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antiseptic1488 [7]

3 years ago

14

A car manufacturer is reducing the number of incidents with the transmission by issuing a voluntary recall. During week 3 of the

recall, the manufacturer fixed 391 cars. In week 13, the manufacturer fixed 361 cars. Assume that the reduction in the number of cars each week is linear. Write an equation in function form to show the number of cars seen each week by the mechanic.

2 answers:

S_A_V [24]3 years ago

7 0

Answer:

y(t) = 391 - 30t

Step-by-step explanation:

The weekly difference is 391-361 = 30

y(t) = 391 - 30t.

With t being the number of weeks.

Nitella [24]3 years ago

4 0

Answer with explanation:

Number of Cars fixed in third week= 391 cars

Number of Cars fixed in 13th week = 361 cars

As it is given that reduction in the number of cars each week is linear.

Number of Week =X axis

Number of Cars fixed = Y axis

Taking two points as (3, 391) and (13,361) and finding the equation of linear function:

Equation of line Passing through two points (3, 391) and (13,361) is given by:

$\Rightarrow \frac{y-y_{1}}{x-x_{1}}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\\Rightarrow \frac{y-361}{x-13}=\frac{391 -361}{3-13}\\\\\Rightarrow \frac{y-361}{x-13}=\frac{30}{-10}\\\\\Rightarrow \frac{y-361}{x-13}=-3\\\\\Rightarrow y-361=-3 x+39\\\\\Rightarrow 3 x+y=361+39\\\\\Rightarrow 3 x+y=400$

Equation of function to show the number of cars seen each week by the mechanic is:

⇒ 3 x+y=400

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4 years ago

For integers a, b, and c, consider the linear Diophantine equation ax C by D c: Suppose integers x0 and y0 satisfy the equation;

Dmitrij [34]

Answer:

a.

$x = x_1+r(\frac{b}{gcd(a, b)} )\\y=y_1-r(\frac{a}{gcd(a, b)} )$

b. x = -8 and y = 4

Step-by-step explanation:

This question is incomplete. I will type the complete question below before giving my solution.

For integers a, b, c, consider the linear Diophantine equation

$ax+by=c$

Suppose integers x0 and yo satisfy the equation; that is,

$ax_0+by_0 = c$

what other values

$x = x_0+h$ and $y=y_0+k$

also satisfy ax + by = c? Formulate a conjecture that answers this question.

Devise some numerical examples to ground your exploration. For example, 6(-3) + 15*2 = 12.

Can you find other integers x and y such that 6x + 15y = 12?

How many other pairs of integers x and y can you find ?

Can you find infinitely many other solutions?

From the Extended Euclidean Algorithm, given any integers a and b, integers s and t can be found such that

$as+bt=gcd(a,b)$

the numbers s and t are not unique, but you only need one pair. Once s and t are found, since we are assuming that gcd(a,b) divides c, there exists an integer k such that gcd(a,b)k = c.

Multiplying as + bt = gcd(a,b) through by k you get

$a(sk) + b(tk) = gcd(a,b)k = c$

So this gives one solution, with x = sk and y = tk.

Now assuming that ax1 + by1 = c is a solution, and ax + by = c is some other solution. Taking the difference between the two, we get

$a(x_1-x) + b(y_1-y)=0$

Therefore,

$a(x_1-x) = b(y-y_1)$

This means that a divides b(y−y1), and therefore a/gcd(a,b) divides y−y1. Hence,

$y = y_1+r(\frac{a}{gcd(a, b)})$ for some integer r. Substituting into the equation

$a(x_1-x)=rb(\frac{a}{gcd(a, b)} )\\gcd(a, b)*a(x_1-x)=rba$

or

$x = x_1-r(\frac{b}{gcd(a, b)} )$

Thus if ax1 + by1 = c is any solution, then all solutions are of the form

$x = x_1+r(\frac{b}{gcd(a, b)} )\\y=y_1-r(\frac{a}{gcd(a, b)} )$

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we first use the Euclidean algorithm to find gcd(15,6); the parenthetical equation is how we will use this equality after we complete the computation.

$15 = 6*2+3\\6=3*2+0$

Therefore gcd(6,15) = 3. Since 3|12, the equation has integral solutions.

We then find a way of representing 3 as a linear combination of 6 and 15, using the Euclidean algorithm computation and the equalities, we have,

$3 = 15-6*2$

Because 4 multiplies 3 to give 12, we multiply by 4

$12 = 15*4-6*8$

So one solution is

$x=-8$ & $y = 4$

All other solutions will have the form

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where $r$ ∈ Ζ

Hence by putting r values, we get many (x, y)

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3 years ago

If g(x)=4x^2-3x+2 find g(-2)

Sholpan [36]

Answer:

24

Step-by-step explanation:

g(x)=4x^2-3x+2=0

if g= -2

g(-2)=4(-2)^2-3(-2)+2=0

=16+6+2

=24

4 0

4 years ago