
Answer:
1.01 × 10⁴ - scientific notation
10,100 - decimal notation
Answer:
6
Step-by-step explanation:
the first thing I did to smome but you know 5AM was a l
The standard form for this parabola is x = a(y-k)^2 + h because this is a sideways-opening parabola. Our h and k values for the vertex are (-4, -1). And it goes through (2,0). We just need to solve for the a. Filling in accordingly, 2 = a(0+1)^2-4 so 2 = a - 4. a = 6. A above.
correct answer is 6!
Answer:
Step-by-step explanation:
A = C^2 / 4 x pi
so if the circumfernce was 10 you would square it to make it 100 and then you would do 4 x pi to get 12.57 ( rounded).
you would then just divide 100 by 12.57 = 7.96 ( rounded)
hope it helped
Answer:
-2, 8/3
Step-by-step explanation:
You can consider the area to be that of a trapezoid with parallel bases f(a) and f(4), and width (4-a). The area of that trapezoid is ...
A = (1/2)(f(a) +f(4))(4 -a)
= (1/2)((3a -1) +(3·4 -1))(4 -a)
= (1/2)(3a +10)(4 -a)
We want this area to be 12, so we can substitute that value for A and solve for "a".
12 = (1/2)(3a +10)(4 -a)
24 = (3a +10)(4 -a) = -3a² +2a +40
3a² -2a -16 = 0 . . . . . . subtract the right side
(3a -8)(a +2) = 0 . . . . . factor
Values of "a" that make these factors zero are ...
a = 8/3, a = -2
The values of "a" that make the area under the curve equal to 12 are -2 and 8/3.
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<em>Alternate solution</em>
The attachment shows a solution using the numerical integration function of a graphing calculator. The area under the curve of function f(x) on the interval [a, 4] is the integral of f(x) on that interval. Perhaps confusingly, we have called that area f(a). As we have seen above, the area is a quadratic function of "a". I find it convenient to use a calculator's functions to solve problems like this where possible.