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3 years ago

If f(1)=3 and f(n)=-2f(n-1)+1,then f(5)=

1 answer:

5 0

F(5) = - 2f(4) + 1
f(4) = -2f(3) + 1
f(3) = -2f(2) + 1
f(2) = -2f(1) + 1
Therefore:
f(2) = -2(3) + 1 = -5
f(3) = -2(-5) + 1 = 11
f(4) = -2(11) + 1 = -21
Therefore f(5) = -2(-21) + 1 = 43

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If 4f(x)+f(5-x)=x2<br><br> What is f(x)?

aksik [14]

We are given that $4f(x)+f(5-x)=x^2$ .

Substitute x with 5-x, then the above equation becomes:

$4f(5-x)+f(5-(5-x))=(5-x)^2$ , that is

$4f(5-x)+f(x)=(5-x)^2$

So, we have the following system of equations:

i) $4f(x)+f(5-x)=x^2$
ii) $4f(5-x)+f(x)=(5-x)^2$

multiply the first equation by -4, so that we eliminate f(5-x)'s

i) $-16f(x)-4f(5-x)=-4x^2$
ii) $4f(5-x)+f(x)=(5-x)^2$

adding the 2 equations side by side we have:

$-15f(x)=-4x^2+(5-x)^2$

expanding the binomial, and collecting same terms we have:

$-15f(x)=-4x^2+(25-10x+x^2)$

$-15f(x)=-3x^2-10x+25$

dividing by -5:

$3f(x)=\frac{3}{5}x^2+2x-5$

dividing by 3:

$\displaystyle{f(x)= \frac{1}{5}x^2+ \frac{2}{3}x-\frac{5}{3}$

Answer: $\displaystyle{f(x)= \frac{1}{5}x^2+ \frac{2}{3}x-\frac{5}{3}$

6 0

3 years ago

Help with this question ASAP!

user100 [1]

Answer:

After 4s

Step-by-step explanation:

Given the ball is initially projected upwards with a velocity of 64ft per sec and we are required to find the time at which it reaches the ground .There are many approaches to solve this problem we will follow this one:

It is also known as the time of flight for the ball which can be found by doubling the time taken for the ball to reach to its maximum height or the point where velocity is zero.

Now $h(t)=-16\times t^{2} +v_{0} \times t+h_{0}$

For the time taken to reach the max height $\frac{dh}{dt} =0$ .

Which implies that -32t+v=0.

∴Time taken to travel halfway through the path =2sec.

∴total time = $2\times 2=4sec$

4 0

2 years ago

Which function is used to model hourly pay?

Maksim231197 [3]

Im pretty sure its A, but dont count on me!!! i hope it helps :/

7 0

3 years ago

Read 2 more answers

Estimate the quotient.

Vika [28.1K]

You divide the two and that's your answer

8 0

3 years ago

Read 2 more answers

4. Lydia cut out her initial from a piece<br><br> of construction paper,

Ratling [72]

Answer:

Option A is correct.

10 square centimeters.

Step-by-step explanation:

Complete Question

The complete Question is attached in the first attached image.

Lydia cut out her initial from a piece of construction paper. How many square centimeters of construction paper are used to make Lydia's initial?

A) 10 square centimeters

B) 11 square centimeters

C) 15 square centimeters

D) 22 square centimeters

Solution

From the second attached image, it is evident that we can split the L-shaped figure into two rectangles of dimensions (3 cm by 1 cm) and (7 cm by 1 cm)

The total area of the figure is thus

(3 × 1) + (7 × 1) = 10 cm²

Hope this Helps!!!

3 0

3 years ago