If p is inversely proportional to the square of q, and p is 28 when q is 3, determine p when q is equal to 2.

Solve for q. a=qb+r What is q equal to? q=a−r−b q=a−r/b q=a/b −r q=a/rb

Mademuasel [1]

The given equation is $a=qb+r$

We need to solve the equation for q.

Value of q:

The value of q can be determined by solving the equation $a=qb+r$ for q.

Thus, subtracting both sides of the equation by r, we get;

$a-r=qb$

Now, dividing both sides of the equation by b, we have;

$\frac{a-r}{b}=\frac{qb}{b}$

Simplifying the terms, we get;

$\frac{a-r}{b}=q$

Therefore, the value of q is $q=\frac{a-r}{b}$

Hence, Option B is the correct answer.

7 0

2 years ago

A) Find a recurrence relation for the number of bit strings of length n that contain a pair of consecutive 0s.

Fed [463]

Answer:

A) $a_{n} = a_{n-1} + a_{n-2} + 2^{n-2}$

B) $a_{0} = a_{1} = 0$

C) for n = 2

$a_{2}$ = 1

for n = 3

$a_{3}$ = 3

for n = 4

$a_{4}$ = 8

for n = 5

$a_{5}$ = 19

Step-by-step explanation:

A) A recurrence relation for the number of bit strings of length n that contain a pair of consecutive Os can be represented below

if a string (n ) ends with 00 for n-2 positions there are a pair of consecutive Os therefore there will be : $2^{n-2}$ strings

therefore for n ≥ 2

The recurrence relation for the number of bit strings of length 'n' that contains consecutive Os

$a_{n} = a_{n-1} + a_{n-2} + 2^{n-2}$

b ) The initial conditions

The initial conditions are : $a_{0} = a_{1} = 0$

C) The number of bit strings of length seven containing two consecutive 0s

here we apply the re occurrence relation and the initial conditions

$a_{n} = a_{n-1} + a_{n-2} + 2^{n-2}$

for n = 2

$a_{2}$ = 1

for n = 3

$a_{3}$ = 3

for n = 4

$a_{4}$ = 8

for n = 5

$a_{5}$ = 19

7 0

2 years ago

Study the graphs, then select the best answers from the drop-down menus.

-Dominant- [34]

1. b 2. a 3. a

100% correct edge 2021

Step-by-step explanation:

7 0

2 years ago

Factor completely 5x^2 − 40.

AVprozaik [17]

Answer:

5(x^2−8

Step-by-step explanation:

There you go

8 0

2 years ago

3- There are 35 cubes in 7 bowls. How many cubes in 3 bowls?

Murrr4er [49]

Answer:

3. 15 Cubes

4. 60 ft per sec , 180 ft

5. 58 yards per min

6. $7.50, $18.00

Step-by-step explanation:

3. Number of Cubes in 7 bowls = 35

Number of Cubes in 1 bowls = $\frac{35}{7}$

Number of Cubes in 3 bowls = $\frac{35}{7} \times 3 = 15$

4. Distance ran by Zebra = 420 ft

Time taken = 7 seconds

Speed = $\frac{Distance}{time}= \frac{420}{7}$ =60 ft per sec

Hence

Distance = speed x time

Distance covered in 30 seconds = 60 x 30 = 180 Ft

5. Distance travelled = 870 yards

Time taken = 15 mins

Speed = $\frac{Distance}{time}= \frac{870}{15}=58$ yards per min

6. Cost of 3 pounds of apple = $4.50

Cost of 1 pounds of apple = $\frac{4.50}{3}$ =$1.50

Cost of 5 pounds of apple = 5 x $1.50 =$7.50

Cost of 12 pounds of apple = 12 x $1.50 =$18.00

6 0

2 years ago