Answer:
The value of cos Ф is ± 
Step-by-step explanation:
There are important rules for sin Ф and cos Ф
∵ sin Ф = 
∴ sin²Ф = 
∴ sin²Ф = 
→ By using the third rule above
∵ cos²Ф = 1 - sin²Ф
∴ cos²Ф = 1 -
∴ cos²Ф = 
→ Take square root for both sides
∴ cos Ф = ±
∴ The value of cos Ф is ±
For this case we have the following table:
x f(x)
<span><span><span>0 2
</span><span>1 5
</span><span>2 10
</span><span>3 17
</span></span></span> The equation that best fits the data in the table, for this case, is given by a quadratic function.
<span><span><span> </span></span></span>The quadratic function in its standard form is:
f (x) = x2 + 2x + 2
Answer:
f (x) = x2 + 2x + 2
Q-2r=4, therefore: q=4+2r.
Plug the value of q into q+r=37, so you get:
4+2r+r=37
3r=37-4=33
3r=33
Therefore: r=11.
q-2r=4, but r=11, so:
q-2(11)=4
q-22=4
Therefore q=26.
Check if the answer is correct using second equation:
q=4+2r=4+2(11)=4+22=26.
So: q=26 and r=11.
see the attached figure with the letters
1) find m(x) in the interval A,BA (0,100) B(50,40) -------------- > p=(y2-y1(/(x2-x1)=(40-100)/(50-0)=-6/5
m=px+b---------- > 100=(-6/5)*0 +b------------- > b=100
mAB=(-6/5)x+100
2) find m(x) in the interval B,CB(50,40) C(100,100) -------------- > p=(y2-y1(/(x2-x1)=(100-40)/(100-50)=6/5
m=px+b---------- > 40=(6/5)*50 +b------------- > b=-20
mBC=(6/5)x-20
3)
find n(x) in the interval A,BA (0,0) B(50,60) -------------- > p=(y2-y1(/(x2-x1)=(60)/(50)=6/5
n=px+b---------- > 0=(6/5)*0 +b------------- > b=0
nAB=(6/5)x
4) find n(x) in the interval B,CB(50,60) C(100,90) -------------- > p=(y2-y1(/(x2-x1)=(90-60)/(100-50)=3/5
n=px+b---------- > 60=(3/5)*50 +b------------- > b=30
nBC=(3/5)x+30
5) find h(x) = n(m(x)) in the interval A,B
mAB=(-6/5)x+100
nAB=(6/5)x
then
n(m(x))=(6/5)*[(-6/5)x+100]=(-36/25)x+120
h(x)=(-36/25)x+120
find <span>h'(x)
</span>h'(x)=-36/25=-1.44
6) find h(x) = n(m(x)) in the interval B,C
mBC=(6/5)x-20
nBC=(3/5)x+30
then
n(m(x))=(3/5)*[(6/5)x-20]+30 =(18/25)x-12+30=(18/25)x+18
h(x)=(18/25)x+18
find h'(x)
h'(x)=18/25=0.72
for the interval (A,B) h'(x)=-1.44
for the interval (B,C) h'(x)= 0.72
<span> h'(x) = 1.44 ------------ > not exist</span>
Answer: 60 decrease or 150 decrease
Step-by-step explanation:
