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2 years ago

Use the discriminant to determine the number of real solutions of the equation. x^2 = -6x - 10

Mathematics

2 answers:

HACTEHA [7]2 years ago

8 0

Answer:

No real solutions.

Step-by-step explanation:

x² + 6x + 10 = 0

a = 1

b = 6

c = 10

D = b² - 4ac = 6² - 4*1*10 = 36 - 40 = - 4

- 4 < 0,

so this equation has no real solutions.

juin [17]2 years ago

3 0

The discriminators is b^2-4ac

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8. Find all the real fourth roots of 256

mezya [45]

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x^4-256=0
(x^2)^2-(16)^2=0
(x^2+16)(x^2-16)=0
either x^2+16=0
it gives complex roots.
or x^2-16=0
or x^2-4^2=0
(x+4)(x-4)=0
either x+4=0,x=-4
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7 0

2 years ago

Find and identify the traces of the quadric surface x2 + y2 − z2 = 36 given the plane. x = k Find the trace. Incorrect: Your ans

AlekseyPX

Answer:

Hyperbola.

Step-by-step explanation:

We start from the function:

$x^{2} +y^{2} -z^{2} =36$

We may get the traces if we cut the surface in planes x=k. This is equivalent to replace x for k:

$k^{2}+y^{2} -z^{2}=36\\y^{2} -z^{2}=36-k^{2}$

The last equation is the equation of an hyperbola, which varies its characteristics depending on K (the plane cut).

3 0

2 years ago

F(x) = e^-x . Find the equation of the tangent to f(x) at x=-1

natima [27]

Answer:

The equation of the tangent line is given by the following equation:

$\displaystyle y - \frac{1}{e} = \frac{-1}{e} \bigg( x - 1 \bigg)$

General Formulas and Concepts:

Algebra I

Point-Slope Form: y - y₁ = m(x - x₁)

x₁ - x coordinate
y₁ - y coordinate
m - slope

Calculus

Differentiation

Derivatives
Derivative Notation

Derivative Property [Multiplied Constant]:
$\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)$

Derivative Rule [Basic Power Rule]:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Derivative Rule [Chain Rule]:
$\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)$

Step-by-step explanation:

*Note:

Recall that the definition of the derivative is the slope of the tangent line.

Step 1: Define

Identify given.

$\displaystylef(x) = e^{-x} \\x = -1$

Step 2: Differentiate

[Function] Apply Exponential Differentiation [Derivative Rule - Chain Rule]:
$\displaystyle f'(x) = e^{-x}(-x)'$
[Derivative] Rewrite [Derivative Rule - Multiplied Constant]:
$\displaystyle f'(x) = -e^{-x}(x)'$
[Derivative] Apply Derivative Rule [Derivative Rule - Basic Power Rule]:
$\displaystyle f'(x) = -e^{-x}$

Step 3: Find Tangent Slope

[Derivative] Substitute in x = 1:
$\displaystyle f'(1) = -e^{-1}$
Rewrite:
$\displaystyle f'(1) = \frac{-1}{e}$

∴ the slope of the tangent line is equal to $\displaystyle \frac{-1}{e}$ .

Step 4: Find Equation

[Function] Substitute in x = 1:
$\displaystyle f(1) = e^{-1}$
Rewrite:
$\displaystyle f(1) = \frac{1}{e}$

∴ our point is equal to $\displaystyle \bigg( 1, \frac{1}{e} \bigg)$ .

Substituting in our variables we found into the point-slope form general equation, we get our final answer of:

$\displaystyle \boxed{ y - \frac{1}{e} = \frac{-1}{e} \bigg( x - 1 \bigg) }$

∴ we have our final answer.

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Learn more about derivatives: brainly.com/question/27163229

Learn more about calculus: brainly.com/question/23558817

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Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

3 0

1 year ago

NEED HELP ASAP ON THIS QUESTION

andrew11 [14]

Answer:

None of these answers are correct.

Step-by-step explanation:

If a²+b²=c², then 7²+5²=c², then if you solve for c this equals about 8. This is none of the answers mentioned which is 8. Also, a good thing to remember is that the hypotenuse is always larger than the two side lengths. So, since the answer is 8 then it is none of the answers.

7 0

2 years ago

Read 2 more answers

For all integers n, if n2 is odd, then n is odd. Use a proof by contraposition, as in Lemma 1.1. Let n be an integer. Suppose th

Reil [10]

Let's assume that the statement "if n^2 is odd, then is odd" is false. That would mean "n^2 is odd" leads to "n is even"

Suppose n is even. That means n = 2k where k is any integer.

Square both sides

n = 2k
n^2 = (2k)^2
n^2 = 4k^2
n^2 = 2*(2k^2)

The expression 2(2k^2) is in the form 2m where m is an integer (m = 2k^2) which shows us that n^2 is also even.

So this contradicts the initial statement which forces n to be odd.

8 0

3 years ago