Add up the subtended arcs that these chords cut to get
44+86 = 130
Then divide that result by 2
130/2 = 65
Final Answer: choice A) 65 degrees
Answer:
Step-by-step explanation:
The rate of change of temperature of the coffee with respect to time is expressed by the differential equation
dT/dt=k(T−A) when k = -1 and A = 23. The equation will become:
dT/dt = -(T-23)
If the coffee cools at the rate of 1°C per minute, then dT/dt = -1 and T = 70
Substituting into the equation:
-1 = k(70-23)
-1 = 47k
k = -1/47
k = -0.0213
Substituting k = -0.0213 into the original equation, the differential equation will be:
dT/dt=k(T−A)
dT/dt = -0.0213(T-23)
dT/dt = -0.0213T+0.489
To get the value of T, we will use variable separable method
dt = dT/-0.0213T+0.489
Integrate both sides
t = -0.0213ln(-0.0213T+0.489)
At t = 1 minute
1 = -0.0213ln(-0.0213T+0.489)
1/-0.0213 = ln(-0.0213T+0.489)
-46.95 = ln(-0.0213T+0.489)
Apply exp to both sides
e^-46.95 = e^ln(-0.0213T+0.489)
4.073×10^-21= -0.0213T+0.489
-0.0213T = 4.073×10^-21-0.489
-0.0213T = -0.489
T = 0.489/0.0213
T = 22.96°C
Answer:
all the households in given state. part 2 is 1565 households surveyed.
Step-by-step explanation:
<u>Question 8</u>
a^2 + 7a + 12
= (a+3)(a+4)
When factorising a quadratic, the product of the two factors should equal the constant term (12), and the sum of the two factors should equal the linear term (7). To find the two factors, list out the factors of 12 (1x12, 2x6, 3x4) and identify the pair that adds up to 7 (3+4).
An alternative method if you get stuck during your exam would be to solve it algebraically using the quadratic formula and then write it in the factorised form.
a = (-7 +or- sqrt(7^2 - 4(1)(12)) / 2(1)
= (-7 +or- sqrt(1))/2
= -3 or -4
These factors are the negative of the values that would go in the brackets when written in factorised form, as when a = -3 the factor (a+3) would equal 0. (If it were positive 3 instead, then in the factorised form it would be a-3).
<u>Question 10</u>
-3(x - y)/9 + (4x - 7y)/2 - (x + y)/18
Rewrite each fraction with a common denominator so you can combine the fractions into one.
= -6(x - y)/18 + 9(4x - 7y)/18 - (x + y)/18
= (-6(x - y) + 9(4x - 7y) - (x + y)) /18
Expand the brackets and collect like terms.
= (-6x + 6y + 36x - 63y - x - y)/18
= (29x - 58y)/18
= 29/18 x - 29/9 y
Answer:
-4
Step-by-step explanation:
So we are given the expression: | y - x | + y - 1, and we have our values for (x,y): (-3,-6).
So, we can just start plugging things in and simplifying, so:
| -6 + 3 | - 6 - 1 = | -3 | -7
= 3 - 7
= -4