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Determine whether the parabola y equals -x2 plus 15x plus 8 opens up down left or right?
when you have y=+/-x2 +whatever, the parabola opens up y=-(x2 +whatever), the parabola opens down x=+/-y2 +whatever, the parabola opens right x=-(y2 +whatever), the parabola opens left so, your answer is up
Is depth in water a negative number?
If measuring from sea level, yes. Technically, though, it is accurate to state depth as a negative number, but unless you have been specifically told, it shouldn't matter whether you do or not. The only exception I can think of is if you are drawing a parabola that shows the depth of a buoyant object over a period of time after being thrown or dropped in. It looks a lot neater to show a positive parabola, as a negative parabola could imply that a non-buoyant object was thrown from the bottom of a body of water. I hope this helped, and ignore the previous paragraph if you want.
What is the equation for the axis of symmetry of the quadratic function f(x) 3x2 12x - 2?
It is x = +/- 2 depending on whether the second term in the equation is -12x or +12x.
What is the square root of 16x squared?
If you square an expression and then take the square root, the squaring and the square root cancel one another, EXCEPT that the sign will be positive. Thus, if you square 16x, and then take the square root, the answer can be 16x or -16x, depending on whether "x" is positive or negative. Or if you only square x, and then take the square root of the entire expression, it would be 4x or -4x (once again, depending on whether "x" is positive or negative).
If you have 266 meters of fencing to enclose a rectangular field what is the maximum area that can be enclosed?
Here you are given a perimeter and told that the field is rectangular. That gives us one equation. 2L + 2W = 266 (A rectangle has two pairs of sides - L and W - that are equal. The sum of all sides is equal to the perimeter by definition.) Area is calculated by multiplying length and width. This gives us our second formula. L * W = Area In the past, in algebra we could solve for one of the variables and then substitute and solve for the other. This is trickier. We CAN solve for one of the variable, for example, for L 2L + 2W = 266 2L = 266 - 2W L = 133 - W When we substitute that in to the other equation, however, we seem to hit a roadblock. (133 - W) * W = Area 133W - W2 = Area Now we still have two variables. but if you think back to the problem, there are multiple possible answers depending on the length and widths that are chosen. In this problem we want to maximize area. So instead, let's think of this problem as finding a maximum point of the following function: f(x) = 133W - W2 To find the rate at which the function (area), we take the derivitive of the function. f'(x) = 133 - 2W When a function reaches its maximum (or minimum point) the rate at which the value of the function is increasing (or decreasing) will go to zero. To better understand this, think of a rollercoaster. As your car climbs up a hill, the extra height you gain is still increasing, but near the top it will slowly level off to where you are not getting any higher (zero) and then decrease after. The same is true for this function. So what does that all mean? By setting the derivitive to zero, we can solve for the point(s) at which this function stops increasing (or decreasing) and hits a maximum (or minimum). f'(x) = 133 - 2W 0 = 133 - 2W 133 = 2W W = 133/2 or 66.5 The big question now is whether this is a minimum point in the function or a maximum. By taking the second derivitive we can test where this part of the function is concave up (like a U) or concave down (like an upside-down U). f''(x) = -2 This means that our function is concave down at all values of X. As the image suggests we are looking at a relative maximum point which is what we are looking for! So going back to our finding, we know that at the maximum area, W = 66.5; now we can solve for Y. 2L + 2W = 266 2L + 2(66.5) = 266 2L + 133 = 266 2L = 133 L = 66.5 So now we know the dimension of our rectangular field is 66.5 x 66.5. Now calculate the area with L x W. L x W = Area 66.5 x 66.5 = 4422.25 The maximum rectangular area that can be enclosed with 266 meters of fencing is 4,422.25 square meters. Double check my work. I have to quick finish this so I cannot check my calculations!
What is maximum or minimum of a parabola depending on whether the parabola opens up or down?
Vertex
How far away is Saturn form the sun in km?
Between 1.35 billion to 1.5 billion kms away...depending on whether you want minimum or maximum, respectively.
How will you describe the graph of a function?
· whether it is linear, quadratic or exponential · whether it has an upper or lower bound · whether it has a minimum or a maximum value · whether it is constant, decreasing or increasing
How do you know if a point is a maximum or a minimum?
Usually at the minimum or maximum of a function, one of the following conditions arises:The derivative is zero.The derivative is undefined.The point is at the end-points of the domain that is being considered (or of the naturally-defined domain, for example, zero for the square root).This will give you "candidate points"; to find out whether each of these candidate points actually is a maximum or a minimum, additional analysis is required. For example, if the second derivative is positive, you have a minimum, if the second derivative is negative, you have a maximum - but if it is zero, it may be a maximum, a minimum, or neither.
Determine whether the parabola y equals -x2 plus 15x plus 8 opens up down left or right?
when you have y=+/-x2 +whatever, the parabola opens up y=-(x2 +whatever), the parabola opens down x=+/-y2 +whatever, the parabola opens right x=-(y2 +whatever), the parabola opens left so, your answer is up
The equivalence point reached when the pH reaches it maximum value?
The equivalence point is reached in a titration when the moles of acid are equal to the moles of base added. At the equivalence point, the pH of the solution is at its maximum or minimum value, depending on whether a strong acid or base is used in the titration.
What is the range of the equation y equals x2 plus 4?
This equation describes a parabola, so it's range on the x-axis will be infinite. To find it's vertex, we can take it's derivative and solve for zero: y = x2 + 4 y' = 2x Let y' = 0 0 = 2x x = 0 Now we plug that x value into the original equation to find y: y = 02 + 4 y = 4 So the vertex is at the point (0, 4). To see whether that's a minimum or a maximum, we need only take it's second derivative and check whether it's positive or negative at that point: y' = 2x y'' = 2 So the rate of change of the slope is positive, which means that the parabola's vertex is a minimum. We can say then that the equation has an infinite x range, and a y range from 4 to infinity.
What is minimum and maximum frequency of have a sex intercourse in a day or nigth?
That depends on a number of factors. First of all, whether the male has an orgasm every time. Secondly, whether the sex lasts very long per session or not. There's more ofcource. But assuming the 'regular' for all variables, if you have a day off and no disturbances, 5 to 7 times should be very well achievable depending on sex drive and such. 12 times should be doable in a day, but take the male 'cooldown period' into consideration. Lastly, the minimum is zero.
What equation describes a parabola that opens up or down and whose vertex at the point (hv)?
This is called the 'standard form' for the equation of a parabola:y =a (x-h)2+vDepending on whether the constant a is positive or negative, the parabola will open up or down.
Definition for decision models and decision variables?
Decision variables are the variables within a model that one can control. They are not random variables. For example, a decision variable might be: whether to vaccinate a population (TRUE or FALSE); the amount of budget to spend (a continuous variable between some minimum and maximum); or how many cars to have in a car pool (a discrete variable between some minimum and maximum).
What is the legal maximum capacity for shotguns per atf guides?
http://www.atf.gov/ - This is the BAFTE website. You can research there. Depending on whether you are talking domestic made or import, the answer will vary.
If I travel 35 to 50 miles per hour in 68.1 hours, How many miles have I driven?
To find out how many miles you have driven, you can use the formula: Distance = Speed × Time Given that you're traveling between 35 to 50 miles per hour and you've driven for 68.1 hours, we'll calculate the distance for both the minimum and maximum speeds: For minimum speed (35 miles per hour): Distance = 35 miles/hour × 68.1 hours For maximum speed (50 miles per hour): Distance = 50 miles/hour × 68.1 hours Let's calculate: For minimum speed: Distance = 35 miles/hour × 68.1 hours = 2383.5 miles For maximum speed: Distance = 50 miles/hour × 68.1 hours = 3405 miles So, you have driven between 2383.5 miles and 3405 miles, depending on whether you were traveling at the minimum or maximum speed.
