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Leya [2.2K]
3 years ago
6

The number 'N' of cars produced at a certain factory in 1 day after 't' hours of operation is given by N(t)=100t-5t^2, 0< or

equal t < or equal 10. If the cost 'C' (in dollars) of producing 'N' cars is C(N)=15,000+8000N, find the cost 'C' as a function of the time 't' of operation of the factory
Then Interpret C(t) when t=5 hours as a new function.
Mathematics
2 answers:
katen-ka-za [31]3 years ago
8 0

Answer:

We know that:

C_{(N)}=15000+8000N

So first we need to substitute the next equation in the C(N) equation

N_{(t)} = 100t-5t^{2}

And therefore we have:

C_{(t)}=15,000 + 8000*(100t-5t^{2})\\C_{(t)}=15,000 + 800000t-40000t^{2}

Finally we replace at t = 5 in the equation above and we have:

C_{(5)}=15,000 + 800000*5-40000*5^{2}\\C_{(5)}= 3015000

The interpretation is that after 5 hours of operation, we have wasted 3015000 dollars producing cars.  

Luden [163]3 years ago
7 0

Given: C(N) = 15,000 + 8000N <span>

In the above equation simply substitute: 
N(t) = 100t - 5t^2 
for N 

</span>

<span>Therefore:
C(t) = 15,000 + 8000{ 100t-5t^2 } 
C(t) =15,000 + 800,000t - 40,000t^2.</span>

 

at t = 5

C(5) = 15,000 + 800,000*5 - 40,000*(5)^2

<span>C(5) = 3,015,000</span>

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Step-by-step explanation: You use the distribution property.


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Find out if the 3 positions are on the same line or not (3,2,0) (1, -1,2) (5,5, 2)
sattari [20]

Answer:

The three positions are not on the same line.

Step-by-step explanation:

We have three points: A:(3,2,0),  B:(1,-1,2) and C:(5,5,2).

Let's build a vector that goes from one point to another; that vector will be the director of a line (if we draw a vector that goes from A to B, that vector will be the direction of the line that pass by A and B because it does not change). In order to build that vector, let's subtract B from A:

A-B=(3,2,0)-(1,-1,2)=(2,3,-2)

The equation of a line is:

p=p_0+rt

Where p is every singular point of the line, p_0 is a particular point of the line (any that we are sure that it is on the line), r is the director vector and t is the independent variable.

Now we have the director vector: (2,3,-2), and we can verify that A and B are on the line:

p=p_0+(2,3,-2)t

Because there is a value for t that satisfies both A and B: If we do p_0=(3,2,0) and t=0, we are going to obtain the point p=A; and if we do t=-1, we are going to obtain p=B. Let's see that:

p=(3,2,0)+(2,3,-2)*0=(3,2,0)\\p=A\\p=(3,2,0)+(2,3,-2)*-1=(1,-1,2)\\p=B\\

If C is also in the same line, C must accomplish the equation: p=(3,2,0)+(2,3,-2)t, so:

C=(5,5,2)=(3,2,0)+(2,3,-2)t

Let's simplify the equation writing the parametric equation, which is just to write the equation for each dimension:

5=3+2t\\5=2-3t\\2=-2t\\

You can verify that there is not a value of t that satisfies all three equations, so, the point C is not on the same line as A and B; which means that A, B and C are not on the same line.

8 0
3 years ago
What is y=4x^2-9x+1 in vertex form
Anna11 [10]

Answer:

y = 4 \left(x - \dfrac{9}{8} \right)^2 - \dfrac{65}{16}

Step-by-step explanation:

y = 4x^2 - 9x + 1

You need to complete the square on the right side.

y = (4x^2 - 9x) + 1

y = 4(x^2 - \dfrac{9}{4}x) + 1

y = 4 \left( x^2 - \dfrac{9}{4}x + \left( \dfrac{9}{8} \right)^2 \right) + 1 - 4\left( \dfrac{9}{8} \right)^2

y = 4 \left(x - \dfrac{9}{8} \right)^2 + 1 - 4 \left( \dfrac{81}{64} \right)

y = 4 \left(x - \dfrac{9}{8} \right)^2 + 1 - \dfrac{81}{16}

y = 4 \left(x - \dfrac{9}{8} \right)^2 + \dfrac{16}{16} - \dfrac{81}{16}

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3 years ago
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kherson [118]

Answer:

Step-by-step explanation:

math is a thing pls like this it was meaningful ;;;;;;;;;0

7 0
3 years ago
Read 2 more answers
PLZ HELP
Scrat [10]

Answer: Ix - 950°C I ≤ 250°.

Step-by-step explanation:

Ok, the limits are:

700°C to 1200°C.

The first step is to find the mean these numbers:

M = (700°C + 1200°C)/2 = 950°C

Now let's find the distance between the mean and the limits (which is equal to half the difference between our numbers)

D = (1200°C - 700°C)/2 = 250°C.

Now we can write our relation as:

Ix - MI ≤ D

Ix - 950°C I ≤ 250°.

if x = 1200°C.

I1200°C - 950°CI = 250°C ≤ 250°C ---- true.

if x = 700°C

I700°C - 950°CI = I-250°CI = 250°C ≤ 250°C ---- true

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