Answer:
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Step-by-step explanation:
The 400th term is 425.There are floor(√400) = 20 squares in the range 1..400, so the 400th term will be at least 420. There are floor(∛420) = 7 cubes in the range 1..400, so the 400th term may be as high as 427. However, there are
![\lfloor\sqrt[6]{427}\rfloor=2](https://tex.z-dn.net/?f=%5Clfloor%5Csqrt%5B6%5D%7B427%7D%5Crfloor%3D2)
numbers that are both squares and cubes. Consequently, the 400th term will be 427-2 =
425.
Answer:
a = 60
b = 90
c = 150
Step-by-step explanation:
Numerele a, b și c sunt direct proporționale cu 2, 3 și 5.
Unde k este constantă de proporționalitate
a ∝ 2
a = 2k
b ∝ 3
b = 3k
c ∝ 5
c = 5k
Dacă media aritmetică a celor trei numere este egală cu 100, determinați numerele a, b și c
= 2k + 3k + 5k / 3 = 100
= 10k / 3 = 100
Cross Multiply
= 10k = 3 × 100
= 10k = 300
Împărțiți ambele părți la 10
k = 300/10
k = 30
Pentru numărul a
a = 2k
a = 2 × 30
a = 60
Pentru numărul b
b = 3k
b = 3 × 30
b = 90
Pentru numărul c
c = 5k
c = 5 × 30
c = 150
Prin urmare, a = 60, b = 90, c = 150
Answer:
2) Equation 1 and Equation 2 have the same number of solutions.
Step-by-step explanation:
The two given equations are
1) 15x + 6 = 41 and 2) 2x + 13 = 28
Solving both equations, we get
Solving (1) : 15x + 6 = 41 ⇒ 15x = 41 - 6 = 35
or, x = 35/15 ⇒ x = 7/3
Solving (2) : 2x + 13 = 28⇒ 2x = 28 - 13 = 15
or, x = 15/2 ⇒ x = 15/2
So, from above solutions we can say that Equation 1 and Equation 2 have the same number of UNIQUE solution.
2/7 ( k+5/8) = 2 and 2/7
2/7 (k+5/8) = 16/7 |multiply by 7
2(k+5/8) = 16 |divide by 2
k+5/8 = 8 |subtract 5/8
k=8-5/8 = 7 and 3/8 = 27/8 = 7.375
