Let's find the derivative of that hyperbola in order to find a slope formula to help us with this equation. We already have an x and y value. The derivative is found this way:
so
. The derivative supplies us with the slope formula we need to write the equation. Sub in the x value of 3 to find what the slope is:
. So in our slope-intercept equation, x = 3, y = 1, and m = -1/3. Use these values to solve for b.
so b = 2. The equation, then, for the line tangent to that hyperbola at that given point is
The total number of students in the four classes is 100 students.
<h3>How to compute the value?</h3>
From the information, the numbers of students in the four sixth-grade classes at Northside School are 26, 19, 34, and 21.
Therefore, the total number of students will be:
= 26 + 19 + 34 + 21
= 100
Therefore there are 100 students.
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Answer: Choice A. (8, 4)
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Explanation:
Because x = 2y, we can replace every copy of x with 2y
Let's do so in the second equation
3x - 4y = 8
3(x) - 4y = 8
3(2y) - 4y = 8 .... x replaced with 2y; now let's isolate y
6y - 4y = 8
2y = 8
y = 8/2 ..... divide both sides by 2
y = 4
Use this y value to find x
x = 2y
x = 2*4
x = 8
So we have x = 8 and y = 4 pair together to get the answer (x,y) = (8, 4) which is choice A.
Answer:
144
Step-by-step explanation:
The sequence is:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946
so you can see the first term larger than 120 is the 144.
