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What is the solution to 6|3x+5| less than equal to 14?

zimovet [89]

In this case there will be 2 solutions to solve for in this equation, both will equal plus and minus the answer. Which is 14.

6(3x + 5) = +_ 14

The solutions will be the following :

(14/6 - 5)/3

(-14/6 - 5)/3.

3 0

3 years ago

Solve the equation for all real values of x.<br> cosxtanx - 2 cos x=-1

IceJOKER [234]

Solution to equation $cosxtanx - 2 cos^2 x=-1$ for all real values of x is $x=2k\pi + \frac{\pi}{6} , x=2k\pi + \frac{5\pi}{6}$ .

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

Here we have , $cosxtanx - 2 cos^2 x=-1$ . Let's solve :

⇒ $cosxtanx - 2 cos^2 x=-1$

⇒ $cosx(\frac{sinx}{cosx}) - 2 cos^2 x=-1$

⇒ $sinx = 2 cos^2 x-1$

⇒ $sinx = 2 (1-sin^2x)-1$

⇒ $sinx = 1-2sin^2x$

⇒ $2sin^2x+sinx-1=0$

By quadratic formula :

⇒ $sinx = \frac{-b \pm \sqrt{b^2-4ac} }{2a}$

⇒ $sinx = \frac{-1 \pm \sqrt{1^2-4(2)(-1)} }{2(2)}$

⇒ $sinx = \frac{-1 \pm3}{4}$

⇒ $sinx = \frac{1}{2} , sinx =-1$

⇒ $sinx = sin\frac{\pi}{6} , sinx = sin\frac{3\pi}{2}$

⇒ $x=\frac{\pi}{6} , x=\frac{3\pi}{2}$

But at $x=\frac{3\pi}{2}$ we have equation undefined as $cos\frac{3\pi}{2}=0$ . Hence only solution is :

⇒ $x=\frac{\pi}{6}$

Since , $sin(\pi -x)=sinx$

⇒ $x=\pi -\frac{\pi}{6} = \frac{5\pi}{6}$

Now , General Solution is given by :

⇒ $x=2k\pi + \frac{\pi}{6} , x=2k\pi + \frac{5\pi}{6}$

Therefore , Solution to equation $cosxtanx - 2 cos^2 x=-1$ for all real values of x is $x=2k\pi + \frac{\pi}{6} , x=2k\pi + \frac{5\pi}{6}$ .

3 0

3 years ago

A heap of grain is shaped as a cone ADCF with height 5 m and base radius 2 m, as shown on the diagram. A and C are points on the

hoa [83]

Answer:

The angle between [A_F] and the base of the cone = 68.2°

The area of the base of the cone ≈ 12.57 m²

Step-by-step explanation:

The given parameters are;

The height of the cone = 5 m

The base radius of the cone = 2 m

The angle which the A $\hat O$ C = 120°

Therefore, we have;

The angle between [A_F] and the base of the cone = The angle between [CF] and the base of the cone

The angle between [CF] and the base of the cone = tan⁻¹(5/2) = tan⁻¹(2.5) ≈ 68.2°

∴ The angle between [A_F] and the base of the cone = The angle between [CF] and the base of the cone = 68.2°

The angle between [A_F] and the base of the cone = 68.2°

The area of the base of the cone = π × r² = π × 2² = 4·π ≈ 12.57

The area of the base of the cone ≈ 12.57 m².

8 0

3 years ago

The entry fee to an Amusement Park is $125 and the cost of each ride is $ 7.25 ( Mon - Thurs) and $ 8.50 ( Fri - Sun). Ava's mom

icang [17]

Answer:

D

Step-by-step explanation:

Well it is Friday so its 8.5 each ride.

8.5r which is basically how many rides she can go on after spending 125 on the admission

8 0

3 years ago

7 multiplied by 5 multiplied by 2 whole over 7 multiplied by 3, the whole raised to the power of 2 multiplied by 5 to the power

Nezavi [6.7K]

It is bassicaly zero

4 0

3 years ago