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Serjik [45]
2 years ago
8

Question 12(Multiple Choice Worth 1 points)

Mathematics
1 answer:
rusak2 [61]2 years ago
7 0

Answer:

\frac1{25}

Step-by-step explanation:

Hello!

Let's use a couple of exponent rules:

  • \frac{a^x}{a^b} = a^{x - b}
  • a^{-x} = \frac{1}{a^x}

Let's utilize the first rule and simplify the fraction.

<h3>Simplify</h3>
  • \frac{5^4}{5^6}
  • 5^{4 - 6}
  • 5^{-2}

Now, we can utilize the second exponent rule, as we have a base to the power of a negative number.

<h3>Simplify</h3>
  • 5^{-2}
  • \frac1{5^2}
  • \frac1{25}

The answer is option 1, \frac{1}{25}.

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Part A: Factor 2x2c2 + 3xc2 − 35c2. Show your work. (4 points)
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3 0
3 years ago
Find a cubic function f(x) = ax3 + bx2 + cx + d that has a local maximum value of 4 at x = −3 and a local minimum value of 0 at
Vinvika [58]
The formula is f(x) = a x ^ 3 + b x ^ 2 + c x  + d 
f '(x) = 3ax^2 + 2bx + c. 
f(- 3) = 3 ==> - 27a + 9b - 3c + d = 3 
f '(- 3) = 0 (being a most extreme) ==> 27a - 6b + c = 0. 
f(1) = 0 ==> a + b + c + d = 0 
f '(1) = 0 (being a base) ==> 3a + 2b + c = 0. 
- 
Along these lines, we have the four conditions 
- 27a + 9b - 3c + d = 3 
a + b + c + d = 0 
27a - 6b + c = 0 
3a + 2b + c = 0 
Subtracting the last two conditions yields 24a - 8b = 0 ==> b = 3a. 
Along these lines, the last condition yields 3a + 6a + c = 0 ==> c = - 9a. 
Consequently, we have from the initial two conditions: 
- 27a + 9(3a) - 3(- 9a) + d = 3 ==> 27a + d = 3 
a + 3a - 9a + d = 0 ==> d = 5a. 
Along these lines, a = 3/32 and d = 15/32. 
==> b = 9/32 and c = - 27/32. 
That is, f(x) = (1/32)(3x^3 + 9x^2 - 27x + 15).
8 0
3 years ago
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