{4}{9} \pi (15 \ cm)^{2} }$
Evaluate Exponents: $\displaystyle \frac{dh}{dt} = \frac{5 \ cm^3/s}{\frac{4}{9} \pi (225 \ cm^2) }$
Evaluate Multiplication: $\displaystyle \frac{dh}{dt} = \frac{5 \ cm^3/s}{100 \pi cm^2 }$
Simplify: $\displaystyle \frac{dh}{dt} = \frac{1}{20 \pi} \ cm/s$

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3 years ago