9514 1404 393
Answer:
- (c1, c2, c3) = (-2t, 4t, t) . . . . for any value of t
- NOT linearly independent
Step-by-step explanation:
We want ...
c1·f1(x) +c2·f2(x) +c3·f3(x) = g(x) ≡ 0
Substituting for the fn function values, we have ...
c1·x +c2·x² +c3·(2x -4x²) ≡ 0
This resolves to two equations:
x(c1 +2c3) = 0
x²(c2 -4c3) = 0
These have an infinite set of solutions:
c1 = -2c3
c2 = 4c3
Then for any parameter t, including the "trivial" t=0, ...
(c1, c2, c3) = (-2t, 4t, t)
__
f1, f2, f3 are NOT linearly independent. (If they were, there would be only one solution making g(x) ≡ 0.)
The surface area of the prism is equal to the summed up area of the faces of the triangular prism.
The bases of the prism would be triangles with an unknown base, b, and height of 3. The area of the base is calculated through the equation,
A = bh/2
where b is base and h is height. Substituting the values,
A = b(3)/2
Since there are two bases, the contribution of the triangles for the surface area is,
2A = 3b
Next we calculate for the area of the triangle sides with length equal to b (same as the base of the triangle).
Area = b(12 km)
There are 3 sides such that the total area becomes,
Area = 36b
Hence, the surface area is,
48.735 km² = 3b + (36b)
The value of b from the equation is 1.25 km
<em>ANSWER: 1.25 km</em>
Answer:
As shown in picture,
volume of cone V = base area x height x (1/3) = pi x (4/2)^2 x 6 x (1/3) = 8 x pi
volume of cup V = base area x height = pi x (3/2)^2 x 3 = 6.75 x pi
(all the volumes are in cubic inches)
A - Incorrect
24 pack of cups: V = 24 x 6.75 x pi = 162 x pi
21 pack of cones: V = 21 x 8 x pi = 168 x pi
162 x pi < 168 x pi
B - Correct
12 pack of cups: V = 12 x 6.75 x pi = 254.5 > 250
C - Correct
14 pack of cones: V = 14 x 8 x pi =351.9 > 350
D - Correct
Volume of cylinder 8 tall, 6 wide: V = pi x (6/2)^2 x 8 = 72 x pi
12 pack of cups: V = 12 x 6.75 x pi = 80.4 x pi > 72 x pi
Hope this helps!
:)
Answer:
The total salary of her is $1066666.66.
Step-by-step explanation:
Given : Allison earns a $40,000 base salary plus a commission equal to 15% of her total sales. If she sold $200,000 worth of goods.
To find : What was her total salary?
Solution :
Let x be the total salary.
Allison earns a $40,000 base salary.
If she sold $200,000 worth of goods.
i.e. the amount is $200,000-$40,000=$160,000
The total salary is given by,
$160,000=15% of x
The total salary of her is $1066666.66.
Answer:
3.25 blocks
Step-by-step explanation:
6.5 * 1.5 = 9.75 blocks
9.75 - 6.5 = 3.25blocks
Farther 3.25 blocks sue ellan need to ride than Bobby ride
