All categories

2 years ago

A city currently has 153 streetlights. As part of a urban renewal program, the city council has decided to

Mathematics

1 answer:

kiruha [24]2 years ago

5 0

Answer:

The explicit function is: $P_x = 153+3x$

And the number of lights after 33 weeks will be 252.

Step-by-step explanation:

Given that:

Total street lights = 153

Let x be the number of weeks

Then the number lights after x weeks will be 3x

This is a linear function where the y-intercept is 153 and slope is 3.

It can be written as: y = mx+b

The function is:

$P_x = 153+3x$

Putting the values for x will give us the number of total lights after that number of weeks.

To find, how many street lights were there at the end of 33rd week,

Putting x = 33

$P_{33} = 153+ 3(33)\\= 153+99 = 252$

Hence.

The explicit function is: $P_x = 153+3x$

And the number of lights after 33 weeks will be 252.

You might be interested in

Show that every triangle formed by the coordinate axes and a tangent line to y = 1/x ( for x > 0)

vfiekz [6]

Answer:

Step-by-step explanation:

given a point $(x_0,y_0)$ the equation of a line with slope m that passes through the given point is

$y-y_0 = m(x-x_0)$ or equivalently

$y = mx+(y_0-mx_0)$ .

Recall that a line of the form $y=mx+b$ , the y intercept is b and the x intercept is $\frac{-b}{m}$ .

So, in our case, the y intercept is $(y_0-mx_0)$ and the x intercept is $\frac{mx_0-y_0}{m}$ .

In our case, we know that the line is tangent to the graph of 1/x. So consider a point over the graph $(x_0,\frac{1}{x_0})$ . Which means that $y_0=\frac{1}{x_0}$

The slope of the tangent line is given by the derivative of the function evaluated at $x_0$ . Using the properties of derivatives, we get

$y' = \frac{-1}{x^2}$ . So evaluated at $x_0$ we get $m = \frac{-1}{x_0^2}$

Replacing the values in our previous findings we get that the y intercept is

$(y_0-mx_0) = (\frac{1}{x_0}-(\frac{-1}{x_0^2}x_0)) = \frac{2}{x_0}$

The x intercept is

$\frac{mx_0-y_0}{m} = \frac{\frac{-1}{x_0^2}x_0-\frac{1}{x_0}}{\frac{-1}{x_0^2}} = 2x_0$

The triangle in consideration has height $\frac{2}{x_0}$ and base $2x_0$ . So the area is

$\frac{1}{2}\frac{2}{x_0}\cdot 2x_0=2$

So regardless of the point we take on the graph, the area of the triangle is always 2.

6 0

3 years ago

As shown in the graph, ΔGHI ≅ ΔG'H'I', since this is a vertical shift, and ΔG'H'I' ≅ ΔG''H''I'', since this is a horizontal shif

77julia77 [94]

D) (X,Y) <span> → (x + 4, y - 5).
HOPE THIS HELPED :-)</span>

4 0

3 years ago

Graph the function y = x3 + x2 – 6x + 5. What are the coordinates, to the nearest tenth, of the relative maximum of the graph? (

Debora [2.8K]

Answer:A

Step-by-step explanation:edge

6 0

3 years ago

Read 2 more answers

Simplify each expression using the distributive property <br><br>9(-7q-6)

hammer [34]

Answer:

-63q-54

Step-by-step explanation:

When using the distributive property, you multiply everything inside of the parentheses by the number outside of the parentheses.

9(-7q-6)

-63q-54

Hope this helps, and have a great day o(*￣▽￣*)ブ

5 0

3 years ago

Leo's model airplane uses O.03 L of fuel each minute it flies.Lf the fuel tank holds O.5 L, how long can the plane fly without r

Keith_Richards [23]

16 minutes

0.03*16=0.48

Closest you can get w/out going over.

3 0

3 years ago