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Kamila [148]
3 years ago
13

When p(x)=x^3+ax+b is divided by x-1 the remainder is 2. When px is divided by x-2 the remainder is 1. Find the values of a and

b?
Mathematics
1 answer:
kvasek [131]3 years ago
5 0

a = - 8 and b = 9

Using the Remainder Theorem.

p(x) divided by (x - a) has remainder p(a)

p(1) = 1³ + a + b = 2⇒ 1 + a +b = 2 ⇒ a + b = 1 ..... (1)

p(2)=2³ + 2a + b = 1 ⇒ 8 +2a + b =1 ⇒ 2a + b = - 7 .....(2)

(2) - (1) gives a = - 8

substitute a = - 8 into (1) : - 8 + b = 1 ⇒ b=9



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An example of consecutive odd integers is 23, 25, 27, and 29. Find four consecutive odd integers with a sum of 160. Show your wo
Andrew [12]
Step1: Define an odd integer.
Define the first odd integer as (2n + 1), for n = 0,1,2, ...,
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Multiplying n by 2 guarantees that 2n will be zero or an even number.
Therefore (2n + 1) is guaranteed to be an odd number.
By adding 2 to the odd integer (2n+1), the next number (2n+3) will also be an odd integer.

Let the four consecutive odd integers be
2n+1, 2n +3, 2n +5, 2n +7 

Step 3: require that the four consecutive integers sum to 160.
Because the sum of the four consecutive odd integers is 160, therefore
2n+1 + 2n+3 + 2n+5 + 2n +7 = 160
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8 0
3 years ago
sebuah topi berbentuk kerucut dengan panjang diameter 18 cm dan tinggi topi tersebut 20cm berapakah volume nya​
madreJ [45]

Answer:

The area of the cone is "1,695.6 cm³".

Step-by-step explanation:

The given values are:

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d = 18 cm

then,

Radius,

r = \frac{d}{2}

 = \frac{18}{2}

 = 9 \ cm

Height,

h = 20 cm

As we know,

⇒  Area of a cone = \frac{1}{3} \pi r^2 h

On substituting the given values in the above formula, we get

⇒                            = \frac{1}{3}\times 3.14\times (9)^2\times 20

⇒                            = \frac{1}{3}\times 3.14\times 81\times 20

⇒                            = 3.14\times 27\times 20

⇒                            = 1,695.6 \ cm^3

8 0
2 years ago
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