The Elements can be defined as a mathematical treatise which comprises 13 books that are attributed to the ancient Greek mathematician who lived in Alexandria, Ptolemaic Egypt c. 300 BC and called Euclid.
Basically, the Elements is a collection of the following geometric knowledge and observations:
DefinitionsPostulatesPropositionsMathematical proofs of the propositions.Based on my experiences so far, an approach to geometry which I prefer is Euclidean geometry because it's much easier than analytical geometry. Also, an approach that is easier to extend beyond two-dimensions is Euclidean geometry because it can be extended to three-dimension.
A situation in which one approach to geometry would prove to be more beneficial than the other is when dealing with flat surfaces. In Euclidean geometry, a correspondence can be established between geometric curves and algebraic equations.
Read more on Euclidean here: brainly.com/question/1680028
#SPJ5
Suppose that $17,699 is invested at an interest rate of 6.6% per year, compounded continuously
a) Find the exponential function that describes the amount in the account after time t, in years.
b) What is the balance after 1 year? 2 years? 5 years? 10 years?
c) What is the doubling time?
[tex]s(t) = 17699(1 .066) {}^{t} [/tex]
b)[tex]s(1) = 17699(1.066) = 18867.13 \\ s(2) = 17699(1.066) {}^{2} = 20112.36 \\ s(5) = 17699(1.066) {}^{5} = 24363.22 \\ s(10) = 17699(1.066) {}^{10} = 33536.73[/tex]
c)[tex]s(t) = 2 \times initial \: capital \: \\ s(t) = 2 \times 17699[/tex]
[tex]17699(1.066) {}^{t} = 2 (17699) \\ 1.066 {}^{t} = 2 \\ t = log¹°⁰⁶⁶(2) = 10.84511 \: years[/tex]
what is the best estiment of the mass of a bowling ball
Step-by-step explanation:
The heaviest legal bowling ball weighs 16 pounds. The lightest weight you can usually find at most bowling alleys is six pounds.
PLEASE MARK ME AS BRAINLIST
12. The base of a triangle with an area of 36 squared inches is 4.2 inches. What is the area of a similar
triangle whose base measures 5.6 inches?
The 4.2 inches base length and 36 in.² area of the given triangle and the 5.6 inches base length of the similar triangle gives the area of the similar triangle as 64 square inches
Which method can be used to find the area of the similar triangle given the dimensions?Area of a triangle = (Base length × Height)/2
Area of the given triangle = 36 in.²
Base length of the given triangle = 4.2 inches
Base length of the similar triangle = 5.6 inches
Therefore;
Area of the given triangle = (Base length × Height)/2
Which gives;
36 = (4.2 × h)/2
Where;
h = Height of the given triangle
36 × 2 = 4.2 × h
[tex]h = \mathbf{\frac{36 \times 2}{4.2}} = 17 \frac{1}{7} [/tex]
Height of the given triangle, h = 17+ 1/7
The ratio of corresponding sides of similar triangles are the same, which gives;
[tex] \frac{5.6}{4.2} = \frac{h'}{17 \frac{1}{7}} [/tex]
Where;
h' = The height of the similar triangle
Which gives;
[tex] h' = \frac{5.6}{4.2} \times 17 \frac{1}{7} = 22 \frac{6}{7} [/tex]
The area, A', of the similar triangle is therefore;
[tex] A' = \frac{1}{2} \times 5.6 \times 22 \frac{6}{7} = 64 [/tex]
The area of the similar triangle A' = 64 in.²The area can also be obtained using the scale factor of area as follows;
(4.2/5.6)² = 36/A'Which gives;
A' = 64 square inchesLearn more about scale factors of calculations here:
https://brainly.com/question/25722260
#SPJ1
Given that a function, g, has a domain of -20 < x < -5 < g(x) <45 and that g(0)= -2 and g(-9)= 6, select the statement that could be true for g.
The given statement that's true about the function is g(-13) = 20 is true for g.
How to illustrate the function?From the information given, the function, g, has a domain of -20 < x < -5 < g(x) <45 and that g(0)= -2 and g(-9)= 6.
Let's analyze the options that are given in the scenario. g(7) = -1. It should be noted that 7 isn't in our domain. Therefore, this isn't possible.
g(-13) = 29
x = 13 is in our domain and 20 is also is in our range. Therefore, this is true for g.
g(0) = 2.
This isn't true because it is given that g(0) = 2
In conclusion, the given statement that's true about the function is g(-13) = 20 is true for g.
Learn more about functions on:
brainly.com/question/10684895
#SPJ1
Miriam charges $5 per trip for deliveries plus $0.50 per mile, If x= the number of miles
Miriam drives for a trip and y = the total cost for a trip, which of these ordered pairs is a
solution to the equation that describes this situation? (1 Point)
(10, 10)
(2,7)
(12, 12)
(5, 6.5)
Answer:
(10,10)
Step-by-step explanation:
y = .5x + 5
If you put in 10 for x, we get 10 for y.
y = .5(10) + 5
y =5 + 5
y = 10
When x is 10, y is 10 (10,10)
A "Shirley Temple" drink is made by a 5.
mixing 2 cups of 7-Up with 4 tablespoons
of grenadine syrup. Write a ratio of
grenadine syrup to 7-Up. (hint: 160 lstot of an
Tablespoons = 1 Cup)
The ratio of grenadine syrup to 7-Up will be 1:8.
How to find the ratio?From the information given, we are told that Shirley Temple" drink is made by a 5 mixing 2 cups of 7-Up with 4 tablespoons of grenadine syrup.
The ratio of grenadine syrup to 7-Up will be:
4 tablespoon : 2 cups
Note that 1 cup = 16 teaspoon
4 : (2 × 16)
= 4:32
= 1:8
Therefore, the ratio of grenadine syrup to 7-Up will be 1:8.
Learn more about ratio on:
brainly.com/question/2328454
#SPJ1
You inherit one million dollars. You invest it all in three accounts for one year. The first account pays 3% compounded annually, the second account pays 4% compounded annually, and the third account pays 2% compounded annually. After one year, you earn $34,000 in interest. If you invest four times the money into the account that pays 3% compared to 2%, how much did you invest in each account?
The amount that was invested are at 3% = 400000, at 4% = 500000 and at 2% = 100000
How to solve for the amount investedWe have x + y + z = 1000000
((1+0.03)x - x)+ ((1+0.04)y - y) + ((1 + 0.02)z-z) = 34000
4z + x + z = 1000000
((1+0.03)4z - 4z)+ ((1+0.04)y - y) + ((1 + 0.02)z-z) = 34000
((1+0.03)4z - 1)+ ((1+0.04)y - 1) + ((1 + 0.02)z-1) = 34000
12/100z + 4/100y +2/100z = 34000
2y + 7z = 1700000
-2y - 10z = -2000000
2y + 7z = 1700000
Solve through the use of the simultaneous linear equation
z = 100000
y = 500000
x = 400000
The amount that was invested are at 3% = 400000, at 4% = 500000 and at 2% = 100000
Read more on compounding here:
https://brainly.com/question/2449900
#SPJ1
Identify the vertex of the parabola ?
Step-by-step explanation:
second one
explanation: trust me bro
Perform the operation and
simplify.
3
x - 3
5
x + 2
-2x + 21
x² + [ ? ]x + [
Answer: -1
Step-by-step explanation:
Here, we are subtracting two fractions; therefore, we must make the denominators the same by finding the least common multiple. Since we have x - 3 for one denominator and x + 2 for the other, we don't have any common factors. Hence, the least common multiple would be their product.
[tex](x-3)(x+2)\\x(x-3)+2(x-3)\\x^2-3x+2x-6\\x^2-x-6[/tex]
The question is looking for the coefficient of the second term. Since there is just a negative sign in front of the x, the "?" can be filled with either a negative sign or a -1.
Tamela plants 6 rows of t tomato plants each. How many tomato plants did she plant?
Answer:
6t tomato plants
Step-by-step explanation:
There are 6 rows, Tamala places t in each row. We multiply 6 by t.
If t were 5, the tomato plants would be 30 since we multiply the rows by the number of tomato plants
Answer:
6t
Step-by-step explanation:
number of rows × number of plants per row = total number of plants
6 × t = 6t
Answer: 6t
Use the midpoint rule with the given value of n to approximate the integral. (Round your answer to four decimal places.)
16
0
sin
x
dx, n = 4
Split up [0, 16] into 4 equally-spaced subintervals of length [tex]\frac{16-0}4=4[/tex],
[0, 16] = [0, 4] U [4, 8] U [8, 12] U [12, 16]
with midpoints 2, 6, 10, and 14, respectively.
Then with the midpoint rule, we approximate the integral to be about
[tex]\displaystyle \int_0^{16} \sin(\sqrt x) \, dx \approx 4 \left(\sin(\sqrt2) + \sin(\sqrt6) + \sin(\sqrt{10}) + \sin(\sqrt{14})\right) \approx \boxed{4.1622}[/tex]
help please.
Malaysia police traffic department claims that 54% of fatal car accidents are caused by driver error. A researcher studies 30 randomly selected accidents and founds that 14 were caused by driver error. Using a = 0.05, is that Malaysia police traffic department's statement is true?
Answer:
The Malaysia police departments statement was true, because 14/30 is extremely close to 54% (roughly 15.5/30).
Type: Probability
Please rate this answer based on how helpful it was!If Emery has $1,400 to invest at 5% per year compounded monthly, how long will it be before he has $2,400? If the compounding is
continuous, how long will it be? (Round your answers to three decimal places.)
Answer:
Step-by-step explanation:
(1400x14.5x5%) + 1400 =2415
Answer: 14.5 months
round 00.963.785 to the nearest. hundredth
Solve the inequality
21≥t+10
The answer is t ≤ 11.
Subtract 10 from each side.21 - 10 ≥ t + 10 - 10t ≤ 11Como derivar cos(2x)/tan(2x)
Use the quotient and chain rules. If
[tex]y = \dfrac{\cos(2x)}{\tan(2x)}[/tex]
then the derivative is
[tex]\dfrac{dy}{dx} = \dfrac{\tan(2x) \frac d{dx}\cos(2x) - \cos(2x) \frac d{dx}\tan(2x)}{\tan^2(2x)}[/tex]
[tex]\dfrac{dy}{dx} = \dfrac{\tan(2x) (-\sin(2x)) \frac d{dx}(2x) - \cos(2x)\sec^2(2x) \frac d{dx}(2x)}{\tan^2(2x)}[/tex]
[tex]\dfrac{dy}{dx} = \dfrac{-2\sin(2x)\tan(2x) - 2 \sec(2x) }{\tan^2(2x)}[/tex]
and we can rewrite this by
• multiplying by [tex]\frac{\cos^2(2x)}{\cos^2(2x)}[/tex],
[tex]\dfrac{dy}{dx} = \dfrac{-2\sin^2(2x)\cos(2x) - 2 \cos(2x) }{\sin^2(2x)}[/tex]
• factorizing,
[tex]\dfrac{dy}{dx} = -\dfrac{2\cos(2x) \left(\sin^2(2x) + 1\right)}{\sin^2(2x)}[/tex]
etc
please help urgently
Answer:
2
Step-by-step explanation:
Substitute:
2(1)(3)+2 / 2(1)(3)-2 =
6 + 2 / 6 - 2 =
8 / 4 =
2.
Hey there!
2ab + 2 / 2ab - 2
= 2(1)(3) + 2 / 2(1)(3) - 2
= 2(3) + 2 / 2(3) - 2
= 6 + 2 / 6 - 2
= 8 / 4
= 2
Therefore, your answer should be: 2
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
if this graph of f(x)=a^(x+g) +k then;
A. the domain is (h,∞) and the range is (-∞,∞)
B. the domain is (-∞,∞) and the range is (h,∞)
C. the domain is (h,∞) and the range is (k,∞)
D. the domain is (-∞,∞) and the range is (k,∞)
The correct option regarding the domain and the range of the function f(x)=[tex]a^{x+g} +k[/tex] is given by that the domain is (-∞,∞) and the range of the function is (k,∞).
Given a function f(x)=[tex]a^{x+g} +k[/tex].
We are told to find the domain and range of the function.
The domain is basically the values which we enters in a function.
The range is basically the values which we are getting by entering some values in the function.
An exponential function is given in the function which has no restrictions hence the domain is (-∞,∞).The range depends on the vertical shift given by k. Hence the range of function is (k,∞).
Hence the correct option regarding the domain and the range of the function f(x)=[tex]a^{x+g} +k[/tex] is given by that the domain is (-∞,∞) and the range of the function is (k,∞).
Learn more about function at https://brainly.com/question/10439235
#SPJ1
Find the missing segment in the image below
Answer:
42
Step-by-step explanation:
similar triangles
24/x = (24+8)/x+14
that looks complicated so we do
8/24 = 14/x
or
24/8 = x/14
3 = x/14
x = 3*14
x = 42
we test it with the first equation
24/42 = 32/56
simplify
4/7 = 4/7
true so 42 is correct
A machinist needs 98 pieces of steel rod. The rods come in bundles of 8 pieces. How many bundles of steel rod does the machinist require?
Given that the pieces of steel rods comes in bundles, the mechanist will require 13 bundles of steel rods to get the 98 pieces of steel rod he needs.
How many bundles of steel rod does the machinist require?Given the data in the question;
Machinist needs 98 pieces of steel rodThe rods come in bundles of 8 piecesNumber of bundles of steel rods required by the mechanist = ?To determine the bundle of steel required, let y represent the bundle.
Since;
1 bundle = 8 piece
y bundle = 98 piece
We cross multiply
y bundle × 8 piece = 1 bundle × 98 piece
y = ( 1 bundle × 98 piece ) / ( bundle × 8 piece )
y = 98 pieces / 8 piece
y = 12.25 ≈ 13
Given that the pieces of steel rods comes in bundles, the mechanist will require 13 bundles of steel rods to get the 98 pieces of steel rod he needs.
Learn more word problems here: brainly.com/question/2610134
#SPJ1
Write an absolute value equation to satisfy the given solution set shown on a number line
(infinity -1/2]u [-1/2 -1/2] u [1/2 infinity)
2) Find the perimeter and area of the figures:
a)
P =
A =
8
8 ft.
b)
P =
A =
12
5m
Answer:
8+8+12+5= 33
Step-by-step explanation:
8+8+12+5=33
Your family borrowed $400,000 from the bank to purchase a new home. If the bank charges 3.8%
interest per year, compounded weekly, it will take 25 years to pay off the loan. How much will each
weekly payment be?
Answer:
472.19
Step-by-step explanation:
$472.19 weekly
Thus the required weekly installment is $402.30 for 25 years.
Given,
The family borrowed $400,000 from the bank to purchase a new home.
the bank charges 3.8% interest per year, compounded weekly, it will take 25 years to pay off the loan. How much will each weekly payment to be determined?
Statistics is the study of mathematics that deals with relations between comprehensive data.
The principle amount to refund = 400,000
Let the principle amount for weekly = P
Rate per year = 3.8%
Tenure = 25 year
For weekly installments,
52 Weeks in a year
Tenure = 25/52
Now,
[tex]Amount = P(1-(1+r)^{-tn})/i\\400000 = P (1-(1+0.038/52)^{-25*52}) / (0.038/52)\\400000 * 0.038/52 = P(1-(52.038)^{-25*52})\\292.30 = P(1-(1.001)^{-1300})\\292.30 = P(1-0.273)\\292.30=P * 0.727\\P = 402.30[/tex]
Thus the required weekly installment is $402.30 for 25 years.
Learn more about Statistics here:
https://brainly.com/question/23091366
#SPJ5
A ball is thrown from an initial height of 2 meters with an initial upward velocity of 25 m/s . The ball's height h (in meters) after t seconds is given by the following.
The value of values of t for which the ball's height is 7 meters then is 4.79secs.
What is velocity?Velocity can be regarded as a vector measurement of the rate as well as direction of motion.
It is the the speed at which something moves in one direction and with the given velocity, the time as well as the distance can be calculated as :
Given:
h=2+25t-5t^2
But h=7
Then 2+25t-5t^2=7
-5t^2++25t +2-7=0
-5t^2+25t -5=0
we can then factorize as :
-5(t^2+5t -1)=0
Solving the equation using quadratic formula, the the roots of equations are: 4.79 and -5.0
The value of values of t for which the ball's height is 7 meters then is 4.79secs.
Learn more about Velocity at;
https://brainly.com/question/6504879
#SPJ1
COMPLETE QUESTION :
A ball is thrown from an initial height of 2 meters with an initial upward velocity of 25 m/s . The ball's height h (in meters) after t seconds is given by the following. h=2+25t-5t^2
Find all values of t for which the ball's height is 7 meters.
Round your answer(s) to the nearest hundredth.
The formula for the perimeter of a rectangle is 2L + 2W = P (L = length, W = Width and P = Perimeter.) The perimeter of a rectangular garden is 400 feet. If the length of one side of the garden is 120 feet, what is the width of one side of the garden?
We conclude that the width of the rectangular garden is 80 feet.
How to get the dimensions of the garden?Let's define the variables:
L = length of the garden.W = width of the garden.The perimeter of a rectangle of length L and width W is given by the simple formula:
P = 2*(L + W)
The perimeter is equal to 400ft, then:
400ft = 2*(L + W)
And we know that the length is 120ft, then:
L = 120ft.
Replacing the length in the perimeter equation we get:
400ft = 2*(120ft + W)
Now we can solve this linear equation for W.
400ft/2 = 120ft + W
200ft = 120ft + W
200ft - 120ft = W
80ft = W
We conclude that the width of the rectangular garden is 80 feet.
If you want to learn more about rectangles:
https://brainly.com/question/17297081
#SPJ1
Caisse can download a maximum of 1000 mb of songs or movies to her smartphone each month. the file of each movie is 85mb, and the file of each song is 4mb. write an inequality that represents the number of movies(M) and songs(S) that Caisse downloads each month?
If Caisse can download a maximum of 1000 mb of songs or movies then the inequality that represents the number of movies and songs that Caisse downloads each month is 85x+4y<1000.
Given that Caisse can download a maximum of 1000 mb of songs or movies to her smartphone each month. the file of each movie is 85mb, and the file of each song is 4mb.
We are required to find the inequality that represents the number movies and songs that Caisse downloads each month.
Inequality is like an equation that shows the relationship between variables that are expressed in greater than, less than , greater than or equal to , less than or equal to sign.
let the number of movies be x and the number of songs be y.
According to question Caisse cannot download more than 1000 mb, so we will use less than towards equation.
It will be as under:
85x+4y<1000.
Hence if Caisse can download a maximum of 1000 mb of songs or movies then the inequality that represents the number of movies and songs that Caisse downloads each month is 85x+4y<1000.
Learn more about inequality at https://brainly.com/question/11613554
#SPJ1
Hello please help asap!! i will mark brainliest and this is worth 20 points!!!!! tysm
The least number of colors you need to correct color in the sections of these pictures so that no two touching sections are the same color is 5 colors. This can be obtained by simply giving colors to the small shapes according to the criteria.
What is the least number of colors?From the question the figure, the number of colored sections with which are not colored with respect to a "touching" colored section, would not be half of the total colored sections since the sections are not alternating as they still meet at a common point.
After all, it notes no two touching sections, not adjacent sections.
There is no equation to calculate this requirement with respect to the total number of sections.
Taking one triangle or square as the starting we can give colors to each small units. This figure will be the start of sequence of other small figures.
If a square were to be this starting shape that have same color as that color of the square.
Now from the remaining given another color to the starting figure. We will get that shapes, that will have same color.
Like that the remaining figures are given colors.
Therefore, the least number of colored sections you can color in the sections meeting the given requirement, is 5 sections for this first figure.
Hence the least number of colors you need to correct color in the sections of these pictures so that no two touching sections are the same color is 5 colors.
Learn more about colored sections here:
brainly.com/question/17110851
#SPJ1
Find the area of figure below,
Answer: 57 cm²
Step-by-step explanation:
We can split this figure into two shapes: the rectangle on the left and the triangle on the right. We can find the area of each separately and add them to get the total area.
RectangleThe area of a rectangle is [tex]lw[/tex], where l is the length and w is the width. We can just multiply 8 and 6 to get the area of the rectangle.
[tex]A=8*6\\A=48[/tex]
TriangleThe area of the triangle is [tex]\frac{1}{2}bh[/tex], where b is the base of the triangle and h is the height. Here' the base would be 6 cm as opposite sides of a rectangle have the same measure, and the height is 3.
[tex]A=\frac{1}{2}(6*3)\\A=\frac{1}{2}(18)\\A=9[/tex]
TotalThe total area would just be the sum of the two separate areas.
[tex]48+9=57[/tex]
Hence, the area of the figure is 57 cm².
Answer: 57 cm^2
Step-by-step explanation:
To find the entire area of the figure, we have to find the area of the rectangle and the triangle and sum it up
The area of the rectangle is 6 * 8 = 48 cm^2
The area of the triangle is 1/2 * 3 * 6(Opposite sides of a rectangle have equal lengths) = 9 cm^2
So the area of the figure is 48 + 9 = 57 cm^2
Which shapes have less than 3 lines of symmetry?
A) B and C
B) A and D
C) B and D
D) A and C
The shapes that have less than 3 lines of symmetry are Isosceles trapezoid and Isosceles triangle
How to determine the shapes that have less than 3 lines of symmetry?The shapes are given as:
Isosceles trapezoidSquareIsosceles triangleRegular PentagonThe lines of symmetry are the lines that, when the shape is rotated through this line, the shape remains the same
As a general rule:
An Isosceles trapezoid and an Isosceles triangle have two lines of symmetry
Hence, the shapes that have less than 3 lines of symmetry are Isosceles trapezoid and Isosceles triangle
Read more about lines of symmetry at
https://brainly.com/question/1460991
#SPJ1
he value of x?
ur answer in the box. need answer quickly! 35 points!
Answer:
x = 46 degrees
Step-by-step explanation:
180 - 134 = 46
Answer:
46°
Step-by-step explanation:
134 + x add to a straight line angle = 180
134+x = 180
x = 46
