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worty [1.4K]
3 years ago
8

Write a function rule for our pattern. 84, 90, 96, 102, 108, …. You may use f(x) or the explicit formula. Use AN for the explici

t formula.
Mathematics
1 answer:
enyata [817]3 years ago
6 0

Answer:

For the given sequence, the function rule is f(x) = 84 + 6(n-1) where 'n' represents the number of the term in the sequence.

Step-by-step explanation:

For any given sequence, you need to first find the pattern, or relationship between the numbers.  In this case, you can see that the numbers increase by six each time.  The general formula for an arithmetic sequence, also called explicit formula, is a(n) = a(1) + d(n-1) where a(n) represents the term in the sequence; a(1) is the first term in the sequence; d=the common difference; and n=term number.  When we plug in the values from the question a(1) = 84 and d = 6 to get our final equation.

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the magnetic field at a distance r from a long straight wire carrying current I can be calculated with the equation:

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A worker at a snack stand opened a new box of cups. The first day he used 30 cups , the second day the worker used 15 percent of
Sholpan [36]

Answer:

Step-by-step explanation:

the first day he used 30 cups

the second day he used 15% of the remaining cups...a total of 90 cups were used on second day.

so 15%of the remaining cups = 90.....so if u let x be the total cups, then the remaining cups would be x - 30

15% of (x - 30) = 90.....turn ur percent to a decimal..." of " means multiply

0.15(x - 30) = 90

0.15x - 4.5 = 90

0.15x = 90 + 4.5

0.15x = 94.5

x = 94.5 / 0.15

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lets check..

start with 630 cups....used 30 the first day....leaving u with 600 cups....15% of the remaining cups = 90.....so 15% of 600 = 90....lets check it

15%of 600 = 0.15(600) = 90...yep, thats correct....there were 630 cups in the new un-opened box

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Cindy claims that 4x/12x= 1/3. Enter a whole number that supports Cindy's claim, and then enter a whole number that does not sup
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EXAMPLE 5 If F(x, y, z) = 4y2i + (8xy + 4e4z)j + 16ye4zk, find a function f such that ∇f = F. SOLUTION If there is such a functi
Valentin [98]

If there is such a scalar function <em>f</em>, then

\dfrac{\partial f}{\partial x}=4y^2

\dfrac{\partial f}{\partial y}=8xy+4e^{4z}

\dfrac{\partial f}{\partial z}=16ye^{4z}

Integrate both sides of the first equation with respect to <em>x</em> :

f(x,y,z)=4xy^2+g(y,z)

Differentiate both sides with respect to <em>y</em> :

\dfrac{\partial f}{\partial y}=8xy+4e^{4z}=8xy+\dfrac{\partial g}{\partial y}

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g(y,z)=4ye^{4z}+h(z)

Plug this into the equation above with <em>f</em> , then differentiate both sides with respect to <em>z</em> :

f(x,y,z)=4xy^2+4ye^{4z}+h(z)

\dfrac{\partial f}{\partial z}=16ye^{4z}=16ye^{4z}+\dfrac{\mathrm dh}{\mathrm dz}

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Integrate both sides with respect to <em>z</em> :

h(z)=C

So we end up with

\boxed{f(x,y,z)=4xy^2+4ye^{4z}+C}

7 0
3 years ago
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