Answer:
(a) 43.6490°N, 70.3928°W
(b) Baker's Field
Step-by-step explanation:
The locations are all within a 7-mile square, so we will make the assumption of a flat Earth with parallel longitude lines. Then the "central" location will be the weighted average of the latitude and longitude coordinates.
(a)Total population is 16000 +22000 +36500 = 74,500. For purposes of the arithmetic, we will subtract 43 from latitude and 70 from longitude, then multiply each fraction by 10. Similarly, we will divide each population by 1000.
The weighted average location is found from ...
(16/74.5)(6.769, 3.717) +(22/74.5)(5.781, 3.222) +(36.5/74.5)(6.795, 4.447)
= (1.4537, 0.7983) +(1.7071, 0.9515) +(3.3291, 2.1787) = (6.490, 3.928)
The center of gravity is about 43.6490°N, 70.3928°W.
__
(b)The coordinate differences from the center of gravity are (in (°lat, °long)) ...
Baker's Field: (0.0294, -0.0101)
Lonesome Acres: (-0.1371, -.0072)
Clearly, Baker's field is closer to the site of part (a).
_____
Additional comment
Distance calculations could be refined further by considering that a degree of longitude at this latitude represents about 0.72 times the distance of a degree of latitude. In this problem, the location of Lonesome Acres has a latitude difference that is several times any of the other coordinate differences, so it is clearly much farther away from the desired location.
The calculations done here are a sort of first-level approximation. The least-significant digits in the coordinates represent a distance of less than 50 feet. If you really want accuracy to that level, then the (approximately) spherical shape of the Earth needs to be accounted for. As a second-level approximation, some reference point needs to be identified, and coordinates in miles (or feet) need to be expressed in relation to that reference. The best accuracy would be obtained using spherical trigonometry to identify the distances.
We expect any school that is constructed to be somewhat larger than 50 feet in any direction, so accuracy to the 4th decimal place in these locations is probably not required--except to satisfy some answer-checker.
Which value of y makes the equation y+4.2=21 true?
I NEED THE ANSWER ASAP I ONLY HAVE 20 MINS TO COMPLETE
A. y = 16.8
B.y=17.2
C.y=17.8
D=25.2
Answer:
A: 16.8
Step-by-step explanation:
4.2 and 16.8 both have decimal place values. If you line up the decimals when you add them, then you get 21.
The next number in the sequence shown below is 156.
1, 15, 155,
The next number of the sequence 1, 15, 155, ...... will be 1555.
What are sequence and series?A sequence is a list of elements that have been ordered in a sequential manner, such that members come either before or after.
A sequence in arithmetic is an enumerated collection of items in which duplicates are permitted and order is important. It has members, just like a set. The distance of the order is defined as the number of items.
The sequence is given below.
1, 15, 155, ......
The next number of the sequence will be given by adding the digit 5 in the one's place. Then the sequence is given as,
1, 15, 155, 1,555, 15,555, 155,555,......
Then the number will be 1555.
More about the sequence link is given below.
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Name.
Solve using
Substitution
L
y = 3x + 2
6x - 2y = 8
Answer:
No solution
Step-by-step explanation:
There is no solution to the system of equations y=3x+2 and 6x-2y=8, meaning that they are parallel to each other on a graph, with no points ever intersecting on each other's lines.
Evaluate the integral:
Substitute x = √7 sin(t) and dx = √7 cos(t) dt. Then
∫ √(7 - x²) dx = ∫ √(7 - (√7 sin(t))²) • √7 cos(t) dt
… = √7 ∫ √(7 - 7 sin²(t)) cos(t) dt
… = 7 ∫ √(1 - sin²(t)) cos(t) dt
… = 7 ∫ √(cos²(t)) cos(t) dt
We require that -π/2 ≤ t ≤ π/2 in order for the substitution we made to be reversible. Over this domain, cos(t) ≥ 0, so
√(cos²(t)) = |cos(t)| = cos(t)
and the integral reduces to
… = 7 ∫ cos²(t) dt
Recall the half-angle identity for cosine:
cos²(t) = (1 + cos(2t))/2
Then the integral is
… = 7/2 ∫ (1 + cos(2t)) dt
… = 7/2 (t + 1/2 sin(2t)) + C
… = 7t/2 + 7/4 sin(2t) + C
Get the antiderivative back in terms of x. Recall the double angle identity for sine:
sin(2t) = 2 sin(t) cos(t)
We have t = arcsin(x/√7), which gives
sin(t) = sin(arcsin(x/√7)) = x/√7
cos(t) = cos(arcsin(x/√7)) = √(7 - x²)/√7
Then
∫ √(7 - x²) dx = 7/2 arcsin(x/√7) + 7/4 • 2 sin(arcsin(x/√7)) cos(arcsin(x/√7)) + C
… = 7/2 arcsin(x/√7) + x/2 √(7 - x²) + C
please help ill mark brainliest
Answer:
it's 11
Step-by-step explanation:
-5, 20, -80, 320, ... is a geometric
sequence.
What is the explicit rule
Answer:
Multiplied by -4
Step-by-step explanation:
-5 (-4) = 20
20 (-4) = -80
-80 (-4) = 320
Help plz no links will mark best answer
Answer:
20
Step-by-step explanation:
you know the ratio is 4:3 so you do 4+3=7 then you do 140÷7=20 so I bar represents 20
How much is 1/9 of 3/8 (in lowest terms)?
A)4/17
B)03/17
C)1/36
D)1/24
Answer:
1/24
Step-by-step explanation:
multiply 1/9 and 3/8. The product of the two factors is 3/ 72. Seeing the two factors on the other hand, we can cancel out 3. Hence the final answer to this problem in lowest terms becomes 1/24.
What are the roots of the equation x^2+18x+90=0x
2
+18x+90=0 in simplest a+bia+bi form?
[tex]x^2 +18x +90 = 0\\\\\text{Apply quadratic formula,}~~ x = \dfrac{-b \pm \sqrt{b^2 -4ac}}{2a} \\\\\text{In this case, a = 1 , b = 18 and c = 90.}\\\\\implies x = \dfrac{-18 \pm \sqrt{18^2 - 4 \cdot 1 \cdot 90}}{2(1)}\\\\\implies x = \dfrac{-18 \pm \sqrt{-36}}2\\\\\implies x = \dfrac{-18 \pm 6i}2\\\\\implies x= -\dfrac{18}2 \pm \dfrac{6i}2\\\\\implies x= -9 \pm 3i[/tex]
Help!!!!!!please help i will fail
Answer:
WHAT is to solve their is notting
Step-by-step explanation:
solve the system using substitution 5x+3y=-4 y-2x=6
Solving steps:-
5x+3y=−4
y−2x=6
-->To solve a pair of equations using substitution, first solve one of the equations for one of the variables. Then substitute the result for that variable in the other equation.
5x+3y=−4,−2x+y=6
-->Choose one of the equations and solve it for x by isolating x on the left hand side of the equal sign.
5x+3y=−4
-->Subtract 3y from both sides of the equation.
5x=−3y−4
--> Divide both sides by 5.
x = 1/5(-3y - 4)
--> Multiply 1/5 −3y−4.
x = -3/5y - 4/5
--> Substitute -3y - 4/ 5 for x n the other equation, −2x+y=6.
-2 (-3/5y - 4/5) + y = 6
--> Multiply −2 times -3y - 4/ 5
6/5y + 8/5 + y = 6
--> Add 6y/5 to y
11/5y + 8/5 = 6
--> Subtract 8/5 from both sides of the equation.
11/5y = 22/5
--> Divide both sides of the equation by 11/5, which is the same as multiplying both sides by the reciprocal of the fraction.
y = 2
--> Substitute 2 for y in x= -3/5y - 4/5. Because the resulting equation contains only one variable, you can solve for x directly.
x = -3/5 x 2 - 4/5
--> Multiply -3/5 times 2.
x = -6 - 4/ 5
--> Add -4/5 to -6/5 by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.
x = -2
--> The equation is now solved.
Answer : x = -2, y = 2
Explanation : If you think this answer is good, please give "Brainliest" or rate/heart my answer. Hope this helps you.
Need help asap! Pls
Answer:
Step-by-step explanation:
The upper right angle is supplement to 130° and a corresponding angle to (3x + 5)
130 + (3x + 5) = 180
3x + 5 = 50
3x = 45
x = 15
Choose correct way to write 7 cents using the dollar symbol.
$.07
$ 7 ¢
$.07 ¢
$.7
Step-by-step explanation:
$.07
$.7
The answer was first one.
Given f(x)=x2-1/x+4 find f(-3)
Find radiuses of circles, if OO1=20cm and 3AK=2BK
Answer:
radius of smaller circle on the left = 8 centimetersradius of larger circle on the right = 12 centimeters=============================================================
Explanation:
The letter O looks very similar to the number zero, so I'm going to use other letters to avoid confusion. For the smaller circle on the left, it'll have center P. The circle on the right will have center Q. See the diagram below.
Based on that, we can say that PQ = 20 cm.
Let x = length of PK
PK + KQ = PQ
KQ = PQ - PK
KQ = 20 - x
We'll keep this in mind for later. I'll refer to this as "Fact 1" when it does come up later.
------------------------
We're given this equation
3AK=2BK
Let's get the numbers to one side and the letters to the other side like so:
3AK=2BK
3AK/BK = 2
AK/BK = 2/3
We'll use this later as well. I'll refer to this as "Fact 2" when it does come up later.
------------------------
Next, draw a segment from P to A to form triangle PAK (also shown in the diagram below). Do the same for points Q and B to form triangle QBK.
The segments PA and PK are radii of the smaller circle, so PA = PK which leads to triangle PAK being isosceles. Triangle QBK is also isosceles for similar reasoning.
The angles AKP and QKB are vertical angles, so they are congruent.
The facts mentioned so far boil down to the two triangles being similar triangles (use the angle angle method to prove).
------------------------
Now that we know the triangles are similar, we can use a proportion to solve for x.
PK/KQ = AK/KB
PK/KQ = 2/3 .... use fact 2
x/(20-x) = 2/3 .... use fact 1
3x = 2(20-x) .... cross multiply
3x = 40 - 2x
3x+2x = 40
5x = 40
x = 40/5
x = 8
So,
PK = x = 8KQ = 20-x = 20-8 = 12The radius of the smaller circle on the left is 8 cm.
The radius of the larger circle on the right is 12 cm.
1. Which of the following is the remainder when the polynomial x^2-5x+3 is divided by (x -8)?
(1) 107
(3) 3
(2) 27
(4) 9
Answer:
27
Step-by-step explanation:
Use synthetic division:
8 | 1 -5 3
__8_24
1 3 | 27
Therefore, (x²-5x+3)/(x-8) = x+3 R27
The mean temperature for the first 7 days in January was 4 °C.
The temperature on the 8th day was 6 °C.
What is the mean temperature for the first 8 days in January?
A bolt has 16 1/2 turns per inch. How many turns would be in 2 1/2 inches of threads?
Answer:
41 1/4 turns
Step-by-step explanation:
create a proportion:
turns / inches = turns / inches
't' = turns
16.5 / 1 = t / 2.5
cross-multiply to get:
t = 41.25 or 41 1/4
IF the domain is {0, 2, -6}, what is the range of y=-2x+3?
Answer:
Range is {3,-1, 15}
Step-by-step explanation:
Answer:
{3, -1, 15} is the range.
Step-by-step explanation:
A- CE=CD
B- CE = CA
C- BF=DF
D- DF=EF
please help!!
The perpendicular bisector theorem gives the statements that ensures
that [tex]\overleftrightarrow{FG}[/tex] and [tex]\overleftrightarrow{AB}[/tex] are perpendicular.
The two statements if true that guarantee [tex]\overleftrightarrow{FG}[/tex] is perpendicular to line [tex]\overleftrightarrow{AB}[/tex] are;
[tex]\overline{CE} = \overline{CD}[/tex] [tex]\overline{DF} = \overline{EF}[/tex]Reasons:
The given diagram is the construction of the line [tex]\mathbf{\overleftrightarrow{FG}}[/tex] perpendicular to line [tex]\mathbf{\overleftrightarrow{AB}}[/tex].
Required:
The two statements that guarantee that [tex]\overleftrightarrow{FG}[/tex] is perpendicular to line [tex]\overleftrightarrow{AB}[/tex].
Solution:
From the point C arcs E and D are drawn to cross line [tex]\overleftrightarrow{AB}[/tex], therefore;
[tex]\overline{CE} = \mathbf{\overline{CD}}[/tex] arcs drawn from the same radius.
[tex]\overleftrightarrow{FG}[/tex] is perpendicular to line [tex]\overleftrightarrow{AB}[/tex], given.
Therefore;
[tex]\overline{DF} = \overline{EF}[/tex] by perpendicular bisector theorem.
Learn more about the perpendicular bisector theorem here:
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subtract the sum of h and 6 from 4
I need help
With this one question
Answer:
$88
Step-by-step explanation:
442.70 rounded to the nearest 10 dollars is 440.
20%= .2.
440 times .2 =
88
NEED NOW PLEASE..........
Answer:
The answer is 6 feet below the surface of the water.
Step-by-step explanation:
So the fish started out as 12m below the surface then went 3m down. If you add 12m and 3m you'll 15m, then minus with a 9m to came up with 6m. But the fish is still below surface, which gives you the answer of " 6 feet below the surface"
Hopes this helped you :)
Which of the lines listed below is parallel to the line with the equation y = 3/2x + 5?
use desmos graphing calculator
Write the following as a mathematical sentence. Use the letter n as your variable.
Seven less than a number is two.
Answer:
n-7=2
Step-by-step explanation:
We can start with one side, which is: seven less than a number
Since the number is n, seven less than it is n-7
The other side 2, as we can see after the word is
The equation, therefore, is
n-7=2
The kindergarten class at Stokes Elementary drinks about 210 pints of milk per week. About how many gallons of milk does the class drink in 10 weeks? Round your answer to the nearest tenth of a gallon if needed.
262.5 gallons of milk does the class drink in 10 weeks.
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
The kindergarten class at Stokes Elementary drinks about 210 pints of milk per week.
as, we know that
1 pint= 0.125 Galloon
So, 210 pints milk = 210 x 0.125 = 26.25 Galloon
Then, In 10 weeks amount of milk drink
= 26.25 x 10
= 262.5 Gallon
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An angle measures 26.9 degrees. What is its complement?
Answer:
63.1°
Step-by-step explanation:
Complementary angles sum 90°
90 - 26.9 = 63.1°
help please use picture
Answer:
y= -1x+4
Step-by-step explanation:
-1/1 is simplified to -1
What is the equation for the line in slope-intercept form?
Enter your answer in the box.
Answer:
y= -4/2x+ -4
Step-by-step explanation:
looked at the graph
Find the slope.
y = 3x – 11
m =[?]
you know that y=mx +c then in the place of m is 3 then answe is also three.