You only have to apply the theorem of Pythagoras here. Remember the square on the hypotenuse (the longest side) is equal to the sum of the squares on the other two sides :
1. AB is the hypotenuse, so, according to the theorem we can write :
AB² = AC² + CB²
c² = 5² + 4²
c²= 25 + 16
c² = 41
applying the square root of 41 we get :
c ≈ 6.40 rounded to the hundred
The next cases are exactly the same thing so there is no need for explanation :
2.
AB is the hypotenuse here because it is the biggest side clearl :
AB² = AC² + CB²
25² = 15² + b²
Thus
b² = 25² - 15²
we just subtracted 15² on each side of the equation
b² = 625 - 225
b² = 400
applying the square root of 400 we get
b = √400 = 20
So AC = 20
3. The longest side is clearly AB = 60
So
AB² = AC² + CB²
60² = 40² + a²
subtracting 40² on each side of the equation we get :
a² = 60² - 40²
I let you finish this using your calculator and doing exactly like the previous cases
4.
AB is the hypotenuse,
AB² = AC² + CB²
23² = b² + 14²
Subtracting 14² from each side of the equation we get
b² = 23² - 14²
5.
AB is the biggest side :
AB² = AC² + CB²
29² = 23² + a²
We subtract 23² on each sides of the equation :
a² = 29² - 23²
You can finish with your calculator
6.
AB² = AC² + BC²
78² = b² + 30²
subtraction...
b² = 78² - 30²
Good luck :)
The bill after applying the coupon = 31.84*(85%) = 27.064
so each of them will pay : 27.064/3 = $9.021
Answer: Present value = $7200
Step-by-step explanation: Given Principal that is the original amount is $6000
Rate is 10% every fourth year
But the total period is eight.
So the interest would be paid 8/4 = 2 times.
Therefore,
Simple interest
= {principal * rate * no of times}/100
= {$6000*10*2}/100
Simple interest = $1200
Present value
= principal + Simple interest
= $6000 + $1200
= $7200.
Answer:
The discriminant b2−4ac < 0, the equation has no real number solutions, it has complex solutions
Step-by-step explanation:
9x² - 4x + 1 = 0 ax² + bx + c = 0
The discriminant: b² - 4ac = (-4)² - 4*9*1 = 16 - 36 = -20
b2−4ac < 0, the equation has no real number solutions, it has complex solutions
Answer:
∅ ≈ 56.31°
Step-by-step explanation:
The bird is spotted flying 6000 ft from a tower . The distance of the tower from the bird is 6000 ft. The height of the tower is 9000 ft because the observer spot the distance from the top of the tower at a distance of 9000 ft.
The illustration forms a right angle triangle. The adjacent side of the triangle is 6000 ft and the height or opposite side of the triangle is 9000 ft. Using tangential ratio the angle of depression from the bird to the observer can be found as follows.
Let
∅ = angle of depression
tan ∅ = opposite/adjacent
tan ∅ = 9000/6000
tan ∅ = 1.5
∅ = tan⁻¹ 1.5
∅ = 56.309932474
∅ ≈ 56.31°
