Answer is D
LMN is similar to PQR
its side are just 3 times greater than PQR scale factor is 3<span />
Answer:
D. Euler Circuit.
Step-by-step explanation:
An Euler Circuit goes through every edge exactly once; starts and stops at the same vertex.
According to the Euler's Theorem, A graph has an Euler path if there are two 2-degree vertices without odd degrees and all other vertices have even degrees.
Mathematically, it is given as;
V+F=2-E
where;
F is the number of faces
V the number of vertices
E the number of edges.
Answer:
1000 miles
Step-by-step explanation:
Given the following :
Number of miles driven :
First trip = 240 miles
Second day = 205 miles
Third day = 315 miles
Fourth day; miles driven before arriving at their final destination = 220 miles
Total number of miles driven after 4 days before reaching their destination :
(240 + 205 + 315 + 220) = 980 miles
However, they still haven't reached their destination ;
Using front end estimation :
We can take the total miles recorded and make an estimation based on the first digit of the recorded miles traveled:
In other to estimate 980 using front end estimation : the actual number is replaced with a number with only one nonzero digit (which is the first digit)
Hence,
980 - - - - > we round the digit after 9 either 1 or 0, since it is greater than 4, then it is rounded to and added to the first digit, all subsequent dots are rounded to zero
Hence 980 - - - - > 1000
Hence, estimated miles driven = 1000 miles
Answer: The required solution is
Step-by-step explanation: We are given to solve the following differential equation :
Let us consider that
be an auxiliary solution of equation (i).
Then, we have
Substituting these values in equation (i), we get
![m^2e^{mt}+10me^{mt}+25e^{mt}=0\\\\\Rightarrow (m^2+10y+25)e^{mt}=0\\\\\Rightarrow m^2+10m+25=0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~[\textup{since }e^{mt}\neq0]\\\\\Rightarrow m^2+2\times m\times5+5^2=0\\\\\Rightarrow (m+5)^2=0\\\\\Rightarrow m=-5,-5.](https://tex.z-dn.net/?f=m%5E2e%5E%7Bmt%7D%2B10me%5E%7Bmt%7D%2B25e%5E%7Bmt%7D%3D0%5C%5C%5C%5C%5CRightarrow%20%28m%5E2%2B10y%2B25%29e%5E%7Bmt%7D%3D0%5C%5C%5C%5C%5CRightarrow%20m%5E2%2B10m%2B25%3D0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~%5B%5Ctextup%7Bsince%20%7De%5E%7Bmt%7D%5Cneq0%5D%5C%5C%5C%5C%5CRightarrow%20m%5E2%2B2%5Ctimes%20m%5Ctimes5%2B5%5E2%3D0%5C%5C%5C%5C%5CRightarrow%20%28m%2B5%29%5E2%3D0%5C%5C%5C%5C%5CRightarrow%20m%3D-5%2C-5.)
So, the general solution of the given equation is
Differentiating with respect to t, we get
According to the given conditions, we have
and
Thus, the required solution is
Answer:
Step-by-step explanation:
a) since acceleration can be expressed as a(t) = dv/dt
We use the chosen rule to obtain
dv/dt = dv/dx * dx/dt = v* dv/dx
We can now set v dv/dx = -kv^2
Taking v from both sides
dv/dx = -kv
Dv/v = -kdx
In (v)= kx+ c
V= e^kx+c
From v (o) = 150
V = 150e^kx
When distance x= 2000ft convert to miles gives 0.378788 mi then velocity v = 15 mi/he
15= 150. e ^ 0.378788k
Lm (o.t) = -0.378788k
K= 6.0788mi
C) we return to dv/dt = -kv^2 = dv/v^2 = -k dt
-1/v = -kt +c
From v(o) = 150, we get - 1/150= c and
1/v - 1/150= kt
We know v= 15mi/hr and k = 6.0788
1/15 - 1/150 = 6.0788t
T = 9.8704.10^-3hr.
