Answer:
The equation of the hyperbola is x²/16 - y²/9 = 1
Step-by-step explanation:
* Lets study the equation of the hyperbola
- The standard form of the equation of a hyperbola with
center (0 , 0) and transverse axis parallel to the x-axis is
x²/a² - y²/b² = 1
- The length of the transverse axis is 2a
- The coordinates of the vertices are (±a , 0)
- The length of the conjugate axis is 2b
- The coordinates of the co-vertices are (0 , ±b)
- The coordinates of the foci are (± c , 0),
- The distance between the foci is 2c where c² = a² + b²
- The distance between the vertex and the focus in-front of it is c - a
* Now lets solve the problem
- The distance from a vertex to the center of the mirror
∵ The vertex of the mirror is (a , 0)
∵ The distance between a vertex and the center of the mirror
is 4 inches
∴ a = 4
∵ The distance between the vertex and a focus in front of the surface
of the mirror is 1
∵ The distance between the vertex and the focus in-front of it is c - a
∴ c - a = 1
∴ c - 4 = 1 ⇒ add 4 to the both sides
∴ c = 5
- The mirror has a horizontal transverse axis and the hyperbola is
centered at (0, 0)
∴ The equation of the hyperbola is x²/a² - y²/b² = 1
- Lets find b from a and c
∵ c² = a² + b²
∵ c = 5 and a = 4
∴ (5)² = (4)² + b²
∴ 25 = 16 + b² ⇒ subtract 16 from both sides
∴ 9 = b² ⇒ take √ for both sides
∴ b = ±3
- Lets write the equation
∴ x²/(4)² - y²/(3)² = 1
∴ x²/16 - y²/9 = 1
* The equation of the hyperbola is x²/16 - y²/9 = 1
The distance of the focus from the center is the sum of the distance from
the focus to the surface and the vertex distance.
Correct response:
[tex]The \ equation \ of \ the \ hyperbola \ that \ models \ the \ mirror \ is \ \underline{\dfrac{x^2}{16} - \dfrac{y^2}{9} = 1}[/tex]Details of the method used to find the equationGiven:
Distance of the vertex from the center = 4 inches
Distance of the focus from the mirror surface = 1 inches
Coordinates of the center of the mirror = (0, 0)
Required:
To write the equation of the hyperbola that can be used to model the mirror
Solution:
The equation of an hyperbola having an horizontal transverse axis is presented as follows;
[tex]\mathbf{\dfrac{(x-h)^2}{a^2} - \dfrac{(y-k)^2}{b^2}} = 1[/tex]Where;
(h, k) = The coordinate of the center
a = Center to vertex distance
b² = c² - a²
Where;
c = The from the center to the vertex
Therefore;
a = 4
(h, k) = (0. 0)
c = 4 + 1 = 5
b² = 5² - 4² = 9
b = √9 = 3
The equation of the hyperbola is therefore;
[tex]\dfrac{(x - 0)^2}{4^2} - \dfrac{(y - 0)^2}{3^2} = \underline{ \dfrac{x^2}{16} - \dfrac{y^2}{9} = 1}[/tex]Learn more about the equation of a hyperbola here:
https://brainly.com/question/9076741
I need help on 8 and 9 i don’t know how to do them lol
Answer:
8) h = 30
r = 16
l= 34
Surface Area= 2514.28
Volume= 8045.71
9) r = 12
h = 2
l = 5/2
Surface Area= 908.08
Volume= 298.42
Step-by-step explanation:
8)
h = 30
r = 16
l=?
Since its is right angled triangle, using pythogras theorem we can find the length of cone
l^2 = h^2 + r^2
l^2 = (30)^2 + (16)^2
l^2 = 900 + 256
l^2 = 1156
Taking square root on both sides
√l^2 = √1156
l = 34
Surface Area = [tex] [tex]\pi r(r+\sqrt{h^2+r^2} )[/tex][/tex]
π = 22/7, r = 16, h=30
Surface Area = [tex]=\frac{22}{7}* 16(16+\sqrt{(30)^2+(16)^2})\\=\frac{22}{7}* 16(16+34)\\=\frac{22}{7}* 800\\=2514.28[/tex]
Volume = [tex]\pi r^2\frac{h}{3}[/tex]
π = 22/7, r = 16, h= 30
Volume = [tex]\frac{22}{7} * (16)^2 *\frac{30}{3}\\=\frac{22}{7} * 256 *10\\= 8045.71[/tex]
9)
r = ?
h = 2
l = 5/2
Since its is right angled triangle, using pythogras theorem we can find the radius of cone
l^2 = h^2 + r^2
(5/2)^2 = (30)^2 + (r)^2
25/4 = 900 + r^2
r^2 = 900 * 4/25
Taking square root on both sides
√r^2 = √144
r = 12
Surface Area = [tex] [tex]\pi r(r+\sqrt{h^2+r^2} )[/tex][/tex]
π = 3.14, r = 12, h=2
Surface Area = [tex]=3.14* 12(12+\sqrt{(12)^2+(2)^2})\\=3.14* 12(12+12.1)\\=3.14* 289.2\\=908.08[/tex]
Volume = [tex]\pi r^2\frac{h}{3}[/tex]
π = 22/7, r = 12, h= 2
Volume = [tex]3.14 * (12)^2 *\frac{2}{3}\\=3.14 * 144 *0.66\\= 298.42[/tex]
Answer:
8) h = 30
Step-by-step explanation:
PLEESE HELP ME I NEED IT PLEASE THIS IS ALL MY PIONTS −4 3/ 5 ÷1 1 /5
let's firstly convert the mixed fractions to improper fractions and then divide.
[tex]\bf \stackrel{mixed}{-4\frac{3}{5}}\implies \cfrac{-4\cdot 5+3}{5}\implies \stackrel{improper}{\cfrac{-23}{5}}~\hfill \stackrel{mixed}{1\frac{1}{5}}\implies \cfrac{1\cdot 5+1}{5}\implies \stackrel{improper}{\cfrac{6}{5}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{-23}{5}\div \cfrac{6}{5}\implies \cfrac{-23}{\begin{matrix} 5 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}}\cdot \cfrac{\begin{matrix} 5 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}}{6}\implies \cfrac{-23}{6}\implies -3\frac{5}{6}[/tex]
Okay I'm assuming this is a mixed fraction -4 ⅗ ÷ 11/5
First step get rid of the mixed fraction.
4 multiplied by 5 is 20 then you add 3 and you get 23
Next step cross cancel
-23 times 11 equals -23
5 5 11
improper fraction so convert to mixed number
answer is -2 1/11
if you're still confused lemme know
Help solve these show little steps if possible
Answer:
a)
x≥3
b)
[tex]t<-\frac{7}{3}[/tex]
c)
y < 28
d)
x > 5/2
Step-by-step explanation:
a)
We have been given the following inequality;
4x-3≥9
add 3 to both sides of the equation,
4x-3+3≥9+3
4x≥12
divide both sides by 4,
x≥3
b)
We have been given the following inequality;
3(t+4)<5
we open the brackets on the left hand side,
3t + 12 <5
subtract 12 on both sides of the equation,
3t + 12 -12 <5-12
3t < -7
divide both sides by 3,
[tex]t<-\frac{7}{3}[/tex]
c)
We have been given the following inequality;
[tex]\frac{2y}{7}<8[/tex]
multiply both sides by 7,
2y < 56
divide both sides by 2,
y < 28
d)
5x + 4 > -3(x-8)
we open the brackets on the right hand side,
5x + 4 > -3x + 24
add 3x to both sides of the inequality,
5x + 4 + 3x > -3x + 24 + 3x
8x + 4 > 24
subtract 4 on both sides,
8x + 4 - 4 > 24 - 4
8x > 20
divide by 8 on both sides,
x > 5/2
Draw a graph that represents the equation y= x-2.
Answer:
Check attached graph
Step-by-step explanation:
Given equation is [tex]y=x-2[/tex].
Now we need to graph the given equation [tex]y=x-2[/tex].
To graph that we can find two points then join them by a straight line.
We are free to plug any number for x say x=0 and x=2
plug x=0
[tex]y=x-2=0-2=-2[/tex]
Hence first point is (0,-2).
plug x=2
[tex]y=x-2=2-2=0[/tex]
Hence first point is (2,0).
Now graph both points and joint them to get final graph as shown below.
Eli ran 9/16 of a mile and walked 1/2 of a mile. How much farther did Eli run than walk?
Write your answer as a fraction or as a whole or mixed number.
Answer: 1/16
Step-by-step explanation:
1/2 would become 8/16 so 9-8 equals 1 and then just add the denominator so 1/16
This is stupid I know lol but I'm having a hard time remembering the difference between a histogram and a bar graph. Can someone please help me find a way for me to remember the differences?
In Bar Graphs;
- Bars have equal space
- One the y-axis, we have numbers & on the x-axis, we have data which can be anything.
In Histograms;
- Bars are fixed
- On the y-axis, we have numbers & and on the x-axis, we have data which in continuous & will always be number.
An easy way you can remember the difference is looking at the spaces of the bars.
A bar graph has gaps
A histogram has no gaps.
Please include explanation! thank you!
L=4 and s=5 I’m to lazy to type it out
Answer:
L= 4
S= 5
Step-by-step explanation:
Given in the question, L+s = 9
So
L= 9-s
Substituting the value of L in the following equation
1.5L + 0.9s = 10.5
1.5 (9-s) + 0.9s = 10.5
13.5 - 1.5s +0.9s = 10.5
13.5 - 10.5 = 1.5s - 0.9s
3= 0.6s
s= 5
Now substituting the value of s in the equation L+s=9, we get the following
L= 9-5
L=4
Find the volume of the sphere.
Either enter an exact answer in terms of Find the volume of π or use 3.14 for Find the volume of the sphere.
Either enter an exact answer in terms π or use 3.14 for π and round your final answer to the nearest hundredth.
Answer:
1436.03 units³
Step-by-step explanation:
The formula for the volume of a sphere of radius r is
V = (4/3)πr³. We'll use 3.14 for π.
Then:
V = (4/3)(3.14)(7 units)³. To the nearest hundredth: 1436.03 units³
Answer:
Step-by-step explanation:
Given
r = 7
pi = 3.14
Formula
V = (4/3) pi * r^3
Solution
V = (4/3) * pi * 343
V = (1.3333) * 3.14 * 343
V = 1435.99 You are going to get a lot of variation in this question: Everything depends on what value you use for 4/3. I used 1.3333 but it does go on. I would try this yourself. Whatever you get, enter it.
You are better off using 3.14 than using pi. You are still going to have to problem of how to represent 4/3
Kim took a total of 8 quizzes over the course of 2 weeks. How many weeks of school will Kim to attend this quarter before she will have taken a total of 20 quizzes? solve using unit rates
5 weeks
8×2.5=20
2×2.5=5
Which is the equation of the given line in standard form?
(3,2) (3,-4)
Options:
x=3
x=-3
y=3
y=3x
Answer:
x = 3
Step-by-step explanation:
Only one of the choices matches the given points:
x = 3
Please help! will mark!
To get the length of AC, you would add AB to BC
AB = 3x
BC = 2x +3
Add together:
3x + 2x +3 = 5x +3
The answer is A.
Your friend is on a weight loss program and has a goal of loosing 15 pounds. So far she has lost 3.5 pounds in the first two weeks. If she keeps up this rate of weight loss, how long can she expect it to take her to meet her weight loss goal?
Lets do the math together.
3.5/2 to find the weight loss per week= 1.75.
We know that every week the friend will reduce her goal by 1.75.
15/1.75= 8.6.
This means that in 8.6 weeks the friend will lose 15 pounds.
I hope this Helps! :)
Hello there! It should take her 8.6 weeks.
Well, the question doesn't specify whether it wants how long it'll take her in weeks, months, or days, so let's go with weeks. To do this, find the unit rate by dividing the amount she lost by the number of weeks it took.
3.5 pounds ÷ 2 weeks = 1.75 pounds lost a week.
Now, divide the total she wants to loose (15 pounds) by the 1.75 pounds a week to see how many she looses in total.
15/1.75 = 8.57142... Which is a little over 8.5 weeks, so we can round up to 8.6 weeks.
What is the product of (6x – y)(2x – y + 2?
Answer:
Step-by-step explanation:
(6x - y)(2x - y + 2)=
= 12x^2 - 6xy + 12x - 2xy + y^2 - 2y
= 12x^2 - 8xy + 12x + y^2 - 2y
Answer:
B 12x2 – 8xy + 12x + y2 – 2y
Step-by-step explanation:
4. A rectangular field has a perimeter of 300m. What is the area of the field if the length of
the field is twice the width of the field?
®
5000 m²
300 m
5000 m
600 m2
The area of the rectangular field given the dimensions of the field is 5000m^2.
What are the equations that can be used to determine the dimensions of the field?a + b = 150 equation 1
a = 2b equation 2
Where:
a = length
b = width
Whats the width?Subsiture for b in equation 1 using equation 2
2b + b = 150
3b = 150
b = 50m
What is the length?a = 2 x 50
q = 100m
What is the area of the field?Area = length x width
100 x 50 = 5000 m^2
To learn more about how to calculate the area of a rectangle, please check: https://brainly.com/question/16595449
The rectangular field is found to be 5000 square meters. Option (1) 5000 m² is the correct answer.
To find the area of a rectangular field given its perimeter and that the length is twice the width, follow these steps:
Let the width of the field be W.Then the length of the field is 2W.The perimeter of the rectangle is given by the formula: Perimeter = 2(Length + Width).Substitute the given values: 300 = 2(2W + W).This simplifies to: 300 = 2(3W) = 6W.Solving for W, we get: W = 50 meters.Given W = 50 meters, the length L is: L = 2W = 100 meters.The area of the rectangle is given by the formula: Area = Length × Width.Substituting the values, we get: Area = 100 × 50 = 5000 m².Plz answer right away
Answer:
1 whole and 1 over 12
Step-by-step explanation:
Answer:
Step-by-step explanation:
7
12
+
3
6
=
7
12
+
3
6
=
7
12
+
1
2
=
7
12
+
6
12
=
7+6
12
=
13
12
(Decimal: 1.083333)
6x = 90 what does x equal?
Answer:
6x=90
Divide by 6 for 6x and 90
6x/6=90/6
x=15
Check answer by using substitution method
6x=90
6(15)=90
90=90
Answer is x=15
Answer:
Step-by-step explanation:
6x = 90 Divide by 6
6x/6 = 90/6
x = 15
-8x + 2x – 16 < -5x + 7x
Answer:
x > 2
Step-by-step explanation:
Given
- 8x + 2x - 16 < - 5x + 7x ← simplify both sides
- 6x - 16 < 2x ( subtract 2x from both sides )
- 8x - 16 < 0 ( add 16 to both sides )
- 8x < - 16 ( divide both sides by - 8 )
Remembering to reverse the symbol as a consequence of dividing by a negative value.
x > 2
The diagram shows the locations of three towns and a library. Each unit on the grid represents 1.5 kilometers.
a. The actual distance between the library and Town A is_km.
b. The approximate distance between the library and Town B is_km.
c. Amelia traveled from Town A to the library to return her books. She then traveled to Town B to meet her friend. She and her friend then traveled to Town C and had dinner. How far did Amelia travel?
Answer:
a. 6km
b. 6.185 km
c. 18.37 km
Step-by-step explanation:
The question is on finding the distance of between two points
The general formulae is given by;
[tex]d= \sqrt{(X2-X1)^2+(Y2-Y1)^2}[/tex]
Where d is the distance
Given that;
1 unit on grid = 1.5 km
a. Finding distance between the library and Town A
A (-2,3) and library (2,3)
[tex]d= \sqrt{(2- -2)^2 + (3-3)^2} \\\\= \sqrt{4^2} \\= 4[/tex]
Actual distance = 4 × 1.5 = 6 km
b. Distance between the library and Town B is
library (2,3) and town B (1, -1)
[tex]d=\sqrt{(1-2)^2+ (-1-3)^2} \\\\\\d=\sqrt{-1^2 +-4^2}\\ \\\\d=\sqrt{1+16} \\\\\\d=\sqrt{17} = 4.123[/tex]
Actual distance = 4.123×1.5 =6.185 km
c. First find the distance between Town B and Town C
Town B (1, -1) and Town C (-3,-2)
[tex]d=\sqrt{(-3-1)^2 + (-2--1)^2} \\\\d=\sqrt{-4^2 + -1^2} \\\\d=\sqrt{16+1} \\\\d=\sqrt{17} \\\\d=4.123[/tex]
Actual distance= 4.123×1.5 =6.185 km
Total distance traveled by Amelia = 6 +6.185 +6.185 =18.37 km
The function p(x) = - 2(x-9)2 + 100 is used to determines the profit on T-shirts sold for x dollars. What would the profit from sales be if the proce of the T-shirts were $15 a piece?
ANSWER
$28
EXPLANATION
The profit function is given as:
[tex]p(x) = - 2 {(x - 9)}^{2} + 100[/tex]
where x is the price of the T-shirt in dollars.
To find the profit on a T-shirt whose price is $15, we substitute x=15 into the function and simplify.
[tex]p(15) = - 2 {(15 - 9)}^{2} + 100[/tex]
We simplify to get:
[tex]p(15) = - 2 {(6)}^{2} + 100[/tex]
[tex]p(15) = -72+ 100[/tex]
[tex]p(15) = 28[/tex]
Which expression is equal to (f - g)(x)?
ANSWER
A. x-8
EXPLANATION
The given functions are:
[tex]f(x) = {x}^{2} - 11x + 24[/tex]
We factor this to get,
[tex]f(x) = (x - 8)(x - 3)[/tex]
and
[tex]g(x) = x - 3[/tex]
[tex]( \frac{f}{g} )(x) = \frac{f(x)}{g(x)} [/tex]
[tex]( \frac{f}{g} )(x) = \frac{ {x}^{2} - 11x + 24}{x - 3} \: for\: x \ne3[/tex]
[tex]( \frac{f}{g} )(x) = \frac{(x - 8)(x - 3)}{x - 3} [/tex]
Cancel the common factors to get,
[tex]( \frac{f}{g} )(x) = x - 8[/tex]
Answer: OPTION A
Step-by-step explanation:
You need to divide the function f(x) by the function g(x):
Then:
[tex](\frac{f}{g})(x)=\frac{x^2-11x+24}{x-3}[/tex]
Now, you need to simplify:
Factor the numerator. Find two numbers whose sum be -11 and whose product be 24. Theses numbers are -8 and -3. Then you get:
[tex](\frac{f}{g})(x)=\frac{(x-8)(x-3)}{x-3}[/tex]
Remember that:
[tex]\frac{a}{a}=1[/tex]
Then, you get that the expresson that is equal to [tex](\frac{f}{g})(x)[/tex] is:
[tex](\frac{f}{g})(x)=(x-8)[/tex]
Maria had $22 to spend on five pencils. After buying them she had $12. How much did each pencil cost?
Answer:
$2
Step-by-step explanation:
Answer:$2.04
Step-by-step explanation:
How do you know if a vertex is a minimum or maximum
If the parabola looks like an “n,” your vertex will be a maximum. If the parabola looks like a “u,” the vertex will be a minimum.
To determine if a vertex is a minimum or maximum, evaluate the behavior of the function at that point. If the function is increasing before the vertex and decreasing after, it is a minimum point. If the function is decreasing before the vertex and increasing after, it is a maximum point.
Explanation:In mathematics, a vertex is a point where two or more lines, curves, or edges meet. When determining if a vertex is a minimum or maximum, we need to look at the behavior of the function or equation at that point.
If the function is increasing before the vertex and decreasing after the vertex, then the vertex is a minimum point. Conversely, if the function is decreasing before the vertex and increasing after the vertex, then the vertex is a maximum point.
For example, consider the parabola y = x^2. The vertex of this parabola is at (0, 0).
Since the parabola opens upwards and the function values increase on either side, the vertex is a minimum point.
mr. and mrs. smiths childeren all play different sports
Answer:
What's your question?
please answer these two before 1:20 pm!!! thanks
Answer: You should use dot plot.
Step-by-step explanation:
1. you should use a dot plot
(correct dot plot)
Its C
How many friends has three pencils?
3
20. dot plot, box plot, and histogram.
help needed asap 20 points if answered right
ANSWER
1. No real roots
2. [tex] \frac{ 7\pm \: \sqrt{33} }{ - 4}[/tex]
3. The discriminant is negative.
EXPLANATION
1. The given equation is
[tex] - 2 {x}^{2} - 9x - 5 = 0[/tex]
We have a=-2,b=-9 and c=-5.
The discriminant is given by:
[tex]D= {b}^{2} - 4ac[/tex]
[tex]D= {( - 9)}^{2} - 4( - 2)( - 5)[/tex]
This simplifies to:
[tex]D= 36 - 40 = - 4[/tex]
Since the discriminant is less than zero, the quadratic equation has no real roots.
2. The given equation is:
[tex] - 2 {x}^{2} - 7x - 2= 0[/tex]
We have a =-2, b=-7 and c=-2.
The roots of this equation are given by;
[tex]x = \frac{ - b \pm \: \sqrt{ {b}^{2} - 4ac } }{2a} [/tex]
We plug in the values to get;
[tex]x = \frac{ - - 7\pm \: \sqrt{ {( - 7)}^{2} - 4( - 2)( - 2) } }{2( - 2)} [/tex]
[tex]x = \frac{ 7\pm \: \sqrt{33} }{ - 4} [/tex]
3. The given graph is hanging downwards. This means that it doesn't have x-intercepts.
Therefore the roots are complex or imaginary.
This implies that, the discriminant of the corresponding equation is negative.
a square painting has an area of 81x^2-90x-25. A second square painting has an area of 25x^2+30x+9. What is an expression that represent the difference of the area of the paintings? show two ways to find the solution
Answer:
The answer in the procedure
Step-by-step explanation:
Let
A1 ------> the area of the first square painting
A2 ----> the area of the second square painting
D -----> the difference of the areas
we have
[tex]A1=81x^{2}-90x-25[/tex]
[tex]A2=25x^{2}+30x+9[/tex]
case 1) The area of the second square painting is greater than the area of the first square painting
The difference of the area of the paintings is equal to subtract the area of the first square painting from the area of the second square painting
D=A2-A1
[tex]D=(25x^{2}+30x+9)-(81x^{2}-90x-25)[/tex]
[tex]D=(-56x^{2}+120x+34)[/tex]
case 2) The area of the first square painting is greater than the area of the second square painting
The difference of the area of the paintings is equal to subtract the area of the second square painting from the area of the first square painting
D=A1-A2
[tex]D=(81x^{2}-90x-25)-(25x^{2}+30x+9)[/tex]
[tex]D=(56x^{2}-120x-34)[/tex]
Final answer:
To find the difference between the areas of two square paintings, subtract the second area from the first to get an expression. By direct subtraction and using the distributive property, both methods yield the expression[tex]56x^2 - 120x - 34[/tex].
Explanation:
To find an expression that represents the difference between the areas of two square paintings, we simply subtract the area of the second painting from the area of the first painting.
The area of the first painting is [tex]81x^2 - 90x - 25,[/tex] and the area of the second painting is [tex]25x^2 + 30x + 9.[/tex]To find the difference, calculate [tex](81x^2 - 90x - 25) - (25x^2 + 30x + 9).[/tex]
Here's the direct subtraction method:
Subtract the [tex]x^2[/tex] terms: [tex]81x^2 - 25x^2 = 56x^2[/tex].
Subtract the x terms: -90x - 30x = -120x.
Subtract the constant terms: -25 - 9 = -34.
Combining these, we get the expression representing the difference in areas:[tex]56x^2 - 120x - 34.[/tex]
Another way to find the solution is using the distributive property to first factor out a negative from the second polynomial, making it easier to subtract:
Rewrite as[tex]: (81x^2 - 90x - 25) - 1*(25x^2 + 30x + 9).[/tex]
Distribute the negative sign:: [tex](81x^2 - 90x - 25) - 1*(25x^2 + 30x + 9)..[/tex]
Now proceed as in the direct subtraction method above.
The final result is the same: [tex]56x^2 - 120x - 34.[/tex]
Tim needs 18 pens he can buy them in packages of 6 9 or 12 he will buy only one type of package which packages could Tim buy write 2 different ways that Tim could buy exactly 18 pens
Answer:
See below.
Step-by-step explanation:
Either 3 packets of 6 pens or
2 packets of 9 pens.
he could buy 3 packs of 6
or 2 packs of 9
PLEASE HELP!!
A motor-powered bike has wheels that travel a linear distance of approximately 62.8 inches in one
revolution. What is the central angle the bike wheels turn through, in degrees, when the bike travels 2
inches?
Answer:
A motor-powered bike has wheels that travel a linear distance of approximately 62.8 inches in one
revolution. What is the central angle the bike wheels turn through, in degrees, when the bike travels 2
inches?
Step-by-step explanation:
PLEASE HELP!!
A motor-powered bike has wheels that travel a linear distance of approximately 62.8 inches in one
revolution. What is the central angle the bike wheels turn through, in degrees, when the bike travels 2
inches?
The central angle the bike wheels turn through, in degrees when the bike travels 2 inches will be 11.46°.
What is a circle?A circle is a geometrical figure which becomes by plotting a point around a fixed point by keeping a constant distance.
Area of the circle = πr² and the perimeter of the circle = 2πr where r is the radius of the circle.
The linear distance in one revolution = perimeter of a circle or wheel
Perimeter = 2πR
R = 62.8/(2π)
R = 9.99 = 10 inches.
When L = 2 inches the center angle will be as,
Ф = L/R
Ф = 2/10 = 0.2 radian
In degree → 0.2 × 180/π = 11.46°
Hence "The central angle the bike wheels turn through, in degrees when the bike travels 2 inches will be 11.46°".
To learn more about the circle,
https://brainly.com/question/266951
#SPJ2
HELP PLS!!! 15 POINTS!
Data Set #2 - Number of books read by students during their 7th grade Year
1,15,8,3,4,6,9,2,1
Median=
Mode=
Mean=
Range=
Answer=
Answer:
See below in bold.
Step-by-step explanation:
Arrange in order first:
1 1 2 3 4 6 8 9 15
Median ( middle number) = 4.
Mode ( the number which occurs most) = 1.
Mean = (1+1+2+3+4+6+8+9+15) = 49/9 = 5.4.
Range = 15 - 1 = 14.
List the numbers in order from smallest to largest:
1, 1 , 2, 3, 4, 6, 8, 9, 15
Median is the Middle value of the set = 4
Mode is the number that appears the most = 1
Mean is the average add the numbers together and divide by the quantity of numbers:
1 + 1 +2 + 3+ 4+ 6 +8 + 9+15 = 49 / 9 = 5.44
Range is the difference between the largest number and smallest number: 15 -1 = 14
Solve the equation.
5+0.5(6n+14)=3
Please explain this to me because I don't get it and feel like cheating going on Brainly.
Answer:
n = - 3
Step-by-step explanation:
It's not cheating unless this question is from a quiz or test.
5+0.5(6n+14)=3 Subtract 5 from both sides.
5-5 + 0.5(6n+14) = 3 - 5 Combine
0.5(6n+14) = - 2 There are two ways to go. I prefer dividing by 0.5
0.5(6n+14)/0.5 = -2/0.5 Do the division
6n + 14 = - 4 Subtract 14
6n+14-14= -4-14 Combine
6n = - 18 Divide both sides by 6
6n/6 = - 18/6 Combine
n = - 3
The solution to the equation 5+0.5(6n+14)=3 will be n = - 3
WE are given the equation as;
5+0.5(6n+14)=3
We need to find the value of n here;
Subtract 5 from both sides.
5-5 + 0.5(6n+14) = 3 - 5
Combine
0.5(6n+14) = - 2
0.5(6n+14)/0.5 = -2/0.5
6n + 14 = - 4
6n+14-14= -4-14
6n = - 18
Divide both sides by 6
6n/6 = - 18/6
n = - 3
Therefore, the solution to the equation 5+0.5(6n+14)=3 is n = - 3
To learn more on Equation:
brainly.com/question/10413253
#SPJ6