A wheelchair ramp has a slope of 1:12 (1 foot of rise over a horizontal distance of 12 feet). To the nearest 0.1 foot, how many feet of ramp will be needed to rise 3 feet? (Round the angle of incline to the nearest 0.01°.)
Answers
1. We must find the value of the angle "α" of the triangle A:
Tan^-1(α)=Opposite Leg/Adjacent leg
Opposite leg=1
Adjacent leg=12
Tan^-1(α)=1/12
α=4.8°
2. Now, let's find the value of its hypotenuse "y":
Sin(α)=Opposite leg/Hypotenuse
Opposite leg=1
Hypotenuse=y
Sin(4.8°)=1/y
y=1/Sin(4.8°
y=12 ft
3. To rise 3 feet, the value of "x" (Feet of ramp), is:
1/12=3/x
x(1)=(3)(12)
x=36 ft
4. The angle of incline is:
Tan^-1(β)=Opposite Leg/Adjacent leg
Opposite leg=3
Adjacent leg=12
Tan^-1(β)=3/12
β=14°
How many feet of ramp will be needed to rise 3 feet?
The answer is: 36 feet
Related Questions
To keep heating costs down for a structure, architects want the ratio of surface area to volume as small as possible. An expression for the ratio of the surface area to volume for the square prism shown is 2b+4h/bh. Find the ratio when b=12 ft and h=18ft.
Answers
Final answer:
The ratio of surface area to volume for the square prism is 4/9 when b = 12 ft and h = 18 ft.
Explanation:
The expression for the ratio of surface area to volume of the square prism is 2b + 4h/bh. To find the ratio when b = 12 ft and h = 18 ft, substitute these values into the expression.
Ratio = 2(12) + 4(18)/(12)(18)
= 24 + 72/216
= 96/216
= 4/9
Therefore, the ratio of surface area to volume for the given square prism is 4/9 when b = 12 ft and h = 18 ft.
The ratio of surface area to volume for a square prism with a base of 12 ft and a height of 18 ft is calculated using the formula 2b + 4h / bh, which results in a ratio of 4 / 9 ft⁻¹.
Explanation:The student has asked to find the ratio of surface area to volume for a square prism when given specific dimensions. The formula provided is 2b + 4h / bh, where b is the base length and h is the height of the prism. To find the ratio for b = 12 ft and h = 18 ft, we substitute these values into the formula:
Ratio = (2 × 12 ft) + (4 × 18 ft) / (12 ft × 18 ft) =
24 ft + 72 ft / 216 ft² =
96 ft / 216 ft².
After performing the calculations, we simplify the expression to get the ratio:
Ratio = 96 ft / 216 ft² = 4 / 9 ft⁻¹.
Thus, the ratio of surface area to volume for a square prism with a base of 12 ft and a height of 18 ft is 4 / 9 ft⁻¹.
the numbers of wins and losses of two local basketball teams are on the table find the probability that a randomly selected game from the season was played by the wolves given that it was a lose
Answers
you know that it is a loss so you can ignore the wins column. Adding up both the losses of the wolves and the losses of the hawks will give you the total losses.
the answer is losses of the wolves/total losses
Probability is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
The probability that a randomly selected game from the season was played by the wolves given that it was a loss is 1/5.
What is probability?It is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
We have,
Total number of wins and losses = 12 + 14 + 16 + 18 = 60
Number of losses wolves has = 12
Now,
The probability that a randomly selected game from the season was played by the wolves given that it was a loss.
= 12/60
= 1/5
Thus,
The probability that a randomly selected game from the season was played by the wolves given that it was a loss is 1/5.
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How many times do you need to divide by ten to get from 3731.7 to 373.17
Answers
What are the solutions to the following system?
Answers
and since we know what "x" is, then let's substitute it on say the 1st equation
[tex]\bf -2x^2+y=-5\implies -2\left( \pm \sqrt{2} \right)^2+y=-5\implies -4+y=-5 \\\\\\ y=-1\\\\ -------------------------------\\\\ \left( \sqrt{2}~,~-1 \right)\qquad \left( -\sqrt{2}~,~-1 \right)[/tex]
Answer:
C
Step-by-step explanation:
Consider the image of ABC for the translation (x, y) --> (x + 4, y - 2). What is the ordered pair of C'?
Answers
In a certain skyscraper, the elevator whisk you a restaurant in the skyscraper at a speed of 500 feet in 60 seconds. If the restaurant is 300 feet up, how long will it take you to reach the restaurant by elevator?
Answers
Answer:
The elevator will take you up at 300 feet in 36 seconds.
Step-by-step explanation:
Let the time taken to go up 300 feet be = t seconds
Given is that the elevator takes you up at 500 feet in 60 seconds.
So, we can derive a relation as:
[tex]\frac{500}{60}= \frac{300}{t}[/tex]
=> [tex]500t=300\times60[/tex]
=> [tex]500t=18000[/tex]
t = 36 seconds
So, the elevator will take you up at 300 feet in 36 seconds.
Which postulate or theorem can be used to prove that △JKL is similar to △MKN?
A. SSS Similarity Theorem
B. ASA Similarity Theorem
C. AA Similarity Postulate
D. SAS Similarity Theorem
Answers
Answer:
The correct option is D.
Step-by-step explanation:
In triangle △JKL,
[tex]\frac{JK}{KL}=\frac{30}{50}=\frac{3}{5}[/tex]
In triangle △MKN,
[tex]\frac{MK}{KN}=\frac{15}{25}=\frac{3}{5}[/tex]
In triangle △JKL and △MKN
[tex]\frac{JK}{KL}=\frac{MK}{KN}[/tex]
[tex]\angle JKL=\angle MKN[/tex] (Vertically opposite angles)
Since two sides are proportional and an inclined angle is congruent, so by SAS theorem of similarity we get
[tex]\triangle JKL=\triangle MKN[/tex]
Therefore option D is correct.
Ramon earns $1,770 each month and pays $53.70 on electricity. To the nearest tenth of a percent, what percent of Ramon's earnings are spent on electricity each month?
Answers
Quick Fix Inc. repairs bikes. The company’s revenue is modeled by the function R(h)=220h−160 for every h hours spent repairing bikes. The company’s overhead cost is modeled by the function C(h)=20h^2−400.
After how many hours does the company break even?
Answers
R(h)=C(h)
220h-160 = 20h²-400
Gather all the variables on one side by subtracting 220h:
220h-160-220h = 20h²-400-220h
-160=20h²-220h-400 (we can move these around so long as we take their respective signs with them)
We want our quadratic equation to equal 0 to solve it, so add 160 to both sides:
-160+160=20h²-220h-400+160
0=20h²-220h-240
All 3 terms of this quadratic are divisible by 20, we can factor 20 out:
0 = 20(h² - 11h - 12)
The quadratic that is left is easily factorable. We want factors of -12 that sum to -11; that would give us -12*1, because -12+1 = -11. Thus we have
0 = 20(h - 12)(h + 1)
Using the zero product property, we know that one of the factors must be 0 in order for the product to be 0. 20 ≠ 0, so it must be either h-12 or h+1:
h-12 = 0
Add 12 to both sides:
h - 12 + 12 = 0 + 12
h = 12
h+1 = 0
Subtract 1 from both sides:
h + 1 - 1 = 0 - 1
h = -1
Since a negative number of hours is not realistic, the answer must be h = 12 hours.
Final answer:
Quick Fix Inc. breaks even after 7 hours of labor. This is determined by setting the revenue function equal to the overhead cost function and solving for the variable h (hours), which results in a quadratic equation that factors to reveal the break-even point.
Explanation:
To find out after how many hours Quick Fix Inc. breaks even, we need to set the company's revenue function equal to its overhead cost function. The revenue function is given by R(h) = 220h - 160 and the overhead cost function is given by C(h) = 20h2 - 400. The break-even point occurs when R(h) = C(h).
To solve for h (hours), we rearrange the equation: [tex]20h^2 - 220h + 160 + 400 = 0, or \\20h^2 - 220h + 560 = 0.[/tex]
Divide through by 20 to simplify: [tex]h^2 - 11h + 28 = 0.[/tex]
Factoring the quadratic equation gives us: (h - 7)(h - 4) = 0.
Set each factor equal to zero and solve for h: h - 7 = 0 or h - 4 = 0, thus h = 7 hours or h = 4 hours.
Since we are looking for a positive number of hours, we need to test which solution makes sense in the context of the problem. After examining both possibilities, we conclude that the company breaks even at 7 hours, because at 4 hours, the cost would still exceed the revenue.
Jack is building a rectangular fence for his ferret. He has 20 feet of fencing and wants the short side of the fence to be 7/2 feet. How long will the other side of the fence be? Write the answer in decimal form.
Answers
the other side of the fence will be 6.5 feet
General Idea:
When we are working with word problems, we need to follow the below steps:
Step 1: Assign variable for the unknown that we need to find.
Step 2: Write a meaningful mathematical equation using the sentence given
Step 3: Solve the equation by Performing reverse operation by Undoing whatever is done to the variable. Solving means find the value of the variable which will make the equation TRUE.
Applying the concept:
Step 1: Let 'x' be the length of longest side of the fence.
Step 2: We need to set up an equation based on the information given.
[tex] Perimeter\; of\; rectangle=\; 2(\; Longest \; side\; +\; Shortest \; side\; ) [/tex]
Substituting 20 for the perimeter of rectangle, x for Longest side and [tex] \frac{7}{2} [/tex] for the shortest side in the above formula, we get the below equation.
[tex] 2(x+\frac{7}{2} )=20 [/tex]
Step 3: Solving the equation.
[tex] 2(x+\frac{7}{2} )=20\\ Distribute \; 2 \; in \; the \; left \; side \; of \; the \; equation\\ \\ 2x+2 \cdot \frac{7}{2} =20\\ Simplify \; in \; the\; left\; side \; of \;the \;equation\\ \\ 2x+7=20\\ Subtract \; 7 \;on\; both \;sides \; of\; the \; equation\\ \\ 2x+7-7=20-7\\ Combine\; like \; terms\\ \\ 2x=13\\ Divide \; by \; 2\;on \; both\; sides\\ \\ \frac{2x}{2} =\frac{13}{2} \\ Simplify \; fraction\;on \; both \; sides\\ \\ x=6.5 [/tex]
Conclusion:
The length of longest side of the fence is 6.5 feet.
John says the transformation rule (x, y) es002-1.jpg (x + 4, y + 7) can be used to describe the slide of the pre-image (4, 5) to the image (0, ???2). What was his error?
Answers
We are given transformation rule
(x, y) --> (x + 4, y + 7).
The coordinate of the pre-image is (4,5).
The coordinate of the transformed image is (0,-2).
Please see, if we apply
(x, y) --> (x + 4, y + 7) rule.
(4,5) coordinate would become (4 +4 , 5+7 ) = (8,12).
But we need (0,-2) instead of (8,12).
Let us reverse operation in the given rule and check.
Let us change (x + 4, y + 7) to (x-4, y-7) and now check.
(4,5) coordinate would become (4-4 , 5-7) = (0,-2).
So, we got exact coordinate of the transformed image.
Therefore, error was
(x, y) --> (x + 4, y + 7) rule should be (x, y) --> (x - 4, y - 7) rule.
Transformation involves changing the position of a point.
John's error is that, he subtracted the points instead of adding them.
The pre-image is given as:
[tex]\mathbf{(x,y) = (4,5)}[/tex]
The image is given as:
[tex]\mathbf{(x,y) = (0,-2)}[/tex]
The transformation rule is given as:
[tex]\mathbf{(x,y) \to (x + 4,y + 7)}[/tex]
When the rule [tex]\mathbf{(x,y) \to (x + 4,y + 7)}[/tex] is applied on [tex]\mathbf{(x,y) = (4,5)}[/tex], we have:
[tex]\mathbf{(x,y) = (4+4,5+7)}[/tex]
[tex]\mathbf{(x,y) = (8,12)}[/tex]
Hence, John's claim is incorrect.
His error is that, he subtracted the points instead of adding them.
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Alex is making a nut mixture to sell at the local farmer's market. He mixes 2 pounds of cashews with a nut mixture that is 40% cashews. The resulting mixture is 52% cashews. How many pounds of nut mixture does Alex make?
Mr. Martinez mixes a 90% sugar cinnamon flavored solution with a 75% sugar cherry flavored solution to make 12 gallons of a new product. The new product is 85% sugar. How much of the cherry flavored solution did he use?
Mr.Acosta works in the lab at a pharmaceutical company. He needs 26 liters of a 36% acid solution to test a new product. His supplier only ships a 42% and a 29% solution. How much of the 42% solution will Mr.Acosta need to use?
PLEASE SHOW WORK!!
Answers
Mr.Acosta works in the lab at a pharmaceutical company. He needs 26 liters of a 36% acid solution to test a new product. His supplier only ships a 42% and a 29% solution. How much of the 42% solution will Mr.Acosta need to use?
We would use the relation c1v1+c2v2=cv
where
v=26 L
c=36%
c1=42%
c2=29%
v1=x
v2=v-x=26-x L
Applying relationship:
42%*x + 29%*(26-x) = 36%*26
Expand
13x+754=936
13x=936-754=182
x=182/13=14 L
Answer: Mr. Acosta will need 14 L of 42% solution, and 12 L of 29% solution to make 26 L of 36% solution.
1. The percentages of cashews available are 100% and 40%. We want to mix these to make 52%. We know that we have used 2 lbs of 100%, and we want to find how much 40% we need.
The first diagram shows the ratio of 40% to 100% will be 48:12. Dividing both terms of this ratio by 6, we get 8:2. This means we will use 8 lbs of 40% cashews with the 2 lbs of 100% cashews, for a total of 10 lbs of mix.
2. The second diagram tells us that 5 out of 15 or 1/3 of the mixture will be cherry-flavored. Of the 12 gallons total, 4 gallons will be cherry-flavored solution.
3. The third diagram shows that 7 of 13 liters will be 42% solution, so to make twice as much mixture, 14 L of 42% solution are needed.
_____
In each diagram, the right-side numbers are the differences between the middle number and the left-side number.
Matthew bought 4 new compact discs at $16.99 each and a carrying case for $35.89. He paid 2007-03-04-00-00_files/i0250000.jpg% sales tax on his purchases. If Matthew paid $112.42 total, determine if he paid the correct amount. a. Matthew paid $0.15 too little for his purchases. b. Matthew paid $0.16 too much for his purchases. c. Matthew paid $0.05 too much for his purchases. d. Matthew paid the correct amount for his purchases.
Answers
20 how much metal is needed to smelt a cubical metal box with outer side 12 inches long if the thickness of its walls should be exactly 3 inches?
Answers
V1=(12 inches)³
V1=1728 inches³
As there are 3 inches of metal on both sides, the widht if the metal box was not completely solid, is:
W=12 inches-(3 inchesx2)
W=6 inches
Then, the volumen of the no solid metal box is:
V2=(6 inches)³
V2= 216 inches³
Therefore, the volume of metal needed to smelt the cubical metal box, is:
V3=V1-V2
V3=1728 inches³-216 inches³
V3=1512 inches³
will give branliest Which events are mutually exclusive?
Jon eats more than 1 apple; Jon eats 3 apples.
Jon eats 4 apples; Jon eats 1 apple.
Jon eats 2 apples; Jon eats more than 2 apples.
Jon eats 2 apples; Jon eats 4 apples.
Answers
Answer:
Jon eats 2 apples; Jon eats more than 2 apples.
Step-by-step explanation:
Mutually exclusive events are events which have no common element between them. They are completely disjoint and the intersection would be a null set
Hence probability for the intersection of mutually exclusive events =0
Here we are given 4 options to select.
Jon eats more than 1 apple; Jon eats 3 apples.
These two are not mutually exclusive as eating 3 apples includes eating 1 apple.
Jon eats 4 apples; Jon eats 1 apple.
These two are not mutually exclusive as eating 4 apples includes eating 1 apple.
Jon eats 2 apples; Jon eats more than 2 apples.
These two are mutually exclusive since he cannot eat 2 applies exactly and also more than 2 apples
Jon eats 2 apples; Jon eats 4 apples.
These two are not mutually exclusive as eating 4 apples includes eating 2 apple.
Hence correct answer is
Jon eats 2 apples; Jon eats more than 2 apples.
what is the vertex of f(x)=5^2+20-16
Answers
.. f(x) = 5x^2 +20x -16
.. = 5(x^2 +4x +4) -16 -20
.. = 5(x +2)^2 -36
The vertex is (-2, -36)
Evaluate g(x) = 0.023x^3 + 0.4x^2 − 2.1x + 8.3 for x = 2 and x = 4.
Answers
for x = 2
g(2) = 0.023(2)³ + 0.4(2)² - 2.1(2) + 8.3
= 0.184 + 1.6 - 4.2 + 8.3
= 5.884
for x = 4
g(4) = 0.023(4)³ + 0.4(4)² - 2.1(4) + 8.3
= 1.472 + 6.4 - 8.4 + 8.3
= 7.772
A person in a rowboat two miles from the nearest point on a straight shoreline wishes to reach a house six miles farther down the shore. if the person can row at a rate of 3 mi/h and walk at a rate of 5 mi/h, find the least amount of time required to reach the house. how far from the house should the person land the rowboat?
Answers
And the answer for this question is: The person should walk 6 - 1.5 miles or 4.5 miles along the shore
Through a time, distance and speed optimization problem, we find the least amount of time to reach the house is approximately 2.11 hours. The person should land the boat 2 miles from the house.
Explanation:The problem given is a classic time, distance and speed optimization problem which can be solved with a bit of calculus and geometric reasoning. The first step is to define variables. Let's say the person decides to row to a point x miles down the shore, and then walk the remaining distance.
The time taken to row is the distance rowed divided by the rowing speed, and since the rowing distance is the hypotenuse of the right triangle formed, it is sqrt(4+[tex]x^2[/tex]) miles. Hence, time rowing is sqrt(4+[tex]x^2[/tex])/3 hours.
The distance walked is 6-x and hence, the time walking is (6-x)/5 hours.
The total time is then T(x)=sqrt(4+[tex]x^2[/tex])/3+(6-x)/5. The task is to find an x that minimizes T(x). To do so, take the derivative of T(x), set it equal to 0 and solve for x. After conducting these steps, you find that the minimum time is attained at x=2. Therefore, the least amount of time required would be T(2) which is approximately 2.11 hours. The person should land the rowboat 2 miles from the house.
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the manager of and apartment complex will install new carpeting in a studio apartment. The floor plan is shown at the right. What is the total area that needs to be carpeted?\
help with 1 and 2 only
Answers
The area of the rectangular section in the middle is given by 15(12)=180ft².
The area to the right can be broken into a rectangle, whose area is 8(10)=80ft², and a triangle, whose area is (1/2)(5)(8)=20ft².
The area to the left can be represented as a rectangle minus a triangular area. The dimensions of the complete rectangle would be 15(5)=75ft². However it is missing a triangle at the top whose area would be (1/2)(5)(5)=12.5ft². Thus we have 180+80+20+75-12.5=242.5ft².
#2)
The area of the weight room is given by 28(30)=840ft². The area of the Dance Studio is given by 33(42)=1386. There is a corner that is counted twice, however. The area of this corner is 14(14)=196ft². Our total area is then 840+1386-196=2030ft².
Anybody have the answer to this?
Answers
One leg measures x.
One leg measures 13.5 cm.
The hypotenuse measures x + 8.45 cm.
With the lengths of the the 3 sides, we can use the Pythagorean theorem and solve for x.
[tex] x^2 + (13.5)^2 = (x + 8.45)^2 [/tex]
[tex] x^2 + 182.85 = x^2 + 16.9x + 71.4025 [/tex]
[tex] 182.25 = 16.9x + 71.4025 [/tex]
[tex] -16.9x = -110.8475 [/tex]
[tex] x = 6.559 [/tex]
Answer: x = 6.6 cm
The area of a room is 396 square feet. The length is x+3, and the width is x+7 feet. Find the dimensions of the room
Answers
(x +7) (x + 3) = 396
x^2 + 7x + 3x + 21 = 396
x^2 + 10x + 21 = 396 Subtract 21 from both sides.
x^2 + 10x = 396 - 21
x^2 + 10x = 375
x^2 + 10x - 375 = 0 This probably factors.
(x + 25)(x - 15)
x + 25 = 0
x = - 25 which makes no sense. Negatives do not describe room dimensions.
x - 15= 0
x = 15. this is fine.
x+3 = 15 + 3 = 18
x + 7 = 15 + 7= 22
Check
=====
Area = L * W = 18 * 22 = 496. It does check.
22 should be the length
18 should be the width.
PLEASE explain this, I'm so lost. 25 points! What is the area of the base of the pyramid? Enter your answer in the box. Express your answer in radical form.
Answers
a can be found using the sine function. Recall sin = (opp)/(hyp)
Here [tex]sin 60 = \frac{a}{8} [/tex]
[tex] \frac{ \sqrt{3} }{2}= \frac{a}{8} [/tex]
[tex]2a=8 \sqrt{3} [/tex]
[tex]a=4 \sqrt{3} [/tex]
The base can be found using the sin of 30 degrees as this is a 30-60-90 right triangle.
[tex]sin30= \frac{b}{8} [/tex]
[tex]\ \frac{1}{2} = \frac{b}{8} [/tex]
[tex]b=4[/tex]
The area of the triangle in the picture is given by [tex]A=( \frac{1}{2} )bh= (\frac{1}{2})(4)( \frac{ \sqrt{3} }{2} )= \sqrt{3} [/tex].
The base of the pyramid is a hexagon which can be divided into 6 triangles each of which is double the area of the one we just found. So the area of the base = 2(area of the triangle we found)(6) = [tex]12 \sqrt{3} [/tex]
The answer is:
area of base = [tex]12\sqrt{3}[/tex]
Hope it helps!
Calculate the slant height for the given square pyramid. Round to the nearest tenth.
Pyramid base = 6 cm
Height = 5 cm
A. 6.2 cm
B. 5.8 cm
C. 7.8 cm
D. 7.2 cm
Answers
the answer would have to be 7.8
Answer: 7.8
Step-by-step explanation:
You roll two fair dice, a green one and a red one. (a) what is the probability of getting a sum of 6? (enter your answer as a fraction.)
Answers
Answer:
Step-by-step explanation:
Which equation is correct for the perpendicular bisector of the line segment whose endpoints are (−1,1) and (7,−5)?
Answers
Perpendicular slope = 4/3
Midpoint = ((-1+7)/2 , (1+(-5))/2) = (3, 3)
equation:
y = mx + c
y = 4/3 x + c
at point (3, 3)
3 = 4/3(3) + c
c = 3 - 4 = -1
y = 4/3 x - 1 or 3y = 4x - 3
When fritz drives to work his trip takes 40 minutes, but when he takes the train it takes 30 minutes. find the distance fritz travels to work if the train travels an average of 15 miles per hour faster than his driving. assume that the train travels the same distance as the car?
Answers
convert minutes to hour first because the question talking about 15 mile per hour
40 mins = 40/60 2/3 hrs
30 mins = 30/60 = 1/2hrs
Assume that s be the speed when Fritz driving, so
s + 15 will be the speed of the train.
We know the time we know the speed, Next
distance that Fritz drive = [tex] \frac{2}{3}s[/tex]
distance the train travel = [tex] \frac{1}{2}(s+15)[/tex]
The question: Assume that the train travels the same distance as the car
==> [tex] \frac{2}{3}s = \frac{1}{2}(s+15)[/tex]
==> [tex] \frac{2}{3}s = \frac{1}{2}s + \frac{15}{2}[/tex]
==> [tex] \frac{2}{3}s - \frac{1}{2}s = \frac{15}{2}[/tex]
==> [tex] \frac{1}{6}s = \frac{15}{2}[/tex]
==> [tex] \frac{6}{1} * \frac{1}{6}s = \frac{15}{2} * \frac{6}{1}[/tex]
==> [tex] s = 45 [/tex]
Now we know that Fritz drive at 45 mph,
distance = [tex] \frac{2}{3} * 45 = 30 miles [/tex]
The diameter of a circle is 8 kilometers. What is the angle measure of an arc kilometers long?
Answers
The circle has a diameter of 8 kilometers, so the perimeter would be:
perimeter= pi * diameter
perimeter= 22/7 * 8 kilometers= 25.14 kilometers
A full perimeter of the circle, which is 25.14km, has 360° angle. So 1km arc would be: 1km/ 25.14 km * 360°= 14.32°
This is the angle measured in radians for an arc that is 1 kilometre long is [tex]\({\theta = \frac{360}{\pi^2}}\)[/tex] radians.
To find the angle measure of an arc in radians, we use the formula:
[tex]\[ \text{Angle in radians} = \frac{\text{Arc length}}{\text{Radius}} \][/tex]
Given that the diameter of the circle is 8 kilometres, we can find the radius by dividing the diameter by 2:
[tex]\[ \text{Radius} = \frac{\text{Diameter}}{2} = \frac{8 \text{ km}}{2} = 4 \text{ km} \][/tex]
The arc length is given as [tex]\(\pi\)[/tex] kilometres. Now we can calculate the angle in radians subtended by the arc:
[tex]\[ \theta = \frac{\text{Arc length}}{\text{Radius}} = \frac{\pi \text{ km}}{4 \text{ km}} = \frac{\pi}{4} \][/tex]
However, this is not the final answer. We need to find the angle measured in degrees. To convert radians to degrees, we use the conversion factor:[tex]\[ 1 \text{ radian} = \frac{180}{\pi} \text{ degrees} \][/tex]
Thus, the angle in degrees is:
[tex]\[ \theta_{\text{degrees}} = \theta_{\text{radians}} \times \frac{180}{\pi} = \frac{\pi}{4} \times \frac{180}{\pi} = \frac{180}{4} = 45 \text{ degrees} \][/tex]
Now, we need to find the angle measured in radians that correspond to an arc length of 1 kilometre. Using the same formula:
[tex]\[ \theta_{\text{1 km}} = \frac{1 \text{ km}}{4 \text{ km}} = \frac{1}{4} \text{ radians} \][/tex]
To find the number of radians in the entire circle, we multiply by [tex]\(2\pi\)[/tex](since the circumference is [tex]\(2\pi r\)[/tex] and the radius is 4 km):
[tex]\[ \text{Full circle in radians} = 2\pi \times 4 \text{ km} = 8\pi \text{ radians} \][/tex]
Now, we want to find how many times the arc length of 1 km fits into the full circle's circumference:
[tex]\[ \text{Number of arcs} = \frac{8\pi \text{ radians}}{1/4 \text{ radians}} = 32\pi \][/tex]
This represents the number of times the 1 km arc goes around the circle, which is also the measure of the angle in radians that corresponds to a 1 km arc. Since the full circle is [tex]\(360\)[/tex] degrees, the angle measured in degrees for the 1 km arc is:
[tex]\[ \theta_{\text{1 km degrees}} = 32\pi \times \frac{180}{\pi} = 32\pi \times \frac{360}{2\pi} = 32 \times 180 = 5760 \text{ degrees} \][/tex]
However, this is not the final answer. We made a mistake in the calculation. We should not multiply the number of arcs by the full circle's degrees. Instead, we should divide the full circle's degrees by the number of arcs to find the angle measure for one arc:
[tex]\[ \theta_{\text{1 km degrees}} = \frac{360}{32\pi} = \frac{360}{\pi} \times \frac{1}{32} = \frac{360}{\pi^2} \times \frac{\pi}{32} = \frac{360}{\pi^2} \text{ degrees} \][/tex]
To convert this back to radians, we multiply by [tex]\(\frac{\pi}{180}\)[/tex]:
[tex]\[ \theta_{\text{1 km radians}} = \frac{360}{\pi^2} \times \frac{\pi}{180} = \frac{360}{\pi^2} \text{ radians} \][/tex]
This is the angle measured in radians for an arc that is 1 kilometre long.
SHALL CROWN BRAINLIEST!
Which sentence uses a double negative correctly?
A. I was not displeased by my performance at the recital.
B. I don't have no hat to wear to the game.
C. Fernando's parents won't give him no money for lunch.
D. Molly never gets no respect from her sister.
I vaguely suspect the answer is A, but I need someone to confirm my suspicions.
Answers
Another example is “We don’t need no education" (and perhaps Pink Floyd was wrong and they did in fact need an education to understand why double negative usage was wrong!)However, it would not be wrong to say "I don’t need an education because I don’t believe education is important." Even though don’t is a negative used twice in the sentence, "I don’t need an education" was one clause and "I don’t believe education is important" is a separate clause entirely.
Answer:
it's A u were correct
Step-by-step explanation:
Can anyone help me please
Answers
A = (-3,3)
B = (-3,1)
C = (-1,1)
Add 5 to each x coordinate. Subtract 2 from each y coordinate
Following those rules, we have A(-3,3) turn into A ' (2, 1)
And the point B(-3,1) turn into B ' (2,-1)
and C (-1,1) turn into C ' (4,-1)
The new vertices A ', B ' and C' are
A ' = (2,1)
B ' = (2,-1)
C ' = (4,-1)
So these vertices are in quadrant I and quadrant IV
A ' is the point in quadrant I
B ' and C ' are in quadrant IV
Using the definitions of odd and even functions , explain why y=sin x+1 is neither odd or even
Answers
[tex]f(-x) = f(x)[/tex]
[tex]f(-x) = -f(x)[/tex]
I'm going to plug in π/2 to check if the odd and even function definition work for this problem or not. Let's do that:
[tex]f(-x) = f(x)[/tex]
[tex]f(- \frac{ \pi }{2} ) = 1 + sin(- \frac{ \pi }{2} ) = 1-1 = 0[/tex]
[tex]f(-x) = -f(x)[/tex]
[tex]f( \frac{ \pi }{2}) = 1+sin( \frac{ \pi }{2}) = 1+1 = 2 [/tex]
As we can see, 0 ≠ 2. Hence, the function is neither odd nor even.
Final answer:
The function y = sin x + 1 is neither even nor odd because it does not satisfy the conditions f(x) = f(-x) for even functions and f(-x) = -f(x) for odd functions after substitution and simplification.
Explanation:
An even function is defined as a function that satisfies the condition f(x) = f(-x), showing symmetry about the y-axis. An odd function, on the other hand, satisfies the condition f(-x) = -f(x), indicating symmetry about the origin. To determine if y = sin x + 1 is an odd or even function, we must check these conditions.
Applying the even function definition, we would expect sin(-x) + 1 = sin(x) + 1 which is not true because sin(-x) = -sin(x) and thus does not satisfy the required symmetry. When we apply the odd function test, we expect -(sin x + 1) = sin(-x) + 1, which also doesn't hold because -sin(x) - 1 does not equal sin(-x) + 1. Therefore, y = sin x + 1 is neither odd nor even.