How many students got eight or more answers correct?

Mathematics

2 answers:

slamgirl [31]3 years ago

7 0

Answer:

Step-by-step explanation:

You have to count the number of dots there are after the number 8. (This includes the dotes above 8.)

Murljashka [212]3 years ago

3 0

Answer:

<em>9 students</em>

Step-by-step explanation:

Assuming that these dots represent students, let us begin with the amount of students that answered 8 questions right;

Students who got 8 answers right ⇒ 4 students,

Students who got 8 answers right ⇒ 3 students,

Students who got 10 answers right ⇒ 2 students

Now we are to compute the value of the students who received 8 or more answers right, provided the questions are out of 10;

Students who received 8 or more answers right; 4 + 3 + 2 = 9 students

<em>Solution; 9 students</em>

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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:

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