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2 years ago

The system of equations has .

2 answers:

7 0

A system of linear equations usually has a single solution, but sometimes it can have no solution (parallel lines) or infinite solutions (same line). This article reviews all three cases. One solution. A system of linear equations has one solution when the graphs intersect at a point.

wolverine [178]2 years ago

6 0

Answer:

A System of Equations has two or more equations in one or more variables Many Variables So a System of Equations could have many equations and many variables.

Step-by-step explanation:

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The function a(t)=t^(1/2)−t^(−1/2) m/s^2 represents the acceleration of a particle moving along a horizontal axis. At time t=0,

garri49 [273]

Answer:

see below

Step-by-step explanation:

a(t)=t^(1/2)−t^(−1/2)

We integrate to find the velocity

v(t) = integral t^(1/2)−t^(−1/2) dt

= t ^ (1/2 +1) t ^ (-1/2 +1)

------------ - ----------------- + c where c is the constant of integration

3/2 1/2

v(t) = 2/3 t^ 3/2 - 2 t^ 1/2 +c

We find c by letting t=0 since we know the velocity is 4/3 when t=0

v(0) = 2/3 0^ 3/2 - 2 0^ 1/2 +c = 4/3

0+c =4/3

c = 4/3

v(t) = 2/3 t^ 3/2 - 2 t^ 1/2 +4/3

To find the position function we need to integrate the velocity

p(t) = integral 2/3 t^ 3/2 - 2 t^ 1/2 +4/3 dt

2/3 t ^ (3/2 +1) 2 t ^ (1/2 +1) 4/3t

------------ - ----------------- + ------------- + c

5/2 3/2 1

p(t) = 4/15 t^ 5/2 - 4/3t ^ 3/2 + 4/3t +c

We find c by letting t=0 since we know the position is -4/15 when t=0

p(0) = 4/15 0^ 5/2 - 4/3 0 ^ 3/2 + 4/3*0 +c = -4/15

0 +c = -4/15

c = -4/15

p(t) = 4/15 t^ 5/2 - 4/3t ^ 3/2 + 4/3t -4/15

8 0

3 years ago

Read 2 more answers

Which statement best describes the area of Triangle ABC shown below?

sergij07 [2.7K]

The answer is b ...........................................................b............b..............

8 0

3 years ago

Read 2 more answers

Which equation represents a line that passes through (–9, –3) and has a slope of –6?

brilliants [131]

$\bf \begin{array}{lllll}
&x_1&y_1\\
% (a,b)
&({{ -9}}\quad ,&{{ -3}})
\end{array}
\\\\\\
% slope = m
slope = {{ m}}= \cfrac{rise}{run} \implies -6
\\\\\\
% point-slope intercept
\stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-(-3)=-6[x-(-9)]
\\\\\\
y+3=-6(x+9)\implies y+3=-6x-54\implies y=-6x-57$

8 0

3 years ago

Mr. Sawyer drove his car from his home to New York at the rate of 45 mph and returned over the same road at the rate of 40 mph.

AveGali [126]

Answer: Time taken by him in going = 8 hours

Time taken by him in returning = 9 hours

Step-by-step explanation:

Let the total distance from home to New York is x miles,

$\text{ Since, Time} = \frac{\text{Distance}}{\text{Speed}}$

Also, he drove his car from his home to New York at the rate of 45 mph,

⇒ $\text{ Time taken by him in going } = \frac{x}{45}\text{ hours}$

And, returned over the same road at the rate of 40 mph.

⇒ $\text{ Time taken by him in returning } = \frac{x}{40}\text{ hours}$

According to the question,

Time taken by him in returning - Time taken by him in going = 30 minutes = 1/2 hours, ( 1 hours = 60 minutes )

⇒ $\frac{x}{40}-\frac{x}{45}=\frac{1}{2}$

⇒ $\frac{9x}{360}-\frac{8x}{360}=\frac{1}{2}$

⇒ $\frac{x}{360} = \farc{1}{2}$

⇒ $2x=720$

⇒ $x=360\text{ miles}$

Hence, the total distance from home to New York = x miles = 360 miles

⇒ $\text{ Time taken by him in going } = \frac{x}{45}\text{ hours}$

$=\frac{360}{45}=8\text{ hours}$

⇒ $\text{ Time taken by him in returning } = \frac{x}{40}\text{ hours}$

$=\frac{360}{40}=9\text{ hours}$

3 0

3 years ago

In parallelogram DEFG, DH = x + 5, HF = 2y, GH = 4x-3 and HE = 4y + 1. Find the values of x and y. The diagram is not drawn to s

GalinKa [24]

Rule: The diagonals of any parallelogram bisect each other. In other words, they cut each other in half.

This means DF is cut into two equal pieces: DH and HF.
Similarly, GE is cut into two equal pieces: GH and HE.

DH = HF
x+5 = 2y
x = 2y-5

GH = HE
4x-3 = 4y+1
4(x)-3 = 4y+1
4(2y-5)-3 = 4y+1 ... x has been replaced with 2y-5
8y-20-3 = 4y+1
8y-23 = 4y+1
8y-4y = 1+23
4y = 24
y = 6

If y = 6, then x is
x = 2y-5
x = 2(6)-5
x = 12-5
x = 7

--------------------------------------------

Answers:
x = 7 and y = 6

5 0

3 years ago