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3 years ago

The first four terms of a sequence are shown below 9,5,1,-3

Mathematics

1 answer:

Debora [2.8K]3 years ago

8 0

Answer:

A. f(1)=9, f(n+1)=f(n)-4 for n> or equal to 1

Step-by-step explanation:

Given the sequence:

9, 5, 1, -3

We can easily calculate the difference of terms:

-3- 1= 1- 5= 5-9= -4

As the difference of terms is same and equal to -4, it is the AP (arithmetic progression)

This sequence can be defined In the form of function as:

f(1)= 9, as the first term is 9
f(n+1)= f(n)- 4, as it is decreasing function with the difference of -4
n ≥ 1, as we count from the first term on

All the above matches the first answer choice:

A. f(1)=9, f(n+1)=f(n)-4 for n> or equal to 1

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jarptica [38.1K]

If the growth rate is a constant, we can model it using a linear equation:

y = b + ax

where b = initial value, a = growth rate.
In this case, x = m = number of months.

Let's find the equation for the growth of each species.

Species A:
Initial height = b = 25 cm
Growth rate = a = 3 cm per month
So its height can be modeled by H(m) = 25 + 3m

Species B:
Initial height = b = 10 cm
Growth rate = a = 8 cm per month
So its height can be modeled by H(m) = 10 + 8m

Thus the answer is A: H(m) = 25 + 3m and B: H(m) = 10 + 8m.

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3 years ago

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sladkih [1.3K]

Answer:

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Step-by-step explanation:

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3 years ago

Given P=1/2x(y+z),find the value of P,if x=6 and y=9 and z=7

GREYUIT [131]

<span>P=1/2 x(y+z)
</span><span>P=1/2 (6)[9 + 7]
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3 years ago

As Sales Manager for ISeeYou Productions, you are planning to review the prices you charge clients for television advertisement

aksik [14]

The development fee p can be modeled by the equation p=-400q+9600 where p is the price the company charges and q is the number of contracts they get. The total revenue R ISeeYou obtains by signing q contracts is found by using the function: $R(q)=-400q^{2}+9600q$ . The cost ISeeYou Productions can be found by using the following function: C(q)=800q+16000. The monthlhy profit of Express ISeeYou Productions if found with the next function: $P(q)=-400p^{2}+8800q-16000$ . ISeeYou should sign 2 or 20 contracts to break even.

a) In order to solve part a of the problem, we will suppose the price will have a linear relation with the amount of contracts they signed, so we need to find two points to build this function.

We know that when signing 6 contracts, the company charges $7,200, so our first point will be:

(6, 7200)

we also know that the company signs 14 contracts when they charge $4,000. So our second point is:

(14, 4000)

so we can use these points to find the slope of the line by using the

slope formula:

$m=\frac{p_{2}-p_{1}}{q_{2}-q_{1}}$

$m=\frac{4000-7200}{14-6}$

so the slope is:

m=-400

We can now use one of those points and the slope to find the function for the price, so we get:

$y-y_{1}=m(x-x_{1})$

$p-p_{1}=m(q-q_{1})$

if we used the point: (6, 7200) we get:

$p-7200=-400(q-6)$

which can now be simplified:

p=-400q+2400+7200

so the price function is:

p=-400q+9600

b) In order to find the revenue equation we need to multiply the price equation by the amount of contracts they signed in a month, so we get:

R(q)=pq

$R(q)=(-400q+9600)q$

$R(q)=-400q^{2}+9600q$

c) The cost can be found by adding the fixed cost and the variable cost, so we get:

C(q)=800q+16000

d) The profit is found by subtracting the montly cost from the monthly revenue, so we get:

P(q)=R(q)-C(q)

$P(q)=-400q^{2}+9600q-(800q+16000)$

so we can now simplify our function to get:

$P(q)=-400q^{2}+9600q-800q-16000$

$P(q)=-400q^{2}+8800q-16000$

e) In order to find the number of contracts for the company to break even, we need to find the q contracts that will give a profit of $0 so we set the function of the previous part of the problem equal to zero so we get:

$P(q)=-400q^{2}+8800q-16000$

$-400q^{2}+8800q-16000=0$