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3 years ago

Perform the indicated operation 5 1/6 - 2 2/3

Mathematics

1 answer:

goldenfox [79]3 years ago

7 0

Answer:

2½

Step-by-step explanation:

First find the Least Common Denominator [LCD], which is 6, then convert 5⅙:

5⅙ → 4 7⁄6

$5 \frac{1}{6} - 2 \frac{2}{3} = 4 \frac{7}{6} - 2 \frac{4}{6} = 2 \frac{3}{6} = 2 \frac{1}{2}$

You see, we regrouped 1 from 5⅙ to make sure that the top mixed number had a higher value than the bottom mixed number, so it is much easier to work with.

I am joyous to assist you anytime.

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Two particles travel along the space curves r1(t) = t, t2, t3 r2(t) = 1 + 2t, 1 + 6t, 1 + 14t . Find the points at which their p

GuDViN [60]

Answer:

A) points at which paths intersect : (1,1,1) ; (2,4,8)

B) DNE

Step-by-step explanation:

A) To find the points in which the particle paths intersect, it is necessary to find the values of t for which the three components of both vectors are equal:

$t_1=1+2t_2\\\\t_1^2=1+6t_2\\\\t_1^3=1+14t_2$

you replace t1 from the first equation in the second equation:

$(1+2t_2)^2=1+6t_2\\\\1+4t_2+4t_2^2=1+6t_2\\\\4t_2^2-2t_2=0\\\\t_2(2t_2-1)=0\\\\t_2=0\\\\t_2=\frac{1}{2}$

Then, for t2 = 0 and t2=1/2 you obtain for t1:

$t_1=1+2(0)=1\\\\t_1=1+2(\frac{1}{2})=2$

Hence, for t1=1 and t2=0 the paths intersect. Furthermore, for t1=2 and t2=1/2 the paths also intersect.

The points at which the paths intersect are:

$r_1(1)=(1,1,1)=r_2(0)=(1,1,1)\\\\r_1(2)=(2,4,8)=r_2(\frac{1}{2})=(2,4,8)$

B) You have the following two trajectories of two independent particles:

$r_1(t)=(t,t^2,t^3)\\\\r_2(t)=(1+2t,1+6t,1+14t)$

To find the time in which the particles collide, it is necessary that both particles are in the same position on the same time. That is, each component of the vectors must coincide:

$t=1+2t\\\\t^2=1+6t\\\\t^3=1+14t$

From the first equation you have:

$t=1+2t\\\\t=-1$

This values does not have a physical meaning, then, the particle do not collide

answer: DNE

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3 years ago

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The answer to Which table represent a function is 1

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3 years ago

a falling stone is at a certain instant 230 feet above the ground. 3 seconds later it is only 14 feet above. From what height wa

vazorg [7]

The falling stone is a certain instant 230 feet above the ground. 3 seconds later it is only 14 feet above. The height that it was dropped is 32 feet. The equation for the answer is;

16t2+h0=230 −16(t+3)2+h0=14

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3 years ago

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Can someone help me with this? sin150° =

marusya05 [52]

Answer:

sin(150°) = 1/2

Step-by-step explanation:

* Lets study how we can solve this problem

- At first the measure of the angle is 150°

- Ask your self in which quadrant can you find this measure

* To know the answer lets revise the four quadrants

# First quadrant the measure of all angles is between 0° and 90°

the measure of any angle is α

∴ All the angles are acute

∴ All the trigonometry functions of α are positive

# Second quadrant the measure of all angles is between 90° and 180°

the measure of any angle is 180° - α

∴ All the angles are obtuse

∴ The value of sin(180° - α) only is positive ⇒ sin(180° - α) = sinα

# Third quadrant the measure of all angles is between 180° and 270°

the measure of any angle is 180° + α

∴ All the angles are reflex

∴ The value of tan(180° + α) only is positive ⇒ tan(180° + α) = tanα

# Fourth quadrant the measure of all angles is between 270° and 360°

the measure of any angle is 360° - α

∴ All the angles are reflex

∴ The value of cos(360° - α) only is positive ⇒ cos(360° - α) = cosα

* Now lets check the angle of measure 150

- It is an obtuse angle

∴ It is in the second quadrant

∴ the value of sin(150) is positive

∴ sin(150°) = sinα

∵ 180 - α = 150 ⇒ isolate α

∵ α = 180° - 150° = 30°

∴ sin(150°) = sin(30°)

∵ sin(30°) = 1/2

∴ sin(150°) = 1/2

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My math final please help

spin [16.1K]

Answer:

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Step-by-step explanation:

Let's solve for x, first:

x + 9 = 3x - 85

9 = 2x - 85

94 = 2x

94/2 = x

47 = x

Now that we have x-value, we can substitute it in any one of the given equation to find angle 3 since, angle 1, 7 and 3 all are congruent:

=> m∠7 = x + 9

=> m∠7 = 47 + 9

=> m∠7 = 56

Since m∠7 ≅ m∠3

and m∠7 = 56, then

m∠3 = 56

Hope this helps!

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3 years ago