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likoan [24]
3 years ago
13

Systems of equations are bundles of equations that all relate to a common problem. For instance, combine two equations that each

give the distance (y) that two different cars drive in a given amount of Systems of equations are bundles of equations that all relate to a common problem. For instance, combine two equations that each give the distance (y) that two different cars drive in a given amount of time(x) to form a system of equations:
y = 60x + 5
y = 40x + 40

One value of x will yield the same value of y in each equation. What does this solution represent in this situation? Can you think of any other scenarios where two linked equations could provide a useful answer? How do systems of equations make problems easier to comprehend?
time(x) to form a system of equations:

Mathematics
2 answers:
never [62]3 years ago
8 0

Answer:

Solution will represent the time at which the distance traveled by both the cars will be the same.

Step-by-step explanation:

we are given with a system of equation . the equations are

y=60x+5

y=40x+40

where y is the distance traveled and x is the time. the solution to the above system of equations represents the time after which they have traveled the same distance .

Another situation could be the total cost of manufacturing of some product.

suppose the cost of the production of pencils in two difference units be given as

C=4n+50

C=5n+35

Where C is the total cost incurred in production of n number of pencils.

The solution to the above system of equation will be representing the number of units for which the cost of production of both the units will be the same.

Sergio [31]3 years ago
3 0
The two equations represent the different speeds (60 and 40) that two cars are traveling and the distances where they began (5 and 40).  The solution represents the time(x) when they have traveled the same distance.  Graphically it is the point where they intersect.  
Other scenarios would be any time you are comparing two things like cost to drive two different cars or internet services.  
Systems of equations help us see each situation, in this problem the time and distance a car travels then relate it to another car's distance traveled at the same times. 

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1000 student and 0.825 participants in sports how many students participate
kondaur [170]
825
You just multiply 1000 × 0.825 = 825 students
6 0
3 years ago
A home improvement contractor is painting the walls and ceiling of a rectangular room. The volume of the room is 1584 cubic feet
liq [111]

Answer:

The room dimensions that will minimize the cost of the paint are 12 ft x 12 ft x 11 ft.

Step-by-step explanation:

We can find first the volume equation using the formula of the volume of a box.

V= xyz

Thus we get the constraint function

1584 = xyz

Then since we are asked to minimize the cost, we can write the cost function which is the area of each one of the walls and ceiling multiplied by the painting cost.

C=0.11 xy+ 2(0.06)xz+2(0.06yz \\ C =0.11 xy+0.12xz+0.12yz

Lagrange Multipliers to find minimum cost.

We can continue finding the partial derivatives to build the system of equations required for Lagrange Multipliers method.

C_x=\lambda V_x \\ C_y = \lambda V_y \\ C_z = \lambda V_z

And the constraint function

xyz=1584

So we get

0.11y+0.12z=\lambda yz \\ 0.11x+0.12z=\lambda xz \\ 0.12x+0.12y=\lambda xy\\ xyz=1584

We can multiply each side of each equation by the dimension which is missing to get the full volume on the right side.

0.11xy+0.12xz=\lambda xyz \\ 0.11xy+0.12yz=\lambda xyz \\ 0.12xz+0.12yz=\lambda xyz

Then we can set each the equations equal to each other, so from the first one and the second equation we get

0.11xy+0.12xz= 0.11xy+0.12yz

We can subtract 0.11xy from both sides.

0.12xz=0.12yz

And we can divide both sides by 0.12z to get

x=y

We can repeat the process by setting the first and third equation equal to each other.

0.11xy+0.12xz= 0.12xz+0.12yz

We can subtract 0.12 xz from both sides

0.11xy=0.12yz

And we can solve by z

z= \cfrac{0.11x}{0.12}\\ z = \cfrac{11x}{12}

So if we replace that as well y = x on the constraint for the volume euqation we get

1584=x(x)\left(\cfrac{11}{12}x\right) \\ 1584=\cfrac{11}{12}x^3

We can then solve for x

x^3 = \cfrac{1584(12)}{11}

And taking the cube root

x = \sqrt[3]{\cfrac{1584(12)}{11}}

x = \sqrt[3]{1728}

x=12 ft

So then we can use the equations we have found for y and z in terms of x

y = x \\ y = 12 ft

And

z= \cfrac{11x}{12}\\z= \cfrac{11(12)}{12} \\ z=11ft

Then the dimensions of the room that will minimize the cost are 12ft x 12 ft x 11 ft. Since you have to enter using commas you can write 12, 12, 11, please check as well if you have to insert the units that are feet for each.

5 0
3 years ago
HELP QUICK PLZ
maks197457 [2]
The answer is D I guess
3 0
2 years ago
Read 2 more answers
7
Gelneren [198K]

Answer:

hard

Step-by-step explanation:

hard

3 0
2 years ago
Meredith borrows 12560 and pays 2 percent simple interest each year for 4 years what is the total amount of interest that she wi
devlian [24]

Answer:

$13564.8

Step-by-step explanation:

Step one:

given data

principal= $12560

rate= 2%= 0.02

time= 4years

<u>Required:</u>

<u>the simple interest</u>

Step two:

the expression for the simple interest is

A= P(1+rt)

substitute

A=12560(1+0.02*4)

A=12560(1+0.08)

A=12560(1.08)

A=13564.8

$13564.8

6 0
3 years ago
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