Answer:
≈ 35.1 ft
Step-by-step explanation:
The model is a right triangle with ladder being the hypotenuse and the angle between the ground and the ladder is 70°
Using the cosine ratio, with l being the length of the ladder.
cos70° = = ( multiply both sides by l )
l × cos70° = 12 ( divide both sides by cos70° )
l = ≈ 35.1 ( to the nearest tenth )
The ladder is approx 35.1 ft long
The answer is going to be: answer B.
Hope this helps =D
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.
Answer: (2;20)
x is the independent variable - number of days (2)
y is the dependent variable - number of tubes (20)
Step-by-step explanation:
Hi to answer this we have to write an equation for each case.
The amount of cookie dough (y) that mike sells is equal to the sum of the 10 already sold tubes and the product of the tubes sold per day (5) and the number of days (x)
Mike ⇒y= 10 + 5x
Same process for Tommy
Tommy⇒ y= 10x
IF they sell l the same amount of cookie dough
y=y
So
10 + 5x =10x
10 =10x-5x
10=5x
10/5 = x
x = 2 days
They will sell the same amount of cookie dough after 2 days .
To find the amount sold in number of tubes, we simply replace the value of "y" by 2 in both equations.
y(2)= 10 + 5(2) = 10+10=20 tubes
y(2)= 10(2) =20 tubes
x is the independent variable - number of days
y is the dependent variable - number of tubes
Represented as an (x,y) coordinate pair. (2; 20)