Answer:
$3.60 per gallon.
Step-by-step explanation:
First, we look for the gallon of gas that will be used for a 172.5 mile trip:
30 miles = 1 gallon of gas
172.5 miles = ?
172.5 ÷ 30 = 5.75 gallons of gas
Let's find the approximate cost of gas in dollars per gallon:
5.75 gallons of gas = $20.70
1 gallon of gas = $?
20.70 ÷ 5.75 = $3.60
The answer is $3.60 per gallon.
sin theta = x , sec theta =y . find cot theta pls answer fast i need to verify my answer . you can directly write the answer no issues
Answer:
[tex]\huge\boxed{\cot\theta=\dfrac{1}{xy}}[/tex]
Step-by-step explanation:
[tex]\bold{METHOD\ 1}[/tex]
[tex]\sin\theta=x\\\\\sec\theta=y\\\\\cot\theta=?\\\\\text{We know:}\\\\\sec x=\dfrac{1}{\cos x};\ \cot x=\dfrac{\cos x}{\sin x}\\\\\sec\theta=y\to\dfrac{1}{\cos \theta}=y\to\dfrac{\cos\theta}{1}=\dfrac{1}{y}\to\cos\theta=\dfrac{1}{y}\\\\\cot \theta=\dfrac{\frac{1}{y}}{x}=\dfrac{1}{xy}[/tex]
[tex]\bold{METHOD\ 2}[/tex]
[tex]\text{We know}\\\\\tan x=\dfrac{\sin x}{\cos x}\\\\\cot x=\dfrac{\cos x}{\sin x}=\dfrac{1}{\tan x}\\\\\sec x=\dfrac{1}{\cos x}\\\\\text{therefore}\\\\(sin x)(\sec x)=(\sin x)\left(\dfrac{1}{\cos x}\right)=\dfrac{\sin x}{\cos x}=\tan x\\\\\dfrac{1}{(\sin x)(\sec x)}=\dfrac{1}{\tan x}=\cot x[/tex]
[tex]\\\sin \theta=x;\ \sec\theta=y\\\\\text{substitute}\\\\\cot\theta=\dfrac{1}{xy}[/tex]
You have already run 4 miles. If you run at a speed of 8 miles per hour, how many total miles will you run in 2 more hours? Choose the correct equation and solution to this problem.
Answer:
20 miles
Step-by-step explanation:
I'm not sure if that is exactly how you solve it but
If its
8x+4 as the equation and x is the number of hours run
the total number of miles run should be 20 miles
8(2)+4=20
Answer:
20 miles
Step-by-step explanation:
miles already covered = 4
rate of speed = 8miles / hour
miles to be covered = 8 miles/hr× 2 hr= 16 miles ( because distance is velocity × time)
total miles covered = 16 + 4 = 20 miles.
8 7 12 7 11
10 7 12
Find:
a)the median
b) the range
c)the mode
Answer:
a) Median: 9
b) Range: 5
c) Mode: 7
Step-by-step explanation:
The median is the number in the middle.
First, you put the numbers in order: 7, 7, 7, 8, 10, 11, 12, 12
The middle of this is 8 and 10, so you plus them and divide by to 2, then it gives 9, so the median is 9.
To find the range, you minus the highest number and the lowest number, 12-7=5.
Mode is the most occurring and repetitive number, in this case, 7, because it is written 3 times.
Hope this helps!!!
Answer:
[tex]\boxed{\mathrm {Median = 9}}[/tex]
[tex]\boxed{\mathrm{Range = 5}}[/tex]
[tex]\boxed{\mathrm{Mode = 7}}[/tex]
Step-by-step explanation:
The observations are:
8,7,12,7,11,10,7,12
In ascending order:
=> 7,7,7,8,10,11,12,12
A) Median => Middlemost no.
Median = 8,10
=> [tex]\frac{8+10}{2}[/tex]
=> [tex]\frac{18}{2}[/tex]
Median = 9
B) Range = Highest No. = Lowest No.
RANGE = 12-7
Range = 5
C) Mode => frequently occurring number
Mode = 7
help with pre algebra
Answer:
The y-axis.
Step-by-step explanation:
This is because it is mirroring across the y-axis, and the x-coordinate's sign is getting changed from positive to negative.
Answer:
Y-axis
Step-by-step explanation:
B is a reflection of point A across theY-axis. The vertical line is Y and the horizontal line is X.
A dilation has center (0, 0). Find the image of each point for the given scale factor. C(3, -6); D(5/3) (C)
A. (-10, 5)
B. (18/5, 9/5)
C. (5, -10)
D. (9/5, 18/5)
Answer: C. (5, -10)
Step-by-step explanation:
When we have a point (x, y) and we do a dilation around (0,0) with a scale factor of A.
The new point will be:
(A*x, A*y)
in this case, the point is (3, -6) and the scale factor is (5/3)
Then the new point will be:
(3*(5/3), -6*(5/3)) = (5, -10)
Please answer this question now
Answer: S = 8.9 or just 9
Step-by-step explanation:
Which of the following is a polynomial with roots - square root of 5, - square root of five and 3
A. X^3 - 3x^2 - 5x +15
B. X^3 + 2x^2 -3x - 6
C. X^3 - 2x^2 - 3x +6
D. X^3 + 3x^2 - 5x - 15
Answer:
A is correct
Step-by-step explanation:
What we need to do here is to multiply all the roots together
The roots are;
3, √5 and -√5
Let’s have them in form of a sum
if x = 3, then the root is x-3
If x = √5, then the root is x-√5
If x = -√5, then the root is x+ √5
Now we need to multiply all these together to arrive at the original polynomial
Let’s start by using the roots
(x-√5)(x+ √5)
we can use the difference of 2 squares here and we arrive at (x^2 -5)
So finally, the polynomial would be;
(x^2-5)(x-3)
= x(x^2-5) -3(x^2-5)
= x^3-5x-3x^2+15
By rearranging, we have;
x^3-3x^2-5x+15
Given the coordinates for the function below, which of the following are
coordinates for its inverse?
Gallons Cost, in
of Gas Dollars
1
2
5
15
20
1.25
2.50
6.25
18.75
25.00
The coordinates of the inverse are (1.25, 1) (2.50, 2), (6.25, 5), (18,75, 15) and (25.00, 20)
How to determine the inverse coordinates?The table of values is given as:
Gallons Cost
1 1.25
2 2.50
5 6.25
15 18.75
20 25.00
The inverse of the above table would have the following header
Cost Gallons
When the inverse table is populated, we have:
Cost Gallons
1.25 1
2.50 2
6.25 5
18.75 15
25.00 20
The coordinates are: (1.25, 1) (2.50, 2), (6.25, 5), (18,75, 15) and (25.00, 20)
Hence, the coordinates of the inverse are (1.25, 1) (2.50, 2), (6.25, 5), (18,75, 15) and (25.00, 20)
Read more about coordinates at:
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If an object is propelled upward from a height of 72 feet at an initial velocity of 90 feet per second, then its height h after t seconds is given by the equation h = − 16 t 2 + 90 t + 72 . After how many seconds does the object hit the ground?
Answer:
6.34 seconds.
Step-by-step explanation:
The object will hit the ground when h = 0.
-16t^2 + 90t + 72 = 0
8t^2 - 45t - 36 = 0
We can then use the quadratic formula to solve.
[please ignore the A-hat; that is a bug]
[tex]\frac{45±\sqrt{45^2 - 4 * 8 * -36} }{2 * 8}[/tex]
= [tex]\frac{45±\sqrt{2025 + 1152} }{16}[/tex]
= [tex]\frac{45±\sqrt{3177} }{16}[/tex]
= [tex]\frac{45±56.36488268}{16}[/tex]
(45 - 56.36488268) / 16 = -0.7103051678
(45 + 56.36488268) / 16 = 6.335305168
Since the time cannot be negative, the object will hit the ground after about 6.34 seconds.
Hope this helps!
Please help don't understand at all
(i) Note that it is given to you that 3a + 2b = 9
You are trying to find the value of 9a + 6b. Find what is multiplied to both the variable a & b. Divide:
(9a + 6b)/(3a + 2b) = 3
Next, multiply 3 to the 9 on the other side of the equation:
3 x 9 = 27
27 is the value of 9a + 6b.
(ii) Note that it is given to you that 8x + 6y = 60
You are trying to find the value of 4x + 3y. Find what is multiplied to both the variable x & y. Divide:
(8x + 6y)/(4x + 3y) = 2
Next, divide 2 from the 60 on the other side of the equation:
60/2 = 30
30 is the value of 4x + 3y.
~
Answer:
(i) 27, (ii) 30
Step-by-step explanation:
i. since 9a + 6b is 3 times 3a + 2b then the and is 3 times 9 = 27
ii. since 4x + 3y is half of 8x + 6y then 60 /2 = 30
Jennifer invested $302 in a simple interest account. The account earns 3.3%/year how much will Jennifer have in her account in 10 months??
Answer: $310.31
Step-by-step explanation:
Invested amount (P) = $302
Interest rate (r) = 3.3% per year
Period = 10 months
Recall, simple interest formula :
A = P(1 + rt) where ; A = final amount
Interest = 3.3% = 3.3/ 100 = 0.033
A = $302 ( 1 + 0.033(10/12))
A = $302 (1 + 0.033(0.8333333))
A = $302 ( 1 + 0.0275)
A = $302 ( 1. 0275)
A = $310.305
A = $310.31
Which statements about the hyperbola are true? Check
all that apply.
There is a vertex at (-3, 6).
The center of the hyperbola is at (-3,5).
There is a vertex at (-5,5).
The transverse axis is vertical.
The directrices are horizontal lines
Answer:
Options (1), (2), (4) and (5) are correct.
Step-by-step explanation:
Characteristics of the given hyperbola,
1). Vertex of the given hyperbola are at (-3, 6) and (-3, 4).
2). Since center of a hyperbola is the center of a line joining vertices of the hyperbola,
Center of the given parabola will be,
[tex](\frac{-3-3}{2},\frac{6+4}{2})[/tex] ⇒ (-3, 5)
3). Vertical line joining the foci of the hyperbola is the transverse axis.
4). A line perpendicular to the transverse axis and passing through the center will be the conjugate axis.
5). Directrices of a horizontal hyperbola are the horizontal lines.
Therefore, Options (1), (2), (4) and (5) are correct.
Answer:
check photo. <3
Step-by-step explanation:
I NEED HELP FAST OR I WILL FAIL!!! What is the approximate solution to the system of equations? Y=x+1, y=3x-2 (-.33, -1.33) (1.4, 2.5) (-.67, .25) (0, 1.5)
Answer:
(1.4, 2.5)
Step-by-step explanation:
[tex]y = x + 1[/tex] ... equ 1
[tex]y =3x - 2[/tex] ... equ 2
subtract equ 1 from 2, we'll have
[tex]0 = 2x - 3[/tex]
[tex]2x = 3[/tex]
[tex]x= 3/2 = 1.5[/tex]
substitute the value of [tex]x[/tex] in equ 1, we'll have
[tex]y = 1.5 +1[/tex]
[tex]y = 2.5[/tex]
therefore, solution to the system of the equation is (1.5, 2.5)
the closest in your option is (1.4, 2.5)
1. Which financial statement reports the amount of cash paid for acquisitions of property, plant, and equipment? In which section (operating, investing, or financing) of this statement is the information reported? 2. Indicate the amount of cash paid for acquisitions of property and equipment in the year ended September 30, 2017.
Answer:
1. Cash flow statements; the investing section
Step-by-step explanation:
The cash flow statements is a useful document that shows where the company receives funds and uses it. Thus, it shows both incoming and outgoing cash flow.
The investment section of the cash flow statement is where all the amount of cash paid for acquisitions of property and equipment is imputed. Usually the transactions are written as capital expenditure.
Can an absolute value function also be a polynomial function? Why or why not?
Answer:
For this case a polynomial is defined with the following expression:
[tex] p(x) =\sum_{i=1}^n a_i x^i[/tex]For all x on the domain considered and n is finite
And by definition the absolute value function is defined as:
[tex] |x|= x, x \geq 0[/tex]
[tex] |x| =-x , x<0[/tex]
If we use the function [tex] f(x) =|x|[/tex] we see that is impossible to obtain the general expression of a polynomial since we can't obtain the form |x| and since we don't satisfy the definition the answer would be:
An absolute value function CANNOT be considered as a polynomial function
Step-by-step explanation:
For this case a polynomial is defined with the following expression:
[tex] p(x) =\sum_{i=1}^n a_i x^i[/tex]For all x on the domain considered and n is finite
And by definition the absolute value function is defined as:
[tex] |x|= x, x \geq 0[/tex]
[tex] |x| =-x , x<0[/tex]
If we use the function [tex] f(x) =|x|[/tex] we see that is impossible to obtain the general expression of a polynomial since we can't obtain the form |x| and since we don't satisfy the definition the answer would be:
An absolute value function CANNOT be considered as a polynomial function
3) The owner of the KiKi Fill Gas Station wishes to determine the proportion of customers who use a credit card or debit card to pay at the pump. He surveys 100 customers and finds that 80 paid at the pump. 1. Estimate the value of the population proportion. 2. Develop a 95% confidence interval for the population proportion. 3. Interpret your findings
Answer:
i) Estimate the value of the population proportion = 0.8
ii) 95% confidence interval for the population proportion
(0.7214 , 0.8784)
iii) Lower bound = 0.7214
upper bound = 0.8784
Step-by-step explanation:
Step(i):-
Given sample size 'n' = 100
Given data he surveys 100 customers and finds that 80 paid at the pump
sample proportion
[tex]p = \frac{x}{n} = \frac{80}{100} = 0.8[/tex]
Step(ii):-
95% confidence interval for the population proportion is determined by
[tex](p^{-} - Z_{\alpha } \sqrt{\frac{p(1-p)}{n} } , p^{-} + Z_{\alpha } \sqrt{\frac{p(1-p)}{n} })[/tex]
Level of significance
∝ =0.05
Z₀.₀₅ = 1.96
[tex](0.8 - 1.96 \sqrt{\frac{0.8 X 0.2)}{100} } , 0.8 + 1.96 \sqrt{\frac{0.8 X 0.2}{100} })[/tex]
On calculation , we get
(0.8 - 0.0784 , 0.8 + 0.0784)
(0.7214 , 0.8784)
Conclusion:-
95% confidence interval for the population proportion
(0.7214 , 0.8784)
The formula for working out the cost of hiring a canoe is : cost=£15+6* number of hours. Megan paid £27 to hire a canoe. How long did she hire the canoe for
Answer:
Megan hired the canoe for 2 hours
Step-by-step explanation:
Given:
Cost(h) = 6h+15 = 27
Solution
6h+15 = 27
6h = 27-15 = 12
h = 2
ese
i). nx n2 =343 (2mks)
I
Answer:
Are you asking what the value of x is if [tex]n^{x} * n^2 = 343[/tex] ?
Step-by-step explanation:
what describes the transformation of g(x)=3(2)-x from the parent function f(x)=2x
Answer:
Reflect across the y-axis, stretch the graph vertically by a factor of 3
Step-by-step explanation:
The question has certain errors, in fact the functions are the following:
g (x) = 3 * (2) ^ - x
f (x) = 2 ^ x
The transformation that we can do to obtain the translated graph, Are given in 2 steps, which are the following:
1. When x is replaced by -x, then it reflects the graph on the y axis.
2. 3 multiplies with the function, it means that it stretches the main function vertically in 3 units.
So to summarize it would be: Reflect across the y-axis, stretch the graph vertically by a factor of 3
A science club is raising money by selling t-shirts. The cost of producing the t-shirts is a one time 550 dollar design and set up fee plus 12
dollars per shirt. If they sell the t-shirts for $17.50 each, what is the minimum number of t-shirts the club can order and still make a profit?
Answer: not sure
Step-by-step explanation:
the scale on the map is 1 cm represents 40 km . the actual straight line distance between 2 cities is about 320 km what is the map distance between these 2 cities
Answer:
8cm
Step-by-step explanation:
the ratio of cm to km is 1 cm on the map equals 40 km. or 1/40 so you have to find what is x/320 using the ratio of 1/40 you gt that x equals 8
Which equation can be used to solve for m, the greater integer? m(m – 3) = 108 m(m + 3) = 108 (m + 3)(m – 3) = 108 (m – 12)(m – 9) = 108
Answer:
m(m-3)=108
Step-by-step explanation:
Complete question below:
Two positive integers are 3 units apart on a number line. Their product is 108.
Which equation can be used to solve for m, the greater integer?
m(m – 3) = 108
m(m + 3) = 108
(m + 3)(m – 3) = 108
(m – 12)(m – 9) = 108
Solution
On the number line,
Let
m= larger integer
The integers are 3 numbers apart on the number line, so
m-3=smaller integer
The product (×) of the larger and smaller integers=108
(m)*(m-3)=108
m(m-3)=108
Therefore, the equation that can be used to solve for m, the larger integer is:
m(m – 3) = 108
Answer:
its a
Step-by-step explanation:
XD
The third, fifth and eighth terms of an AP are the first 3 consecutive terms of a GP. Given that the first term of the AP is 8, calculate the common difference
Answer:
The common difference = 2.
Step-by-step explanation:
An AP can be written as a1, a1 + d, a1 + 2d, a1 + 3d, a1 + 4d, a1 + 5d, a1 + 6d , a1 + 7d.
where a1 = first term and d is the common difference.
Here first term = a1 = 8
3rd term = a1 + 2d = 8 + 2d
5th term = a1 + 4d = 8 + 4d
8th term = 8 + 7d
First 3 terms of a GP are a , ar and ar^2
So from the given information:
a = 8 + 2d
ar = 8 + 4d
ar^2= 8 + 7d
Dividing the second equation by the first we have
r = (8 + 4d)/(8 + 2d)
Dividing the third by the second:
r = (8 + 7d) / (8 + 4d)
Therefore, eliminating r we have:
(8 + 4d)/(8 + 2d) = (8 + 7d)/(8 + 4d)
(8 + 4d)^2 = (8 + 2d)(8 + 7d)
64 + 64d + 16d^2 = 64 + 72d^ + 14d^2
2d^2 - 8d = 0
2d(d^2 - 4) = 0
2d = 0 or d^2 = 4, so
d = 0, 2.
The common difference can't be zero so it must be 2.
x: 13, 17, 21, 25 y: 0, 6, 12, 18 is the relationship linear, exponential or neither
━━━━━━━☆☆━━━━━━━
▹ Answer
Linear
▹ Step-by-Step Explanation
As x increases by 4, y increases by 6.
13 + 4 = 17
17 + 4 = 21
21 + 4 = 25
0 + 6 = 6
6 + 6 = 12
12 + 6 = 18
Hope this helps!
CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
[tex]\mathfrak{\huge{\pink{\underline{\underline{AnSwEr:-}}}}}[/tex]
Actually Welcome to the Concept of the GRAPHS AND FUNCTIONS.
This here, from the graph we can see that it's a EXPONENTIAL GROWTH.
Thus the relationship is Exponential.
solve the equation 2/3x-2=7
Answer: x = 27/2
Step-by-step explanation:
2/3x-2=7
2/3x=9
2/3x=27/3
2/3x(3/2)=27/3(3/2)
x=81/6
x=27/2
Answer: x = 27/2
Step-by-step explanation: In this equation, our first step is to isolate the x term by adding 2 to both sides.
On the left, -2 and +2 cancel out and were left
with 2/3x and on the right, 7 + 2 simplifies 9.
So we have 2/3x = 9.
In order to get x by itself, since it's being multiplied by a fraction,
we multiply both sides of the equation by the reciprocal of that fraction.
The reciprocal of a fraction is just that fraction
flipped so the reciprocal of 2/3 is 3/2.
So we have (3/2)(2/3x) = 9(3/2).
On the left, the 2's cancel and the 3's cancel.
On the right, 9(3/2) is 27/2.
So x = 27/2
What is the value of discontinuity of x^2+8x+4/x^2-x-6? Choices:
Answer:
-2
Step-by-step explanation:
Hello,
First of all, let's check the denominator.
[tex]x^2-x-6 \ \ \text{ *** How to factorise it ...? ***}\\\\\text{*** The product of the roots is -6=-2*3 and their sum is 1 ***}\\\\x^2-x-6=x^2-3x+2x-6=x(x-3)+2(x-3)=(x+2)(x-3)[/tex]
Now, let's see the numerator.
[tex]x^2+8x+4 \ \text{ *** -2 is not a zero as ***}\\\\(-2)^2+8*(-2)+4=4-16+8=-4\\\\\text{*** 3 is not a zero as ***}\\\\3^2+8*3+4=9+24+4=37\\[/tex]
So we cannot factorise the numerator with (x+2) or (x-3)
Then, -2 and 3 are the the discontinuities of the expression.
There is only -2 in the list, this is the correct answer.
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Find the solution of y= -x - 3 for x= -2.
Answer:
x=-2 and y=-1
Step-by-step explanation:
If x = -2 then:
y = -(-2)-3
y = 2-3
so y = -1
I hope this helps! And plz mark me brainliest!!!
Answer:
(-2,-1)
Step-by-step explanation:
Well if x is -2 we can plug it in to find y,
y = -(-2) - 3
y = 2 - 3
y = -1
(-2, -1)
Thus,
the solution is (-2,-1)
Hope this helps :)
Find the largest integer which belongs to the following interval: (−∞; 31]
Answer:
The largest integer that belongs to the interval (-∞, 31] is 31
Step-by-step explanation:
The given interval is (-∞, 31], from which the round bracket indicates that the number next to the bracket is not included in the inequality while the square [] (closed) bracket indicates that the number next to the bracket is included in the inequality
Therefore, 31 is inclusive in the inequality while -∞ is excluded.
The find the largest integer that belongs to the interval (-∞, 31] the numbers are arranged on the number line as follows
The numbers presented in number line form -∞, .....-1, 0, 1, 2,..., 31
Giving 31 as the largest integer in the inequality
PLEASE HELP!! Which two solid figures have the same volume?
Answer:
B. a rectangular solid with a base of 6 cm^2 and a height of 12cm
D. An oblique solid with a base of 6cm^2 and a slant height of 12cm
The rectangular solid with a base of 6 cm² and height of 12 cm and oblique prism of base area 6 cm² , height 12 cm has the same volume
What is the Volume of a Rectangle?The volume of the rectangle is given by the product of the length of the rectangle and the width of the rectangle and the height of the rectangle
Volume of Rectangle = Length x Width x Height
Volume of Rectangle = Area of Rectangle x Height
Given data ,
Let the base and height of the rectangular solid be 6 cm² and 12 cm respectively
So , volume of rectangle = 6 x 12 = 72 cm³
Now , the base and height of the oblique prism be 6 cm² and 12 cm respectively
So , the volume of prism = 6 x 12 = 72 cm³
Hence , the volume of rectangle and prism are same
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three people are watching a hot air balloon travel over their town. at a certain point in time, one person stands directly below the balloon, and the others look at it at certain angles. in the following image, a,b, and c are people, and d is the balloon. person c is 384m directly below the balloon, person b is 200m away from person c, and the angle between person a, the balloon, and person b is 33 degrees. how far is person a from the hot air balloon
Answer:
Distance between balloon and a is = 383.67 m
Step-by-step explanation:
The given situation can be represented as the given diagram as attached in the answer area.
cd = 384 m
cb = 200 m
[tex]\angle adb = 33^\circ[/tex]
To find:
Distance between balloon and a i.e. side ad = ?
Solution:
First of all, let us consider the right angled [tex]\triangle bcd[/tex].
We know the trigonometric identity that:
[tex]tan\theta = \dfrac{Perpendicular}{Base}[/tex]
[tex]tan\angle cbd =\dfrac{cd}{cb}\\\Rightarrowtan\angle cbd =\dfrac{384}{200}\\\Rightarrowtan\angle cbd =1.92\\\Rightarrow \angle cbd = tan^{-1}(1.92) = 62.49^\circ[/tex]
Now, using the external angle property for the external [tex]\angle cbd[/tex] for the [tex]\triangle abd[/tex]:
(External angle is equal to the sum of two opposite angles of the triangle.)
[tex]\angle cbd = \angle adb+\angle a[/tex]
[tex]\Rightarow \angle a =62.49-33 =29.49^\circ[/tex]
Now, let us consider the right angled [tex]\triangle acd[/tex].
We have the value of [tex]\angle a[/tex] and perpendicular dc.
We have to find the hypotenuse ad.
Let us use the sine identity:
[tex]sin\theta =\dfrac{Perpendicular}{Hypotenuse}\\\Rightarrow sin\angle a =\dfrac{cd}{ad}\\\Rightarrow sin(29.49^\circ) =\dfrac{384}{ad}\\\Rightarrow ad = \dfrac{384}{0.49}\\\Rightarrow \bold{ad = 783.67\ m}[/tex]
So, the answer is:
Distance between balloon and [tex]\bold{a}[/tex] is = 383.67 m