Answer:
p-q= -4
p=q-4
x^2 + px + q=0
=> x^2 + (q-4)x + q = 0
d= b^2-4ac
=(q-4)^2 - 4(1)(q)
= q^2 + 16 -8q - 4q
=q^2 -12q+16
given that D=16
q^2 -12q+16 = 16
=> q^2 -12q = 0
=> q^2 = 12q
=> q = 12q/q
=> q= 12
Therefore the value of q is 12 and the value of p is q-4 = 12-4= 8
Hope you understood............
1. You must use the formula for calculate the volume of a rectangular prism, which is:
V=(h)(l)(w)
V: It is the volumen of the rectangular prism (V=1152 inches³).
h: It is the height of the rectangular prism (h=18-w).
l:It is the lenght of the rectangular prism (l=2w+4).
2. When you substitute these calues into the formula, you obtain:
V=(h)(l)(w)
1152=(18-w)(2w+4)(w)
(18-w)(2w+4)(w)-1152=0
3. Then, you should mutiply them:
36w²-2w³+72w-4w²-1152=0
32w²-2w³+72w-1152=0
4. When you factor, you obtain:
2(w-16)(w-6)(w+6)
w1=16
w2=6
w3=-6
5. The problem says that the height is greater than the width, therefore, the widht is:
w=6 inches
6. The length is:
l=2w+4
l=2(6)+4
l=16 inches
7. And the height is:
h=18-w
h=18-6
h=12 inches
What are the dimensions of the bag?
The dimensions of the bag are:
l=16 inches
h=12 inches
w=6 inches
Answer:
x=7
y=9
Step-by-step explanation:
x+7y=70 ...(1)
3x-6y=-33
divide by 3
x-2y=-11 ...(2)
(1)-(2) gives
x+7y-x+2y=70+11
9y=81
y=9
x-2*9=-11
or x=-11+18=7
Answer:
P = 6200 / (1 + 5.2e^(0.0013t))
increases the fastest
Step-by-step explanation:
dP/dt = 0.0013 P (1 − P/6200)
Separate the variables.
dP / [P (1 − P/6200)] = 0.0013 dt
Multiply the left side by 6200 / 6200.
6200 dP / [P (6200 − P)] = 0.0013 dt
Factor P from the denominator.
6200 dP / [P² (6200/P − 1)] = 0.0013 dt
(6200/P²) dP / (6200/P − 1) = 0.0013 dt
Integrate.
ln│6200/P − 1│= 0.0013t + C
Solve for P.
6200/P − 1 = Ce^(0.0013t)
6200/P = 1 + Ce^(0.0013t)
P = 6200 / (1 + Ce^(0.0013t))
At t = 0, P = 1000.
1000 = 6200 / (1 + C)
1 + C = 6.2
C = 5.2
P = 6200 / (1 + 5.2e^(0.0013t))
You need to change the exponent from negative to positive.
The inflection points are where the population increases the fastest.
Answer:
x = 4.7
Step-by-step explanation:
30x - 140 -(x - 4)
Multiply the -1 into (x - 4)
30x - 140 - x + 4
Add/subtract
29x - 136 = 0
+136
