Hot dogs and Hamburgers:
1.)
The caterer for your class picnic charges $1 for each hotdog and $2 for each hamburger. You have $48 to spend. Write a model that shows the different numbers of hot dogs and hamburgers that you could purchase...
2.) Airplane landing: An Airplane's altitude is 100 feet as it is descending for a landing on a runway whose touchdown point is 5000 feet away. Let the x-axis represent the distance on the ground and the y-axis represent the airplane's altitude.
WHAT IS THE SLOPE OF THE AIRPLANE'S DESCENT????
3.) WRITE AN EQUATION of the line that follows the path of the airplane's descent.
1. d+2h=48
2. So when the plane starts to descend at 100 feet, its at 0 on the X axis, so your point is (0, 100). It's touchdown point is 5000 feet away, so it will be at 5000 on the x axis and 0 on the y axis, so your point is (5000, 0). Now you have two points so you can find the slope using the slope formula, (y2-y1) / (x2-x1), so that would be (0-100) / (5000-0), which gives you -100/5000, or -1/50. The y intercept is 100 because that's what y was when x was 0. Now you have the slope and the y intercept, so go ahead and put in into slope-intercept form, y=mX-b when m=the slope and b=the y intercept, so you have
y=-1/50x+100. Hope I helped!!!!!
3. Sorry cant help with that one!!
1.) Let's represent the number of hot dogs as "x" and the number of hamburgers as "y." Based on the information given, we know that a hot dog costs $1 and a hamburger costs $2. We also have $48 to spend. Therefore, we can create the following equation:
1x + 2y = 48
This equation represents the total cost of the hot dogs and hamburgers, which cannot exceed $48.
2.) Since the altitude is decreasing as the distance on the ground increases, the slope of the airplane's descent represents the rate of change of the altitude with respect to the distance on the ground.
In this case, the altitude is decreasing by 100 feet as the airplane travels a horizontal distance of 5000 feet. The slope can be calculated as the change in altitude divided by the change in distance:
Slope = (change in altitude) / (change in distance)
= -100 feet / 5000 feet
= -0.02
Therefore, the slope of the airplane's descent is -0.02.
3.) To find the equation of the line that represents the path of the airplane's descent, we can use the slope-intercept form, which is given by:
y = mx + b
where "m" represents the slope and "b" represents the y-intercept.
In this case, we know that the slope (m) is -0.02. To find the y-intercept (b), we need to know the altitude at a specific point on the ground. However, the information provided does not specify this.
Therefore, without further information, we cannot write the precise equation of the line that follows the path of the airplane's descent.
1.) To determine the different numbers of hot dogs and hamburgers that you could purchase, you can use a system of equations. Let's use the variables "h" for the number of hot dogs and "b" for the number of hamburgers.
The cost of each hot dog is $1, so the total cost of hot dogs would be h dollars. Similarly, the cost of each hamburger is $2, so the total cost of hamburgers would be 2b dollars.
Since you have a total of $48 to spend, we can set up the equation:
1h + 2b = 48
To find the different combinations of h and b that satisfy this equation, you can use trial and error or solve the equation algebraically. For trial and error, start by assuming a value for one variable and solve for the other. For example, you could start with assuming h = 0, which would give you 2b = 48 or b = 24. This means you could buy 0 hot dogs and 24 hamburgers. Repeat this process with different values of h to find other possible combinations.
Alternatively, you can solve the equation algebraically using techniques like substitution or elimination to find the values of h and b that satisfy the equation.
2.) The slope of the airplane's descent can be determined by finding the change in altitude (the difference in y-values) divided by the change in distance on the ground (the difference in x-values).
Given that the starting altitude is 100 feet and the touchdown point is 5000 feet away, we need to find the change in altitude and the change in distance. The change in altitude is 0 - 100 = -100 feet (assuming the descent is a straight line). The change in distance is 5000 - 0 = 5000 feet.
The slope is calculated as: slope = (change in altitude) / (change in distance)
Therefore, slope = -100 feet / 5000 feet = -0.02
So, the slope of the airplane's descent is -0.02.
3.) To write an equation that represents the path of the airplane's descent, we can use the slope-intercept form of a linear equation: y = mx + b, where "m" represents the slope and "b" represents the y-intercept.
We already found that the slope of the descent is -0.02. The initial altitude at the starting point is given as 100 feet. Since the x-axis represents the distance on the ground and the touchdown point is 5000 feet away, the y-intercept is (0, 100).
Plugging in these values, the equation of the line representing the path of the airplane's descent is:
y = -0.02x + 100