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kumpel [21]
2 years ago
13

What is the 5th term of the expansion of (3x+y^4)^7

Mathematics
1 answer:
chubhunter [2.5K]2 years ago
8 0

9514 1404 393

Answer:

  945x^3·y^16

Step-by-step explanation:

The 5th term will be ...

  C(7,4)(3x)^3(y^4)^4 = 35·27·x^3·y^(4·4)

  = 945x^3·y^16

_____

The coefficients of the expansion are C(n, k) where n is the exponent of the binomial, and k+1 is the term number. This is n!/(k!(n-k)!). The general (k-th) term of the expansion (a+b)^n is C(n, k)a^(n-k)b^(k) where k ranges from 0 to n.

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A wedge of cheese is shaped like a triangular prism. The wedge of cheese is 7 inches tall. The base of the cheese is shaped like
Gala2k [10]

Answer:

193 in

Step-by-step explanation:

Volume of a triangular prism:

The volume of a triangular prism is the base area multiplied by the wedge, that is:

V = A_bw

The base area is one half times the triangle base times it's height, so:

V = 0.5*b*h*w

The wedge of cheese is 7 inches tall.

This means that w = 7

The base of the cheese is shaped like a triangle with a base of 11 and a height of 5 inches.

This means that b = 11, h = 5

Volume:

V = 0.5*b*h*w = 0.5*11*5*7 = 192.5

Rounding, approximately 193 in.

4 0
3 years ago
Given that A and B are true and X and Y are false, determine the truth value of the following proposition: ~[(A ⊃ Y) v ~(X ⊃ B)]
Anni [7]

Answer:

The value of the proposition is FALSE

Step-by-step explanation:

~[(A ⊃ Y) v ~(X ⊃ B)] ⋅ [~(A ≡ ~X) v (B ⊃ X)]

Let's start with the smallest part: ~X. The symbol ~ is negation when X is true with the negation is false and vice-versa. In this case, ~X is true (T)

~[(A ⊃ Y) v ~(X ⊃ B)] ⋅ [~(A ≡ T) v (B ⊃ X)]

Now the parts inside parenthesis:  (A ⊃ Y),(X ⊃ B),(A ≡ T) and (B ⊃ X). The symbol ⊃ is the conditional and A ⊃ Y is false when Y is false and A is true, in any other case is true. The symbol ≡ is the biconditional and A ≡ Y is true when both A and Y are true or when both are false.

(A ⊃ Y) is False (F)

(X ⊃ B) is True (T)

(A ≡ T) is True (T)

(B ⊃ X) is False (F)

~[(F) v ~(T)] ⋅ [~(T) v (F)]

The two negations inside the brackets must be taken into account:

~[(F) v F] ⋅ [F v (F)]

The symbol left inside the brackets v is the disjunction, and A v Y is false only  with both are false. F v (F) is False.

~[F] ⋅ [F]

Again considerating the negation:

T⋅ [F]

Finally, the symbol ⋅ is the conjunction, and A v Y is true only with both are true.

T⋅ [F] is False.

5 0
3 years ago
PLEASE HELP ASAP!!!!
Bogdan [553]

Step-by-step explanation:

I think C. objects color and texture distributed thoughout the photo

6 0
3 years ago
Decrease 40 by 12.5%
vredina [299]

Answer:

35

Step-by-step explanation:

Multiply 40 by 0.125 (12.5%) and you get 5

Subtract 5 from 40

35

6 0
3 years ago
Tina’s bedroom is in the shape of a rectangular prism 15 feet long, 12 feet wide, and 10 feet high. It has no windows. Tina want
Tanya [424]

Answer:

720ft²

Step-by-step explanation:

Wall 1&2 = lh = 15*10=150

Wall 3&4 = wh = 12*10=120

Ceiling = lw = 12*15=180

120+150+120+150+180=720ft²

7 0
3 years ago
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