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3 years ago

I need help with this.

Mathematics

1 answer:

e-lub [12.9K]3 years ago

8 0

Answer:

its 512 cubic centimeters

Step-by-step explanation:

8×8×8=512

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Find the general term of sequence defined by these conditions.

disa [49]

Answer:

$\displaystyle a_{n} = (2)^{2n -1} - (3) ^{n-1 }$

Step-by-step explanation:

we want to figure out the general term of the following recurrence relation

$\displaystyle \rm a_{n + 2} - 7a_{n + 1} + 12a_n = 0 \: \: where : \: \:a_1 = 1 \: ,a_2 = 5,$

we are given a linear homogeneous recurrence relation which degree is 2. In order to find the general term ,we need to make it a characteristic equation i.e

${x}^{n} = c_{1} {x}^{n - 1} + c_{2} {x}^{n - 2} + c_{3} {x}^{n -3 } { \dots} + c_{k} {x}^{n - k}$

the steps for solving a linear homogeneous recurrence relation are as follows:

Create the characteristic equation by moving every term to the left-hand side, set equal to zero.
Solve the polynomial by factoring or the quadratic formula.
Determine the form for each solution: distinct roots, repeated roots, or complex roots.
Use initial conditions to find coefficients using systems of equations or matrices.

Step-1:Create the characteristic equation

${x}^{2} - 7x+ 12= 0$

Step-2:Solve the polynomial by factoring

factor the quadratic:

$( {x}^{} - 4)(x - 3) = 0$

solve for x:

$x = \rm 4 \:and \: 3$

Step-3:Determine the form for each solution

since we've two distinct roots,we'd utilize the following formula:

$\displaystyle a_{n} = c_{1} {x} _{1} ^{n } + c_{2} {x} _{2} ^{n }$

so substitute the roots we got:

$\displaystyle a_{n} = c_{1} (4)^{n } + c_{2} (3) ^{n }$

Step-4:Use initial conditions to find coefficients using systems of equations

create the system of equation:

$\begin{cases}\displaystyle 4c_{1} +3 c_{2} = 1 \\ 16c_{1} + 9c_{2} = 5\end{cases}$

solve the system of equation which yields:

$\displaystyle c_{1} = \frac{1}{2} \\ c_{2} = - \frac{1}{3}$

finally substitute:

$\displaystyle a_{n} = \frac{1}{2} (4)^{n } - \frac{1}{3} (3) ^{n }$

$\displaystyle \boxed{ a_{n} = (2)^{2n-1 } - (3) ^{n -1}}$

and we're done!

7 0

3 years ago

At a football game, a vender sold a combined total of 201

gizmo_the_mogwai [7]

We know that soda + hot dog =201

soda is 2x

hot dog is x

2x+x=201

3x=201

divide each side by 3

x=67

2x=134

They sold 134 sodas and 67 hotdogs

5 0

3 years ago

cesar left the college traveling 12 mph. Then, 4 hours later, Gabriel left traveling the same direction at 24 mph. How long will

Sloan [31]

Answer:

Step-by-step explanation:

Given that cesar left the college traveling 12 mph. Then, 4 hours later, Gabriel left traveling the same direction at 24 mph.

Before Gabriel started Cesar would have travelled for 4 hours

So distance travelled by Cesar in 4 hours $=4(12) =48 miles$

Thus Cesar is ahead of Gabriel by 48 miles

Difference of speed $=(24-12) =12 mph$

So to catch Cesar time required = 48/difference in speed

= 4 hours

It will take 4 hours.

8 0

3 years ago

Deanna knows that the floor in her kitchen is a square with an area of 169 ft2. The perimeter of her kitchen floor is found by a

Savatey [412]

Answer:

52 ft

Step-by-step explanation:

area of a square is l x w. all sides are equal so the l = w

A = 169 ft^2 so each side is the square root of 169 which is 13 ft

perimeter of the floor would be all four sides added or length of 1 side multiplied by 4 since they are all equal

Perimeter = 13ft × 4 = 52 ft

so:

6 0

3 years ago

Read 2 more answers

Hi help with these please and thank yu? :)

ryzh [129]

Answer:

the first one is A

b/c when you calculate it comes 0 = 6

And the second one is D

b/c when you calculate it comes 0 = 2

if it's helpful ❤❤❤

THANK YOU.

7 0

3 years ago

I need help with this.​

I need help with this.