MATHEMATICS HIGH SCHOOL

Complete the following item based on the given information.The volume of a box(V) varies directly with its length(l). Using k for the constant of proportionality, express the relationship between V and l if V varies directly with l.
V = _______

Answers

Answer 1

Answer:

Answer:

$V = kl$

Step-by-step explanation:

The direct variation states:

if $y \propto x$ , then the equation is in the form of:

$y=kx$ ; where k is the constant of proportionality.

As per the statement:

The volume of a box(V) varies directly with its length(l).

⇒ $V \propto l$

Using the above definition we have;

$V = kl$

where,

k represents for the constant of proportionality.

Therefore, the relationship between V and l if V varies directly with l is,

$V = kl$

Answer 2

Answer: $Volume\ V\ varies\ directly\ with\ length\ l\ proportion\ is\n\n (V)/(l)=k\ \ |*l\n V=kl$

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If a function f ( x ) has values f ( 4 ) = 6 and f ( 8 ) = 18, use what you have learned about function patterns to find f ( 16 ) = if f ( x ) is: a.) Linear function: f ( 16 ) = b.) Power function: f ( 16 ) = c.) Exponential function: f ( 16 ) = d.) Logarithmic function: f ( 16 ) =

Answers

Answer:

a) f(16) = 42

b) f(16) = 54

c) f(16) = 162

d) f(16) = 30

Step-by-step explanation:

a) y = mx + b ∧ m = (f(8) - f(4))/(8-4) ⇒ m = (18 - 6)/(8 - 4) = 3

b = y - mx = 6 - 3(4) = 6 - 12 = - 6

f(16) = 3(16) - 6 = 42

b) y = kxⁿ ∧ f(4) = 6 = k4ⁿ ∧ f(8) = 18 = k8ⁿ ⇒ 18/6 = (k8ⁿ)/(k4ⁿ) ⇒ 3 = 2ⁿ

n = ㏑(3) / ㏑(2) ⇒ k = y/xⁿ ⇒ k = 6/4ⁿ = 2/3

f(16) = 2/3 × 16ⁿ = 54

c) y = aeᵇˣ ∧ f(4) = 6 = aeᵇ⁴ ∧ f(8) = 18 = aeᵇ⁸ ⇒ 18/6 = (aeᵇ⁸)/(aeᵇ⁴) ⇒ 3 = e⁴ᵇ

b = ㏑(3/4) ∧ a = y / eᵇˣ ⇒ a = 6 / e⁴ᵇ = 2

f(16) = 2eᵇ¹⁶ = 162

d) y = a㏑(bx) ∧ f(4) = 6 = a㏑(b4) ∧ f(8) = 18 = a㏑(b8)

⇒ 18 - 6 = a㏑(b8) - a㏑(b4) ⇒ 12 = a㏑(8b/4b) ⇒ a = 12 / ㏑(2)

f(4) = 6 = a㏑(4b) ⇒ b = (√2)/4

f(16) = a㏑(b16) = 30

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C.
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D.
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Answers

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Answers

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Answers

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Answers

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