Answer:
It is not a subspace.
Step-by-step explanation:
So, the polynomial degree of at most 3 is given below as;
V = { p (z) = b0 + b1z + b2z^ + ... + bnz^n. |n is less than or equal to 3 and b0, b1, b2,... are integers.
To determine whether a subset is a subspace of Pn, we have to check for the properties below;
(1). Zero vector property : that is, when polynomial, p(z) = 0 and 0 is an integer.
(2). Addition property= here, we have; p(z) + h(z) = (b0 + b1z + b2z^2 +....+ bnz^n) + ( c0 + c1z + c^2z^2 +... + cnz^n). That is the sum of integers.
(3). Scaler multiplication property: the coefficient here may not be real numbers therefore, the condition is not followed here.
Therefore, it is not a subspace of Pn.
Answer:
3z
2
Step-by-step explanation:
Answer:
dy/dx = (cos y + y sin x) / (cos x + x sin y)
Step-by-step explanation:
y cos x = x cos y
y (-sin x) + dy/dx cos x = x (-sin y dy/dx) + cos y
-y sin x + dy/dx cos x = -x sin y dy/dx + cos y
dy/dx (cos x + x sin y) = cos y + y sin x
dy/dx = (cos y + y sin x) / (cos x + x sin y)
The first thing that we want to do is simplify both side of this equation.
2(m-8).
The first thing we have to do, is multiple 2 by m and -8, also called distributing. So, when we do that, we get
2(m-8)=2*m + 2*-8 = 2m-16
4(m+6)
Now, we do the same thing we did for the first parenthesis, and that's multiple 4 by m and 6.
4(m+6)=4*m + 4*6 = 4m+24
Now, we need to get m by itself on one side. So, lets bring the equation from the right to the left
2m-16 = 4m + 24 (bring 4m to the other side by subtracting)
2m-16-4m = 24 (bring -16 to the right by adding)
-2m=24+16
-2m=40 (divide both sides by -2 to get your value for m)
m=40/-2 = -20
So, our answer is m = -20
The correct answer to this question is letter "D. x = 21, y = 14."
18 : 12
27 : x - 3
24 : y + 2
18 / 12 = 27 / x - 3
3 / 2 = 27 / x - 3
54 = 3x - 9
3x = 54 + 9
3x = 63
x = 21
18 / 12 = 24 / y + 2
3 / 2 = 24 / y + 2
48 = 3y + 6
3y = 48 - 6
3y = 42
y = 14
