Answer:
Observe that if the vector is in W then it satisfies:
This means that each vector in W can be expressed as a linear combination of the vectors
Also we can see that those vectors are linear independent. Then the set
is a basis for W and the dimension of W is 2.
Answer:
Jordan got 222 calories from pizza
Step-by-step explanation:
Given:
slices of pizza ate by Kasey =10
cups of fruit salad by Kasey= 5
slices of pizza ate by Jordan = 6
cups of fruit salad by Jordan= 7
Kasey's calorie count = 3070
Jordan calorie count = 2522
To Find:
calories Jordan got from pizza =?
Solution:
Let the calorie of one slice of pizza be x
and the calorie of one cup of fruit salad be y
According to the question, the equation that represents the Kasey's Scenario is
10x + 5y = 3070-------------------------------------(1)
Similarly the equation that represents the Jordan Scenario is
6x + 7y = 2522--------------------------------------(2)
multiply eq(1) by 6 we get
60x + 30y = 18420---------------------------------(3)
multiply eq(2) by 10 we get,
60x + 70y = 25220----------------------------------(4)
Subtracting eq (3) from (4) we get
60x + 70y = 25220
60x + 30y = 18420
(-) (-) (-)
-----------------------------------
0x + 40y = 6800
---------------------------------
=>40 y = 6800
=>y =
=> y = 170
So calorie of one cup fruit salad is = 170 calories
substituting the y values in eq 1 we get
10x + 5(170) = 3070
10x + 850 = 3070
10x = 3070 - 850
10x = 2220
x =
x= 222
So calorie of one pizza slice = 222 calories
Now we know that Jordan ate 6 slices of pizza
calories Jordan get from pizza = number of pizza he ate X calore per pizza slice
=> 6 x 222
=>1332 calories
The function
... y = 1/x
has derivative
... y' = -1/x²
which has no zeros. It is undefined at x=0, the only critical point. The derivative is negative for all values of x, so the function is decreasing everywhere in its domain.
Your function
... y = (x+1)/(x-3)
can be written as
... y = 1 +4/(x-3)
which is a version of y = 1/x that has been vertically scaled by a factor of 4, then shifted 1 unit up and 3 units to the right. Shifting the function to the right means x=3 is excluded from the domain (and the interval on which the function is decreasing).
The critical point is x=3.
The function is decreasing on (-∞, 3) ∪ (3, ∞), increasing nowhere.
