Answer: 86.6ft closer to the ground.
Step-by-step explanation:
The diameter of the wheel is 200ft
Then the radius, half of the diameter, is: r = 200ft/2 = 100ft.
Initially, the seat is at the same level that the center of the wheel.
And the distance between the center of the wheel and the bottom is the radius.
Then the initial position is at an angle of 0° from the x-axis. (where the (0,0) of this axis coincides with the center of the wheel=
Now, the wheel rotates 60°. (downwards, so we actually could use -60° measuring from the positive x-axis)
And thinking in this as a triangle rectangle, where the opposite angle is 60°, we can calculate the displacement in the vertical direction as:
y = sin(-60°)*R
y = sin(-60°)*100ft = -86.6ft
So the seat is 86.6ft closer to the ground.
The seat is [tex]86.6feet[/tex] closer to the ground
The seat will be closer by the height it drops when the Ferris wheel turns downwards by [tex]60^{\circ}[/tex].
The height, and the radius of the Ferris wheel form the opposite and the hypotenuse of a [tex]60^{\circ}[/tex] right-angled triangle. Since the diameter of the Ferris wheel is 200feet, the radius will be 100feet. So we have
[tex]sin60^{\circ}=\frac{opp}{hyp}=\frac{h}{100}\\\\h=100\times sin60^{\circ}\\=100\times 0.8660\\=86.6[/tex]
So the seat is [tex]86.6feet[/tex] closer to the ground
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Alex’s house (point F) lies on the same street as her school (point H). Alex’s bus stop (point G) lies between her house and her school.
Given FG = (2x) meters, GH = 1,000 meters, and FH = 1,200 meters, what is x?
The value of x in the expression will be 100.
What is a line segment?A line segment in geometry is a section of a line that has two clearly defined endpoints and contains every point on the line that lies within its confines.
Given that FG = (2x) meters, GH = 1,000 meters, and FH = 1,200 meters,
The value of x will be calculated by making an equation for the line segment below:-
FG + GH = FH
2X+1000=1200
2X = 1200 - 1000
2X = 200
X = 100 meters
2X + 1000= 1200
Therefore, the value of x in the expression will be 100.
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Can I write (3x-1)(3x+1) as (x-1/3)(x+1/3)?
Answer:
yes
Step-by-step explanation:
[tex](3x-1)(3x+1)=9x^{2}-1[/tex] [tex]=\frac{9x^{2} }{9}-\frac{1}{9}=[/tex] [tex]x^{2} -\frac{1}{9}[/tex]
[tex](x-1/3)(x+1/3)=x^{2} -\frac{1}{9}[/tex]
If a = 3 and b = 4, then find the value of 2a + 3b A. 15 B. 16 C. 17 D. 18
Answer:
18
Step-by-step explanation:
2a+3b
2•3+3•4
6+12
18
Answer:
2124+272cd
Step-by-step explanation:
Help please! Any help is appreciated
Answer: The answer is (-∞, ∞)
Step-by-step explanation:I hope this helps!
Yesterday at 4pmn, I was 95 degrees outside. Every hour after that, the temperature dropped 3 degrees. What was the temperature at 8pm
Answer:
83 degress
Step-by-step explanation:
We know that every hour it dropped 8 degress. If it dropped from 4pm to 8pm, that means it dropped 4 times. 3x4=12 so we do 95-12 which equals 83.
What integer describes gaining 14 pounds ?
Answer:
14
Step-by-step explanation:
Since gaining fourteen pounds means going in a positive direction, we can say the gain of fourteen pounds numerically as 14.
Let x, y, z be numbers. (x2 yz4)3 =
Which point is located in quadrant IV?
What is rhe price of the computer be after the mark down?
Answer:
C.$150
Step-by-step explanation:
The sales man told her that he would sell it to he for ⅓ of the marked price.
Given:
Marked Price= $450
⅓
Required:
⅓ of the marked price or $450
Formula:
⅓*$450
Solution:
⅓ of $450
⅓*$450
$450/3
$150
Hope this help ;) ❤❤❤
Answer:
A.180
Step-by-step explanation:
Solve for x: 5x +1(3x + 6) > 14
Answer:
5x+3x+6>14
8x>14-6
8x>8
divide both sides by 8
x>1
What is the value of a if (2a+3)−(4a−8)=7?
Answer:
Step-by-step explanation:
2a + 3 - 4a + 8 = 7
-2a + 11 = 7
-2a = -4
a = 2
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{a = 2}}}}}[/tex]
Step-by-step explanation:
[tex] \sf{(2a + 3) - (4a - 8) = 7}[/tex]
When there is a ( - ) in front of an expression in parentheses , change the sign of sign of each term in the expression
[tex] \longrightarrow{ \sf{2a + 3 - 4a + 8 = 7}}[/tex]
Collect like terms
[tex] \longrightarrow{ \sf{ - 2a + 3 + 8 = 7}}[/tex]
Add the numbers: 3 and 8
[tex] \longrightarrow{ \sf{ - 2a + 11 = 7}}[/tex]
Move 11 to right hand side and change it's sign
[tex] \longrightarrow{ \sf{ - 2a = 7 - 11}}[/tex]
Subtract 11 from 7
[tex] \longrightarrow{ \sf{ - 2a = - 4}}[/tex]
Divide both sides by -2
[tex] \longrightarrow{ \sf{ \frac{ - 2a}{ - 2} = \frac{ - 4}{ - 2} }}[/tex]
Calculate
[tex] \longrightarrow{ \sf{a = 2}}[/tex]
Hope I helped!
Best regards! :D
19. Amy has 8 coins worth $1.40. Some of the coins are nickels and some are quarters. How
many of each coin does Amy have?
Answer:
5 quarters and 3 nickels
Step-by-step explanation:
x = nickels
y = quarters
x + y = 8
x(0.05) + y(0.25) = 1.40
3 + 5 = 8
3(0.05) + 5(0.25) = 1.40
0.15 + 1.25 = 1.40
1.25 + 0.15 = 1.40
Let f be the function defined by f(x)=cx−5x^2/2x^2+ax+b, where a, b, and c are constants. The graph of f has a vertical asymptote at x=1, and f has a removable discontinuity at x=−2. (a) Show that a=2 and b=−4. (b) Find the value of c. Justify your answer. (c) To make f continuous at x=−2, f(−2) should be defined as what value? Justify your answer. (d) Write an equation for the horizontal asymptote to the graph of f. Show the work that leads to your answer.
Answer:
a) [tex]a = 2[/tex] and [tex]b = -4[/tex], b) [tex]c = -10[/tex], c) [tex]f(-2) = -\frac{5}{3}[/tex], d) [tex]y = -\frac{5}{2}[/tex].
Step-by-step explanation:
a) After we read the statement carefully, we find that rational-polyomic function has the following characteristics:
1) A root of the polynomial at numerator is -2. (Removable discontinuity)
2) Roots of the polynomial at denominator are 1 and -2, respectively. (Vertical asymptote and removable discontinuity.
We analyze each polynomial by factorization and direct comparison to determine the values of [tex]a[/tex], [tex]b[/tex] and [tex]c[/tex].
Denominator
i) [tex](x+2)\cdot (x-1) = 0[/tex] Given
ii) [tex]x^{2} + x-2 = 0[/tex] Factorization
iii) [tex]2\cdot x^{2}+2\cdot x -4 = 0[/tex] Compatibility with multiplication/Cancellative Property/Result
After a quick comparison, we conclude that [tex]a = 2[/tex] and [tex]b = -4[/tex]
b) The numerator is analyzed by applying the same approached of the previous item:
Numerator
i) [tex]c\cdot x - 5\cdot x^{2} = 0[/tex] Given
ii) [tex]x \cdot (c-5\cdot x) = 0[/tex] Distributive Property
iii) [tex](-5\cdot x)\cdot \left(x-\frac{c}{5}\right)=0[/tex] Distributive and Associative Properties/[tex](-a)\cdot b = -a\cdot b[/tex]/Result
As we know, this polynomial has [tex]x = -2[/tex] as one of its roots and therefore, the following identity must be met:
i) [tex]\left(x -\frac{c}{5}\right) = (x+2)[/tex] Given
ii) [tex]\frac{c}{5} = -2[/tex] Compatibility with addition/Modulative property/Existence of additive inverse.
iii) [tex]c = -10[/tex] Definition of division/Existence of multiplicative inverse/Compatibility with multiplication/Modulative property/Result
The value of [tex]c[/tex] is -10.
c) We can rewrite the rational function as:
[tex]f(x) = \frac{(-5\cdot x)\cdot \left(x+2 \right)}{2\cdot (x+2)\cdot (x-1)}[/tex]
After eliminating the removable discontinuity, the function becomes:
[tex]f(x) = -\frac{5}{2}\cdot \left(\frac{x}{x-1}\right)[/tex]
At [tex]x = -2[/tex], we find that [tex]f(-2)[/tex] is:
[tex]f(-2) = -\frac{5}{2}\cdot \left[\frac{(-2)}{(-2)-1} \right][/tex]
[tex]f(-2) = -\frac{5}{3}[/tex]
d) The value of the horizontal asympote is equal to the limit of the rational function tending toward [tex]\pm \infty[/tex]. That is:
[tex]y = \lim_{x \to \pm\infty} \frac{-10\cdot x-5\cdot x^{2}}{2\cdot x^{2}+2\cdot x -4}[/tex] Given
[tex]y = \lim_{x \to \infty} \left[\left(\frac{-10\cdot x-5\cdot x^{2}}{2\cdot x^{2}+2\cdot x-4}\right)\cdot 1\right][/tex] Modulative Property
[tex]y = \lim_{x \to \infty} \left[\left(\frac{-10\cdot x-5\cdot x^{2}}{2\cdot x^{2}+2\cdot x-4}\right)\cdot \left(\frac{x^{2}}{x^{2}} \right)\right][/tex] Existence of Multiplicative Inverse/Definition of Division
[tex]y = \lim_{x \to \pm \infty} \left(\frac{\frac{-10\cdot x-5\cdot x^{2}}{x^{2}} }{\frac{2\cdot x^{2}+2\cdot x -4}{x^{2}} } \right)[/tex] [tex]\frac{\frac{x}{y} }{\frac{w}{z} } = \frac{x\cdot z}{y\cdot w}[/tex]
[tex]y = \lim_{x \to \pm \infty} \left(\frac{-\frac{10}{x}-5 }{2+\frac{2}{x}-\frac{4}{x^{2}} } \right)[/tex] [tex]\frac{x}{y} + \frac{z}{y} = \frac{x+z}{y}[/tex]/[tex]x^{m}\cdot x^{n} = x^{m+n}[/tex]
[tex]y = -\frac{5}{2}[/tex] Limit properties/[tex]\lim_{x \to \pm \infty} \frac{1}{x^{n}} = 0[/tex], for [tex]n \geq 1[/tex]
The horizontal asymptote to the graph of f is [tex]y = -\frac{5}{2}[/tex].
Using asymptote concepts, it is found that:
a) Building a quadratic equation with leading coefficient 2 and roots 1 and -2, it is found that a = 2, b = -4.
b) c = -10, since the discontinuity at x = -2 is removable, the numerator is 0 when x = -2.
c) Simplifying the function, it is found that at [tex]x = -2, f(x) = -\frac{5}{3}[/tex].
d) The equation for the horizontal asymptote to the graph of f is [tex]y = -\frac{5}{2}[/tex]
-------------------------
Item a:
Vertical asymptote at [tex]x = 1[/tex] and discontinuity at [tex]x = -2[/tex] means that the the roots of the quadratic function at the denominator are [tex]x = 1[/tex] and [tex]x = -2[/tex].The leading coefficient is given as 2, thus, we build the equation to find coefficients a and b.[tex]2(x - 1)(x - (-2)) = 2(x - 1)(x + 2) = 2(x^2 + x - 2) = 2x^2 + 2x - 4[/tex]
[tex]2x^2 + ax + b = 2x^2 - 2x - 4[/tex]
Thus a = 2, b = -4.
-------------------------
Item b:
Removable discontinuity at [tex]x = -2[/tex] means that the numerator when [tex]x = -2[/tex] is 0, thus:[tex]-2c - 5(-2)^2 = 0[/tex]
[tex]-2c - 20 = 0[/tex]
[tex]2c = -20[/tex]
[tex]c = -\frac{20}{2}[/tex]
[tex]c = -10[/tex]
-------------------------
Item c:
With the coefficients, the function is:
[tex]f(x) = \frac{-10x - 5x^2}{2x^2 + 2x - 4} = \frac{-5x(x + 2)}{2(x - 1)(x + 2)} = -\frac{5x}{2(x - 1)}[/tex]
At x = -2:
[tex]-\frac{5(-2)}{2(-2 - 1)} = -\frac{-10}{-6} = -(\frac{5}{3}) = -\frac{5}{3}[/tex]
Thus, simplifying the function, it is found that at [tex]x = -2, f(x) = -\frac{5}{3}[/tex]
-------------------------
Item d:
The horizontal asymptote of a function is:
[tex]y = \lim_{x \rightarrow \infty} f(x)[/tex]
Thus:
[tex]y = \lim_{x \rightarrow \infty} \frac{-10x - 5x^2}{2x^2 + 2x - 4} = \lim_{x \rightarrow \infty} \frac{-5x^2}{2x^2} = \lim_{x \rightarrow \infty} -\frac{5}{2} = -\frac{5}{2}[/tex]
The equation for the horizontal asymptote to the graph of f is [tex]y = -\frac{5}{2}[/tex]
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−0.75 − (−
5
2
)+0.4+(−
4
3
)
Answer:
-13
Step-by-step explanation:
Evaluate the following function over the domain {0,1,2,3}. What is the range?
Answer:Another way to identify the domain and range of functions is by using graphs. Because the domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the x-axis. The range is the set of possible output values, which are shown on the y-axis.
range is The zero doesn't matter. You still subtract the lowest number from the highest. If zero is the lowest number, then the highest number is the range. If the set consists of negative numbers, and zero is the highest number, then the lowest number (without its negative sign) is the range.
0
Is the expression 2 • 4x equal to the expression 8x?
Answer:
YESStep-by-step explanation:
[tex]2 . 4x =\\2 \times 4x\\\mathrm{Multiply\:the\:numbers:}\:2\times \:4=8\\\\= 8x[/tex]
Which are examples of unit rates? Check all that apply.
100 students for every 2 buses
1 teacher per 25 students
4 pencils for each student
8 students per team
Answer: 8 students per team and 4 pencils each student
Step-by-step explanation:
Answer:
Both C and D
Step-by-step explanation:
You roll a single die numbered from 1 to 6 twice. The probability of rolling an even number the first time and a 6 the second is the setup. What is the probability "rolling an even number the first time"? (Answer in percentage)
Answer:
The answer is 50%Step-by-step explanation:
step one :
first and foremost we are going to list the sample space related to a die
the same space is S= {1,2,3,4,5,6}= 6
step two:
now the even numbers in the sample space are ={2,4,6}= 3
hence we can solve for the probability of obtaining an even number to be
Pr(even number)= 3/6= 1/2.
step three:
since we are to provide the answer in percentage format, we can easily do this by multiplying the answer by 100 to get the percentage
(1/2)*100= 0.5*100= 50%
aaron walks 2 1/8 miles to his friends house. then, they walk 5/6 miles to the park .finally, aaron walks 1 3/4 miles to get back home.how far did aaron walk today
Answer:did you check and see if anybody asked this question before??
Step-by-step explanation:
The total distance did Aaron walk today is 4.70 miles.
It is required to find the total distance.
What is distance?
The distance of an object can be defined as the complete path travelled by an object .Distance is a scalar quantity that refers to "how much ground an object has covered" during its motion.
Given :
Aaron walks 2 1/8 miles to his friends.
He walk 5/6 miles to the park.
Again he walks 1 3/4 miles to get back home.
Total distance=
2 1/8 miles+5/6 miles+ 1 3/4 miles
=17/8+5/6+7/4
=4.70 miles
Therefore, the total distance did Aaron walk today is 4.70 miles.
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How can you determine what type of solution an equation has when solving? Explain.
Answer: Answer is in the steps
Step-by-step explanation:
If the system of equations have the same slope and same y-intercepts then it means that they have infinitely many solutions.
if the system of equations have the same slope but different y-intercepts it means that they have no solution because they will never intersect but will always form parallel lines.
If the system of equations have different slopes and different y-intercepts or have same y-intercepts and different slopes it means that they have exactly on solution.
Can anyone explain to me why I got this wrong
Answer:
I think your suppose to multiply the lengths together then you multiply the width together and the add those two
Step-by-step explanation:
srry if i am wrong lol
[tex]5(m - 1) = - 25[/tex]
can u help me solve it?
Answer:
-4.
Step-by-step explanation:
5(m - 1) = -25
m - 1 = -5
m = -4.
Answer:
m = -4
Step-by-step explanation:
Divide both sides by the numeric factor on the left side, then solve.
m = -4
Please answer asapWhat is the measure of an exterior angle of a regular 13-sided polygon? Enter your answer as a decimal in the box. Round to the nearest tenth of a degree.
Answer:
Step-by-step explanation:
it is given by the formula=4× 90/ n
where n = number of sides
exterior angle= 4 x 90/13
=360/13=[tex]27.7[/tex]°
5/k = 15/20 what would the k be?
Answer:
20/3
Step-by-step explanation:
5/k=15/20
5/k=3/4
5 x 4/3 = k
k=20/3
Given segment XZ and point Y that lies on XZ find XZ if XY = 7 and YZ = 17
Answer:
24
Step-by-step explanation:
We are given segment XZ and point Y. First, draw a number line. Draw X and Z on either side of the number line. We know that Y is between X and Z since there are the distances of XY and YZ. To find XZ, add the distance of XY and YZ, which are respectively 7 and 17. Adding 7 and 17, we get 24 as the answer.
The value of XZ is 24.
What are Arithmetic operations?Arithmetic operations can also be specified by adding, subtracting, dividing, and multiplying built-in functions. The operator that performs the arithmetic operation is called the arithmetic operator.
+ Addition operation: Adds values on either side of the operator.
For example 12 + 2 = 14
What is a Line Segment?A line segment is defined as a measured path between two places. Line segments can make up any polygon's sides because they have a set length.
The figure given below shows a line segment XZ, where the length of line segment XZ refers to the distance between its endpoints, X and Z.
Given that a line segment XZ and point Y that lies on XZ
XY = 7 and YZ = 17
Here XZ = XY + YZ
X_____________Y_______________Z
⇒ XZ = XY + YZ
Substitute the values of XY = 7 and YZ = 17, we get
⇒ XZ = 7 + 17
Apply the addition operation in the above equation,
⇒ XZ = 24
Therefore, the value of XZ is 24.
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What is the solution of this equation -4z = 24
Answer:
z = -6
Step-by-step explanation:
[tex]-4z=24\\\\\frac{-4z=24}{-4}\\\\ \boxed{z=-6}[/tex]
Hope this helps.
Which value of x is the solution of the equation (2/3)x+(1/2) =(5/6)
Answer:
1/2
Step-by-step explanation:
Step 1:
4/6x + 3/6 + 5/6
Step 2:
4/6x = 2/6
Step 3:
2/6 times 6/4
Answer:
1/2
Hope This Helps :)
please answer ASAP ......
Explain why it might be easier to solve the multiplication problem by changing it from this: 5×87×2, to this: 5×2×87. Use a property of multiplication to justify your reasoning.
Answer:
It makes the calculation easy and quick.
Step-by-step explanation:
Commutative Property of multiplicationThe product of two or more real numbers is not affected by the order in which they are being multiplied. In other words, real numbers can be multiplied in any order because the product remains the same.When you multiply as it is given:
5×87×2=870Step 1) 5×87 = 435Step 2) 435×2 = 870Using the commutative property makes it much easier:
5×2×87 = 870Step 1) 5×2 = 10Step 2) 10* 87 = 870Answer:
see below.
Step-by-step explanation:
its a commutative property of multiplication.
it doesn't matter in order or not... the result will always be the same.
form your example 5×87×2, if you use a calculator it doesn't matter which number you start.
say 2 x 87 x 5 = 870
or 87 x 5 x 2 = 870
or 5 x 2 x 87 = 870
see the results are all the same no matter which way you go.
Which option best completes the following statement?
As a unit of account, money provides a way to determine and compare
OA) money over time.
B) apples.
O C) value.
OD) people.
Apples and people don't make much sense as an answer here, so we can rule out B and D. Choice A can be ruled out as it seems redundant to say "money compares money over time". It makes more sense to say "Money compares value (over time)".