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Ronch [10]
3 years ago
11

Find the first 4 terms in the expansion of ( 1 + x 2 ) 8. Use your answer to find the value of ( 1.01 ) 8

Mathematics
1 answer:
anyanavicka [17]3 years ago
7 0

(1+x^2)^8

=(1+8x^2+8*7/(1*2)x^4+8*7*6/(1*2*3)x^6+8*7*6*5/(1*2*3*4)x^8+....)

=1+8x^2+28x^4+56x^6+70x^8+....)

For x<1, higher power terms diminish in value, hence we can approximate powers of numbers.

1.01=(1+0.1^2) => x=0.1 in the above expansion

(1.01)^8

=1+8(0.1^2)+28(0.1^4)+56(0.1^6) [ limited to four terms, as requested]

=1+0.08+0.0028+0.000056 (+0.00000070)

=1.082856 (approximately)

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Please answer this correctly
Eva8 [605]

Answer:

Surface Area is 56π cm²

Step-by-step explanation:

The area for a cylinder's surface area is

a=2πrh+2πr²

The cylinder base's radius is 4 cm

The cylinder's height is 3 cm

Putting into the equation:

a=2×π×4×3+2×π×4²

a=2π×4×3+2×π×4²

a=8π×3+2×π×4²

a=24π+2×π×4²

a=24π+2×π×16

a=24π+2π×16

a=24π+32π

a=56π

The surface area of the cylinder is 56π cm².

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3 years ago
Can you help me out please
borishaifa [10]
Picture on the left: y = 1/2x + 3

Picture on the right: y = -2x - 3

Mark me as brainliest please?
7 0
3 years ago
R is the midpoint of QS, if QR=2x and RS=x+3, what is RS?
lbvjy [14]
Q -------------R------------S

suppose this is your line,

R is the mid point

and it's given that

QR = 2x
and
RS = x+3

as R is the mid point of QS
so,
QR = RS
then,
2x = x + 3
2x - x =3
x = 3


as,
it's given that RS = x + 3
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3 years ago
A large but sparsely populated county has two small hospitals, one at the south end of the county and one at the north end. The
Readme [11.4K]

Answer:

Step-by-step explanation:

Probability distribution of this type is a vicariate distribution because it specifies two random variable X and Y. We represent the probability X takes x and Y takes y by

f(x,y) = P((X=x,Y=y) ,

and given that the random variables are independent the joint pmf isbgiven by:

f(x,y) = fX(x) .fY(y) and this gives the table (see attachment)

(b) the required probability is given by considering X=0,1 and Y =0,1

f(x,y) = sum{(P(X ≤ 1, Y ≤ 1) }

= [0.1 +0.2 ] × [0.1 + 0.3]

= 0.3 × 0.4

= 0.12

Now we find

fX(x) = sum{[f(x.y)]} for y =0, 1 and similarly for fY(y)= sum{[f(x,y)]} for x=0, 1

fX(x) = sum{[f(x,y)]}= 0.1+0.3

= 0.4

fY(y) = sum{[f(x.y)]} = 0.1 + 0.2

= 0.3

Since fY(y) × fX(x) = 0.4 × 0.3

= 0.12

Hence f(x,y) = fX(x) .fY(y), the events are independent

(c) the required event is give by: [P(X<=1, PY<=1)]

= P(X<=1) . P(Y<=1)

= [sum{[f(x.y]} over Y=0,1] × [sum{[f(x.y)]}, over X= 0, 1

= 0.4 × 0.3

= 0.12

(d) the required event is given by the idea that: either The South has no bed and the North has or the the North has no bed and the South has. Let this event be A

A =sum[(P(X = 1<= x<= 4, Y =0)] + sum[P(X =0 Y= 1 <= x <= 3)]

A = [0.02 + 0.03 + 0.02 + 0.02] + [0.03 + 0.04 + 0.02]

A = [0.09] + [ 0.09]

A = 0.18

Pls note the sum of the vertical column X=2 is 0.3

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Indica el valor del 3 en cada uno de los siguientes números 35.097 _ 753.978 _ 7.543 _ 312.501
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