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2 years ago

What are the approximate solutions of 4x^2 + 3 = -12x to the nearest hundredth

Mathematics

2 answers:

iVinArrow [24]2 years ago

4 0

Approximate solutions are

X subset 2 is approximately equal to -2.72

X subset 1 is approximately equal to -0.28

shutvik [7]2 years ago

4 0

Hello from MrBillDoesMath!

Answer: -.28 and -2.72

Discussion:

This is a quadratic equation (where a = 4, b +12, and c = 3 using the standard notation involved in the solution)

4x^2 + 3= -12x => (given). Add 12x to both sides

4x^2 + 12x + 3 = 0.

From the quadratic formula:

x = ( -12 +\- sqrt ( 12^2 - 4(4)(3) ) )/ (2 * 4)

x = ( -12 +\- sqrt (144 -48))/ (2 * 4)

x = ( -12 +\- sqrt (96)) / (2 * 4)

x = ( -12 +\- sqrt(16*6) ) / (2 * 4)

The "+" solution, x = -12/8 + ( 4 /8)sqrt(6) = -3/2 + 1/2 (sqrt(6)) = -.28

The "-" solution x = -12/8 - ( 4 /8)sqrt(6) = -3/2 - 1/2 (sqrt(6)) = -2.72

Regards,

MrB

Read more on transformations here:

brainly.com/question/4289712

#SPJ1

3 0

1 year ago

Find sin(a)&cos(B), tan(a)&cot(B), and sec(a)&csc(B).

Reil [10]

Answer:

Part A) $sin(\alpha)=\frac{4}{7},\ cos(\beta)=\frac{4}{7}$

Part B) $tan(\alpha)=\frac{4}{\sqrt{33}},\ tan(\beta)=\frac{4}{\sqrt{33}}$

Part C) $sec(\alpha)=\frac{7}{\sqrt{33}},\ csc(\beta)=\frac{7}{\sqrt{33}}$

Step-by-step explanation:

Part A) Find $sin(\alpha)\ and\ cos(\beta)$

we know that

If two angles are complementary, then the value of sine of one angle is equal to the cosine of the other angle

In this problem

$\alpha+\beta=90^o$ ---> by complementary angles

$sin(\alpha)=cos(\beta)$

Find the value of $sin(\alpha)$ in the right triangle of the figure

$sin(\alpha)=\frac{8}{14}$ ---> opposite side divided by the hypotenuse

simplify

$sin(\alpha)=\frac{4}{7}$

therefore

$sin(\alpha)=\frac{4}{7}$

$cos(\beta)=\frac{4}{7}$

Part B) Find $tan(\alpha)\ and\ cot(\beta)$

we know that

If two angles are complementary, then the value of tangent of one angle is equal to the cotangent of the other angle

In this problem

$\alpha+\beta=90^o$ ---> by complementary angles

$tan(\alpha)=cot(\beta)$

<em>Find the value of the length side adjacent to the angle alpha</em>

Applying the Pythagorean Theorem

Let

x ----> length side adjacent to angle alpha

$14^2=x^2+8^2\\x^2=14^2-8^2\\x^2=132$

$x=\sqrt{132}\ units$

simplify

$x=2\sqrt{33}\ units$

Find the value of $tan(\alpha)$ in the right triangle of the figure

$tan(\alpha)=\frac{8}{2\sqrt{33}}$ ---> opposite side divided by the adjacent side angle alpha

simplify

$tan(\alpha)=\frac{4}{\sqrt{33}}$

therefore

$tan(\alpha)=\frac{4}{\sqrt{33}}$

$tan(\beta)=\frac{4}{\sqrt{33}}$

Part C) Find $sec(\alpha)\ and\ csc(\beta)$

we know that

If two angles are complementary, then the value of secant of one angle is equal to the cosecant of the other angle

In this problem

$\alpha+\beta=90^o$ ---> by complementary angles

$sec(\alpha)=csc(\beta)$

Find the value of $sec(\alpha)$ in the right triangle of the figure

$sec(\alpha)=\frac{1}{cos(\alpha)}$

Find the value of $cos(\alpha)$

$cos(\alpha)=\frac{2\sqrt{33}}{14}$ ---> adjacent side divided by the hypotenuse

simplify

$cos(\alpha)=\frac{\sqrt{33}}{7}$

therefore

$sec(\alpha)=\frac{7}{\sqrt{33}}$

$csc(\beta)=\frac{7}{\sqrt{33}}$

6 0

2 years ago

2. Find the general relation of the equation cos3A+cos5A=0

mars1129 [50]

<h2>Answer:</h2>

$A=\frac{\pi}{8}+\frac{n\pi}{4}or\ A=\frac{\pi}{2}+n\pi$

<h2>Step-by-step explanation:</h2>

<h3>Find angles</h3>

$cos3A+cos5A=0$

________________________________________________________

<h3>Transform the expression using the sum-to-product formula</h3>

$2cos(\frac{3A+5A}{2})cos(\frac{3A-5A}{2})=0$

________________________________________________________

<h3>Combine like terms</h3>

$2cos(\frac{8A}{2})cos(\frac{3A-5A}{2})=0\\\\ 2cos(\frac{8A}{2})cos(\frac{-2A}{2})=0$

________________________________________________________

<h3>Divide both sides of the equation by the coefficient of variable</h3>

$cos(\frac{8A}{2})cos(\frac{-2A}{2})=0$

________________________________________________________

<h3>Apply zero product property that at least one factor is zero</h3>

$cos(\frac{8A}{2})=0\ or\ cos(\frac{-2A}{2})=0$

________________________________________________________

<h3>Cross out the common factor</h3>

$cos\ 4A=0$

________________________________________________________

<h3>Solve the trigonometric equation to find a particular solution</h3>

$4A=\frac{\pi}{2}or\ 4A=\frac{3\pi}{2}$

________________________________________________________

<h3>Solve the trigonometric equation to find a general solution</h3>

$4A=\frac{\pi}{2}+2n\pi \ or\\ \\ 4A=\frac{3 \pi}{2}+2n \pi\\ \\A=\frac{\pi}{8}+\frac{n \pi}{4\\}$

________________________________________________________

<h3>Reduce the fraction</h3>

$cos(-A)=0$

________________________________________________________

<h3>Simplify the expression using the symmetry of trigonometric function</h3>

$cosA=0$

________________________________________________________

<h3>Solve the trigonometric equation to find a particular solution</h3>

$A=\frac{\pi }{2}\ or\ A=\frac{3 \pi}{2}$

________________________________________________________

<h3>Solve the trigonometric equation to find a general solution</h3>

$A=\frac{\pi}{2}+2n\pi\ or\ A=\frac{3\pi}{2}+2n\pi,n\in\ Z$

________________________________________________________

<h3>Find the union of solution sets</h3>

$A=\frac{\pi}{2}+n\pi$

________________________________________________________

<h3>Find the union of solution sets</h3>

$A=\frac{\pi}{8}+\frac{n\pi}{4}\ or\ A=\frac{\pi}{2}+n\pi ,n\in Z$

<em>I hope this helps you</em>

5 0

1 year ago

Quadrilateral ABCD is a rectangle.

jeka94

Answer:

Step-by-step explanation:

The diagonals of a rectangle are congruent and bisect each other, so

AC = BD

2AG = 2DG, that is

AG = DG, substitute values

- 7y + 5 = 2y + 68 ( subtract 2y from both sides )

- 9y + 5 = 68 ( subtract 5 from both sides )

-9y = 63 ( divide both sides by - 9 )

y = - 7

Hence

BD = 2(2y + 68)

= 4y + 136

= (4 × - 7) + 136

= - 28 + 136

= 108 → A

5 0

2 years ago

Given the following chemical reaction:

Marizza181 [45]

Answer:

The answer to your question is 12 moles of water.

Step-by-step explanation:

Reaction

2 O₂ + CH₄ ⇒ CO₂ + 2 H₂O

If Oxygen is in excess, then the limiting reactant is methane and we calculate the moles of water produced considering the moles of methane.

1 mol of methane -------------- 2 moles of water

6 moles of methane --------- x

x = (6 x 2) / 1

x = 12 moles of water

5 0

2 years ago