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3 years ago

Which of the following uses a variable to represent a person, place, or thing that is unknown

Mathematics

1 answer:

maw [93]3 years ago

4 0

Answer:

Mr X

Step-by-step explanation:

his identity is a variable ; it could be anybody of the male gender.

all the other ones denote known designations, i.e, B+ grade

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When can you say that there is no solution for a system of linear equation

SCORPION-xisa [38]

Answer:

You can say there is no solution for a system of linear equation when the graphs are PARALLEL to each other.

ONE solution: when both lines intersect at one point

INFINITE solution: when the line goes on forever

NO solution: is when the lines are parallel to each other.

5 0

3 years ago

Y''+y'+y=0, y(0)=1, y'(0)=0

mars1129 [50]

Answer:

$y=e^{\frac{-t}{2}}\left ( \cos\left ( \frac{\sqrt{3}t}{2} \right )+\frac{1}{\sqrt{3}}\sin \left ( \frac{\sqrt{3}t}{2} \right ) \right )$

Step-by-step explanation:

A second order linear , homogeneous ordinary differential equation has form $ay''+by'+cy=0$ .

Given: $y''+y'+y=0$

Let $y=e^{rt}$ be it's solution.

We get,

$\left ( r^2+r+1 \right )e^{rt}=0$

Since $e^{rt}\neq 0$ , $r^2+r+1=0$

{ we know that for equation $ax^2+bx+c=0$ , roots are of form $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ }

We get,

$y=\frac{-1\pm \sqrt{1^2-4}}{2}=\frac{-1\pm \sqrt{3}i}{2}$

For two complex roots $r_1=\alpha +i\beta \,,\,r_2=\alpha -i\beta$ , the general solution is of form $y=e^{\alpha t}\left ( c_1\cos \beta t+c_2\sin \beta t \right )$

i.e $y=e^{\frac{-t}{2}}\left ( c_1\cos\left ( \frac{\sqrt{3}t}{2} \right )+c_2\sin \left ( \frac{\sqrt{3}t}{2} \right ) \right )$

Applying conditions y(0)=1 on $e^{\frac{-t}{2}}\left ( c_1\cos\left ( \frac{\sqrt{3}t}{2} \right )+c_2\sin \left ( \frac{\sqrt{3}t}{2} \right ) \right )$ , $c_1=1$

So, equation becomes $y=e^{\frac{-t}{2}}\left ( \cos\left ( \frac{\sqrt{3}t}{2} \right )+c_2\sin \left ( \frac{\sqrt{3}t}{2} \right ) \right )$

On differentiating with respect to t, we get

$y'=\frac{-1}{2}e^{\frac{-t}{2}}\left ( \cos\left ( \frac{\sqrt{3}t}{2} \right )+c_2\sin \left ( \frac{\sqrt{3}t}{2} \right ) \right )+e^{\frac{-t}{2}}\left ( \frac{-\sqrt{3}}{2} \sin \left ( \frac{\sqrt{3}t}{2} \right )+c_2\frac{\sqrt{3}}{2}\cos\left ( \frac{\sqrt{3}t}{2} \right )\right )$

Applying condition: y'(0)=0, we get $0=\frac{-1}{2}+\frac{\sqrt{3}}{2}c_2\Rightarrow c_2=\frac{1}{\sqrt{3}}$

Therefore,

$y=e^{\frac{-t}{2}}\left ( \cos\left ( \frac{\sqrt{3}t}{2} \right )+\frac{1}{\sqrt{3}}\sin \left ( \frac{\sqrt{3}t}{2} \right ) \right )$

3 0

3 years ago

Teddy is writing a proof about the figure shown on the coordinate plane below. He wants to show that quadrilateral WXYZ is a par

faltersainse [42]

B is the answer show that segments WX AND YZ have equal lengths

6 0

3 years ago

Read 2 more answers

If a=(-1, -3) and b=(11, -8) what is the length of ab?

professor190 [17]

Answer: D. The length is 13 units.

Step-by-step explanation:

(-1, -3 ) Find the difference between the x values and y values.

(11, -8)

-3-(-8) = 5

-1-11 = -12 now find the absolute values.

The absolute value of 5 is 5 . The absolute value of -12 is 12.

Now use the Pythagorean Theorem formula a^2 + b^2 =c^2 where c square is the length between AB.

5^2 + 13^2 = C^2

25 + 144 = c^2

169=c^2

c= 13

8 0

3 years ago

A train travels 250 km with a average speed of 75 km/hr and 350 km with 70km/hr and 200 km with average speed of 30km/hr. What w

pentagon [3]

Answer:

53 1/3 km/h

Step-by-step explanation:

average speed = (total distance)/(total time)

average speed = distance/time

time * average speed = distance

time = distance/(average speed)

250 km at 75 km/h

distance = 250 km

time = (250 km)/(75 km/h) = 3.33333... hours

350 km at 70 km/h

distance = 350 km

time = (350 km)/(70 km/h) = 5 hours

200 km at 30 km/h

distance = 200 km

time = (200 km)/(30 km/h) = 6.6666... hour

total distance = 250 km + 350 km + 200 km = 800 km

total time = 3.33333... hours + 5 hours + 6.66666... hours = 15 hours

average speed = (total distance)/(total time)

average speed = (800 km)/(15 hours)

average speed = 53 1/3 km/h

3 0

3 years ago