Answer:
proportional
Step-by-step explanation:
Answer:
<u>y = w and ΔABC ~ ΔCDE</u>
Step-by-step explanation:
Given sin(y°) = cos(x°)
So, ∠y + ∠x = 90° ⇒(1)
And as shown at the graph:
ΔABC is aright triangle at B
So, ∠y + ∠z = 90° ⇒(2)
From (1) and (2)
<u>∴ ∠x = ∠z </u>
ΔCDE is aright triangle at D
So, ∠x + ∠w = 90° ⇒(3)
From (1) and (3)
<u>∴ ∠y = ∠w</u>
So, for the triangles ΔABC and ΔCDE
- ∠A = ∠C ⇒ proved by ∠y = ∠w
- ∠B = ∠D ⇒ Given ∠B and ∠D are right angles.
- ∠C = ∠E ⇒ proved by ∠x = ∠z
So, from the previous ΔABC ~ ΔCDE by AAA postulate.
So, the answer is <u>y = w and ΔABC ~ ΔCDE</u>
Answer: x=38/7
Step-by-step explanation:
Answer:
Mean= 10.83
Median= 9.5
Step-by-step explanation:
Given number,
10, 15, 8, 11, 9, 12
N= 6
As we know,
Mean= Ex/N
=10+15+8+11+9+12/6
=65/6
=10.83
Therefore, Mean= 10.83
Now,
Median(MD)= (N+1/2)th item
= 6+1/2
=7/2
=3.5th item
So, Median(MD)= 3th+4th/2 item
= 8+11/2
= 19/2
= 9.5
Therefore, Median= 9.5
Answer:
Step-by-step explanation:
Let P be the population of the community
So the population of a community increase at a rate proportional to the number of people present at a time
That is
![\frac{dp}{dt} \propto p\\\\\frac{dp}{dt} =kp\\\\ [k \texttt {is constant}]\\\\\frac{dp}{dt} -kp =0](https://tex.z-dn.net/?f=%5Cfrac%7Bdp%7D%7Bdt%7D%20%5Cpropto%20p%5C%5C%5C%5C%5Cfrac%7Bdp%7D%7Bdt%7D%20%3Dkp%5C%5C%5C%5C%20%5Bk%20%5Ctexttt%20%7Bis%20constant%7D%5D%5C%5C%5C%5C%5Cfrac%7Bdp%7D%7Bdt%7D%20-kp%20%3D0)
Solve this equation we get
where p is the present population
p₀ is the initial population
If the initial population as doubled in 5 years
that is time t = 5 years
We get
Apply In on both side to get
Substitute 
in 
to get
Given that population of a community is 9000 at 3 years
substitute t = 3 in 
<h3>Therefore, the initial population is 5937.8</h3>
