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3 years ago

Solve for y. 5x-10y=-40

Mathematics

2 answers:

marusya05 [52]3 years ago

4 0

Y=4

-10/-10 = -40/-10

-40/-10 = 4

Andru [333]3 years ago

4 0

This is the answer x = 8 + 2y

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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

5 0

3 years ago

Help! Please? The ratio (by volume) of milk in a certain solution is 3 to 8. If the total volume of the solution is 187 cubic fe

DIA [1.3K]

We know that the total volume of the solution is 187 cubic feet.
187=3x+8x
187=11x
17=x
Now we know that the ratio 3 to 8 is 51 to 136.
Double check, (3*17)+(8*17)=187.
I'm not sure which part of the ratio is water, but knowing this information, you should be able to solve it. I believe it may be this:
The total volume of milk is 51. If the rest of the solution is water, then 187-51=136.

6 0

4 years ago

Answer 1-10 Need before 10:00 CN

forsale [732]

Answer:

1. 1 4/5

2. 1 1/30

3. 2 3/20

4. 1 1/5

5. 1 13/20

6. 1 13/30

7. 1 29/60

8. 1 3/20

9. 1 7/10

10. 1 9/20

Hope this helps :)

8 0

3 years ago

The sum of three consecutive even integers is 108. What is the largest number?

horrorfan [7]

Answer:

The largest of three numbers is 38.

Step-by-step explanation:

Given : The sum of three consecutive even integers is 108.

We have to find the largest of three consecutive even integer.

Consecutive integers are integer having a difference of one between each term . example 14 , 15, 16 ..

consecutive even integers are integers having a difference of two between them such that first term is in the form of 2n , where n is integers.

Consider the three consecutive even integers are 2n , 2n + 2 , 2n + 4

Also, given The sum of three consecutive even integers is 108.

that is 2n + 2n + 2 + 2n + 4 = 108

Simplify, we get,

6n + 6 = 108

Subtract 6 both side, we get,

6n = 102

Divide by 6 both side, we get,

n = 17

Thus, numbers are 2n = 2 × 17 = 34

2n + 2 = 34 + 2 = 36

2n + 4 = 34 + 4 = 38

Thus, The sum of three consecutive even integers is 108 then integers are 34, 36, 38 .

Thus, The largest of three numbers is 38.

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3 years ago

peter played his favorite video game for 10 hours last week. today, peters parents restricted him to 5 additional hours each wee

never [62]

f(x) is the function that models Peters total video game time.
Peter played his favorite video game for 10 hours last week.
Peters parents restricted him to 5 additional hours each week for the next 8 weeks.
After 8 weeks Peter will have played f(x) hours video game.
f(x)=10+8*x , where x is the number of hours Peter plays every week and this number is smaller than 5 (his parents restricted this number) , x<5

7 0

3 years ago