Mathematics: Evaluate 0.985 using the binomial theorem. write 0.98 as a binomial: (1 +

Evaluate 0.985 using the binomial theorem. write

amandaiscool22

14.03.2022

The value of 0.98^5 is 0.9039207968.

Step-by-step explanation:

We need to find the value of 0.98^5 .

According to the binomial theorem,

$(a+b)^n=^nC_0a^n+^nC_{1}a^{n-1}b+...+^nC_{n-1}a^1b^{n-1}+^nC_nb^n$

Write 0.98 as a binomial: (1 - 0.02)

Write 0.98 as a binomial: (1 + (-0.02))

0.98^5=(1 + (-0.02))^5

Using binomial theorem, we get

0.98^5=^5C_0(1)^5+^5C_1(1)^4(-0.02)^1+^5C_2(1)^3(-0.02)^2+^5C_3(1)^2(-0.02)^3+^5C_4(1)^1(-0.02)^4+^5C_5(1)^0(-0.02)^5

0.98^5=(1)+5(-0.02)^1+10(-0.02)^2+10(-0.02)^3+5(-0.02)^4 +1(-0.02)^5

0.98^5=(1)+(-0.1)+(0.004)+(-0.00008)+0.0000008+(-0.0000000032)

0.98^5=0.9039207968

Therefore the value of 0.98^5 is 0.9039207968.

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rbeltran24

16.09.2022

x = 44.3°

Step-by-step explanation:

Redrawing the triangle,

To obtain x, we can apply the trigonometric relation :

Sin x = opposite / hypotenus

Opposite side = 6.5

Hypotenus = 9.3

Sin x = 6.5/9.3

x = sin^-1(6.5 / 9.3)

x = 44.34

x = 44.3°

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