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VARVARA [1.3K]
3 years ago
8

What is the constant of proportionality in the equation y =2.5xy=2.5 xy

Mathematics
2 answers:
Inessa [10]3 years ago
8 0
What is the constant of proportionality in the equation y =2.5x

2.5
kenny6666 [7]3 years ago
5 0

Answer: 2.5

Step-by-step explanation:

We know that the constant of proportionality is the ratio between two directly proportional quantities.

The equation of direct variation between two quantities x and y is given by :-

y=kx, where k is the constant of proportionality,

The given equation : - y =2.5xy

When we compare to the general direct variation equation , we get

k=2.5

hence, the constant of proportionality in the equation  2.5

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Step-by-step explanation:

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30+ Points!!!<br> 5. Solve the following inequalities.<br> a) 2 log3x – 2 logx3 -3 &lt;0
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Answer:

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2 log3x – 2 logx3 -3 <0

\mathrm{Subtract\:}2\log ^3\left(x\right)\mathrm{\:from\:both\:sides}

2\log ^3\left(x\right)-2logx^3-3-2\log ^3\left(x\right)

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\mathrm{Add\:}3\mathrm{\:to\:both\:sides}

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Multiply\:both\:sides\:by\:-1\:\left(reverse\:the\:inequality\right)

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2lx^3og>2\log ^3\left(x\right)-3

\mathrm{Divide\:both\:sides\:by\:}2lx^3o;\quad \:l>0

\frac{2lx^3og}{2lx^3o}>\frac{2\log ^3\left(x\right)}{2lx^3o}-\frac{3}{2lx^3o};\quad \:l>0\\

\mathrm{Simplify}

g>\frac{2\log ^3\left(x\right)-3}{2lx^3o};\quad \:l>0

Step-by-step explanation:

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Write a recursive rule and an explicit rule for the<br> sequence<br> 3,7,11,15
m_a_m_a [10]

Answer:

The Recursive formula for the sequence is:

aₙ = aₙ₋₁ + d

The Explicit formula for the sequence is:

a_n=4n-1

Step-by-step explanation:

Given the sequence

3,7,11,15

Here:

a₁ = 3

computing the differences of all the adjacent terms

7 - 3 = 4, 11 - 7 = 4, 15 - 11 = 4

The difference between all the adjacent terms is the same and equal to

d = 4

We know that a recursive formula basically defines each term of a sequence using the previous term(s).

The recursive formula of the Arithmetic sequence always involves the first term.

a₁ = 3

We know that, in the Arithmetic sequence, every next term can be obtained by adding the common difference and the preceding term.

so

The recursive formula of the sequence is:

aₙ = aₙ₋₁ + d

substitute n = 2 to find the 2nd term

a₂ = a₂₋₁ + d

a₂ = a₁+ d

substitute a₁ = 3 and d = 4

a₂ = 3 + 4

a₂ = 7

Thus, the recursive formula for the sequence 3,7,11,15 is:

aₙ = aₙ₋₁ + d

<u>An explicit rule for the sequence</u>

Given the sequence

3,7,11,15

We already know that

a₁ = 3

d = 4

An arithmetic sequence has a constant difference 'd' and is defined by  

a_n=a_1+\left(n-1\right)d

substituting a₁ = 3 and d = 4

a_n=4\left(n-1\right)+3

a_n=4n-4+3

a_n=4n-1

Therefore, an explicit rule for the  sequence

a_n=4n-1

6 0
2 years ago
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