Answer:
Volume of the Crockpot = πr^2h
= 3.14 x 6 x 6 x 15
= 3.14 x 540 in^3
Volume of double batch of chili = 900 x 2 = 1800 in^3
3.14 x 540/1800 = 9.42/10 = 0.942 < 1
Since the value we found by dividing the volume of Crockpot by double batch of chili is less than 1, we can say that the Crockpot will not hold the double batch of chili
Hope this helps!
Answer:
The equation does not have a real root in the interval ![\rm [0,1]](https://tex.z-dn.net/?f=%5Crm%20%5B0%2C1%5D)
Step-by-step explanation:
We can make use of the intermediate value theorem.
The theorem states that if 
is a continuous function whose domain is the interval [a, b], then it takes on any value between f(a) and f(b) at some point within the interval. There are two corollaries:
- If a continuous function has values of opposite sign inside an interval, then it has a root in that interval. This is also known as Bolzano's theorem.
- The image of a continuous function over an interval is itself an interval.
Of course, in our case, we will make use of the first one.
First, we need to proof that our function is continues in , which it is since every polynomial is a continuous function on the entire line of real numbers. Then, we can apply the first corollary to the interval , which means to evaluate the equation in 0 and 1:
Since both values have the same sign, positive in this case, we can say that by virtue of the first corollary of the intermediate value theorem the equation does not have a real root in the interval . I attached a plot of the equation in the interval ![\rm [-2,2]](https://tex.z-dn.net/?f=%5Crm%20%5B-2%2C2%5D)
where you can clearly observe how the graph does not cross the x-axis in the interval.
6.5c + 9.7a = 1721.4
a = 4c
6.5c + 9.7(4c) = 1721.4
6.5c + 38.8c = 1721.4
45.3c = 1721.4
c = 1721.4 / 45.3
c = 38...so there were 38 childrens' tickets <==
and 152 adult tickets
Answer:
8x + 1/2 or 8x + 0.5
Step-by-step explanation:
-6x + 3 3/4 + 14x - 3.25
u can either convert the fraction to a decimal or convert the decimal into a fraction, i'm going to do the latter
-6x + 3 3/4 + 14x - 3 1/4
rearrange to make it easier, don't need to do this i'm just doing this for the sake of it
-6x + 14x + 3 3/4 - 3 1/4
8x + 2/4, simplify this
8x + 1/2
The decimal way if u want:
-6x + 3 3/4 + 14x - 3.25
-6x + 3.75 + 14x - 3.25
-6x + 14x + 3.75 - 3.25
8x + 0.5
