Answer:
Area covered by the fences will be 16.1 unit²
Step-by-step explanation:
Let the first parabola is represented by the function f(x) = 6x²
and second parabola by g(x) = x² + 9
point of intersection of the graphs will be determined when f(x) = g(x)
6x² = x² + 9
5x² = 9
x² = 1.8
x = ± 1.34
Now we will find the area between these curves drawn on the graph.
Area = ![\int_{-1.34}^{1.34}[f(x)-g(x)]dx=\int_{-1.34}^{1.34}[6x^{2}-(x^{2}+9)]dx](https://tex.z-dn.net/?f=%5Cint_%7B-1.34%7D%5E%7B1.34%7D%5Bf%28x%29-g%28x%29%5Ddx%3D%5Cint_%7B-1.34%7D%5E%7B1.34%7D%5B6x%5E%7B2%7D-%28x%5E%7B2%7D%2B9%29%5Ddx)
= 
= ![[\frac{5}{3}x^{3}-9x]_{-1.34}^{1.34}](https://tex.z-dn.net/?f=%5B%5Cfrac%7B5%7D%7B3%7Dx%5E%7B3%7D-9x%5D_%7B-1.34%7D%5E%7B1.34%7D)
= ![[\frac{5}{3}(-1.34)^{3}-9(-1.34)-\frac{5}{3}(1.34)^{3}+9(1.34)]](https://tex.z-dn.net/?f=%5B%5Cfrac%7B5%7D%7B3%7D%28-1.34%29%5E%7B3%7D-9%28-1.34%29-%5Cfrac%7B5%7D%7B3%7D%281.34%29%5E%7B3%7D%2B9%281.34%29%5D)
= ![[-4.01+12.06-4.01+12.06]](https://tex.z-dn.net/?f=%5B-4.01%2B12.06-4.01%2B12.06%5D)
= 16.1 unit²
Answer:
1/60
Step-by-step explanation:
Since there are 6 possible outcomes for the first event and 10 possible outcomes for the second event, and they are independent of each other, one outcome of the experiment would have a 1/(6*10)=1/60 chance of happening. Hope this helps!
A. (8,4) because you can tell in the second pattern
Answer:
White roses - 7
Red roses - 17
Step-by-step explanation:
Set up proportional equations
White roses = x
Red roses = 3x - 4
Set equal to 24
x + 3x - 4 = 24
4x - 4 = 24
4x = 28
x = 7
x is white roses, so there are 7
Plug x value into red rose equation
3(7)-4
21-4 = 17 red roses
Check
17+7 = 24
Answer:
<em>* Siobhan's profit at the grocery store ⇒ $ 10.8 *</em>
Step-by-step explanation:
See below;
Priya's 40% profit in the grocery store ⇒ 40/100 * 9 = 2/5 * 9 = 18/5 ⇒ $ 3.6,
Priya's profit at the grocery store ⇒ 9 + 3.6 ⇒ $ 12.6,
Siobhan's 15% of Priya's profit from the store ⇒ 15/100 * 12.6 = $ 1.8
Siobhan's profit at the grocery store ⇒ 12.6 - 1.8 = $ 10.8
<em>* Siobhan's profit at the grocery store ⇒ $ 10.8 *</em>