Answer:
value of a.b = -4
Step-by-step explanation:
We need to find a.b
a= 4i-4j
b = 4i+5j
We know that i.i =1, j.j=1, i.j =0 and j.i=0
a.b = (4i-4j).(4i+5j)
a.b = 4i(4i+5j)-4j(4i+5j)
a.b = 16i.i +20i.j-16j.i-20j.j
a.b = 16(1) +20(0)-16(0)-20(1)
a.b = 16 +0-0-20
a.b = 16-20
a.b =-4
So, value of a.b = -4
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Answer:
- Exact distance =
feet - Approximate distance = 127.2792 feet.
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Explanation:
The area of the square is 8100 square feet, abbreviated ft^2.
Apply the square root to find the distance from any base to its adjacent counterpart (eg: from 1st to 2nd base). So we get sqrt(8100) = 90 ft as that side distance. Notice that 90*90 = 8100.
If you were to draw a line from 1st base to 3rd base, then you would split the square into two congruent right triangles. Each right triangle is isosceles (the two legs being 90 ft each).
Use the pythagorean theorem to find the hypotenuse.
![a^2 + b^2 = c^2\\\\c = \sqrt{a^2+b^2}\\\\c = \sqrt{90^2+90^2}\\\\c = \sqrt{2*90^2}\\\\c = \sqrt{2}*\sqrt{90^2}\\\\c = \sqrt{2}*90\\\\c = 90\sqrt{2} \ \text{ ... exact distance}\\\\c \approx 127.2792 \ \text{ ... approximate distance}\\\\](https://tex.z-dn.net/?f=a%5E2%20%2B%20b%5E2%20%3D%20c%5E2%5C%5C%5C%5Cc%20%3D%20%5Csqrt%7Ba%5E2%2Bb%5E2%7D%5C%5C%5C%5Cc%20%3D%20%5Csqrt%7B90%5E2%2B90%5E2%7D%5C%5C%5C%5Cc%20%3D%20%5Csqrt%7B2%2A90%5E2%7D%5C%5C%5C%5Cc%20%3D%20%5Csqrt%7B2%7D%2A%5Csqrt%7B90%5E2%7D%5C%5C%5C%5Cc%20%3D%20%5Csqrt%7B2%7D%2A90%5C%5C%5C%5Cc%20%3D%2090%5Csqrt%7B2%7D%20%5C%20%5Ctext%7B%20...%20exact%20distance%7D%5C%5C%5C%5Cc%20%5Capprox%20127.2792%20%5C%20%5Ctext%7B%20...%20approximate%20distance%7D%5C%5C%5C%5C)
The distance from 1st to 3rd base is roughly 127.2792 feet.
Answer:
The probability the student studies Art and
Biology is 0.2143.
Step-by-step explanation:
Denote the events as follows:
A = a students studies Art
B= a students studies Biology
The information provided is:
N = 42
n (An B) = 9
n (A' n B) = 10
n (A' n B') =7
Then the number of students who study Art
but not Biology is:
n(An B') = N -n (An B) -n (A' nB) - n (A'n B')
= 42 - 10 - 7 - 9
= 16
The number of students who study Art but
not Biology is 16.
Compute the probability the student studies
Art and Biology as follows:
P(ANB)
n(ANB)
= 0.2143
Thus, the probability the student studies Art
and Biology is 0.2143.
Answer:
69
Step-by-step explanation: