1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Valentin [98]
3 years ago
5

Lerna's Hydra is a mythological character that appears in some stories such as the 12 Tasks of Hercules. The Hydra was a one-hea

ded monster but when it is cut off, 2 more heads grow in its place. If a hero tried to conquer it by cutting off all of its heads every day, how many heads would the Hydra have on the third day? And at the end of 10 days of trying to kill it? *
Mathematics
1 answer:
cluponka [151]3 years ago
4 0

Answer:

Step-by-step explanation:

Initially the monster is one-headed, when it is cut off, 2 more heads grow in its place, when the two heads are cut off, 4 will grow in its place. This will go on an on and the amount of heads that grows each day will form a geometric sequance as shown;

1, 2, 4...

The nth term of an arithmetic sequence is expresses as;

T_n = ar^{n-1} where;

a is the first term

r is the common ratio

n is the number of terms

To get the number of heads that the Hydra have on the third day, we will have to find the fourth term of the sequence since the first cutting was done the next day (second day).

from the sequence above;

a = 1

r = 2/1 = 4/2 = 2

T4 = 1(2)^{4-1}

T4 = 2^3

T4 = 8

Hence the hydra will have 8 heads on the third day.

To know the number of heads at the end of 10 days, we will find the 11th term of the progression

T11 = 1(2)^{11-1}

T4 = 2^10

T4 = 1024

He will have 1024 heads after 10 days of trying to kill the monster.

You might be interested in
Negative fractions on the number line
goblinko [34]
The answer is D
Let me know if it’s right!
8 0
2 years ago
Read 2 more answers
S (3, -5), T (0, -2), U (-3, -5)<br><br> scale factor = 4<br><br> S' = <br><br> T' = <br><br> U'=
Svetach [21]
S’(12,-20) T’(0,-8) U’(-12,-20)
3 0
3 years ago
Prime factorization of 1408
V125BC [204]

Answer:

There are 7 copies of 2 and 1 copy of 11 in the product:

1408 = 2^7×11

Step-by-step explanation:

Factor the following integer:

1408

The last digit of 1408 is 8, which means it is even. Therefore 1408 is divisible by 2:

1408 = 2 704:

1408 = 2×704

The last digit of 704 is 4, which means it is even. Therefore 704 is divisible by 2:

704 = 2 352:

1408 = 2×2×352

The last digit of 352 is 2, which means it is even. Therefore 352 is divisible by 2:

352 = 2 176:

1408 = 2×2×2×176

The last digit of 176 is 6, which means it is even. Therefore 176 is divisible by 2:

176 = 2 88:

1408 = 2×2×2×2×88

The last digit of 88 is 8, which means it is even. Therefore 88 is divisible by 2:

88 = 2 44:

1408 = 2×2×2×2×2×44

The last digit of 44 is 4, which means it is even. Therefore 44 is divisible by 2:

44 = 2 22:

1408 = 2×2×2×2×2×2×22

The last digit of 22 is 2, which means it is even. Therefore 22 is divisible by 2:

22 = 2 11:

1408 = 2×2×2×2×2×2×2×11

11 is not divisible by 2 since 11 is odd and 2 is even:

1408 = 2×2×2×2×2×2×2×11 (11 is not divisible by 2)

The sum of the digits of 11 is 1 + 1 = 2, which is not divisible by 3. This means 11 is not divisible by 3:

1408 = 2×2×2×2×2×2×2×11 (11 is not divisible by 2 or 3)

The last digit of 11 is not 5 or 0, which means 11 is not divisible by 5:

1408 = 2×2×2×2×2×2×2×11 (11 is not divisible by 2, 3 or 5)

Divide 7 into 11:

| | 1 | (quotient)

7 | 1 | 1 |  

- | | 7 |  

| | 4 | (remainder)

11 is not divisible by 7:

1408 = 2×2×2×2×2×2×2×11 (11 is not divisible by 2, 3, 5 or 7)

No primes less than 11 divide into it. Therefore 11 is prime:

1408 = 2×2×2×2×2×2×2×11

There are 7 copies of 2 and 1 copy of 11 in the product:

Answer: 1408 = 2^7×11

8 0
3 years ago
Please help, I’m not good at math and I’m struggling lol how fun
hram777 [196]

Answer:

D. Y = x + 2

Step-by-step explanation:

The slope increases at a rate of 1 / 1, which is written as just x. The line starts at 2, which is at the y-intercept, a.k.a, where you get the +2 from.

3 0
3 years ago
Read 2 more answers
Angles: can somebody tell me the angles of X, Y, Z please p.s 25 points if answered correctly
antoniya [11.8K]

Answer:

X=30; Z=80; Y=70

Step-by-step explanation:

The straight lines equal 180 and you subtract 180 to 150 and 180 to 100 to get 30 and 80 and the inside of a triangle is 180 and you subtract 30 and 80 to 180 to get 70.

3 0
3 years ago
Other questions:
  • An employee at plant A receives a salary of $350 per week and a 2.9% bonus on the production sales for the week. If the sales fo
    7·1 answer
  • -11=a+7 dolce equation
    5·2 answers
  • The histogram shows the number of hours volunteers worked one week.
    15·1 answer
  • I need help with this math problem please
    13·1 answer
  • Without actually solving the equation, explain why the equation √(x+1 + 2=0 has no solution.
    10·1 answer
  • Suppose a baby weighed 8 pounds at birth and gained about 1.2 pounds each month during the first year of life to the nearest pou
    11·1 answer
  • 1131 divided by 29 \
    14·2 answers
  • Simplify the variable expression: g - 16/4 + 2
    7·1 answer
  • (Giving brainlyiest)<br><br><br> 25 POINTS
    10·1 answer
  • A shopkeeper bought 24 bottles of fruit juice for $63 dollars.
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!