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padilas [110]
3 years ago
13

What are the restrictions for (x^2+10x+25)/(x^2-3x-28) 0,14 -4,7 0,7 4,7

Mathematics
1 answer:
nirvana33 [79]3 years ago
5 0
The answer is -4,7

The denominator can't equal zero. Factor the denominator:
x^2 - 3x - 28=
(X - 7)(x + 4); next set each set of parentheses equal to 0;
x - 7 = 0; so x=7 is one value
x + 4 = 0; so x=-4 is the other
Remember, x = 7 and x= -4 make the denominator zero, which is a "restriction" because you can't divide by zero.
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Find the 2nd Derivative:<br> f(x) = 3x⁴ + 2x² - 8x + 4
ad-work [718]

Answer:

f''(x)=36x^2+4

Step-by-step explanation:

Let's start by finding the first derivative of f(x)= 3x^4+2x^2-8x+4. We can do so by using the power rule for derivatives.

The power rule states that:

  • \frac{d}{dx} (x^n) = n \times x^n^-^1

This means that if you are taking the derivative of a function with powers, you can bring the power down and multiply it with the coefficient, then reduce the power by 1.

Another rule that we need to note is that the derivative of a constant is 0.

Let's apply the power rule to the function f(x).

  • \frac{d}{dx} (3x^4+2x^2-8x+4)

Bring the exponent down and multiply it with the coefficient. Then, reduce the power by 1.

  • \frac{d}{dx} (3x^4+2x^2-8x+4) = ((4)3x^4^-^1+(2)2x^2^-^1-(1)8x^1^-^1+(0)4)

Simplify the equation.

  • \frac{d}{dx} (3x^4+2x^2-8x+4) = (12x^3+4x^1-8x^0+0)
  • \frac{d}{dx} (3x^4+2x^2-8x+4) = (12x^3+4x-8(1)+0)
  • \frac{d}{dx} (3x^4+2x^2-8x+4) = (12x^3+4x-8)
  • f'(x)=12x^3+4x-8

Now, this is only the first derivative of the function f(x). Let's find the second derivative by applying the power rule once again, but this time to the first derivative, f'(x).

  • \frac{d}{d} (f'x) = \frac{d}{dx} (12x^3+4x-8)
  • \frac{d}{dx} (12x^3+4x-8) = ((3)12x^3^-^1 + (1)4x^1^-^1 - (0)8)

Simplify the equation.

  • \frac{d}{dx} (12x^3+4x-8) = (36x^2 + 4x^0 - 0)
  • \frac{d}{dx} (12x^3+4x-8) = (36x^2 + 4(1) - 0)
  • \frac{d}{dx} (12x^3+4x-8) = (36x^2 + 4 )

Therefore, this is the 2nd derivative of the function f(x).

We can say that: f''(x)=36x^2+4

6 0
2 years ago
Read 2 more answers
Miguel saved $355 in 5 weeks. He saved equal amounts of money each week. How much money would he save in 15.5 weeks ?
Andrei [34K]

Answer:

A

Step-by-step explanation:

$355:5

$355 divided by 5=$71

5 divided by 5=1

$71 per week

$71x15.5=$1,100.50

$1,100.50 in 15.5 weeks

7 0
3 years ago
X^2=1/4 please help me
skelet666 [1.2K]
X² = 1/4 ⇒√⇒ x₁ = 1/2, x₂ = -1/2
5 0
3 years ago
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In programming, what is a floating-point number?
Cerrena [4.2K]

Answer: A floating-point number is one where the position of the decimal point can "float" rather than being in a fixed position within a number. floating point is a variable type that is used to store floating-point number values.

5 0
3 years ago
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Solve for x.<br> 5<br> 10<br> 12<br> 13
zysi [14]

Answer: B)  4 & 1/6

Nice work on getting the correct answer.

============================================================

Explanation:

x is opposite the marked acute angle

5 is opposite the corresponding acute angle

So x and 5 are proportional to each other. We can form the ratio x/5

Similarly, 10 and 12 are proportional to one another. We can form the ratio 10/12.

Set those ratios equal to each other and solve for x

x/5 = 10/12

12x = 5*10 ... cross multiply

12x = 50

x = 50/12 ...... divide both sides by 12

x = (25*2)/(6*2)

x = 25/6

x = (24+1)/6

x = 24/6 + 1/6

x = 4 + 1/6

x = 4 & 1/6 which shows why <u>choice B</u> is the answer.

Side note: 25/6 = 4.167 approximately

8 0
3 years ago
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