Answer:
a=20 m²
b=21 cm²
c=36 dm²
Step-by-step explanation:
A) 12²+16²=a²
144+256=a²
400=a²
√400=a
a=20
B) 28²+b²=35²
784+b²=1225
b²=1225-784
b²=441
b=√441
b=21
C) c²+15²=39²
c²+225=1521
c²=1296
c=√1296
c=36
<u>Hint </u><u>:</u><u>-</u>
- Break the given sequence into two parts .
- Notice the terms at gap of one term beginning from the first term .They are like
. Next term is obtained by multiplying half to the previous term . - Notice the terms beginning from 2nd term ,
. Next term is obtained by adding 3 to the previous term .
<u>Solution</u><u> </u><u>:</u><u>-</u><u> </u>
We need to find out the sum of 50 terms of the given sequence . After splitting the given sequence ,
.
We can see that this is in <u>Geometric</u><u> </u><u>Progression </u> where 1/2 is the common ratio . Calculating the sum of 25 terms , we have ,
![\implies S_1 = a\dfrac{1-r^n}{1-r} \\\\\implies S_1 = \dfrac{1}{2}\left[ \dfrac{1-\bigg(\dfrac{1}{2}\bigg)^{25}}{1-\dfrac{1}{2}}\right]](https://tex.z-dn.net/?f=%5Cimplies%20S_1%20%3D%20a%5Cdfrac%7B1-r%5En%7D%7B1-r%7D%20%5C%5C%5C%5C%5Cimplies%20S_1%20%3D%20%5Cdfrac%7B1%7D%7B2%7D%5Cleft%5B%20%5Cdfrac%7B1-%5Cbigg%28%5Cdfrac%7B1%7D%7B2%7D%5Cbigg%29%5E%7B25%7D%7D%7B1-%5Cdfrac%7B1%7D%7B2%7D%7D%5Cright%5D%20)
Notice the term 
will be too small , so we can neglect it and take its approximation as 0 .
![\implies S_1\approx \cancel{ \dfrac{1}{2} } \left[ \dfrac{1-0}{\cancel{\dfrac{1}{2} }}\right]](https://tex.z-dn.net/?f=%5Cimplies%20S_1%5Capprox%20%5Ccancel%7B%20%5Cdfrac%7B1%7D%7B2%7D%20%7D%20%5Cleft%5B%20%5Cdfrac%7B1-0%7D%7B%5Ccancel%7B%5Cdfrac%7B1%7D%7B2%7D%20%7D%7D%5Cright%5D%20)
Now the second sequence is in Arithmetic Progression , with common difference = 3 .
![\implies S_2=\dfrac{n}{2}[2a + (n-1)d]](https://tex.z-dn.net/?f=%5Cimplies%20S_2%3D%5Cdfrac%7Bn%7D%7B2%7D%5B2a%20%2B%20%28n-1%29d%5D%20)
Substitute ,
![\implies S_2=\dfrac{25}{2}[2(4) + (25-1)3] =\boxed{ 908}](https://tex.z-dn.net/?f=%5Cimplies%20S_2%3D%5Cdfrac%7B25%7D%7B2%7D%5B2%284%29%20%2B%20%2825-1%293%5D%20%3D%5Cboxed%7B%20908%7D%20)
Hence sum = 908 + 1 = 909
Answer:
22.25
Step-by-step explanation:
1302-1124/2016-2008
For the 11 the first one is x = 4y and for the 2 one it will be x=−6−2y
Answer/Step-by-step explanation:
Let's solve your equation step-by-step.
4−(2y+5)=3(1−4y)
Step 1: Simplify both sides of the equation.
4−(2y+5)=3(1−4y)
4+−1(2y+5)=3(1−4y)(Distribute the Negative Sign)
4+−1(2y)+(−1)(5)=3(1−4y)
4+−2y+−5=3(1−4y)
4+−2y+−5=(3)(1)+(3)(−4y)(Distribute)
4+−2y+−5=3+−12y
(−2y)+(4+−5)=−12y+3(Combine Like Terms)
−2y+−1=−12y+3
−2y−1=−12y+3
Step 2: Add 12y to both sides.
−2y−1+12y=−12y+3+12y
10y−1=3
Step 3: Add 1 to both sides.
10y−1+1=3+1
10y=4
Step 4: Divide both sides by 10.
10y
10
=
4
10
y=
2
5
Answer:
y=
2/5
yw
