The height of the kite above the ground is 58.68 ft
Let x be the height of the kite above Chee's hand.
The height of the kite above Chee's hand, the string and the horizontal distance between Chee and the kite form a right angled triangle with hypotenuse side, the length of the string and opposite side the height of the kite above Chee's hand.
Since we have the angle of elevation from her hand to the kite is 29°, and the length of the string is 100 ft.
From trigonometric ratios, we have
tan29° = x/100
So, x = 100tan29°
x = 100 × 0.5543
x = 55.43 ft.
Since Chee's hand is y = 3.25 ft above the ground, the height of the kite above the ground, L = x + y
= 55.43 ft + 3.25 ft
= 58.68 ft to the nearest hundredth of a foot
So, the height of the kite above the ground is 58.68 ft
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Answer: the first term of the series is 128
Step-by-step explanation:
In a geometric sequence, the consecutive terms differ by a common ratio. The formula for determining the sum of n terms, Sn of a geometric sequence is expressed as
Sn = a(1 - r^n)/(1 - r)
Where
n represents the number of term in the sequence.
a represents the first term in the sequence.
r represents the common ratio.
From the information given,
r = 1/4 = 0.25
n = 4
S4 = 170
Therefore, the expression for the sum of the 4 terms, S4 is
170 = a(1 - 0.25^4)/(1 - 0.25)
170 = a(1 - 0.00390625)/(1 - 0.25)
170 = a(0.99609375)/(0.75)
170 = 1.328125a
a = 170/1.328125
a = 128
Answer:
6. E
7. D
8. 5,-8,34
Step-by-step explanation:
A. Parallel to the y-axis and passes through the point (3,5)
For it to be parallel to the y-axis, what this means is that it has an x-intercept and no y intercept.
So what this means is that x = 3 is our line so E is correct
B. Perpendicular to the y-axis means it is parallel to the x-axis
It means is has no x intercept and thus its x value at any point in time is zero
So the equation is y = -5
or simply y + 5 = 0 which means D is correct
C. It is parallel to the line 5x -8y + 12 = 0
Thus: 8y = 5x + 12
dividing both sides by 8
y = 5x/8 + 12/8
y = 5x/8 + 3/2
y = 5x/8 + 1.5
Comparing this with the general equation of a straight line ;
y = mx + c
where m is that slope, this means that 5/8 is the slope of the line
Mathematically if two lines are parallel, they have equal slopes.
So we can say the slope of the other line too is 5/8
Now to find the equation of the other line, we can use the point-slope method
y-y1 = m(x-x1)
where (x1,y1) in this case is (-2,3)
So we have;
y-3 = m(x-(-2))
y-3 = 5/8 (x + 2)
8(y-3) = 5(x + 2)
8y -24 = 5x + 10
5x + 10 + 24 -8y = 0
5x -8y + 34 = 0
So A, B, C = 5, -8, 34
Answer: A. 1.2
Step-by-step explanation:
Given : Sample size : n= 64
Standard deviation: 
The formula to find the standard error of mean is given by :-
Therefore, the standard error of the mean= 1.2
Hence, A is the right option.
Step-by-step explanation:
Equation for circle centered at origin:
x² + y² = r².
Therefore r² = (-4)² + (-2)² = 20, r = √20.
Hence d = 2r = 2√20 = 8.94 (2d.p.)
