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3 years ago

(a) Find the first 3 terms in ascending powers of x of the binomial expansion of (2+x/2)^6

Mathematics

1 answer:

Firdavs [7]3 years ago

3 0

Answer:(2+x/2)^6=64(1+3x/2+15x^2/16+5x^3/16+....) (2.05)^6=74.2203

Step-by-step explanation:

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What multiplies to -29 and adds to 1

Margarita [4]

First set up equation
x times y=xy

so
xy=-29
and
x+y=1
subtract x from both sides
y=1-x
subsitute 1-x for y in first equation
x(1-x)=-29
distribute
x-x^2=-29
add x^2 to both sides
x=-29+x^2
subtract x from both sides
0=x^2-x-29
so we can use the quadratic formula to solve for x if the equation=0 and it is in ax^2+bx+c form so

if
ax+bx+c=0 then x= $\frac{ -b+/-\sqrt{b^2-4ac} }{2a}$ that means x= $\frac{ -b-\sqrt{b^2-4ac} }{2a}$ or x= $\frac{ -b-\sqrt{b^2-4ac} }{2a}$ so

x^2-x-29
a=1
b=-1
c=-29
$\frac{ -(-1)-\sqrt{-1^2-4(1)(-29)} }{2(1)}$ = $\frac{ +1-\sqrt{1^2-(-116)} }{2(1)}=\frac{ +1-\sqrt{1^2+116} }{2}=\frac{ +1-\sqrt{117} }{2}= \frac{1-10.816653826392}{2} = [tex] \frac{-9.816653826392}{2}= -4.908326913196$

the second number is
$\frac{ -(-1)+\sqrt{-1^2-4(1)(-29)} }{2(1)}=\frac{ +1+\sqrt{1^2+(-116)} }{2(1)}= \frac{1+10.816653826392}{2} = \frac{ +1+\sqrt{117} }{2}= \frac{10.816653826392}{2}=5.908326913196$

the two numbers are
5.908326913196 and
-4.908326913196

7 0

3 years ago

What does x equal in 3(x+3)-2<25

Phantasy [73]

3x+9-2<20

3x+7-25<25-25

3x-18=0

x=18/3

x=6

8 0

4 years ago

If a reflection over the line y=x occurs, then the rule for this reflection is

Anni [7]

If you reflect over the line y = -x, the x-coordinate and y-coordinate change places and are negated (the signs are changed).

7 0

3 years ago

The sum of two numbers is 50. One number is 28 more than the other. Find the numbers.

Lady bird [3.3K]

Answer:

Step-by-step explanation:

28+22 is 50

3 0

3 years ago

Read 2 more answers

Two number cubes are rolled sequentially. What is the probability that the first number cube shows a five and the other number c

nexus9112 [7]

The probability of first number cube shows a five and the other number cube shows an even number is $\frac{1}{12}$ .

Solution:

Two cubes are rolled sequentially.

Sample space when two dies are rolled

$=\left\{\begin{array}{l}{(1,1),(1,2),(1,3),(1,4),(1,5),(1,6)} \\{(2,1),(2,2),(2,3),(2,4),(2,5),(2,6)} \\{(3,1), 3(, 2),(3,3),(3,4),(3,5),(3,6)} \\{(4,1),(4,2),(4,3),(4,4),(4,5),(4,6)} \\{(5,1),(5,2),(5,3),(5,4),(5,5),(5,6)} \\{(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)}\end{array}\right\}$

Number of sample space = 36

Even numbers getting when two cubes rolled are 2, 4, 6.

First number cube shows a five and the other number cube shows an even number = {(5, 2), (5, 4), (5 6)}

Number of first number cube shows a five and the other number cube shows an even number = 3

Probability of first number cube shows a five and the other number cube shows an even number

$=\frac{\text{Number of outcomes}}{\text{Total number of sample space}}$

$$=\frac{3}{36}$

$$=\frac{1}{12}$

Hence, the probability of first number cube shows a five and the other number cube shows an even number is $\frac{1}{12}$ .

8 0

3 years ago