9514 1404 393
Answer:
m^2 = 35/9
Step-by-step explanation:
The line will be tangent to the ellipse where there is one point of intersection between the line and the ellipse. We can find that case by looking at the discriminant of the quadratic.
x^2 +9(mx +2)^2 = 1
x^2 +9(m^2x^2 +4mx +4) = 1
(9m^2 +1)x^2+36mx +35 = 0 . . . . subtract 1, collect terms
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Then the discriminant is ...
(36m)^2 -4(9m^2 +1)(35)
We want it to be zero, so we have ...
1296m^2 -1260m^2 -140 = 0 . . . . eliminate parentheses
36m^2 = 140 . . . . . . . . . . . . . . . add 140
m^2 = 140/36 . . . . . . . . . . . . divide by 36
m^2 = 35/9
1. 4(n+3)=16, n+3=4, n=1
2. m/4+3=24, m/4=21, m=84
1. three added to a number n implies n+3, 4 times that sum is 4 (n+3), to solve divide both sides by 4 then subtract three from both sides.
2. a number divided by 4 means n/4 adding it to three n/4+3, to solve subtract 3 from both sides then multiply both sides by 4
Answer:look below
Step-by-step explanation: The prime factorization of number is the break down into factors which are prime numbers (numbers without factors except 1 and itself). The factors 22 and 32 are composite numbers since they have more than 1 and itself as factors. They are not prime.
However, the factorization of 22 * 32 * 5 will equal a number. 22*32*5 = 3, 520. But it does not match the solutions given.
The angle between two vectors is:
CosФ = u - v / Magnitude(u) x magnitude(v)
Magnitude of u = SQRT(7^2 + -2^2) = SQRT(49 +4) = SQRT(53)
Magnitude of v = SQRT(-1^2 +2^2) = SQRT(1 +4) = SQRT(5)
u x v = (7 x -1) + (-2 x 2) = -7 + -4 = -11
cosФ = -11 / sqrt(53) x sqrt(5)
cosФ = -11sqrt265) / 265
Ф =cos^-1(-11sqrt265) / 265)
Ф=132.51 degrees.
Answer:
x=-5/11, y=-9/11. (-5/11, -9/11).
Step-by-step explanation:
3x+2y=-3
y=4x+1
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3x+2(4x+1)=-3
3x+8x+2=-3
11x=-3-2
11x=-5
x=-5/11
y=4(-5/11)+1
y=-20/11+11/11
y=-9/11
