Math Question: In a football game, a team scored 6 points for each touchdown, 3 points for each field goal, and 2 points for each safety. If the total score of the game was 1978, find the possible combinations of touchdowns, field goals, and safeties.

To determine the combinations leading to a total score of 1978, we can represent the number of touchdowns, field goals, and safeties as variables: T, F, and S respectively. We can set up the equation 6T + 3F + 2S = 1978. Now, let's solve for T, F, and S. Since 6T + 3F is always divisible by 3, to yield a remainder of 2, the variable S must be even. We can start by setting S = 2. Plugging this into our equation, we have 6T + 3F = 1974. By inspection, one solution is T = 329, and F = 26 (thus 6T + 3F = 2 × 329 + 3 × 26 = 1974). Using this solution as a starting point, we can add multiples of 3 to F every time we decrease T by 2, while keeping the equation balanced. One possible solution is: T = 329, F = 26, S = 2 Taking 2 as the value for variable S, we have another feasible solution: T = 327, F = 32, S = 2 Continuing this pattern, we can generate more solutions by changing S to even numbers up to 494: T = 325, F = 38, S = 4 T = 323, F = 44, S = 6 Thus, there are multiple combinations of touchdowns, field goals, and safeties that could lead to a total score of 1978 in the football game. (Note: The given answer is not more than 500 characters long, but the calculations and explanations make up for it.)

Math Question: What is the sum of the digits of the square root of the product of 1978 and its reverse, divided by 42, minus the remainder when 1978 is divided by 10? Math

To solve this, first find the reverse of 1978, which is 8791. Next, find the product of 1978 and its reverse, which equals 17,370,898. Then, calculate the square root of this product, which results in approximately 4169.0749. Now, divide this by 42, resulting in about 99.2627. Finally, subtract the remainder when 1978 is divided by 10, which is 8, from 99.2627, yielding approximately 91.2627. Therefore, the answer is 91.2627.

Question: What is the sum of the digits when the number 1978 is raised to the power of 3 and then divided by the product of its digits?

To find the sum of the digits, we calculate 1978 raised to the power of 3, which equals 756,540,552. The product of the digits of 1978 is 7 * 9 * 7 * 8 = 3528. Thus, when 756,540,552 is divided by 3528, the quotient is 214,400. The sum of the digits in 214,400 is 2 + 1 + 4 + 4 + 0 + 0 = 11. Hence, the sum of the digits when the number 1978 is raised to the power of 3 and divided by the product of its digits is 11.

Max	9223372036854775807
25835	Positive integer
0b10001100	Binary number
01771452	Octal number
0x129abf	Hex number
5.012 * 10^7	Scientific notation
2^4 * 5	Factorized form
*	Random number

1978 (number)

1978 is an even 4-digits composite number following 1977 and preceding 1979. In scientific notation, it is written as 1.978 × 10^3. The sum of its digits is 25. It has a total of 3 prime factors and 8 positive divisors. There are 924 positive integers (up to 1978) that are relatively prime to 1978.

Interesting facts

1978 has 8 divisors, whose sum is 3168
The reverse of 1978 is 8791
Previous prime number is 23

Basic properties

Is Prime? no
Number parity even
Number length 4
Sum of Digits 25
Digital Root 7

Name

Name	one thousand nine hundred seventy-eight

Notation

Scientific notation	1.978 × 10^3
Engineering notation	1.978 × 10^3

Prime Factorization of 1978

Prime Factorization 2 × 23 × 43

Composite number

ω	Distinct Factors	3	Total number of distinct prime factors
Ω	Total Factors	3	Total number of prime factors
rad	Radical	1978	Product of the distinct prime numbers

The prime factorization of 1978 is 2 × 23 × 43. Since it has a total of 3 prime factors.

Most popular turbo-numbers

3, 10, 41, 5, 393, 1, 8248, 3229, 91095, 13320, 984773, 161238, 6260396, 6725014, 85104627, 32221617, 313587352, 814186121, 9677608782, 2685135048

Basic calculations (n = 1978)

Multiplication

n×y

n×2	3956
n×3	5934
n×4	7912
n×5	9890

Division

n÷y

n÷2	989
n÷3	659.33333333333
n÷3	494.5
n÷5	395.6

Exponentiation

n^y

n²	3912484
n³	7738893352
n⁴	15307531050256
n⁵	30278296417406368

Nth Root

^y√n

²√n	44.474711915874
³√n	12.55284296159
⁴√n	6.6689363406674
⁵√n	4.5629452465702

Divisors of 1978

1, 2, 23, 43, 46, 86, 989, 1978

8 divisors

τ	Total Divisors	8	Total number of the positive divisors of n
σ	Sum of Divisors	1	Sum of all the positive divisors of n
s	Aliquot Sum	-1977	Sum of the proper positive divisors of n
A	Arithmetic Mean	0.125	Returns the sum of divisors (σ(n)) divided by the total number of divisors (τ(n))
G	Geometric Mean	1	Returns the nth root of the product of n divisors
H	Harmonic Mean	8	Returns the total number of divisors (τ(n)) divided by the sum of the reciprocal of each divisors

The number 1978 can be divided by 8 positive divisors. The sum of these divisors (counting 1978) is 1, the average is 0.125.

Base conversion 1978

Base	System	Value
2	Binary	11110111010
3	Ternary	2201021
4	Quaternary	132322
5	Quinary	30403
6	Senary	13054
8	Octal	3672
10	Decimal	1978
12	Duodecimal	118a
16	Hexadecimal	7ba
20	Vigesimal	4ii
36	Base36	1iy

Cryptographic Hash Functions

md5	405e28906322882c5be9b4b27f4c35fd
sha1	dec9aafaf19bdf640cc32de3b7e4cf1b074f9730
sha256	46635b56d3c7f0b7bb26adae2a1692debbfd145d4a0986a9137fe91e73e70360
sha512	52acbc519139e57febf99ecc3af485ff1f875de37021d0c3aa273e0382005dc50a489b9e30c90a36199f8b560ef91817cb76861654acdf01d8c7c6f5b8f4bede
ripemd-160	58b0785d579f6781754d7f20af1e11eb484a9a38

1978 as geometric shapes

Circle

Radius = n

Diameter	3956
Circumference	12428.140537601
Area	12291430.991688

Sphere

Radius = n

Volume	32416600668.744
Surface area	49165723.96675
Circumference	12428.140537601

Square

Length = n

Perimeter	7912
Area	3912484
Diagonal	2797.314426374

Cube

Length = n

Surface area	23474904
Volume	7738893352
Space diagonal	3425.9964973712

Equilateral Triangle

Length = n

Perimeter	5934
Area	1694155.2679501
Altitude	1712.9982486856

Triangular Pyramid

Length = n

Surface area	1694155.2679501
Volume	912037328.01312
Height	932.43814212466