Answer:
, ∠C ≅∠Z
, ∠A≅∠X
Step-by-step explanation:
we know that
If two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent
so
In this problem
The corresponding sides are
BA and YX
BC and YZ
AC and XZ
The corresponding angles are
∠A and ∠X
∠B and ∠Y
∠C and ∠Z
so
and
∠A≅∠X
∠B≅∠Y
∠C ≅∠Z
therefore
, ∠C ≅∠Z
, ∠A≅∠X
Let:
x = hours of travel
y = velocity
slope= rise/run slope=(y2-y1)/(x2-x1)
(x1,y1) = (2,50) (x2,y2) = (6,54)
sub values back into the equation m = (54-50)/(6-2) m = 1
POINT SLOPE FORMy-y1 = m(x-x1) y-50= 1(x-2) y = x -2 +50
y = x + 48
B)
the graph within the first seven hours can be obtained at point B
x = 7
y = 7+48 = 55
B(7,55)
Answer:
1 1/2
Step-by-step explanation:
The first step is to figure out the lightest and the heaviest bad. The lightest bag is 4 1/4 and the heaviest is 5 3/4. Now to subtract, you can't subtract this as a mixed fraction so turn each fraction into an improper fraction by multiplying the whole number by the denominator then adding the numerator to the product of the whole number multiplied by the denominator (if you didn't know numerator is the top and the denominator is the bottom. To find out 4 1/4 as an improper fraction follow these steps (4*4+1=17) so 4 1/4=17/4. The process is the same for 5 3/4 (5*4+3=23) so 5 3/4= 23/4. Now to subtract, you subtract the numerator but not the denominator. You subtract because the question asks how many more and that means to subtract 23/4-17/4= 6/4. Last step is to turn this back into a mixed fraction do that by dividing the numerator by the denominator, 6 divided by 4 equals 1.5 and turn the decimal into a fraction 1 is a whole number so you don't change that but the 5 behind the decimal needs to be changed so now 1.5= 1 5/10 and last step is simplify 1 1/2. Hope this helped :).
Answer:
As per the given statement:
The region bounded by the given curves about the y-axis, 
, y=0, x = 0 and x = 1
Using cylindrical shell method:
The volume of solid(V) is obtained by rotating about y-axis and the region under the curve y = f(x) from a to b is;
where 
where x is the radius of the cylinder
f(x) is the height of the cylinder.
From the given figure:
radius = x
height(h) =f(x) =y=
a = 0 and b = 1
So, the volume V generated by rotating the given region:
![V =2 \pi \int_{0}^{1} x ( 13e^{-x^2}) dx\\\\V=2\pi\left [ -\frac{13}{2}e^{-x^2} \right ]_{0}^{1}\\\\V=2\pi\left (-\frac{13}{2e}-\left(-\frac{13}{2}\right) \right )\\\\V=-\frac{13\pi }{e}+13\pi](https://tex.z-dn.net/?f=V%20%3D2%20%5Cpi%20%5Cint_%7B0%7D%5E%7B1%7D%20x%20%28%2013e%5E%7B-x%5E2%7D%29%20dx%5C%5C%5C%5CV%3D2%5Cpi%5Cleft%20%5B%20-%5Cfrac%7B13%7D%7B2%7De%5E%7B-x%5E2%7D%20%5Cright%20%5D_%7B0%7D%5E%7B1%7D%5C%5C%5C%5CV%3D2%5Cpi%5Cleft%20%28-%5Cfrac%7B13%7D%7B2e%7D-%5Cleft%28-%5Cfrac%7B13%7D%7B2%7D%5Cright%29%20%5Cright%20%29%5C%5C%5C%5CV%3D-%5Cfrac%7B13%5Cpi%20%7D%7Be%7D%2B13%5Cpi%20)
therefore, the volume of V generated by rotating the given region is 
