Answer:Section 6.1
Solutions and Hints
by Brent M. Dingle
for the book:
Precalculus, Mathematics for Calculus 4
th Edition
by James Stewart, Lothar Redlin and Saleem Watson.
If you remember nothing else from this section remember:
arc length = radius * angle
s = r * q
where the angle, q, is measured in radians.
There are other formulas, but that one is pretty important.
48. A circular arc of length 3 feet subtends a central angle of 25.
Find the radius of the circle.
Start with s = r*q , s = 3 feet, q = 25 = 25*(p/180) = (5/36)p radians
3 = r * (5/36)p Å 3*(36/5) = r*p Å 21.6 = p*r Å r = 21.6/p feet
52. Memphis, Tennessee and New Orleans Louisiana lie approximately on
the same meridian. Memphis has latitude 35 N and New Orleans 30 N.
Find the distance between the cities, given the radius of the earth is
3960 miles.
Again start with s = r*q,
with r = 3960 miles and q = 35 – 30 = 5 = 5*(p/180) = (1/36)p.
and we need to find s = arc length = distance between the cities.
s = 3960*(1/36)p = 110p miles.
60. A sector of a circle of radius 24 miles has an area of 288 square miles.
Find the central angle of the sector.
For this you need a new formula.
The area of a sector of circle = A = ½*r
2
*q ,
where q is the central angle of the sector measured in radians
and r of course is the radius of the circle.
For this problem r = 24 miles, A = 288 sq. miles and we need to find q.
288 = (½)*24
2
*q Å 288 = 288*q Å 1 radian = q (or about 57.3)
62. Three circles with radii 1, 2 and 3 feet are externally tangent to one
another. Find the area of the sector of the circle of radius 1 that is
cut off by the line segments joining the center of that circle to the
centers of the other two circles.
So you start out with:
Notice you know the length of ALL the sides of the triangle, because you know
the radius of each circle. From this you might discern that: 5
2
= 3
2
+ 4
2
. Thus you
have the (length of the hypotenuse)
2
= (length of side A)
2
+ (length of side B)
2
.
And from that you may conclude the triangle is a right triangle, or rather the angle
we are interested in is 90. Thus we use the area formula given in the text:
The area of a sector of circle = A = ½*r
2
*q ,
For this problem r = 1 foot, q = 90 = p/2, and we need to find A
A = ½ * 1
2
* p/2 = p/4 square feet.
Step-by-step explanation:
The linear speed of a point on the equator in miles per hour is 1037 mph. Therefore, option D is the correct answer.
Given that, the radius of the earth is approximately 3960 miles.
What is the linear speed?Linear speed is the measure of the concrete distance travelled by a moving object. The speed with which an object moves in the linear path is termed linear speed. In easy words, it is the distance covered for a linear path in the given time. Linear Speed Formula is articulated as s=rθ/t.
Any point in the equator would complete a 360° or 2π, revolution in 24 hours. Therefore, the linear speed would be s=rθ/t.
where r is the radius of the Earth and θ is the angular distance (in rad) after time t
Hence, the linear speed would be
s= (3960×2π)/24
= (3960×2×3.14)/24
= 24868.8/24
= 1036.7
≈1037 mph
The linear speed of a point on the equator in miles per hour is 1037 mph. Therefore, option D is the correct answer.
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How many centiliters are in 5 quarts? quarts Right-arrow liters Right-arrow centiliters StartFraction 5 quarts Over 1 EndFraction times StartFraction a Over b EndFraction times StartFraction c Over d EndFraction = 475 centiliters a = b = c = d =
Answer:
a = 0.95 liters
b = 1 quart
c = 100 centiliters
d = 1 liter
Step-by-step explanation:
on edge.
Answer:
A: 0.95 Liters
B: 1 quart
C: 100 centilitres
D: 1 Liter
Step-by-step explanation:
Got it right in edge 2020
I need the answer now!!!!
(3c2 + 2d)(–5c2 + d)
Select all of the partial products for the multiplication problem above.
2d2
3cd3
–15c4
–10c2 d
–15c2
3c2 d
Answer:
A C D F
Step-by-step explanation:
edg 2020
What is the image point of (3, -3) after a translation left 3 units and up 4 units?.
Answer:
(0, 1)
Step-by-step explanation:
(x, y)
Left and Right movement deals with the x value
Up and Down movement deals with the y value
3 units left = -3
4 units up = +4
(x - 3, y + 4)
(3 - 3, -3 + 4)
(0, 1)
The image point of (3, -3) after a translation of [tex](-3, 4)[/tex] is [tex](0,1)[/tex].
Determination of the coordinates of resulting point after translationGeometrically speaking, a translation is determined by following formula:
[tex]V'(x,y) = V(x,y) + T(x,y)[/tex] (1)
Where:
[tex]V(x,y)[/tex] - Original point[tex]T(x,y)[/tex] - Translation vector[tex]V'(x,y)[/tex] - Resulting pointIf we know that [tex]V(x,y) = (3, -3)[/tex] and [tex]T(x,y) = (-3, 4)[/tex], then the coordinates of the resulting point are, respectively:
[tex]V'(x,y) = (3, -3) + (-3, 4)[/tex]
[tex]V'(x,y) = (0, 1)[/tex]
The image point of (3, -3) after a translation of [tex](-3, 4)[/tex] is [tex](0,1)[/tex]. [tex]\blacksquare[/tex]
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A farmer collected 1,957 eggs from her chickens she puts them into a carton that each hold 48 eggs how many cartons will the farmer need to hold all of the eggs
Answer:
41 cartons will be needed
Step-by-step explanation:
here, we need to know the number of cartons the farmer needs to hold all the eggs
To calculate this, we simply make a division of the number of eggs by the number of eggs in a carton
That would be 1957/48 = 40.77
The closest number of cartons here is 41
Please answer correctly !!!!!!!!!!!!!!!!!! Will mark brainliest !!!!!!!!!!!!!!!!!!!
Answer:
92 degrees
Step-by-step explanation:
<HEF and <AED are vertical angles.
How much should your average everyday coin weigh?
Answer:
About 0.080 ounces
A nickle weighs exactly 5.00 grams,
A cent weighs exactly 2.50 grams,
and so on...
Is this any better for you guys
Answer:
According to the pattern, Samuel will swim 64 laps on Monday.
The pattern rule: Start at 88 and subtract 8 each time.
Explanation:
There is a clear pattern. 88 - 80 - 72. The number 8 is subtracted each time day after day. Since he is doing 8 laps less each day, it can be assumed that we subtract 8 from Sunday, which is 72.
72 - 8 = 64
I hope this was helpful to you! If it was, please consider rating, pressing thanks, and marking my answer as 'Brainliest.' It would really help. Have a great day! :)
Answer:
64 Laps
Step-by-step explanation:
It looks like the Samuel swam 8 less laps than the previous day.
88 - 8 = 80
80 - 8 = 72
So, we sohuld subtract 8 from 72.
72 - 8 = 64
Samuel should swim 64 laps on Monday.
Hope this helps!
ILL MARK BRAINLIEST please help :( 32 points too
Answer:
Hope this helps!
Step-by-step explanation:
21. 1/1000
22. 1 second
23. 0.16666666666
24. 0.1
25. 0.2
26. 5/48
27. 33.9 kilometers
You work 4 hours on Monday, 4.5 hours on Tuesday, 7.25 hours on Thursday, and 12 hours on Saturday. If you get paid $11.52 per hour, what is your total pay for the week?
Answer:
319.68
Step-by-step explanation:
How many is equivalent to 10/12
Answer:
10/12 =5/6
Step-by-step explanation:
Answer:
5/6
Step-by-step explanation:
I believ you meant what is the simplest version of that fraction and that would be 5/6. Both 10 and 12 are divisable by 2 and 5 can not be reduced
A t-shirt vendor is thinking about changing the number of t-shirts he brings to an event. Which size should he bring more of?
Answer: B. Medium
Step-by-step explanation:
A.P.E.X
Answer:
A Medium
Step-by-step explanation:
AP. EX
what is 411, 600, 000 in scientific notation
Answer:
4.116 × 108
Step-by-step explanation:
I simply used a Scientific Notation Converter
Answer:
The answer would be 4.116 x 10 exponent of 8
Step-by-step explanation:
In scientific notation, the answer has to be between 1-10, so to make this number between one and ten, you must create a decimal behind the number in the one's place and move it until you get to the first number (in this case, you would move it eight times, so your equation would be 4.116 x 10 to the eight power (exponent of eight). If you need to round the number to the tenth place, it's 4.1 x 10^8
Hope this helps!
Is 46 a number in the sequence generated by 5n + 1
Answer:
231
Step-by-step explanation:
5.46+1
230+1
231
answer this?
Answer:
yes
Step-by-step explanation:
Equate 5n + 1 and 46 to find n, that is
5n + 1 = 46 ( subtract 1 from both sides )
5n = 45 ( divide both sides by 5 )
n = 9
Thus 46 is the ninth term in the sequence
scott gained a total of 72 yards in his team's first football game of the season what intenger represents the average number of yards scott gained each quarter?
Answer:
Scott gained 18 yards every quarter
Step-by-step explanation:
72 divided by 4 is equal to 18, so every 1/4 of a season he gained 18 yards.
For g(x) = 12x – 2, evaluate g (1/4)
Replace x with 1/4 and solve:
12(1/4) - 2
3-2 =1
The answer is 1
Answer:
the answer is 1
Step-by-step explanation:
g(1/4)=12(1/4)-2
=12/4-2
=3-2
=1
What percent is equivalent to 2/5?
Answer:
40%
Step-by-step explanation:
In order to turn a fraction into a decimal or percentage, you need to make the denominator 100. In this case you just need to multiply the numerator and denominator by 20:
2/5 --> 2*20/5*20 --> 40/100
So, it is 40%. Though if you want to turn ANY fraction (specifically fractions with hard to multiply denominators) into a percentage, just follow this rule:
(100n/d)%
The 2/5 is equivalent to 40%.
To calculate what percent is equivalent to 2/5, we can use the formula:
Percent = (Part / Whole) * 100
In this case, the part is 2 and the whole is 5.
Percent = (2 / 5) * 100
Now, perform the division:
Percent = 0.4 * 100
To find the percentage, multiply 0.4 by 100:
Percent = 40%
Therefore, 2/5 is equivalent to 40%. To understand this better, consider that 2 out of 5 parts is 40% of the whole. The percentage represents the proportion of the part (2) in relation to the whole (5) expressed as a fraction of 100. In this scenario, 2/5 is equivalent to 40%, indicating that 40% of the whole is represented by the fraction 2/5.
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can you simplify the fraction 4/-3 any more
Answer:
No
Step-by-step explanation:
you can't simplify it anymore no matter how low of a number you simplify it by
HELP!!! please look at the photo attached, its really confusing me so even if you dont know the answer can you atleast give me tips on how to do it?
note: the rectangle is 4cmx11.5cm, scaled up it is 8mx23m
The area of the rectangle in meters = 8x 23 = 184 square meters.
The area of one board = 1.2 x 1 = 1.2 square meters
Total area of all the boards = 1.2 x 150 = 180 square meters.
180 is less than 184 so she does not have enough boards.
1)What value for y makes the equation 2(y-4)+8=12+y true?
A. -6
B. 12
C. 6
D. 8
2)Which number below does not satisfy the given inequality: -4x - 6 > -14?
A. -4
B. -2
C. 0
D. 2
Answer:
1. Option B- y=12
2. Option D - 2
Step-by-step explanation:
1. 2(y - 4) + 8 = 12 + y
2y - 8 + 8 = 12 + y
add like terms -8 + 8 is 0 so
2y = 12 + y
Subtract y
1y = 12
Divide by 1
y= 12
2. -4(2) - 6 > -14
-8 - 6 > -14
-14 > -14
This is not true because -14 is not greater than -14, they are equal.
Hope this helps.
Plz I'm sooooo confuzzled: If you reflect any shape across the x-axis and then across the y-axis, do you get the same result that you would if you rotated it 180° about the origin? What does that mean?
Answer:
the answer is true
Step-by-step explanation:
If the shape is in the upper left quadrant then you reflect it across the x-axis it would be in the lower left quadrant, next you reflect across the y-axis it would be in the lower right quadrant, finally, if you rotate it 180 degrees it would be where it started.
Answer:
it's correct because even though rotating 90° is not the same as reflecting about the y-axis, when you reflect again about the x-axis, it becomes the same as reflecting an additional 90°.
so reflecting about y and then about x is the same as rotating 180°.
Step-by-step explanation:
if you reflect (x, y) in 180° it becomes (-x,-y)
when you reflect about the y-axis, (x,y) becomes (-x,y).
when you reflect again about the x-axis, (-x,y) becomes (-x,-y) which is the same as the 180°
Suppose 36 gallons of water came out of a pipe in 9 minutes what was the rate in gallons per minute?
NEED HELP ASAP!!!! please! 25 points!
Answer: 2-4= -2
Step-by-step explanation: hope it helps
Answer: (0 + 2) + ( 2 - 4)
Step-by-step explanation:
Find 3/8 of £42.plz show the correc working out
Answer:
3X (1/8) X 42. This is 126 X (1/8). Answer: 15 3/4
Step-by-step explanation:
Answer:
15.75
Step-by-step explanation:
42 / 8 = 5.25
5.25 x 3 = 15.75
Plzzzzzz help me with all 3 answers
Answer:
1) is arithmetic (because your adding 10)
2) is not arithmetic
3) is arithmetic ( because your adding 10)
Step-by-step explanation:
Explain why 173 degrees cannot be an interior angle from any regular polygon.
173 cannot be an interior angle of any regular polygon because the number of sides would be negative.
Why can't the interior angle of the polygon be 173 degrees?
The formula that can be used to determine one of the one interior angle of an n-sided polygon is [180(n−2)]/n .
In order to determine the value of n, take the following steps:
[180(n - 2) ]/ n = 173
Multiply both sides of the equation by n
180(n - 2) = 173n
Divide both sides by 180
n - 2 = 0.961111n
Combine similar terms
n - 0.96n = 2
0.038889n = 2
n = 51.4
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what points are solutions to the linear equality graph? Select all that apply.
A. (0,0)
B. (-1,2)
C. (-3,0)
D. (3,0)
E. (-4,-1)
F. (2,2)
solve (2x + 3) - (9x - 3)
Answer:
-7x + 6
Step-by-step explanation:
WILL MARK BRAINLIESTS
and go on my last question please!
Answer:
125*125
Step-by-step explanation:
Plz help me with this question if you can also explain that would be great but you don’t have to
Answer:
I'm pretty sure it's D: y= 23x
Step-by-step explanation:
Pleaseeee help.
Will give extra points.
Brainliest to the one that explains well.
Find the equation of the circle with center (0,-6) and tangent to the x-axis.
