Answer:
66.42°
Step-by-step explanation:
<u>Given:</u>
A(5, 3t+2, 2)
B(1, 3t, 2)
C(1, 4t, 3)
BA • BC = 4
Step 1: Find t.
First we have to find vectors BA and BC. We do that by subtracting the coordinates of the initial point from the coordinates of the terminal point.
In vector BA B is the initial point and A is the terminal point.
BA = OA - OB = (5-1, 3t+2-3t, 2-2) = (4, 2, 0)
BC = OC - OB = (1-1, 4t-3t, 3-2) = (0, t, 1)
Now we can find t because we know that BA • BC = 4
BA • BC = 4
To find dot product we calculate the sum of the produts of the corresponding components.
BA • BC = (4)(0) + (2)(t) + (0)(1)
4 = (4)(0) + (2)(t) + (0)(1)
4 = 0 + 2t + 0
4 = 2t
2 = t
t = 2
Now we know that:
BA = (4, 2, 0)
BC = (0, 2, 1)
Step 2: Find the angle ∠ABC.
Dot product: a • b = |a| |b| cos(angle)
BA • BC = 4
|BA| |BC| cos(angle) = 4
To get magnitudes we square each compoment of the vector and sum them together. Then square root.
Rounded to two decimal places:
Answer:
x = 2
Step-by-step explanation:
Answer:
5 years.
Step-by-step explanation:
Every year the population increases by a factor 103.5% or 1.035.
The equation relating population and time in years is:
P = 6000(1.035)^t (This is an example of exponential growth)
So we have:
7100 = 6000(1.035)^t
(1.035)^t = 7100/6000
(1.035)^t = 1.1833
t ln 1.035 = ln 1.1833
t = ln 1.1833/ln 1.035
= 4.89.
Median: 29
Range: 25
IQR: 14.5
Explanations:
**Median:**
(To find the median, we need to first order all the elements)
Ordered —> 15, 18, 18, 20, 23, 28, 30, 33, 33, 34, 38, 40
(Since there are an even number of elements, we need to add the two elements in the middle and divide by 2)
Median = (28 + 30)/2 = 58/2 = 29
**Range:**
(To find the range, you just have the subtract the smallest one from the largest)
Range = 40 - 15 = 25
**IQR:**
First half of elements —> 15, 18, 18, 20, 23, 28
Second half of elements —> 30, 33, 33, 34, 38, 40
Q1 (Quartile 1) = Median of first half = (18 + 20)/2 = 38/2 = 19
Q3 (Quartile 3) = Median of second half = (33 + 34)/2 = 67/2 = 33.5
IQR = Q3 - Q1 = 33.5 - 19 = 14.5
It would take (100 km/hr)= 0.01 hr or 36 seconds.
