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3 years ago

1) Write these using index notation: a. 2 X 2 X 2 X 2 b. 5 X 5 X 5 X 7 X 7

Mathematics

1 answer:

mrs_skeptik [129]3 years ago

3 0

Answer:

a) $2^{4}$

b) $5^{3}$ x $7^{2}$

Step-by-step explanation:

You can group together like base values, so 3 x 3 x 3 x 3 x 3 becomes 3 to the power of 5. All it means is that you are multiplying the base value (in this case 3) by itself 5 times.

Index notation makes it easier in more complex equations to solve, as its simpler and doesn't take up as much space.

Hope this helped : )

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Use Remainder Theorem to determine if x-2 is a factor of the polynomial f(x)=3x^5 - 7x^3 -

morpeh [17]

Answer:

(x - 2) is not a factor of f(x) = 3x^5 - 7x^3 - 11x^2 + 2

Step-by-step explanation:

According to the Remainder Theorem, when a polynomial f(x) is divided by a term (x - r), then the remainder must be f(r).

So first we will divide f(x) by (x - 2) using long division to get:

(3x^5 - 7x^3 - 11x^2 + 2) / (x - 2)

= 3x^4 + (6x^4 - 7x^3 - 11x^2 + 2) / (x-2)

= 3x^4 + 6x^3 + (5x^3-11x^2+2) / (x - 2)

= 3x^4 + 6x^3 + 5x^2 (-x^2 + 2) / (x - 2)

= 3x^4 + 6x^3 + 5x^2 -x -2 - (2) / (x -2)

= $\frac{-2 + 3x^{5} - 7x^{3} - 11x^{2} + 2x}{x - 2} - 2$

Therefore the remainder is -2.

Now check x = 2 for 3x^5 - 7x^3 - 11x^2 + 2:

3(2)^5 - 7(2)^3 - 11(2)^2 + 2 = -2

The Remainder Factor theorem also states that if (x - r) is a factor of f(x) then f(r) must be 0.

So we found that f(2) = -2, therfore (x - 2) is not a factor of f(x) .

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Answer:

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3 years ago

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You are standing above the point (2,5) on the surface z=30−(2x2+2y2). (a) in which direction should you walk to descend fastest?

3241004551 [841]

(a) Use u = -∇z(2, 5)/||∇f(2, 5)||

= -<-4x, -4y>/||<-4x, -4y>|| {at (2, 5)} 
= <8, 20>/√((-8)^2 + (-20)^2)
= <2, 5>/√29

(b) Du f(2, 5) = ∇z(2, 5) · u 
= ∇z(2, 5) · -∇z(2, 5)/||∇f(2, 5)|| 
= -||∇z(2, 5)||^2 / ||∇f(2, 5)|| 
= -||∇z(2, 5)|| 
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4 years ago

find the HCF and LCM of 92 and 510 by method of prime factorization hence verify that HCF into a cm equal to product of two give

Daniel [21]

Answer:

Step-by-step explanation:

92 = 2² × 23

510 = 2 × 3 × 5 × 17

HCF = 2

LCM = 2² × 3 × 5 × 17 × 23 = 23460

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3 years ago

Help plz

solong [7]

Answer:

Question 1: 8

Question 2: -32.5

Step-by-step explanation:

Laura gets paid 8 dollars an hour to baby sit

8x represents how much Laura gets paid by the hour.

Laura owes her friend 32.50

-32.50 represents the amount she owes her friend

Combine

y = 8x - 32.50

Answer

Question 1: 8

Question 2: -32.5

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