Answer:
Its b.
Step-by-step explanation:
m < 3 = m < 4 (vertical angles)
m < 1 = m < 5 ( alternate angles)
Therefore the triangles are similar.
F=5.77X10^9(1.032^(y-1985)), we want to know when this is:
2.2X10^12=5.77X10^9(1.032^(y-1985))
381.2825=1.032^(y-1985)
ln(3,812825)=(y-1985)ln(1.032)
ln(3.812825)/ln(1.032)=y-1985
y=1985+ln(3.812825)/ln(1.032)
y≈2027.5
So GDP will reach 2.2 trillion during the year 2027.
Four gigabytes (4.9)
$73.5-$49=$24.5
$24.5/$5 =4.9
Answer:
She hiked 1,554 kilometers in all.
Step-by-step explanation:
Let the hiking kilometers for morning be x
Given that:
Hiking kilometers in afternoon = 666
According to given condition that afternoon kilometers are 25% less than morning:
x = 666 + 25% of x
By simplifying:
x = 666 + 0.25x
x - 0.25x = 666
0.75x = 666
Dividing both sides by 0.75 we get:
x = 666/0.75
x = 888 kilometers
She hiked 888 kilometers in morning
And
Total = 888 + 666 =1554 km
i hope it will help you!
A) There are a number of ways to compute the determinant of a 3x3 matrix. Since k is on the bottom row, it is convenient to compute the cofactors of the numbers on the bottom row. Then the determinant is ...
1×(2×-1 -3×1) -k×(3×-1 -2×1) +2×(3×3 -2×2) = 5 -5k
bi) Π₁ can be written using r = (x, y, z).
Π₁ ⇒ 3x +2y +z = 4
bii) The cross product of the coefficients of λ and μ will give the normal to the plane. The dot-product of that with the constant vector will give the desired constant.
Π₂ ⇒ ((1, 0, 2)×(1, -1, -1))•(x, y, z) = ((1, 0, 2)×(1, -1, -1))•(1, 2, 3)
Π₂ ⇒ 2x +3y -z = 5
c) If the three planes form a sheath, the ranks of their coefficient matrix and that of the augmented matrix must be 2. That is, the determinant must be zero. The value of k that makes the determinant zero is found in part (a) to be -1.
A common approach to determining the rank of a matrix is to reduce it to row echelon form. Then the number of independent rows becomes obvious. (It is the number of non-zero rows.) This form for k=-1 is shown in the picture.