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2 years ago

Determine the constant of proportionality in each of the representations below.

Mathematics

2 answers:

cluponka [151]2 years ago

7 0

Answer:

Pretty sure is 15

Step-by-step explanation:

90 divided by 6 is 15.

katen-ka-za [31]2 years ago

3 0

Answer:

The constant of proportionality, k is 15

Step-by-step explanation:

The constant of proportionality is the ratio between two directly proportional quantities.

Proportional quantities can be described by the equation y = kx, where k is a constant ratio.

Here, "x" is the number of tickets and "y" is the number of dollars.

k = 30/2 = 15/1 or 15

k = 15

k = 60/ 4 = 30/2 = 15/1 or 15

k = 15

k = 90/6 = 30/2 = 15/1 0r 15

k = 15

When we take the ratio of x and y for all the given values, we get an equal value for all the ratios.

Therefore, the constant of proportionality, k is 15

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A bus travels 36 miles in 45 minutes. How many miles will the bus travel in 60 minutes at this rate. Show a ratio.

ankoles [38]

A rate is a special ratio in which the two terms are in different units. A rate is a little bit different than the ratio, it is a special ratio. For this case, the rate would have units of miles per minutes. We calculate as follows:

rate = 36 miles / 45 min = 0.8 miles per min
distance traveled = 0.8 miles per min ( 60 min ) = 48 miles

3 0

2 years ago

During a period of extreme cold, the average daily temperature dropped decreased by 1. Feach day. How many days did it take for

PtichkaEL [24]

Answer:

The answer is 9 days

Step-by-step explanation:

First, we realise

-1.F = 1 day

-9.F = 9 days

The -1.F times 9 gives us one so the days times 9 as well.

Answer = 9

4 0

2 years ago

1Jada made 6 cups of blueberry jam and divided the jam equally among 4 containers. How much jam went in each container? I pick

creativ13 [48]

Answer:

That would be 1.5

Step-by-step explanation:

Here it is.

3 0

2 years ago

Find the slope and y intercept of the line represented by each table

d1i1m1o1n [39]

5. m=3 because 6/2 is the slope. b= 1

6. m= -4 because -20/5 is the slope. b= 140

5 0

2 years ago

Can someone please help me with this

Mama L [17]

Answer:

27.

Equation of 2 tangent lines at the given curve going through point P is:

y = -7x + 1

y = x + 1

28.

Part 1: 400 feet

Part 2: Velocity is +96 feet/second (or 96 feet/second UPWARD) & Speed is 96 feet per second

Part 3: acceleration at any time t is -32 feet/second squared

Part 4: t = 10 seconds

29.

Part 1: Average Rate of Change = -15

Part 2: The instantaneous rate of change at x = 2 is -8 & at x = 3 is -23

Step-by-step explanation:

27.

First of all, the equation of tangent line is given by:

$y-y_1=m(x-x_1)$

Where m is the slope, or the derivative of the function

Now,

If we take a point x, the corresponding y point would be $x^2-3x+5$ , so the point would be $(x,x^2-3x+5)$

Also, the derivative is:

$f(x)=x^2-3x+5\\f'(x)=2x-3$

Hence, we can equate the DERIVATIVE (slope) and the slope expression through the point given (0,1) and the point we found $(x,x^2-3x+5)$

The slope is $\frac{y_2-y_1}{x_2-x_1}$

So we have:

$\frac{x^2-3x+5-1}{x-0}\\=\frac{x^2-3x+4}{x}$

Now, we equate:

$2x-3=\frac{x^2-3x+4}{x}$

We need to solve this for x. Shown below:

$2x-3=\frac{x^2-3x+4}{x}\\x(2x-3)=x^2-3x+4\\2x^2-3x=x^2-3x+4\\x^2=4\\x=-2,2$

So, this is the x values of the point of tangency. We evaluate the derivative at these 2 points, respectively.

$f'(x)=2x-3\\f'(-2)=2(-2)-3=-7\\f'(2)=2(2)-3=1$

Now, we find 2 equations of tangent lines through the point (0,1) and with respective slopes of -7 and 1. Shown below:

$y-y_1=m(x-x_1)\\y-1=-7(x-0)\\y-1=-7x\\y=-7x+1$

and

$y-y_1=m(x-x_1)\\y-1=1(x-0)\\y-1=x\\y=x+1$

So equation of 2 tangent lines at the given curve going through point P is:

y = -7x + 1

y = x + 1

28.

Part 1:

The highest point is basically the maximum value of the position function. To get maximum, we differentiate and set it equal to 0. Let's do this:

$s(t)=160t-16t^2\\s'(t)=160-32t\\s'(t)=0\\160-32t=0\\32t=160\\t=\frac{160}{32}\\t=5$

So, at t = 5, it reaches max height. We plug in t = 5 into position equation to find max height:

$s(t)=160t-16t^2\\s(5)=160(5)-16(5^2)\\=400$

max height = 400 feet

Part 2:

Velocity is speed, but with direction.

We also know the position function differentiated, is the velocity function.

Let's first find time(s) when position is at 256 feet. So we set position function to 256 and find t:

$s(t)=160t-16t^2\\256=160t-16t^2\\16t^2-160t+256=0\\t^2-10t+16=0\\(t-2)(t-8)=0\\t=2,8$

At t = 2, the velocity is:

$s'(t)=v(t)=160-32t\\v(2)=160-32(2)\\v(2)=96$

It is going UPWARD at this point, so the velocity is +96 feet/second or 96 feet/second going UPWARD

The corresponding speed (without +, -, direction) is simply 96 feet/second

Part 3:

We know the acceleration is the differentiation of the velocity function. let's find it:

$v(t)=160-32t\\v'(t)=a(t)=-32$

hence, the acceleration at any time t is -32 feet/second squared

Part 4:

The rock hits the ground when the position is 0 (at ground). So we equate the position function, s(t), to 0 and find time when it hits the ground. Shown below:

$s(t)=160t-16t^2\\0=160t-16t^2\\16t^2-160t=0\\16t(t-10)=0\\t=0,10$