The area of the rectangle ABEF = 2sa = 2ss/(2*tan(180/8)) = s^2/(tan(180/8)).
What is an octagon?
An octagon is a polygon with eight straight sides and eight angles. It is a closed two-dimensional shape with eight sides of equal length. A regular octagon is an octagon in which all sides and angles are equal.
When it comes to the area of a regular octagon, the area of a regular polygon can be calculated using the formula
A = (ns^2)/(4tan(180/n)) where A is the area, n is the number of sides and s is the length of each side.
In case of a regular octagon, the area of an octagon is (8s^2)/(4tan(180/8))
A rectangle ABEF is made up of two congruent sides with the length of the side of the octagon, and two congruent sides with the length of the apothem of the octagon.
An apothem of a regular polygon is the distance from the center of the polygon to the midpoint of any side. The apothem of a regular octagon can be calculated by using the formula
a = s/(2*tan(180/8)) where a is the apothem and s is the side of the octagon.
Hence, the area of the rectangle ABEF = 2sa = 2ss/(2*tan(180/8)) = s^2/(tan(180/8)).
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3 times what equals 5?
Answer: its 1.6667.
Answer:
Step-by-step explanation
3*X=5
X=5/3
X=1.67
A city planner make a cale drawing of a propoed playground. The length of the actual playground i 78 feet, and the width i 42 feet. Suppoe a cale of 0. 5 inch = 6 feet i ued. Which dimenion repreent the playground on the cale drawing?
The dimensions size on the scale drawing is 6.5 inches by 3.5 inches.
Dimensions in mathematics are the measure of the size or distance of an object or region or space in one direction. In simpler terms, it is the measurement of the length, width, and height of anything.
In Geometry we can have different dimensions, The number of dimensions is how many values are needed to locate points on a shape.
Multiplying the actual dimensions by the scale gives the scale dimensions:
(0.5 in)/(6 ft) × {78 ft, 42 ft}
= {39/6 in, 21/6 in}
= {6.5 in, 3.5 in}
Therefore, the dimensions size on the scale drawing is 6.5 inches by 3.5 inches.
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Ishi walked a total of 2 miles on a treadmill. He walked at a constant rate of 4 miles per hour. Which expression shows how long, in minutes, Ishi walked on the treadmill? 2.5 miles : 4 moles/hour x 60 minutes/1 hour 2.5 miles : 4 mmoles/hour x 60 minutes/1 hour 2.5 miles : 4 mom/10 mg x 60 minutes/1 hour 2.5 miles : 4 milem/hour x 60 minutes/1 hour
Ishi walked on the treadmill time for 37.5 minutes, which is equivalent to 2.5 miles at a rate of 4 miles/hour. To find the time Ishi walked on the treadmill, we need to use the equation, Distance (miles) / Rate (miles/hour) x Time (hours) = Time (minutes).
Answer: 2.5 miles : 4 milem/hour x 60 minutes/1 hour
Ishi walked on the treadmill time for 37.5 minutes, which is equivalent to 2.5 miles at a rate of 4 miles/hour.
To find the time Ishi walked on the treadmill, we need to use the equation, Distance (miles) / Rate (miles/hour) x Time (hours) = Time (minutes).
Therefore, 2.5 miles / 4 miles/hour x 1 hour = 0.625 hour or 37.5 minutes.
Ishi walked on the treadmill for time 37.5 minutes, which is equivalent to 2.5 miles at a rate of 4 miles/hour.
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Hi I need some help through this problem: Find the equation of a line parallel to 2x+4y-12=0 that passes through the point (-2,5).
equation in slope-intercept form.
Answer:
y = - [tex]\frac{1}{2}[/tex] x + 4
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
given
2x + 4y - 12 = 0 ( subtract 2x - 12 from both sides )
4y = - 2x + 12 ( divide through by 4 )
y = - [tex]\frac{2}{4}[/tex] x + [tex]\frac{12}{4}[/tex]
y = - [tex]\frac{1}{2}[/tex] x + 3 ← in slope- intercept form
with slope m = - [tex]\frac{1}{2}[/tex]
• Parallel lines have equal slopes , then
y = - [tex]\frac{1}{2}[/tex] x + c ← is the partial equation of the parallel line
to find c substitute (- 2, 5 ) into the partial equation
5 = - [tex]\frac{1}{2}[/tex] (- 2) + c = 1 + c ( subtract 1 from both sides )
4 = c
y = - [tex]\frac{1}{2}[/tex] x + 4 ← equation of parallel line
Answer:
y = -(1/2)x + 4
Step-by-step explanation:
Lets look for an equation of the form y=mx+b, where m is the slope and b is the y-intercept (the value of y when x = zero). Lets rewrite the given equation to conform to this format:
2x+4y-12=0
4y = -2x+12
y = -(2/4)x +(12/4)
y = -(1/2)x +3
This line has a slope of -(1/2). Parallel lines have the same slope as the reference line. So the new line will also have a slope of -(1/2) and we can write the new line equation as:
y = -(1/2)x + b
Any line with a slope of -(1/2) will be parallel. Any value of b is acceptable. But we want this line to intersect the point (-2,5), so we need to pick a value of b that forces the line through this point. To find the value of b to make that happen, enter the point (-2,5) in the parallel line equation from above:
y = -(1/2)x + b
5 = -(1/2)*(-2) + b for point (-2,5)
5 = 1+b
b = 4
The parallel line that intersects (-2,5) is
y = -(1/2)x + 4
See the attached graph.
If you were going to place a streetlight so it was equidistant from three sidewalks, would you use the incenter or circumcenter to find the best location?
We can use the incenter to find the best location, because the point that is equidistant to all sides of a triangle is called the incenter.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Now, We know that;
The incenter is equidistant from the sides of the triangle and the point that is equidistant to all sides of a triangle.
Hence, We can use the incenter to find the best location, to place a streetlight so it was equidistant from three sidewalks.
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Wyatt has $780 to spend at a bicycle store for some new gear and biking outfits. assume all prices listed include tax.
he buys a new bicycle for $398.35.
he buys 2 bicycle reflectors for $19.41 each and a pair of bike gloves for $35.27.
he plans to spend some or all of the money he has left to buy new biking outfits for $46.60 each.
write and solve an inequality which can be used to determine oo, the number of outfits wyatt can purchase while staying within his budget.
The inequality which can be used to determine too, the number of outfits Wyatt can purchase while staying within his budget is:
780 ≥ 472.44 + 46.60x
Inequality:
In mathematics, equations are not always balanced on both sides using equal signs. It can also be about "not equal" relationships, such as one being greater than the other or less than the other. In mathematics, an inequality refers to a relationship in which two numbers or other mathematical expressions do not compare equally. These formulas belong to algebra and are called inequalities.
An inequality means that two things are not the same. One of them may be less than, greater than, less than or equal to, greater than or equal to the other.
p ≠ q means p is not equal to qp < q means p is less than qp > q means p is greater than qp ≤ q means p is less than or equal to qp ≥ q means p is greater than or equal to qAccording to the question:
As based on the information,
he can't spent more than $780.
Four cycle reflector cost = 2 × $19.41
= $38.82
Let maximum number of outfit = x
and Cost = 46.60x
and the the pair of glove is for $35.27.
Therefore,
New bicycle + Bicycle reflectors + Biker gloves + Biking Outfit ≤ 780
⇒ $398.35 + $ 38.82 + $ 35.27 + $46.60 x ≤ 780
⇒ 472.44 + $ 46.60x ≤ 780
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Help w number 1 please super confused
An equilateral triangle is one that has all three of its sides be in line with one another.A slash mark is used to indicate the congruent sides.Congruent angles are ∠L and ∠X, ∠G and ∠Y, and ∠F and ∠T.
How do you identify congruent angles?An equilateral triangle is one that has all three of its sides be in line with one another.A slash mark is used to indicate the congruent sides.An equilateral triangle always has angles that are 60° in length.
It is referred to as an isosceles triangle when a triangle's two sides are identical. When the corresponding sides and angles of two angles match, the angles are said to be congruent.
When stacked, two angles are also congruent if they match.
If they line up with each other after turning or moving it, then.
Also creating equivalent vertex angles are a parallelogram's diagonals.
Congruent sides - L and X, G and Y, and F and T.
Congruent angles - ∠L and ∠X, ∠G and ∠Y, and ∠F and ∠T.
ΔLGF ≅ ΔXYT
Congruent angles are ∠L and ∠X, ∠G and ∠Y, and ∠F and ∠T.
Congruent sides are L and X, G and Y, and F and T.
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A torch and a battery cost 2. 50 altogether. The torch costs 1. 50 more than the battery. What fraction of the total price is the torch?Give your answer in its simplest form
The fraction of the total price that the torch is is 4/5.
Let x be the cost of the battery.
We know that the torch cost is 1.50 more than the battery cost. So, the cost of the torch is
x + 1.50
The total cost is the sum of the cost of the battery and the torch, so:
x + (x + 1.50) = 2.50
2x + 1.50 = 2.50
Solving this equation we get,
x = 0.50
Therefore the cost of the battery is 0.50 and the cost of the torch is 2.00.
To find the fraction of the total price that the torch is, we divide the cost of the torch by the total cost:
= (2.00) / (2.50)
= 4/5
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A rocket is set to blast from the surface of Earth. What speed will it need to achieve in order to stay in orbit around the Earth at an altitude of 300 km? Note distance here to the center of the Earth is 6.7*10^6 km and the mass of Earth is 6*10^24.
Answer:
For example, a spacecraft leaving the surface of Earth needs to be going 7 miles per second, or nearly 25,000 miles per hour to leave without falling back to the surface or falling into orbit.
Convert 17 cm to decimeters
Answer: 1.7
Step-by-step explanation: First, let's see how many decimeters are in 1 cm. To find it, we must divide the cm by 10. So, we can do 17 / 10 or move the decimal one spot left. They should both = 1.7. I hope this helped!
Find the Wronskian of the following vector functions: u(t) = [3t - 1 -2t], v(t) = [-2t + 1 3t] a). 12 t^2 b). -12 t^2 - t c). -13 t^2 - t d). -5 t^2 + 2t e). 5t^2 - t f). None of the above.
The Wronskian of the given vector functions is [tex]5t^2-t[/tex]. So the option e is correct.
In the given question, we have to find the Wronskian of the following vector functions:
[tex]u(t) = \left [ \begin{matrix}3t - 1\\ -2t\end{matrix} \right ][/tex] and [tex]u(t) = \left [ \begin{matrix}-2t + 1\\ 3t\end{matrix} \right ][/tex]
Thomas Muir gave the Wronskian determinant its name after Józef Hoene-Wroski introduced it in 1812. It is applied to the study of differential equations, and in some cases, it can reveal linear independence among a group of solutions.
Wronskian vector functions = [tex]\left | \begin{matrix}3t - 1 & -2t\\ -2t + 1 & 3t\end{matrix} \right |[/tex]
Now solving the vector
Wronskian vector functions = (3t-1)3t - (-2t)(-2t+1)
Wronskian vector functions = [tex]9t^2-3t + 2t(-2t+1)[/tex]
Wronskian vector functions = [tex]9t^2-3t -4t^2+2t[/tex]
Wronskian vector functions = [tex]5t^2-t[/tex]
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In the diagram, if PW = 12 and PT = 9, find PX.
The length of segment PX in this problem is given as follows:
PX = 9.
How to obtain the length of segment PX?The theorem used to solve this problem is given as follows:
A line parallel to one side of a triangle divides the other two proportionately.
In this problem, all the horizontal lines are parallel, hence the side is divided proportionality, as the resulting triangles in the context of this problem are all similar.
PX is three-fourths of the length of the segment PW = 12, hence it's length is given as follows:
PX = 3 x 12/4
PX = 3 x 3
PX = 9 units.
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here are the number of hours that 9 students spend on the computer on a typical day: 1 6 7 6 8 11 6 12 15 the data from the above 9 students form what type of distribution?
The data from the 9 students represents the number of hours that they spend on the computer on a typical day. It forms a distribution known as a frequency distribution.
A frequency distribution is a tabular representation of data that shows how often each value or set of values of a variable occurs in a data set. The data set is typically divided into a number of classes or bins, and the frequency of each class is recorded.
In this case, the data represents the number of hours that 9 students spend on the computer on a typical day. Each student is represented by one data point, and the frequency of each value (the number of hours) is recorded.
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Please Help me out!!
The solution to f(g(h(x))) = [tex]x^{2} - 12x^{3/2} + 54x -108\sqrt{x} + 87[/tex]
f(x) = [tex]x^{4} + 6[/tex]
g(x) = [tex]x-3[/tex]
h(x) = [tex]\sqrt{x}[/tex]
Therefore to find f(g(h(x))),
fogoh(x) = f(g(h(x)))
We first substitute the value of h(x) as above,
f(g([tex]\sqrt{x}[/tex] )) ....... as h(x) = [tex]\sqrt{x}[/tex]
Now, we substitute the value of g(x) where x is [tex]\sqrt{x}[/tex]
f([tex]\sqrt{x} -3[/tex]) ....... as g(x) = [tex]x-3[/tex]
Then we substitute the value of x in f(x) with [tex]\sqrt{x} -3[/tex]
[tex](\sqrt{x} -3)^{4} + 6[/tex]
Now we further solve to find a simpler form of the equation,
[tex](\sqrt{x} -3)^{4} + 6[/tex]
= [tex](x^{2} -12x^{3/2} +54x- 108\sqrt{x} +81) + 6[/tex]
= [tex]x^{2} - 12x^{3/2} + 54x -108\sqrt{x} + 87[/tex]
Therefore, fogoh(x) = f(g(h(x))= [tex]x^{2} - 12x^{3/2} + 54x -108\sqrt{x} + 87[/tex]
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Can anyone help me answer this question?
In a geometric progression, the first term is 7, the last term 448 and the sum 889. Find
the common ratio.
Answer:
Step-by-step explanation:
Given : In a GP the first term is 7
the last term is 448
and the sum 889
To find : Common ratio ? The number of terms is 7.
The common ratio is 2
Answer:
common ratio (r) = 2
Step-by-step explanation:
solution in picture
A school has a square courtyard and wants to create diagonal walkways. the length of
each side of the courtyard is 25 meters. approximately how long is each walkway?
The length of each side of the courtyard is 25 meters. Then 35.36 meters long is each walkway.
In the given question, a school has a square courtyard and wants to create diagonal walkways.
The length of each side of the courtyard is 25 meters.
We have to find how long is each walkway.
By dividing the square in half to form a right triangle, you can find the solution. The Pythagorean theorem can then be used to find the hypotenuse.
According the Pythagorean Theorem
[tex]a^2+b^2 = c^2[/tex]
[tex](25)^2+(25)^2=c^2[/tex]
Now solving,
625 + 625 = [tex]c^2[/tex]
[tex]c^2[/tex] = 1250
Taking square root on both side, we get
c = 35.36 meters.
Hence, 35.36 meters long is each walkway.
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If h(x) = -x(1 - x), find h(-3).
Answer:
12
Step-by-step explanation:
h(-3)= -(-3)(1-(-3))=
3(4)=12
If a square is 12 cm 8 cm and 10 cm what is the volume 
Answer: 960cm^2
Step-by-step explanation: 12 x 8 = 96 x 10 = 960
Answer:
a) 1728 [tex]cm^{3}[/tex]
b) 512 [tex]cm^{3}[/tex]
c) 1000 [tex]cm^{3}[/tex]
Step-by-step explanation:
(I think your question is ...a little mixed up as a square has same length for all of its respective sides. So I will attempt to do them a little differently as I believe the question must have had three different sub questions)
a) [tex]V = s^{3}[/tex]
"s" here represents the respective length for the sides.
The answer for if a side was 12 centimeters, then the volume would be
[tex]V = 12^{3}[/tex]
Which would give us a volume of 1728 [tex]cm^{3}[/tex]
b)[tex]V = s^{3}[/tex]
"s" here represents the respective length for the sides.
The answer for if a side was 8 centimeters, then the volume would be
[tex]V = 8^{3}[/tex]
Which would give us a volume of 512 [tex]cm^{3}[/tex]
c)[tex]V = s^{3}[/tex]
"s" here represents the respective length for the sides.
The answer for if a side was 10 centimeters, then the volume would be
[tex]V = 10^{3}[/tex]
Which would give us a volume of 1000 [tex]cm^{3}[/tex]
In ΔKLM, k= 1.2 cm, � m∠L=93° and � m∠M=6°. Find the length of I, to the nearest 10th of a centimeter
Using the law of sines, the length of l is: 12.1 cm.
What is the Law of Sines?The Law of Sines is a theorem in triangle geometry that relates the lengths of the sides of a triangle to the sine of its angles. It states that for any triangle, the ratio of the length of a side to the sine of the angle opposite that side is the same for all three sides.
Given the following:
k = 1.2 cm
m<L = 93°
m<M = 6°
m<K = 180 - 93 - 6 = 81°
Using the law of sines, sin K/k = sin L/l:
sin 81/1.2 = sin 93/l
Find l:
(sin 81)(l) = (sin 93)(12)
l = (sin 93)(12)/(sin 81)
l = 12.1 cm
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suppose car gas mileage is normally distributed with a mean of 25 miles per gallon. if 67% of cars get at least 23 miles per gallon, what percentage of cars get less than 30 miles per gallon? a
So, on solving the provided question, we can say that percentage = 1/15 X 100 = 15%
What is percentage?A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used. It is frequently denoted using the percent symbol "%," though. The amount of percentages has no dimensions. With a denominator of 100, percentages are basically fractions. To show that a number is a percentage, place a percent symbol (%) next to it. For instance, if you correctly answer 75 out of 100 questions on a test (75/100), you receive a 75%. To compute percentages, divide the amount by the total and multiply the result by 100. The percentage is calculated using the formula (value/total) x 100%.
car gas mileage is normally distributed with a mean of = 25 miles per gallon
67% of cars get at least 23 miles per gallon
percentage of cars get less than 30 miles per gallon
25-23/30
2/30
1/15
percentage = 1/15 X 100 = 15%
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Area under the curve
f(x) = x 2 + 2x
g(x) = x + 2
Answer: The area under the curve refers to the area between the curve of a function and the x-axis. To find the area under the curve of a function, you would typically integrate the function with respect to x and then evaluate the definite integral between a set of limits.
For example, to find the area under the curve of f(x) = x^2 + 2x from x=0 to x=a, we would integrate the function with respect to x,
∫[0,a] (x^2 + 2x) dx = (1/3)x^3 + x^2 evaluated from x=0 to x=a,
Similarly, to find the area under the curve of g(x) = x + 2 from x=0 to x=a, we would integrate the function with respect to x,
∫[0,a] (x + 2) dx = (1/2)x^2 + 2x evaluated from x=0 to x=a
It's important to note that the definite integral is only defined if the function is continuous and has no vertical asymptotes on the interval.
Step-by-step explanation:
The citizens of a certain community were asked to choose their favorite pet. The pie chart below shows the distribution of the citizens' answers. If there are 130,000citizens in the community, how many chose Cats, Dogs, or Birds
On solving the provided question, we can say that be equation the value we obtain Number of citizens × total percentage = 140,000 x (23%+11%) = 47,600
What is equation?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.
number of citizens who chose cat or fish is 47,600
Number of citizens × total percentage
140,000 x (23%+11%)
140,000 x 34%
= 47,600
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What is the lateral surface area of this figure in cm2? Round to the nearest 10th. Hint: you will need Pythagorean Theorem to solve.
The surface area of the prism in this problem is given as follows:
46 cm².
What is a surface area?A surface area is given by the sum of all the areas that compose the figure.
The prism in this problem is composed as follows:
One square of side length s = 2 cm.Two right triangles of dimensions 2 cm and 7 cm.Two rectangles of dimensions 2 cm and 7 cm.The area of the square is given by the side squared, hence:
As = 2² = 4 cm².
The area of a right triangle is given by half the multiplication of the side lengths, hence:
At = 2 x 0.5 x 2 x 7 = 14 cm².
The area of a rectangle is given by the multiplication of the dimensions, hence:
Ar = 2 x 2 x 7 = 28 cm².
Hence the surface area of the prism is then obtained as follows:
S = As + At + Ar
S = 4 + 14 + 28
S = 46 cm².
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Dr. Coleman is a zoologist who studies giant pandas. Giant pandas are very tiny when they are born but grow to be quite large. The function f(x) gives the weight, in pounds, of a particular female panda when she was x years old. What does f(4)=f(30) tell you?
The information shows that f(4)=f(30) tells us that the weight of a particular female panda at 4 years old is the same as her weight at 30 years old.
What is the function?It is a mathematical expression, rule, or law that establishes the relationship between an independent variable and a dependent variable (the dependent variable).
In this case, Dr. Coleman is a zoologist who studies giant pandas. Giant pandas are very tiny when they are born but grow to be quite large. The function f(x) gives the weight, in pounds, of a particular female panda when she was x years old.
The function illustrated shows that the weights are the same.
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What is the 4 in front of the formula called?
The 4 in front of the formula is called a coefficient.A coefficient is a number that is multiplied by a variable or a constant in an algebraic expression.
In this case, the 4 is being multiplied by the formula, which makes it a coefficient.
A coefficient is a numerical value that is used in an algebraic expression or equation. It is placed in front of a variable or a constant, and it is multiplied by that particular element. The coefficient is used to adjust the value of the expression or equation, and it can be any number, including fractions, negative numbers, and decimals. For example, if a formula were written as 4x + 2 = 10, then the 4 in front of the x is the coefficient. This number is used to adjust the value of the expression, and it can be changed to any other number in order to alter the equation. Coefficients are very useful in mathematics, and they can be used to solve many types of equations and problems.
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what is the maximum of the sinusoidal function? enter your answer in the box.
Answer:
Step-by-step explanation:
B
Zell invested $80,000 in two different types of stocks. The first type earned 9% and the second type earned 12%. If the profit on the 12% stocks was $150 more than the profit on the 9% stocks, how much did Zell invest in the 9% stock?
Zell invested $80,000 in two different types of stocks. Solving for x gives us the amount invested in the 9% stock:
x = $45000
What is stock?Generally, Let x be the amount invested in the 9% stock.
Then (80,000 - x) is the amount invested in the 12% stock.
The profit on the 9% stock is 0.09 * x and the profit on the 12% stock is
0.12 * (80,000 - x).
We know that the profit on the 12% stock is $150 more than the profit on the 9% stock.
So we can set up the following equation:
0.12 * (80,000 - x)
= 0.09 * x + 150
x=45000
Therefore, Zell invested $80,000 in two different types of stocks. the amount invested in the 9% stock is $45000
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Answer:
$45,000
Step-by-step explanation:
refer to exercise 75. how surprising would it be for more than 4 elk in the sample to survive to adulthood? calculate an appropriate probability to support your answer.
According to the given possibility the event of more than 4 elk surviving to adulthood is not surprising and the appropriate probability is 0.1402.
Here we have given that it be for more than 4 elk in the sample to survive to adulthood.
Then the probability is calculated by using the binomial probability,
And here we have to use the addition rule for mutually exclusive event, then we get,
=> P(AUB) = P(A or B) = P(A) + P(B)
At the possibility of k = 5 we have the binomial probability to be evaluated as follows:
=> P(X = 5) = 21 (0.44)⁵ (0.56)² ≈ 0.1086
At the possibility k = 6 then the binomial probability to be calculated as,
=> P(X = 6) = 7(0.44)⁶ (0.56)¹ ≈ 0.0284
Finally at the value of k = 7 then the binomial probability to be evaluated as,
=> P(X = 7) = 1 (0.44)⁷(0.56)° ≈ 0.0032
Therefore the two different numbers of successes are impossible on same simulation is by applying the addition rule for mutually exclusive events is calculated as,
=> P(X > 4) = P(X = 5) + P(X = 6) + P(X = 7)
=> 0.1086 +0.0284 + 0.0032
=> 0.1402
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give the equation of the line in slope intercept form of the line with a slope of -4/3 and that passes through the point (3,-3)
[tex](\stackrel{x_1}{3}~,~\stackrel{y_1}{-3})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{4}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-3)}=\stackrel{m}{- \cfrac{4}{3}}(x-\stackrel{x_1}{3}) \implies y +3= -\cfrac{4}{3} (x -3) \\\\\\ y+3=-\cfrac{4}{3}x+4\implies {\Large \begin{array}{llll} y=-\cfrac{4}{3}x+1 \end{array}}[/tex]
By what factor would you need to change the radius of a sphere, such that its volume increased by a factor of 7? Please include step by step calculations!
The factor by which radius of the sphere be changed is 1.91, which is calculated by applying the concepts of surface area and volume on the assigned problem.
What do you mean by volume?
Volume is defined as the 3D measurement that deals with the amount of space required by an object. It is always calculated in cubic units. Its basic unit is cubic metre.
Calculation of the change in radius of sphere when its volume is increased by 7Let the radius and volume of sphere be r and v respectively
Volume of sphere, v = 3.16 × ( r )3 —- 1
Now, changed radius, R = xr
Where x is the factor, we need to calculate
Changed volume, V = 7v = 3.16 × ( R )3 -— 2
From equations 1 and 2, we get,
7v / v = ( R )3 / ( r )3
7 = ( xr )3 / ( r )3
7 = (x)3 × 1
Taking cube root both sides,
x = 1.913
Hence, the factor by which radius of the sphere be changed is 1.91.
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