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3 years ago

Approximate two of the roots of x³-3x²+x+1 by drawing 2 graphs on the interval 0≤x≤3.

Mathematics

1 answer:

Elina [12.6K]3 years ago

5 0

Answer:

The answer to your question is below

Step-by-step explanation:

See the graph below.

I recommend you to evaluate the function when x = (-1, 0, 1, 2, 3, and 4) to get the values of y.

Then, in the graph we look for the points where the line crosses the x-axis, these points will be the roots.

In the graph we observe that the root are x = 1 and x = 2.4

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If cosine theta equals negative square root of three over two and pi over two less than theta less than pi, what are the values

Natalka [10]

<h2>Answer:</h2>

The values of sinθ and tanθ are:

$\sin \theta=\dfrac{1}{2}$

and

$\tan \theta=-\dfrac{1}{\sqrt{3}}=-\dfrac{\sqrt{3}}{3}$

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

It is given that:

$\cos \theta=-\dfrac{\sqrt{3}}{2}$

where

$\dfrac{\pi}{2}$

i.e. the angle θ lie in the second quadrant.

Also, we know that in the second quadrant sine and cosecant function is positive.

whereas cosine,secant, tangent and cotangent functions are negative.

Now, we know that:

$\cos (\dfrac{5\pi}{6})=-\dfrac{\sqrt{3}}{2}$

i.e. here

$\theta=\dfrac{5\pi}{6}$

Hence, we have:

$\sin (\theta)=\sin (\dfrac{5\pi}{6})\\\\i.e.\\\\\sin \theta=\dfrac{1}{2}$

Also,

$\tan \theta=\dfrac{\sin \theta}{\cos \theta}\\\\i.e.\\\\\tan \theta=\dfrac{\dfrac{1}{2}}{\dfrac{-\sqrt{3}}{2}}\\\\i.e.\\\\\tan \theta=\dfrac{1}{-\sqrt{3}}\\\\i.e.\\\\\tan \theta=-\dfrac{1}{\sqrt{3}}$

Now, on rationalizing we have:

$\tan \theta=-\dfrac{\sqrt{3}}{3}$

7 0

4 years ago

Read 2 more answers

In QRS, Q = S, SQ = 5 and RS = 11. Find the length of QR.

IRINA_888 [86]

Angle Q = 31°

Angle R = 118°

Angle S = 31°

6 0

3 years ago

M(5, 7) is the mid-point of the l.ine segment joining A (3,4) to B. Find the coordinates of B.

Nina [5.8K]

Answer:

B(7,10)

Step-by-step explanation:

$M(5,7)=(x ,y)\\A(3,4)=(x_1,y_1)\\B(x_2,y_2)\\\\Endpoint ;\\x = \frac{x_1+x_2}{2}\\ \\5 = \frac{3+x_2}{2}\\ Cross\:Multiply\\5\times 2 =3+x_2\\10=3+x_2\\10-3 =x_2\\7=x_2\\\\\\y = \frac{y_1+y_2}{2} \\\\7 = \frac{4+y_2}{2}\\ Cross\:Multiply\\7\times 2 =4+y_2\\14 =4+y_2\\14-4 =y_2\\10 =y_2\\\\\\B(7,10)$