Answer:
Step-by-step explanation:
I discounted the 2-m ramp. If we are supposed to be looking for the length of time the ride is above 38 m from the ground, that translates to 36 m from the very bottom of the circle that is the Ferris wheel (where the wheel would meet the "ground"). I first found the circumference of the circle:
C = 48(3.1415) so
C = 150.792 m
I enclosed this circle (the Ferris wheel is a circle) in a square and then split the square in 4 parts. Each square has a quarter of the circle in it. If you divide the circumference by 4, that means that the arc length of each quarter circle is a length of 37.698 m. But that doesn't put us 36 m above the ground, that only puts us 24 m above the ground (remember the diameter of the circle is 48, so half of that is 24, the side length of each of the 4 squares). What that means to us (so far, and we are not at the answer yet) is that when the height off the ground is 24 m, a car that starts at the bottom of the ride has traveled 37.698 m around the circle. Traveling in an arc around the outside of the circle is NOT the same thing as a height off the ground. Going around a circle takes longer because of the curve. In other words, if the car has traveled 37.698 m around the outside of the circle, it is NOT 37.698 m above the ground...it's only 24 m above the ground. Hence, the reason I enclosed the circle in a square so we have both the circle's curve {arc length} and height above the ground {side of the square}). As the car travels farther along the outside of the circle it gets higher off the ground. If one quarter of the circle is 24 m above the ground, we need to figure out how much farther around the circle we need to go so we are 36 m above the ground. The height difference is 36 - 24 = 12m. we need now to find how long the arc length of the circle is that translates to another 12 m (the difference between the 24 we found and the 36 total). Using right triangle trig I found that arc length to be 12.566. The total arc length on the circle that translates to 36 m above the ground is 50.26437 m.
Going back to the beginning of the problem, the circumference of the circle is 150.792, and it makes one complete revolution in 5 minutes. That means that a car will travel 30.1584 m in 1 minute. Since this is the case, we can use proportions to solve for how long it takes to get 36 m above the ground:
[tex]\frac{m}{min}:\frac{30.1584m}{1min}=\frac{50.26437m}{xmin}[/tex] and cross multiply:
30.1584x = 50.26437 so
x = 1.6667 minutes, the time it takes to reach a height of 36 m. BUT this is not what the question is asking. The question is asking how long it's HIGHER than that 36 m. Let's think.
The car starts at the bottom of the ride, gets to a height of 36 m, keeps going around the circle to its max height of 48 m, then eventually comes back down and keeps going til it's back on the ground. That means that there is a portion at the top of the wheel that is above 36 m. If it goes 50.2647 m around the circle til it's at 36 m, then when it passes the max height and drops back to 36 m, it's 50.2647 m around the other side of the circle. We just found that to travel that 50.2647 m, it took the car 1.6667 minutes. We travel this distance twice (once meeting the height going up and then again coming down) so that takes up 3.3334 minutes.
5 minutes - 3.3334 minutes leaves us off 36 m above the ground for 1.6664213 minutes.
Doanh nghiệp bán trả góp 1 bất động sản có giá thanh toán là 32.000trđ . Thu điều cả vốn lẫn lãi trong 10 năm với lãi suất trả chậm là 10% / năm . Xác định số vốn phải thu ở năm thứ 6 ?
Answer:
Step-by-step explanation:
Eight years ago, the daughters age was thrice the son's age. Now the daughter's age is 4 years more than the son's age. Find their present ages.
Answer:
Let s be the son’s current age and d be the daughter’s current age. The system of equations is:
s - 10 = 2(d - 10)
s = 3 + d
Since s is already set to an equation, we can use the substitution method for s in the other equation:
s = 3 + d
s - 10 = 2(d - 10)
3 + d - 10 = 2(d - 10)
Simplify and solve for d:
3 + d - 10 = 2(d - 10)
-7 + d = 2d - 20
-7 = d - 20
13 = d
The daughter is 13 years old. To solve for the son’s age, we will plug in the solution for d into one of the equations. The second one is simpler so we will use that:
s = 3 + d
s = 3 + 13
s = 16
The son is 16 years old. Let us use the other equation to check our solutions:
s - 10 = 2(d - 10)
16 - 10 = 2(13 - 10)
6 = 2(3)
6 = 6
It checks out. The son is 16 years old, and the daughter is 13 years old.
The present age of the daughter and son are 14 and 10 years respectively.
Let the age of the daughter be x
Let the age of the son be y
If the daughter's age is 4 years more than the son's age now, then,
x = y + 4 ............. 1
If Eight years ago, the daughters' age was thrice the son's age, then;
Daughter = x - 8
Son = y - 8
Hence, x - 8 =3(y - 8).................. 2
Substitute equation 1 into 2 to have:
x - 8 =3(y - 8).
y + 4 - 8 = 3(y - 8)
y - 4 = 3y - 24
y - 3y = -20
-2y = -20
y = 10
Recall that x = y + 4
x = 10 + 4
x = 14
Hence the present age of the daughter and son are 14 and 10 years respectively.
LEarn more here: https://brainly.com/question/16510024
Which system of linear inequalities is graphed?
Answer:
The first one.
Step-by-step explanation:
Graph lines as if the inequalities were equal signs.
X = -3 is a vertical line at x = -3, because it's less than we shade to the left. All numbers less than -3 are to the left. The line is dashed because there is no equal to. Only less than. The line is not included in the solution set.
y = -x - 1 is a line with a y-intercept of -1 and a slope of -1. All values that are less that y are below the line. Because it's less than or equal to the line is solid.
Answer:
A
Step-by-step explanation:
The vertical line is dotted at -3 and shaded to the left
x < -3
This gives us two choices left
A and C
The other line has a y intercept at -1 and is solid and shaded to the left
It is of the form
y ≤ mx+1
We know the slope is negative since is goes down from left to right
The only Choice is A
the length of a photograph is 11.4 inches if the photo is enlarged so that its length is increased by 2.25 inches what the new length
We know
[tex] \\ \sf \longmapsto \: new \: length = length + increased \: length \\ \\ \sf \longmapsto \: new \: length = 11.4 + 2.25 \\ \\ \sf \longmapsto \: new \: length = 13.65in[/tex]
sin pi/3 __ __ pi/6 = 1/2(sin pi/2 + sin pi/6)
I think I’m just supposed to fill in the blank? (question off of a p e x) please give explanation!
Notice that
• π/2 = π/3 + π/6
• π/6 = π/3 - π/6
Recall the angle sum identities for sine:
sin(x + y) = sin(x) cos(y) + cos(x) sin(y)
sin(x - y) = sin(x) cos(y) - cos(x) sin(y)
By adding these together, we get
sin(x + y) + sin(x - y) = 2 sin(x) cos(y)
==> sin(x) cos(y) = 1/2 (sin(x + y) + sin(x - y))
Now take x = π/3 and y = π/6 :
sin(π/3) cos(π/6) = 1/2 (sin(π/2) + sin(π/6))
So the blank should be filled with cos.
I only need the answer
Answer:
1
Step-by-step explanation:
The given equation of the function is y = -a·(x - h)² + 1
The positive constants of the equation = a, and h
The points the function crosses the x-axis = 2, and 4
Where the function crosses the x-axis, y = 0, and x = 2, and 4, therefore, when x = 2, we have;
y = 0 = -a·(2 - h)² + 1
When x = 4, we have;
0 = -a·(4 - h)² + 1
-a·(2 - h)² + 1 = -a·(4 - h)² + 1
-a·(2 - h)² = -a·(4 - h)²
(2 - h)² = (4 - h)²
±(2 - h) = +#±(4 - h)
When
(2 - h) is negative, and (4 - h) is positive, but the same magnitude, we have';
-(2 - h) = +(4 - h)
2·h = 4 + 2 = 6
h = 3
0 = -a·(4 - h)² + 1 = -a·(4 - 3)² + 1 = -a + 1
Therefore, a = 1
The graph shows the function f(x) = 2x
What is the value of x when fx) = 8?
Answer:
4 = x
Step-by-step explanation:
f(x) =2x
Let f(x) = 8
8 =2x
Divide each side by 2
8/2 = 2x/2
4 = x
Answer:
4
Step-by-step explanation:
f(x) = 2x
When f(x) = 8, x = 8/2 = 4.
Hope this helped,
~cloud
Two linear equations are shown.
A coordinate grid with 2 lines. The first line is labeled y equals StartFraction one-third EndFraction x plus 2 and passes through (negative 6, 0) and (0, 2). The second line is labeled y equals StartFraction 4 over 3 EndFraction minus 5.
What is the solution to the system of equations?
(7, 4)
(7, StartFraction 13 over 3 EndFraction)
(8, StartFraction 14 over 3 EndFraction)
(9, 7)
Answer:
(7, 13/3)
Step-by-step explanation:
Given the expressions
y = 1/3x + 2 and the second line y = 4/3x - 5
Equating both expressions
1/3x + 2 = 4/3x - 5
1/3x - 4/3x = -5 - 2
-3/3x = -7
-x = -7
x = 7
Substitute x = 7 into any of the equations
Using y = 1/3 x + 2
y = 1/3(7) + 2
y = 7/3 + 2
y = (7+6)/3
y = 13/3
Hence the solution to the system of the equation is (7, 13/3)
Answer:
(7,13/3) is your answer, otherwise known as answer choice B.
Step-by-step explanation:
sec²x + cosec²x ≡sec²xcosec²x
proving qn pls i nd it by tdy
Step-by-step explanation:
sec²x + cosec²x = sec²x.cosec²x
1/cos²x + 1/sin²x = 1/cos²x.1/sin²x
or, (sin²x+cos²x)/sin²x.cos²x = 1/(sin²x.cos²x)
or, 1/(sin²x.cos²x) = 1/(sin²x.cos²x)
Hence,
sec²x + cosec²x = sec²x.cosec²x proved!!
Find the distance between the points (-2, -10) and (-9,-5) on a coordinate plane.
Answer:
√74
Step-by-step explanation:
Plans for a new shopping center call for buildings directly across the sidewalk from each other to be congruent. This computer printout shows a clothing store.
If the vertices of a home improvement store are located at (−x1,y1), (−x2,y2), (−x3,y3), and (−x4,y4), will the home improvement store be congruent to the clothing store?
Answer:
Yes, both stores will be congruent
Step-by-step explanation:
The given coordinates of the vertices of the home improvement store are;
(-x₁, y₁), (-x₂, y₂), (-x₃, y₃) and (-x₄, y₄)
The coordinates of the vertices of the clothing store are;
(x₁, y₁), (x₂, y₂), (x₃, y₃) and (x₄, y₄)
Therefore, the coordinates of the vertices of the home improvement store, corresponds to the coordinates of the vertices of the image of the reflection of the clothing store across the sidewalk (which is the y-axis)
A reflection of (x, y) across the y-axis gives (-x, y)
Given that a reflection is a rigid transformation, the dimensions (lengths and angles between corresponding sides) of the home improvement store and the clothing store are equal, therefore, the home improvement store will be congruent to the clothing store.
Answer: yes, because the home improvement store is a reflection of the clothing store.
Step-by-step explanation:
Imagine math!!!
Find the value of x that will make L||M.
6x + 8
4x + 2
X =[?]
Answer:
6x+8+4x+2=180
so!! 10x+10=180
10x=170
x=17
Answer:
[tex]x=17[/tex]
Step-by-step explanation:
The two angles labelled [tex]6x+8[/tex] and [tex]4x+2[/tex] are co-interior angles. When two parallel lines are cut by a traversal, co-interior angles are supplementary, meaning they add up to 180 degrees. Therefore, if line L is parallel to line M, [tex]6x+8[/tex] and [tex]4x+2[/tex] must be supplementary:
[tex]6x+8+4x+2=180[/tex]
Combine like terms:
[tex]10x+10=180[/tex]
Subtract 10 from both sides:
[tex]10x=170[/tex]
Divide both sides by 10:
[tex]x=\frac{170}{10}=\boxed{17}[/tex]
PLEASE HELP ASAP 30 POINTS
Answer:
I don't know how to do please let me I will try solve the question
help help............
Answer:
please send the pic again clearly
Answer:
I hope it will help you
Step-by-step explanation:
please make me brainlestthank u
I'm not sure how to answer this!!
Answer:
I think it's a
Step-by-step explanation:
hsjshbwibs hshhsvsu hshsbsbus
Solve using the Pythagorean identity
Answer:
Solution given
Cos[tex]\displaystyle \theta_{1}=\frac{3}{5}[/tex]
consider Pythagorean theorem
[tex]\bold{Sin²\theta+Cos²\theta=1}[/tex]
Subtracting [tex]Cos²\theta[/tex]both side
[tex]\displaystyle Sin²\theta=1-Cos²\theta[/tex]
doing square root on both side we get
[tex]Sin\theta=\sqrt{1-Cos²\theta}[/tex]
Similarly
[tex]Sin\theta_{1}=\sqrt{1-Cos²\theta_{1}}[/tex]
Substituting value of [tex]Cos\theta_{1}[/tex]
we get
[tex]Sin\theta_{1}=\sqrt{1-(\frac{3}{5})²}[/tex]
Solving numerical[tex]Sin\theta_{1}=\sqrt{1-(\frac{9}{25})}[/tex]
[tex]Sin\theta_{1}=\sqrt{\frac{16}{225}}[/tex]
[tex]Sin\theta_{1}=\frac{\sqrt{2*2*2*2}}{\sqrt{5*5}}[/tex]
[tex]Sin\theta_{1}=\frac{4}{5}[/tex]
Since
In IVquadrant sin angle is negative
[tex]\bold{Sin\theta_{1}=-\frac{4}{5}}[/tex]
Answer:
[tex]\sin(\theta_1)=-\frac{4}{5}[/tex]
Step-by-step explanation:
We'll use the Pythagorean Identity [tex]\cos^2(\theta)+\sin^2(\theta)=1[/tex] to solve this problem.
Subtract [tex]\cos^2(\theta)[/tex] from both sides to isolate [tex]\sin^2(\theta)[/tex]:
[tex]\sin^2(\theta)=1-\cos^2(\theta)[/tex]
Substitute [tex]\cos(\theta)=\frac{3}{5}[/tex] as given in the problem:
[tex]\sin^2(\theta_1)=1-(\frac{3}{5}^2)[/tex]
Simplify:
[tex]\sin^2\theta_1=1-\frac{9}{25}[/tex]
Combine like terms:
[tex]\sin^2\theta_1=\frac{16}{25}[/tex]
For [tex]a^2=b[/tex], we have two solutions [tex]a=\pm \sqrt{b}[/tex]:
[tex]\sin\theta_1=\pm \sqrt{\frac{16}{25}},\\\begin{cases}\sin \theta_1=\frac{4}{5},\\\sin \theta_1=\boxed{-\frac{4}{5}}\end{cases}[/tex]
Since the sine of all angles in quadrant four return a negative output, [tex]\frac{4}{5}[/tex] is extraneous and our answer is [tex]\boxed{\sin(\theta_1)=-\frac{4}{5}}[/tex]
a bag contains 3 red marbles, 5 yellow marbles, and 2 green marbles. what is the probability that you will select 2 green marbles in a row if you do not replace the first marble? A) 0.020 B) 0.02 C) 0.040 D) 0.200
Answer:
B
Step-by-step explanation:
find the probability of picking the first green marble, which would be 2/10
then afterwards once the marble is removed, it would be 1/9
Multiply both 2/10 and 1/9 to get 0.022, which rounds to 0.02
Answer:
0.02
Step-by-step explanation:
3+5+2 = 10
to choose 1 green the probability is 2/10 = 1/5
if we do not replace it, then there are now 9 marbles left and only 1 green left, so 1/9
to find them both in a row, multiply
1/5 * 1/9 = 1/45 = 0.02222
A container of cream cheese weighs 250 grams, which is equivalent to 8.8 ounces. Calculate the missing conversions
Answer:
the picture below has the answer
Step-by-step explanation:
The missing numbers are 312.5 and 35.2
Mọi người giúp em với
Answer:
bka bla bla bla sorry I newbie
Instructions: Point R is the centroid. Find DU if DR = 14.
Which number is rational?
√2
Pi
Square root of 10
Square root of 16
Answer:
[tex]\sqrt{16}[/tex] is rational number
Step-by-step explanation:
Rational number is of the form p/q, where q ≠ 0. It may be a terminating number or non terminating repeating number.
√2 is irrational number as it is non terminating non repeating number
π is irrational number as it is non terminating non repeating number
√10 is irrational number as it is non terminating non repeating number.
[tex]\sqrt{16}=\sqrt{4*4}=4[/tex]
[tex]\sqrt{16}[/tex] is a rational number
Which is the angle of elevation from C to B?
Answer:
Angle of elevation = ∠4
Step-by-step explanation:
Angle of elevation of a point point from another point is the angle formed between the line joining these points and the horizontal line.
Therefore, angle of elevation of point B from a point C = ∠4
Option with angle 4 will be the answer.
Can someone help me with this math homework please!
Answer:
(-3,-6) and (-3,2)
Step-by-step explanation:
A line with an undefined slope is vertical. In this case it must have x coordinates equal to -3
If x=3 ,y=4 than what is the value?
[ INDICES]- Simplify :
1. [tex] \large{ \tt{\frac{ {13}^{ \: 2x + 1} - 5 \times {169}^{x} }{9 \times {169}^{x} } }}[/tex] [ Ans : 2 ]
2. [tex] \large{ \tt{ \frac{ {9}^{ \: n + 2} + 10 \times {9}^{n} }{ {9}^{n + 1} \times 11 - 8 \times {9}^{n} }}}[/tex] [ Ans : 1 ]
- Please show your workings! :)
Step-by-step explanation:
Hey there!
Please see attached picture for your answer!
Hope it helps!
Answer is in the attachment.
note:
make a slight change in question 1;
Scarlett made a profit of $250.00 with her mobile car wash company
Not enough information to solve..... Please make your question more clear
The ordered pair (2, −4) is a solution of which system?
Answer:
option 1
Step-by-step explanation:
y ≤ x - 2
-4 ≤ 2-0
-4 ≤ 2 Satisfies the inequality
y ≥ - x - 4
-4 ≥ - 2- 4
-4 ≥ - 6 (2 , -4) satisfies the inequality
find the sum of (x²+3xy+y²)+(x³+3x²y+2xy²+y³)
1 Which one of the following expression represents the sum of the expressions (5x - 13xy + 14y) and (12xy - 6x - 12y)?
Answer:
(12xy-6x -12y)
12xy-18xy
6xy
Answer:
- xy - x + 2y
Step-by-step explanation:
5x - 13xy + 14y + 12xy - 6x - 12y ← collect like terms
= (- 13xy + 12xy) + (5x - 6x) + (14y - 12y)
= - xy - x + 2y
Can someone help me with this math homework please!
Answer:
Step-by-step explanation:
