Use the term equal groups to describe the division problem shown below. 123 divided by 5 equals 24r3
1 answer:
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A passenger flies on a heading of N40W with an airspeed of 240 km/h. His actual ground velocity is 250 km/h at a bearing of N60E. the speed and direction of the wind are V=245.15kw/h at N83.46E. This is further explained below.
<h3>What is the speed and direction of the wind.?</h3>Generally, the equation for the cosine rule is mathematically given as
a2 = b2 + c2 – 2bc cos ∠x.
Therefore
V^2 = (240^2 + 250^2) – (2(240*250)* cos 100)
V^2=140937.7813
V=375.42kw/h
In conclusion, the sine rule is mathematically given as
Sin x/240=sin60/375.42kw/h
Therefore
sin x=sin100*250/375.42kw/h
x=40.981
Hence
Direction N83.46E
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<h2>Answer:</h2>
√44
2 Real Roots
<h2>Step-by-step explanation:</h2>Looking at the image attached, the discriminant is the value under the square root.
In the equation given:
a = 1
b = -8
c = 5
The discriminant is therefore:
√(b²- 4ac) = √(-8²- (4*1*5)) = √(64-20) = √44
√44 is a positive number. Because it is positive, there must be 2 real roots.
If it were negative, there would be 2 imaginary roots.
If it were zero, there would be 1 real root.
<h3>Answer: Largest value is a = 9</h3>
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Work Shown:
b = 5
(2b)^2 = (2*5)^2 = 100
So we want the expression a^2+3b to be less than (2b)^2 = 100
We need to solve a^2 + 3b < 100 which turns into
a^2 + 3b < 100
a^2 + 3(5) < 100
a^2 + 15 < 100
after substituting in b = 5.
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Let's isolate 'a'
a^2 + 15 < 100
a^2 < 100-15
a^2 < 85
a < sqrt(85)
a < 9.2195
'a' is an integer, so we round down to the nearest whole number to get
So the greatest integer possible for 'a' is a = 9.
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Check:
plug in a = 9 and b = 5
a^2 + 3b < 100
9^2 + 3(5) < 100
81 + 15 < 100
96 < 100 .... true statement
now try a = 10 and b = 5
a^2 + 3b < 100
10^2 + 3(5) < 100
100 + 15 < 100 ... you can probably already see the issue
115 < 100 ... this is false, so a = 10 doesn't work