The length of a rectangular picture frame is 4 inches less than three times the width. The perimeter is 136 inches. Find the len
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Answer:
triangular pyramid
Step-by-step explanation:
Let's make the central triangle the "base", or the bottom face, of our polyhedron. Try to visualise what will happen if we fold up the three triangles so that their top vertices meet at the center top (see diagram).
If we can do that, we'll see that it's a pyramid with a triangular base, so it's a triangular pyramid.
Hi there!
We can calculate dy/dx using implicit differentiation:
xy + y² = 6
Differentiate both sides. Remember to use the Product Rule for the "xy" term:
(1)y + x(dy/dx) + 2y(dy/dx) = 0
Move y to the opposite side:
x(dy/dx) + 2y(dy/dx) = -y
Factor out dy/dx:
dy/dx(x + 2y) = -y
Divide both sides by x + 2y:
dy/dx = -y/x + 2y
We need both x and y to find dy/dx, so plug in the given value of x into the original equation:
-1(y) + y² = 6
-y + y² = 6
y² - y - 6 = 0
(y - 3)(y + 2) = 0
Thus, y = -2 and 3.
We can calculate dy/dx at each point:
At y = -2: dy/dx = -(-2) / -1+ 2(-2) = -2/5.
At y = 3: dy/dx = -(3) / -1 + 2(3) = -3/5.
Using <u>linear function concepts</u>, it is found that the correct option is:
The amount of calories in a cheeseburger increases by 1.42 for every one gram of fat. The calorie amount estimated by this model is 121 if there are zero grams of fat.
A linear function is modeled by:
In which:
- m is the slope, which represents by how much y changes when x changes by 1.
- b is the y-intercept, which is the value of y when x = 0.
In this problem:
- The explanatory variable fat is the input.
- The response variable calories is the output.
The equation is:
- The slope is of 1.42, which means that the amount of calories increases by 1.42 when the amount of fat increases by 1 gram.
- The y-intercept is of 121, which means that if there are 0 grams of fat, there will be 121 calories.
Thus, the correct option is:
The amount of calories in a cheeseburger increases by 1.42 for every one gram of fat. The calorie amount estimated by this model is 121 if there are zero grams of fat.
A similar problem is given at brainly.com/question/16302622