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3 years ago

Can you see attachment below

Mathematics

2 answers:

padilas [110]3 years ago

8 0

Answer:

yes

Step-by-step explanation:

Kaylis [27]3 years ago

7 0

Yess I can seee the attendees

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Consider the sequence: 1536,768, 384, 192,96, --- Determine the 11th term of the sequence.

Naya [18.7K]

Answer:

1.5

Step-by-step explanation:

Note there is a common ratio between consecutive terms, that is

768 ÷ 1536 = 0.5

384 ÷ 768 = 0.5

192 ÷ 384 = 0.5

96 ÷ 192 = 0.5

This indicates that the terms form a geometric sequence with

$a_{n}$ = a $(r)^{n-1}$

where a is the first term and r the common ratio

Here a = 1536 and r = 0.5, thus

$a_{11}$ = 1536 × $(0.5)^{10}$ = 1.5

7 0

3 years ago

Read 2 more answers

An athlete eats 65 grams of protein per day while training. How much is this in milligrams

spayn [35]

65 grams=65,000 miligrams

5 0

2 years ago

Read 2 more answers

Robert's car uses 5 gallons of gas to cover 170 miles. At this rate, how many gallons will he need for a 255-mile trip?

Talja [164]

170/5 = 34 mi/gallon
255/34 = 7.5 gallons

4 0

3 years ago

Mr. Smith Junior wishes to buy a used car in a year's time when he turns 18, and he is willing to spend $5,000. He plans to work

ArbitrLikvidat [17]

This will be a additional Price = $282.51 Time to maturity = 10 years Annual payment = $50 Rate of the Return = 12%

Hope This helps!

5 0

3 years ago

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

3 0

2 years ago