The radius of such a cylinder will be 8 and height=8/3.
What is a cylinder?
Cylinder is one of the basic 3d shapes, in geometry, which has two parallel circular bases at a distance. The two circular bases are joined by a curved surface, at a fixed distance from the center. The line segment joining the center of two circular bases is the axis of the cylinder. The distance between the two circular bases is called the height of the cylinder. LPG gas-cylinder is one of the real-life examples of cylinders.
Since, the cylinder is a three-dimensional shape, therefore it has two major properties, i.e., surface area and volume. The total surface area(TSA) of the cylinder is equal to the sum of its curved surface area and area of the two circular bases. The space occupied by a cylinder in three dimensions is called its volume(V).
V=πr²h and TSA=2πr²+2πrh where r=radius and h=height.
Now,
In any case, we can let the radius of the inscribed cylinder be x
. That must therefore mean that the height of the cylinder is 8−4/6x
. This makes the volume of the cylinder
V=πx^2(8−2/3x)=π(8x^2−2/3*x^3)
To find the maximum volume of the cylinder we take the derivative of V
with respect to x
and set it to 0
dV/dx=π(16x−2x^2)=0⇒16x−2x^2=2x(8−x)=0
x=0 leads to a trivial case, which leaves us with x=8
. This means that the height is 8−2/3*8=8/3
, and the volume is therefore
V=π⋅8^2⋅8/3
V=512/3π.
To know more about cylinder visit the link
https://brainly.com/question/16134180?referrer=searchResults
#SPJ1
• The dimensions of a rectangle are 3x by 4x-9. Find x if the perimeter is 52.
Draw a picture if you need a visual
Answer:
x = 6, length of the rectangle is 18cm, and width is 21cm
Step-by-step explanation:
To solve this problem, we can use the perimeter of a rectangle formula: P = 2l + 2w.
Here, l = 3x and w = 4x - 9, so the perimeter is P = 2(3x) + 2(4x - 9) = 52.
Solving for x, we get x = 6.
Therefore, the length of the rectangle is 3x = 18 cm, and the width is 4x - 9 = 21 cm.
A painter is making a mural on the side of a building. In planning this project, he first creates the same painting on a normal sized sheet of paper at a scale of 2 in. to 5 ft. If the width of the paper drawing is 4.9 inches, what will be the width of the mural (in feet) when it is finished?
The width of the mural (in feet) when it is finished is equal to 12.25 feet.
What is scale factor?In Geometry, a scale factor is the ratio of two corresponding side lengths or diameter in two similar geometric figures which can be used to either horizontally or vertically enlarge (increase) or reduce (decrease or compress) a function that represents their size.
Scale factor = 2/5
For the width of the mural (in feet), we have:
2/5 = 4.9/x
x = (5 × 4.9)/2
x = 24.5/2
x = 12.25 feet.
Read more on scale factor here: brainly.com/question/7482670
#SPJ1
What is the equation of the following graph? Use equation y = mx + b (picture included)
heellllpp guys i will give brainlist
R
102°
o
S
What is the measure of arc RT?
102 degrees
156 degrees
204 degrees
88 degrees
Previous
E
Please help
The measure of arc RT is: C. 204 degree.
How to find the measure of arc RT?arc ORT = 102° - 90°
arc = 12°
arc ROT = 180° - 2×12°
arc ROT = 180° - 24°
arc ROT = 156°
Hence:
Measure of arc RT
arc RT= 360° - 156°
arc RT = 204°
Therefore the correct option is C.
Learn more about measure of arc RT here:https://brainly.com/question/28045005
#SPJ1
How do you solve it WITHOUT using graph paper?
Line A passes through the points (-4, 3) and (-2, -1).
Line B passes through the points (-4, 4) and (-5, 7).
At what point do the lines intersect?
A step by step explanation please!
Answer: To find the point of intersection of two lines without using graph paper, we can use the method of solving a system of equations.
First, we need to find the slope-intercept form of each line. The slope-intercept form of a line is y = mx + b, where m is the slope of the line and b is the y-intercept.
To find the slope of Line A, we can use the slope formula: m = (y2 - y1)/(x2 - x1). Plugging in the given points, we get: m = (-1 - 3)/(-2 - (-4)) = -4/2 = -2.
Therefore, Line A can be written as y = -2x + b. To find the y-intercept, b, we can plug in one of the points, such as (-4,3) and solve for b: 3 = -2(-4) + b, so b = 11.
So, the slope-intercept form of Line A is y = -2x + 11
We can use the same process to find the slope-intercept form of Line B: m = (7 - 4)/(-5 - (-4)) = 3/1 = 3. So Line B can be written as y = 3x + b. Plugging in one of the points, (-4,4), we get 4 = 3(-4) + b, so b = 16.
So, the slope-intercept form of Line B is y = 3x + 16
Now we have two equations: y = -2x + 11 and y = 3x + 16. To find the point of intersection, we need to find the values of x and y that make both equations true. To do this, we can set the two equations equal to each other:
-2x + 11 = 3x + 16
Subtracting 3x from both sides:
-5x = 5
Dividing both sides by -5:
x = -1
Now we can substitute this value of x back into either equation to find the corresponding value of y. Using y = -2x + 11:
y = -2(-1) + 11 = -2 + 11 = 9
So the point of intersection of Line A and Line
Step-by-step explanation:
What is the expanded form for 72 cubed?
Answer:373248
Step-by-step explanation:
72^3 = 373248
In parallelogram ABCD, AB = 6x-4, CD = 5x + 1, and BC = 2x.
What is the perimeter of ABCD?
D
Perimeter =
A
units
C
B
Answer:
15x-3
Step-by-step explanation:
Recall that parallelograms, as the name implies, have two pairs of parallel sides. In this case, line segments AB and CD are parallel to each other, and then BC and DA are parallel to each other:
Perimeter = AB + BC + CD + DA = (6x-4) + (2x) + (5x+1) + (2x) = 15x - 3
Enter the resulting inequality.
11 > −2; Subtract 11 from both sides.
The resulting inequality is
If 11 is Subtracted from both sides, the resulting inequality is 9 > -4
How find the resulting inequality?
An inequality is a relationship that makes a non-equal comparison between two numbers or other mathematical expressions e.g. 2x > 4
Initially, you have 11 > −2
If you subtract 11 from both sides, you will have:
11 -2 > −2-2
9 > -4
Thus, the resulting inequality will be 9 > -4
Learn more about inequality on:
brainly.com/question/25275758
#SPJ1
Create a table from y=5x. You can just do numbers like
Y 7. 9. 6
X 4. 7. 4 or sum I just need the table
When y = 5x the possible outcome of table is 2.8 when x = 4 , 3.88 when x= 7 and 3.33 when x= 4 .
Function range :A function's range can refer to one of two closely related ideas: The function's image is its codomain. Given two sets, X and Y, a function is a binary relation between X and Y if, for every x in X, there is exactly one y in Y that corresponds to f. Take a look at the function y = f(x). The range of the function is the spread of all the y values from the lowest to the highest. Substitute all of x's values into the given expression for y to determine whether it is positive, negative, or equal to other values.
if y=5 x
y= 7 and X = 4 , then
7= 5(4)
7 = 20
= 20/7
= 2.8
when Y =9 and X = 7 then,
9 = 5(7)
9 = 35
35/9
= 3.88
when Y = 6 and X = 4 then,
6= 5(4)
6= 20
20/6
= 3. 33
Missing function of table are 2.88 , 3.88,3.33
What is the range of the function?
The range is (0;+∞). The values are all positive (if a positive number is raised to a power, the result cannot be negative), and the value cannot be zero, so the range is (0;+∞).
Incomplete question :
Create a table from y=5x. You can just do numbers like
Y 7. 9. 6
X 4. 7. 4 or sum I just need the table
Complete the table for the given rule.
Rule:y=5x
x, y
5,4,2
Learn more about function range :
brainly.com/question/28801359
#SPJ1
16/1 x 3/8 in simplest form
Answer: 6
Step-by-step explanation:
1. 16/1 × 3/8= 48/8
2. 48/8= 6
give three points that lie on a line with a slope of -2/5
The three points that lie on a line y = -2/5x with a slope -2/5 will be:
(0, 0)
(5, -2)
(10, -4)
How to illustrate the slope?Given slope = m = -2/5. We suppose the line passes through the origin, so b = 0
substituting m = -2/5 and b = 0 in the slope-intercept form
y = -2/5x + 0
y = -2/5x
Thus, the equation of line with the slope m = -2/5 and passes through the origin (0, 0) will be:
y = -2/5x
As the equation of line passes through (0, 0), thus the point (0, 0) lies on the line.
Putting x = 0 in the equation y = -2/5x
y = -2/5 × (0)
y = 0
Thus, (0, 0) is the point which also passes through the line
Putting x = 5 in the equation y = -2/5x
y = -2/5 × 5
y = -2
Thus, (5, -2) is the point which also passes through the line.
Learn more about slope on:
https://brainly.com/question/16949303
#SPJ1
Please Help. I'll give Brainliest
Answer: Number 2
Step-by-step explanation:
Angle 1 + Angle 2 + Angle 3 = 180 degrees because its a straight line, so we immediately eliminate number 1 and 4 (Because it says the angles add up to 270). Next, we look at 2 and 3. 3 is incorrect because with just 1 right angle, QRST might be a rectangle. Therefore, number 2 is correct. :>
The monthly rents for five apartments advertised in a newspaper were $670, $670, $790, $1550, and $810. Use the mean, median, mode, and range of the rents to answer the following question: Which measure of central tendency best described the advertised rents? Calculate the four measures of central tendency and provide two to four sentences supporting the answer. (I already calculate the four, I just need help with picking out the best one. Range: 880. Mode: 670. Mean: 898. Median: 790)
The MEAN best describes the monthly rents.
The best one is Mean : 898
Now, According to the question:
The monthly rents for five apartments advertised in a newspaper were $670, $670, $790, $1550, and $810.
We are required to use the mean, median and mode to explain which measure of central tendency best describes the monthly rent.
The mean, median and mode (as calculated) are the measures of central tendency for the data set given.
This measures which value is closest to the center such that it can conveniently represent every other data. Observe carefully that the least value is 670 while the highest is 1550.
Also, observe that the value which is "more central" to both extremes is the mean.
The median is closer to the lowest value and much farther from the highest value.
The mode is actually at the lowest end of the data set.
However, the mean is safely between both ends. Its farther away from the least value than the median which means its moving closer to the "center" unlike the other two measures.
Learn more about Mean , median and mode at:
https://brainly.com/question/4001516
#SPJ4
What is the length of CD when;
C: (-3 , -4)
D: (1 , -2)
CD is about 2.83 in length when C: (-3 , -4) D: (1 , -2) in coordinate geometry.
How is this determined?In coordinate geometry, the distance formula, which is the square root of (x2 - x1)2 + (y2 - y1)2, can be used to determine the length of CD.
In this instance, point C's coordinates are (-3, -4) and point D's coordinates are (1, -2). Using the distance formula with these values as input, we obtain:
√((1 - (-3))^2 + ((-2) - (-4))^2) = √(4 + 4) = √8 = 2.8284271247461903
In simpler terms, you can use the distance formula, which is the square root of the sum of the differences of their x- and y-coordinates squared, to determine the separation between two points in a coordinate plane.
Learn more about Coordinate geometry here:
brainly.com/question/18269861
#SPJ1
Find the values of the variables for the parallelogram.
Answer:
which parallelogram?
Step-by-step explanation:
repost it and add a pic
Find the measures of the numbered angles.
Answer: ∠1= 75°, ∠2= 105°, ∠3=105°, ∠4=75°, ∠6=105°, ∠7= 105°, ∠8=75°
Step-by-step explanation:
∠1 is corresponding to angle 75° which make them equal.
∠2 is supplementary to ∠1 which means they add up to 180°. Since ∠1 is 75° you would subtract 75° from 180° to get 105°.
∠3 is vertical to ∠2 which makes them equal.
∠4 is vertical to ∠1 which makes them equal.
∠6 is corresponding to ∠2 which makes them equal.
∠7 is vertical to ∠6 which makes them equal.
∠8 is vertical to 75° which makes them equal.
Find a unit vector that has the same direction as the given vector. -3i + 7j
The unit vector that has the same direction as the given vector is[tex]& (3 / \sqrt{ } 58) \mathrm{i}-(7 / \sqrt{58}) \mathrm{j}[/tex].
The given vector(v) is -3i+7j
The unit vector is found by dividing the vector by its magnitude
Unit vector of [tex]$v=\frac{v}{\|v\|}$[/tex]
A vector is a quantity that has both magnitude, as well as direction. A vector that has a magnitude of 1 is a unit vector. It is also known as Direction Vector.The formula of unit vector in the direction of a given vector is:
Unit Vector = Vector/Vector's magnitudeWe have to find the magnitude first
So,
[tex]& \|v\|[/tex] =[tex]\sqrt{(3)^{2}+(-7)^{2} } =\sqrt{9+49} =\sqrt{58}[/tex]
[tex]& \|v\|=\sqrt{58}[/tex]
The unit vector is:
The i, j, and k are the unit vectors in the directions of the x-axis, y-axis, and z-axis respectively in a 3-dimensional plane. i.e.,
|i| = 1|j| = 1|k| = 1[tex]$$\begin{aligned}& =(1 / \sqrt{58})(3 \mathrm{i}-7 \mathrm{j}) \\& =(3 / \sqrt{ } 58) \mathrm{i}-(7 / \sqrt{58}) \mathrm{j}\end{aligned}$$[/tex]
Therefore, the unit vector is [tex]& =(3 / \sqrt{ } 58) \mathrm{i}-(7 / \sqrt{58}) \mathrm{j}[/tex].
For more such questions on unit vector
https://brainly.com/question/28028700
#SPJ4
t
he points that are on the graph of the function defined by y=2x+3
.
The point that lies on the function defined by the equation is (2, 7)
How to determine the point that lies on the graph of the equationFrom the question, we have the following parameters that can be used in our computation:
y = 2x + 3
The point in the ordered pair that lies on the graph of the equation is the solution set
Take for instance, we set x = 2
So, we have the following representation
y = 2 * 2 + 3
Evaluate the product and the sum
This gives
y = 7
When repesented as an ordered pair, we have
(2, 7)
Hence, the point is (2, 7)
Read more about linear equation at
brainly.com/question/2030026
#SPJ1
a family eats at a restaurant. the bill is $38.00. the family leaves a tip and spends $44.27. how much was the tip as a percentage of the bill?
Answer:
14.16%
Step-by-step explanation:
[tex]=(\frac{44.27-38}{44.27} )(100)=(\frac{6.27}{44.27} )(100)=\frac{627}{44.27} =14.16[/tex]
Hope this helps
Systems of Linear Inequalities
PLEASE HELP
Th systems of Linear Inequalities are:
x>=-7,
y<6-2x/3,
y<=-1,
y>3/5x-5,
y<6+5x
How to solve the linear inequalities?Step1:
x>=-7,y<6-2x/3,y<=-1,y> 3/5x-5,y<6+5x: [x>=-7]
[y<6-2x/3]
[y<=-1]
[ y>3/5x-5]
[y<6+5x]
x>=-7
[tex]3y+2x < 6\sy < =-1\sy > \frac{3}{5}[/tex]
x-5\sy-5x<6
Separate y for 3y+2x6 as follows: y6-2x/3 3y+2x6
Step2:
shuffle twice to the right side
Divide both sides by 3 using the formula 3y/6/3-2x/3.
simplify
3y/3<6/32x/3
Simplify 3y/3 by dividing it by y.
3/3=1
simplify 6/3-2x/3: 6-2x/3
6/3-2x/3
Apply the formula a/c + b/c = a+-b/c = 6-2x/3 y 6-2x/3
Identify y for y-5x6: y6+5x y-5x6.
Y=6+5x move the right side by 5x.
To learn more about linear inequalities refers to;
https://brainly.com/question/19526736
#SPJ1
Quadrilateral ABCD'is a reflection of quadrilateral ABCD over the x-axis.
What is the length of A'D' ?
A. 3 units
B. 7 units
C. 4 units
D. 6 units
option D is correct- The length of quadrilateral of A’D’ is 6. When it is reflected ,the lengths don’t change.
image is attached below,
Quadrilateral
A quadrilateral is defined as a two-dimensional shape with four sides, four vertices, and four angles. There are two main types: concave and convex. There are also various subcategories of convex quadrilaterals, such as trapezoids, parallelograms, rectangles, rhombi, and squares.
Reflection
A reflection is a mirror image of the shape. An image will reflect through a line, known as the line of reflection. A figure is said to reflect the other figure, and then every point in a figure is equidistant from each corresponding point in another figure.
Learn more about quadrilateral here:-
https://brainly.com/question/29934291
#SPJ4
find the rate of change between the points (-1,30) and (-6,10)
Answer:
Step-by-step explanation:
The rate of change, also known as the slope, between two points can be found using the formula:slope = (y2 - y1) / (x2 - x1)where (x1, y1) and (x2, y2) are the coordinates of the two points.To find the slope between the points (-1, 30) and (-6, 10), we can plug in the coordinates into the formula:slope = (10 - 30) / (-6 - (-1)) = -20/-5 = 4So the rate of change or the slope between the points (-1,30) and (-6,10) is 4.This means that the y-value of the second point is 4 units lower than the y-value of the first point for every unit you move to the left on the x-axis.
D. Ray saved $4 on a shirt that was was originally
$32. What percent was the discount?
Answer: The percent was 12.5%
The equation y =7400x represents the number of miles, y, that the satellite Space Explorer flies in x hours. Find the rate of change.
If the equation "y = 7400x" represents the number of miles(y) , that satellite space explorer files in x hours , then the rate of change is 7400 miles per hour.
The Rate Of Change is also known as "Slope" ,
The rate of change can be found by taking the derivative of the equation ⇒ y = 7400x with respect to x.
The derivative of the equation "y = 7400x" with respect to x is ;
⇒ dy/dx = d/dx(7400x) = 7400 .
Therefore , rate of change of the equation "y = 7400x" is 7400 miles per hour , that means the satellite explorer files will cover 7400 miles in 1 hour .
Learn more about Rate Of Change here
https://brainly.com/question/29802077
#SPJ4
Somebody help me please with this question!!
A local hamburger hop old a combined total of 491 hamburger and cheeeburger on Friday. There were 59 fewer cheeeburger old than hamburger. How many hamburger were old on Friday?
The hamburger shop sold a total of 491 hamburgers and cheeseburgers on Friday. There were 59 fewer cheeseburgers sold than hamburgers, so the number of hamburgers sold on that day was 275.
432 hamburgers.
We can write an equation to represent the information given.
Hamburgers + Cheeseburgers = 491
Cheeseburgers = Hamburgers - 59
Substitute the second equation into the first equation:
Hamburgers + (Hamburgers - 59) = 491
Solve for 'Hamburgers':
2Hamburgers - 59 = 491
2Hamburgers = 550
Hamburgers = 275
Since the question asks for the number of hamburgers, the answer is 275 hamburgers.
The hamburger shop sold a total of 491 hamburgers and cheeseburgers on Friday. There were 59 fewer cheeseburgers sold than hamburgers, so the number of hamburgers sold on that day was 275.
learn more about number here
https://brainly.com/question/10547079
#SPJ4
hi help pls n thanks
The required domain is x ≥ -4.So option(4) is correct.
What is domain?The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.
According to question:From the graph, we can see that curve is starting from -4 to infinity in x direction.
By baby curve method
x ≥ -4
Thus, required domain is x ≥ -4.So option(4) is correct.
To know more about Domain visit:
brainly.com/question/28135761
#SPJ1
find the measures of <X <Y.
The missing interior angles of the hexagon is as follows:
∠X = 135 degrees
∠Y = 135 degrees
How to find the angles in a polygon?The polygon above has 6 sides. Therefore, the polygon is a hexagon. The sum of interior angles of a polygon is ( n − 2 ) × 180°.
where
n = number of sidesThe sum of interior angles in an hexagon is calculated as follows:
180(6 - 2) = 180(4) = 720 degrees
Therefore, the angles of x and y are congruent.
Hence,
let
∠x = ∠y = a
Therefore,
2a + 91 + 149 + 100 + 110 = 720
2a = 720 - 450
2a = 270
a = 270 / 2
a = 135 degrees
Therefore,
∠x = ∠y = 135 degrees.
learn more on angles here: https://brainly.com/question/10725953
#SPJ1
an automobile manufacturer claims that their van has a 57.2 miles/gallon (mpg) rating. an independent testing firm has been contracted to test the mpg for this van. after testing 91 vans they found a mean mpg of 56.9 with a standard deviation of 1.8 mpg. is there sufficient evidence at the 0.025 level that the vans underperform the manufacturer's mpg rating? state the null and alternative hypotheses for the above scenario.
The null and alternative hypotheses for the above scenario are
H0: Their van has a miles/gallon (MPG) rating equal to 57.2 miles/gallon
Ha: Their van has a miles/gallon (MPG) rating that is different from 57.2 miles/gallon
Given that,
One automaker says that their van gets 57.2 miles per gallon (mpg). An impartial testing business has been hired to evaluate the mpg for this van. They tested 91 vans, and the results showed that the average mileage was 56.9 with a standard deviation of 1.8 mpg. Is there adequate proof that the vans don't meet their mpg rating at the 0.025 level
To find: state the null and alternative hypotheses for the above scenario.
The null and alternative hypotheses for the above scenario are
H0: Their van has a miles/gallon (MPG) rating equal to 57.2 miles/gallon
Ha: Their van has a miles/gallon (MPG) rating that is different from 57.2 miles/gallon
To know more about alternative hypotheses click here:
brainly.com/question/28331914
#SPJ4