20Ne, 19F and Mg₂+ are all examples of species or chemical ions.
How will you describe these ions?20Ne is a stable isotope of Neon, 19F- is a negatively charged fluoride ion, and Mg₂+ is a positively charged magnesium ion. They all have a specific number of protons and electrons, which gives them their chemical properties and their unique behavior.
Chemical ions are atoms or molecules that have gained or lost one or more electrons, resulting in a net electrical charge. This charge can be positive (cation) or negative (anion). Examples of common ions include sodium (Na+) and chloride (Cl-), which combine to form table salt (NaCl).
Therefore, the correct answer is as given above
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Tomhas$84,076inasavingsaccountthatearns15%annually.Theinterestisnotcompounded.Tothenearestdollar,howmuchinterestwillheearnin6months?
Use the formula i = prt, where i is the interest earned, p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years.
$75668.4 is the interest earned in 6 months.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Tom has $84,076 in a savings account that earns 15% annually.
The interest is not compounded.
We have to find the interest he earned in 6 months.
Use the formula i = prt,
where i is the interest earned,
p is the principal (starting amount),
r is the interest rate expressed as a decimal,
and t is the time in years.
i=84076×15/100×6
=84076×0.15×6
=$75668
Hence, $75668.4 is the interest earned in 6 months.
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In an interval whose length is z seconds, a body moves (32z + 2z^ 2 ) ft. What is the average speed v of the body in this interval?
The average speed of the body in the given interval is 32 + 2z ft/s.
The average speed v of a body in an interval of z seconds can be calculated using the formula v = d/t, where d is the distance traveled and t is the time taken.
In this case, the distance d is (32z + 2z^ 2 ) ft and the time taken is z seconds.
Therefore, the average speed v of the body in this interval is:
v = (32z + 2z^ 2 ) ft / zs
v = 32 + 2z ft/s
Therefore, the average speed of the body in the given interval is 32 + 2z ft/s.
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Benjamin gets to go to festival with his friend for $120 The cost covers $45 for his lodging and 2 tickets to the festival, including all of his meals.
How much is a ticket to the festival?
Answer:
is $27.50 per each teacket
711
Put the measures of the angles in order from least to greatest
Answer: [tex]m\angle YOZ, m\angle VOS, m\angle UOZ, m\angle XOS, m\angle TOZ[/tex]
Step-by-step explanation:
[tex]m\angle VOS=90^{\circ}\\\\m\angle UOZ=180^{\circ}-56^{\circ}=124^{\circ}\\\\m\angle YOZ=180^{\circ}-143^{\circ}=37^{\circ}\\\\m\angle XOS=126^{\circ}\\\\m\angle TOZ=180^{\circ}-33^{\circ}=147^{\circ}[/tex]
2. If -2 is the root of a quadratic equation x²-5x+c=0, find
a: the value of c
b: the other root
The value of c according to the given equation as described is; -14.
The other root of the equation in discuss is; 7.
What is the value of c and determine the other root?As evident in the task content; if -2 is the root of a quadratic equation x²-5x+c=0, then x = -2 holds true for the equation; therefore, we have;
a). (-2)² - 5 (-2) + c = 0
4 + 10 + c = 0
c = -14
Hence, the value of c is; -14.
b). By substituting into the equation; we have;
x² - 5x - 14 = 0
(x - 7) (x + 2) = 0
x = 7 OR x = -2.
Therefore, the other root of the equation is; 7.
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Examine the number line,and then choose the correct symbol to complete each statement
After examine the number line,and then the correct symbol to complete each statement is -2/4<-1/4; 3/4>2/4;-1/4<0.
What is Number line ?
A number line is a diagram of a graduated straight line used to represent real numbers in introductory mathematics. It is assumed that every point on a number line corresponds to a real number, and that every real number corresponds to a point.
What is Symbol?
A mark, sign, or term that denotes, denotes, or is taken to denote an idea, an item, or a relationship is known as a symbol. By connecting seemingly unrelated ideas and events, symbols help people look beyond the known and the visible.
In the question given some relation between the real number which are
a) -2/4 < -1/4 because negative number has the property that the those numbers which is smaller is always greater.
b) 3/4 > 2/4 both numbers are positive so clearly it 3/4 comes after 2/4 so it is greater.
c) -1/4 < 0 zero is always greater than the negative numbers
So, after examine the number line,and then the correct symbol to complete each statement is -2/4<-1/4; 3/4>2/4;-1/4<0.
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given vector u equals open angled bracket negative 10 comma negative 3 close angled bracket and vector v equals open angled bracket 4 comma 8 close angled bracket comma what is projvu? open angled bracket negative 640 over 109 comma negative 192 over 169 close angled bracket open angled bracket negative 256 over 109 comma negative 512 over 109 close angled bracket open angled bracket negative 8 comma negative 3 close angled bracket open angled bracket negative 16 over 5 comma negative 32 over 5 close angled bracket
The correct answer is open angled bracket negative 16 over 5 comma negative 32 over 5 close angled bracket, as it is the vector u.
The projection of vector u onto vector v is given by the formula:
projv(u) = (u . v/||v||^2) * v
where u . v is the dot product of vectors u and v,and ||v|| is the magnitude of vector v
Given that u = <-10, -3> and v = <4, 8>, we can substitute these values into the formula and find projv(u)
projv(u) = ( (-10)(4) + (-3)(8) )/ (4^2 + 8^2) * <4,8>
projv(u) = ((-40 - 24)/ (16 + 64))* <4,8>
projv(u) = (-64/80) * <4,8>
projv(u) = (-4/5) * <4,8>
projv(u) = <-16/5,-32/5>
The vector u is already parallel to the vector v, that's why the projection of vector u on vector v is equal to vector u itself.
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Evaluate the integral below by interpreting it in terms of areas. In other words, draw a picture of the region the integral represents, and find the area using geometry.-5 ∫5 sqrt(5^2−x^2) dx my lower limit is -5 and my upper is 5. How do I solve this problem? do i graph this equation and use left or right approximation?
Answer:
[tex]\frac{25\pi}{2}\approx39.27\text{ units}^2[/tex]
Step-by-step explanation:
I assume your problem is [tex]\displaystyle \int\limits^{5}_{-5} {\sqrt{5^2-x^2}} \, dx[/tex]. Recognize that [tex]\sqrt{5^2-x^2}=\sqrt{25-x^2}[/tex] is a semi-circle directly above the x-axis with a radius of 5. The bounds cover the whole area of the semicircle, so its area is just half the area of a circle with a radius of 5. You probably know that the area of a circle is [tex]A=\pi r^2[/tex], so the area of a semicircle would be [tex]A=\frac{\pi r^2}{2}[/tex]. Thus, the area using geometry is [tex]A=\frac{\pi (5)^2}{2}=\frac{25\pi}{2}\approx39.27\text{ units}^2[/tex].
You buy 4 small candles and 2 large candles for $14. Your friend buys 5 small candles and 3 large candles for $20. What is the cost of each small candle? of each large candle?
Each small candle costs $_ and each large candle costs $_.
Using simultaneous equations, each small candle costs $1.00 and each large candle costs $5.00.
What are simultaneous equations?Simultaneous equations are two or more equations solved concurrently.
Simultaneous equations are also known as a system of equations.
Small Candle Large Candle Total Cost
You buy 4 2 $14
A friend buys 5 3 $20
Let the cost of the small candle each = s and the cost of the large candle each = l
Equations:Equation 1: 4s + 2l = 14
Equation 2: 5s + 3l = 20
Multiply Equation 1 by 1.5:
Equation 3: 6s + 3l = 21
Subtract Equation 2 from Equation 3:
6s + 3l = 21
-
5s + 3l = 20
s = 1
= $1
From Equation 1:
4s + 2l = 14
4 + 2l = 14
2l = 10
l = 5
= $5
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The segments GA and GB are tangent to a circle at A and B, and AGB is a 48-degree angle. Given that GA = 12 cm, find the distance from G to the nearest point on the circle.
The distance from G to the nearest point on the circle is going to be 5.61 cm.
The given figure (image attached below) has the segments GA and GB tangent to a circle at A and B, and AGB is at a 48-degree angle. We have been told that GA = 12 cm. We have to find the distance from G to the nearest point on the circle.
For this, first what we need to do is draw radii to A and B. Next draw OG which bisects the 48-angle G into two 24-angles. Let P be the point where OG intersects the circle. This becomes the distance from G to the nearest point on the circle which we need to find (image attached below).
In the right triangle AOG, radius AO is the side opposite angle AGO-
= Tangent = Perpendicular / Base
= tan(24) = r / 12
= r = 12tan(24) (i)
For OG -
= cos(24) = Base / Hypotenuse = 12 / OG
= OG = 12cos(24) (ii)
Now, we subtract (i) and (ii) -
= 12tan(24) - 12cos(24)
= 5.61 cm
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The polygon in the diagram is a square with center P. The length from the center to the vertex is [tex]6\sqrt{2} in[/tex]. Find the area of the square to the nearest tenth of an inch.
A) 24.0 [tex]in^{2}[/tex]
B) 72.0 [tex]in^{2}[/tex]
C) 36.0 [tex]in^{2}[/tex]
D) 144.0 [tex]in^{2}[/tex]
The area the polygon in the diagram with, a length from the center to the vertex 6√2 in is 144.0 in².
What is polygon?Any closed curve that consists entirely of connected line segments (sides) without any intersections is known as a polygon in geometry. The three simplest polygons are pentagons, triangles with three sides, and quadrilaterals with four sides (five sides). The two types are concave and convex polygons.
Convex polygons are those without any extended sides crossing over them. Equilateral refers to a polygon with equal sides. Interior angles of equiangular shapes are equal. Every equilateral and equiangular polygon is a regular polygon (e.g., an equilateral triangle or a square).
As all sides are equal, all diagonals are equal too, and the angle of adjacent diagonals are 90° with vertical opposite angle.
Therefore,
Each side = [tex]\sqrt{\text {diagonal}^2+ \text {diagonal}^2}[/tex]
Each side = [tex]\sqrt{(6\sqrt{2} )^2+(6\sqrt{2} )^2}[/tex]
Each side = [tex]\sqrt{(36\times 2+36\times 2}[/tex]
Each side = [tex]\sqrt{144}[/tex]
Each side = 12 inch
Area = 12 × 12
= 144.0 in²
Thus, the area the polygon in the diagram with, a length from the center to the vertex 6√2 in is 144.0 in².
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Divide the following and then check by multiplying.
7)84
Select the correct choice below and, if necessary, fill in the answer box to complete your choice
OA. The quotient does not have a remainder. The quotient is
B. The quotient has a remainder not equal to 0. The quotient is
OC. The quotient is undefined.
When dividing 84 by 7 then the quotient does not have a reminder and the quotient will be 12.
What is division?
A division in mathematics is the process of dividing a specific amount into equal parts. The division is the inverse of multiplication.
We can find a division fact if we know a multiplication fact: For instance, 3 5 = 15, so 15 / 5 = 3.
Also 15 / 3 = 5.
Here given that,
We have to divide 87/7,
By dividing,
we know that 8/7 gives reminder 1, and a quotient of 1.
Then divide 14 by 7,
which gives reminder 0 and quotient 2.
So by dividing 84 / 7 we get reminder 0 with a quotient of 12.
Therefore the correct option is option A. With a quotient of 12.
Hence, When dividing 84 by 7 then the quotient does not have a reminder and the quotient will be 12.
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find the equations of the lines that pass through the point (5,6) and are parallel to and perpendicular to the line with equation y =4x
The equation of this parallel line is y = 4x - 22. Railroad tracks, sidewalk edges, ladder rails, endless rail tracks, opposing sides of a ruler, opposite edges of a pen, an eraser, and other real-world objects are instances of parallel lines.
What is meant by parallel line?In a plane, lines that are consistently spaced apart from one another are referred to as parallel. Parallel lines don't ever intersect. Perpendicular lines are those that intersect at a 90-degree angle.Parallel lines are two lines that are never crossed and are equally spaced apart from one another.They could be horizontal or vertical. Parallel lines can be found in our daily life in the form of nearby train tracks, rows of notebooks, and zebra crossings.Since there is no "b" in the conventional equation y = mx + b, the line y = 4x has a slope of 4 and an intercept of 0. Any parallel line will have the same slope as the slope (m = 4) in this case. The slope of all parallel lines will be the same.
So let's return to the conventional format and replace the m with a "4".
y = 4x + b
Now that the values have been entered into the equation, let's solve for "b" using the point that sits on the line.
-6 = 4(4) + b
-6 - 16 = b
b = -22
The equation of this parallel line is y = 4x - 22
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Interpreting Polynomials
5x+9
A. 5
B. 9
C.
O
D. 1
What is the degree of the
polynomial?
Choice A
O Choice B
Choice C
O Choice D
Answer:
Give the degree of the polynomial.
6x5+5x4−3x2+x7
Answers:
18
5
6
9
7
Hope it helps :)
Mariah made a cylinder out of clay that had a radius of 6 cm and a volume of 72π cm^3. She painted the entire surface of the cylinder purple. How many square centimeters of the cylinder did Mariah paint in terms of π?
Enter the correct answer in the box/blank in terms of π.
_______ cm^2 (squared)
[tex]Answer:\ \boxed{96\pi }\ cm^2[/tex]
Step-by-step explanation:
[tex]R=6\ cm \ \ \ \ V_c=72\pi \ cm^3\ \ \ \ S_c=?[/tex]
[tex]V_c=\pi R^2H\\[/tex]
[tex]72\pi =\pi 6^2H\\\\72=36H\\[/tex]
Divide both parts of the equation by 36:
[tex]2=H\\\\Thus,\ H=2\ cm[/tex]
[tex]S_c=2(\pi R^2)+2\pi R(H)\\\\S_c=2\pi (6^2)+2\pi 6(2)\\\\S_c=2\pi(36)+12\pi (2) \\\\S_c=72\pi +24\pi \\\\S_c=96\pi\ cm^2[/tex]
Consider the following data: 13,11,5,2,9,14 Step of 3 : Calculate the value of the sampe variance Round your answer to one decimal place.Refer to Exercise 3. Calculate and interpret the standard deviation of the random variable X.
The sample variance of the given data 13,11,15,2,9,14 is 356.6.
Sample variance can be defined as the expectation of the squared difference of data points from the mean of the data set. It is an absolute measure of dispersion and is used to check the deviation of data points with respect to the data's average.
we have data 13, 11, 5, 2, 9, 14, and we have to determine the sample variance of given data.
Sample variance is given by,
[tex]S^2=\frac{\sum^n_1(X_i-X')^2}{(n-1)}[/tex]
where X' is the sample mean,
the mean of given data is,
[tex]X'=\frac{(13+11+5+2+9+14)}{6} \\\\X'=\frac{54}{6} \\\\X'=9[/tex]
now the sample variance is given by,
[tex]S^2=\frac{(13+9)^2+(11+9)^2+(5+9)^2+(9+9)^2+(14+9)^2}{6-1} \\\\S^2=\frac{(484+400+289+81+529)}{5} \\\\S^2=356.6[/tex]
Hence the sample variance is 356.6.
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Airline passengers get heavier In response to the increasing weight of airline passengers, the Federal Aviation Administration (FAA) in 2003 told airlines to assume that passengers average 190 pounds in the summer, including clothes and carry-on baggage. But passengers vary, and the FAA did not specify a standard deviation. A reasonable standard deviation is 35 pounds. Weights are not Normally distributed, especially when the population includes both men and women, but they are not very non-Normal. A commuter plane carries 30 passengers.
• (a) Explain why you cannot calculate the probability that a randomly selected passenger weighs more than 200 pounds.
• (b) Find the probability that the total weight of the passengers on a full flight exceeds 6000 pounds. Show your work. (Hint: To apply the central limit theorem, restate the problem in terms of the mean weight.)
The probability that the total weight of the passengers on a full flight exceeds 6000 pounds is about 0.0147 or 1.47%.
What is the Central Limit Theorem?
The Central Limit Theorem states that the sum of a large number of independent and identically distributed random variables is approximately Normally distributed.
(a) The reason why you cannot calculate the probability that a randomly selected passenger weighs more than 200 pounds is that the weight of passengers is not Normally distributed.
The Normal distribution is a symmetric bell-shaped distribution that is defined by its mean and standard deviation.
The weight of passengers is not symmetric and it may not follow a bell shape.
Therefore, we cannot use the Normal distribution to calculate the probability of a weight greater than 200 pounds.
(b) To calculate the probability that the total weight of the passengers on a full flight exceeds 6000 pounds, we can use the Central Limit Theorem.
Since we don't know the exact distribution of the weight of the passengers, we can use the Central Limit Theorem to approximate the total weight of the passengers on a full flight.
The mean weight of a passenger is 190 pounds, and the standard deviation is 35 pounds. Since a full flight carries 30 passengers, the mean weight of the passengers on a full flight is 19030 = 5700 pounds and the standard deviation is 35sqrt(30) = 175 pounds.
To find the probability that the total weight of the passengers on a full flight exceeds 6000 pounds, we can use the standard normal distribution table.
z = (6000 - 5700) / 175 = 2.2857
Probability P(X > 6000) = P(Z > 2.2857) = 1 - P(Z < 2.2857) = 1 - 0.9853 = 0.0147
Hence, the probability that the total weight of the passengers on a full flight exceeds 6000 pounds is about 0.0147 or 1.47%.
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LA REPRESA POZA HONDA ALMACENA 11 MILLONES DE METROS CÚBICOS DE AGUA. ¿CUÁNTOS KILÓMETROS DE AGUA ALMACENA?
Porfavor ayudenme es para Matematicas
Answer: 11/1000 o 1.1%
Step-by-step explanation:
11 ÷ 1000
0.011
11/1000 o 1.1%
A rectangle is partitioned into 5 regions as shown. Each region is to be painted a solid color-red. orange, yellow, blue, or green-so that regions that touch are painted different colors, and colors can be used more than once. How many different colorings are possible? (A) 120 (B) 270 (C) 360 (D) 540 (E) 720
The 5 different colorings are possible.
The rectangle is partitioned into 5 regions.
The objective is to find the different of color.
There are 5 rectangle and 5 colors
Each region is to be painted a solid color-red. orange, yellow, blue, or green
Need to color 5 rectangles by using given five colors.
Then, we need to use 5! colors.
The factorial of a whole number is the function that multiplies the number by every natural number below it. Symbolically, a factorial can be represented by using the symbol "!". So, "n factorial" is the product of the first n natural numbers and is represented as n!
The formula for n factorial is:
n! = n × (n - 1)!=5×4×3×2×1
=120
Therefore, the possible colorings are 5.
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For the function given below, find a formula for the Riemann sum obtained by dividing the interval [a,b] into n equal subintervals and using the right-hand endpoint for each [tex]c_k[/tex]. Then take a limit of this sum as [tex]n[/tex]→∞ to calculate the area under the curve over [a,b].
[tex]f(x)=2x[/tex] over the interval [1,5]
The Riemann sum formula is ∫(1,5) 2x = 24
How to determine the Riemann sum formulaFrom the question, we have the following parameters that can be used in our computation:
f(x) = 2x over the interval [1, 5]
The Riemann sum for f(x) = 2x over the interval [1,5] using the right-hand endpoint for each subinterval is given by the formula:
(Δx/2) * (2c1 + 2c2 + ... + 2cn) where c1, c2, ..., cn are the right-hand endpoints of the subintervals and Δx = (b - a)/n.
As a general rule:
As n approaches infinity, the width of the subintervals approaches zero,
Also, we have the Riemann sum approaches the definite integral of f(x) = 2x over the interval [1,5], which is x² evaluated at the interval's endpoints.
So, the formula becomes
∫(1,5) 2x = x²
Substitute the intervals
∫(1,5) 2x = 5² - 1²
Evaluate
∫(1,5) 2x = 24
Hence, the formula is ∫(1,5) 2x = 24
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Find the 10th term of the sequence below
Answer:
10th term = 94
Step-by-step explanation:
Given equation,
→ Tn = n² - n + 4
Now the 10th term will be,
→ Tn = n² - n + 4
→ T10 = (10)² - 10 + 4
→ T10 = 100 - 6
→ [ T10 = 94 ]
Hence, the answer is 94.
A school is arranging a field trip to the zoo. The school spends 885.69 dollars on passes for 37 students and 2 teachers. The school also spends 325.23 dollars on lunch for just the students. How much money was spent on a pass and lunch for each student?
The $31.309 money was spent on a pass and lunch for each student
What is Equation?Two or more expressions with an Equal sign is called as Equation.
School spends on a pass for each student,885.69/39
$22.97
School spends on a lunch for each student,
325.23/39
$8.339
Therefore, total money spent on a pass and lunch for each student
= 22.97 + 8.339
= $31.309
Hence, the $31.309 money was spent on a pass and lunch for each student
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You pick a card at random. Without putting the first card back, you pick a second card at random. 1 2 3 4 What is the probability of picking a 2 and then picking a 1? Write your answer as a fraction or whole number.
The probability of picking a 2 and then picking a 1 would be = 1/2
What is probability?Probability is definitely as the expression that to represents the number of outcomes of an event.
The number of cards such as 1,2,3,4 = 4 cards.
The cards picked at random = a 1 and a 2
Therefore, the probability = 2/4 = 1/2
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A dentist was making note of his upcoming appointments with different aged patients and the reasons for their visits.
The probability that an appointment is with a patient under 18 years old is 0.9, the probability that it is for a regular cleaning is 0.15, and the probability that it is with a patient under 18 years old and is for a regular cleaning is 0.14.
What is the probability that a randomly chosen appointment is with a patient under 18 years old or is for a regular cleaning?
Write your answer as a whole number, decimal, or simplified fraction.
The probability that a randomly chosen appointment is with a patient under 18 years old or is for regular cleaning is 0.95.
The probability of a random appointment being with a patient under 18 or for regular cleaning is calculated as P(Under 18 or Regular Cleaning) = P(Under 18) + P(Regular Cleaning) - P(Under 18 and Regular Cleaning).
P(Under 18) = 0.9
P(Regular Cleaning) = 0.15
P(Under 18 and Regular Cleaning) = 0.14
So, P(Under 18 or Regular Cleaning):
= 0.9 + 0.15 - 0.14
Apply the arithmetic operation, and we get
= 0.91.
Thus, the required probability is 0.91.
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A kite is flying 20 ft off the ground. It’s line is pulled taut and casts a 15 feet shadow
Answer:ts line is pulled taut and casts a 15 ft - shadow. Find the length of the line. If necessary, round your answer to the nearest tenth.
Step-by-step explanation:
match the given side lengths to the correct inequality that represents the range of the 3rd side. (9 cards will be left over)
A triangle's third side must always be between (but not exactly equal to) the other two sides' total and difference in length. Take the numbers 2, 6, and 7 as an example. In light of this, the third side length must be more than 4 and lower than 8.
What is triangle?Three edges and three vertices make up a triangle, which is a polygon. It is among the fundamental shapes in geometry. Triangle ABC refers to a triangle with the vertices A, B, and C. Any three points in Euclidean geometry that are not collinear determine a singular triangle and a singular plane simultaneously. In geometry, a triangle is a three-sided polygon with three sides, three vertices, and three edges.The fact that a triangle's internal angles can be added up to equal 180 degrees is its most significant characteristic. Triangle's angle sum property is what this characteristic is known as. When three straight lines cross, a triangle is the result. There are always three sides and three corners to a triangle (angles). A triangle's vertex is the location at which two of its sides meet.To learn more about triangle, refer to:
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A man bought one almirah for Rs 3640 and the other for Rs 4800. He sold the first almirah for a loss of 15% and the other at a profit of 13 1/3 %. How much did he gain or lose in the whole transaction.
Please tell the answer .
Answer:
Rs. 94
Step-by-step explanation:
We will denote the almirahs as A1 and A2 for ease of explanation. I am omitting currency until the final answer
For the following computations note that x% = x/100 in decimal so
15% = 15/100 = 0.15
13 1/3% = 13 1/3 ÷ 100 = 40/3 ÷ 100 = 40/300
Cost of A1 = 4800
A1 was sold for a loss of 15%
Loss = 15% of 3640 = 0.15 x 3640 = Rs 546
A2 bought at 4800 was sold at a gain of 13 1/3%
Gain from sale = 13 1/3% of 4800 = 40/300 x 4800 =Rs 640
We have to treat gain as positive and loss as negative to arrive at the answer
Net gain/loss = 640 - 546 = Rs. 94
the sums of the measures of the interior angles of a polygon is three times the sum of its exterior angles. how many sides does it have. please help
The sums of the measures of the interior angles of a polygon is three times the sum of its exterior angles then it has 8 sides .
What is Polygon?
A polygon is a two-dimensional, closed form that is flat or planar and is limited by straight sides. Its sides are not curled. A polygon's edges are another name for its sides. The vertices (or corners) of a polygon are the places where two sides converge. Here are some illustrations of polygons.
What is interior angles?
Interior angles are those that are located within the confines of two parallel lines that are intersected by a transversal.
What is exterior angles?
The angles that are created outside of a triangle are its external angles. In other terms, the angle created between one of a triangle's sides and its neighboring extended side is the triangle's external angle.
We know that sum of interior angle of regular polygon is ;
(n-2) x 180°
Where n = no. of sides
We also know that sum of exterior angle of regular polygon is 360°.
The fact that the sum of a polygon's internal angles is three times the sum of its outside angles is now a given;
Therefore;
sum of interior angles of a regular polygon = 3 x sum of exterior angle
⇒ (n-2) x 180°
⇒3 x 360°
Simplify the equation we have above by:
⇒(n-2) = 3 x 360°/180° = 6
⇒ n = 6+2 = 8
Therefore the sides of the regular polygon is 8.
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Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. sketch the region, the solid, and a typical disk or washer.
y=2−12x, y=0, x=1, x=2; rotate about the x-axis.
The Volume of the solid obtained by rotating the region bounded by the curves is 5 cm³.
Volume of a solid plain:
The volume of a solid is a measure of the space occupied by an object. It is measured by the number of unit cubes required to fill the solid.
Given in the question:
y = 2 - 1/2x
y = 0 , x = 1 and x = 2
As we know that:
We can write 19π / 12 as
(19× 22/7 )÷ 12
= 209/ 42
= 4.97 ≈ 5 cm³
Therefore, the volume is 5 cm³
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The acceleration function (in m/s2) and the initial velocity are given for a particle moving along a line.
a(t) = t + 4, v(0) = 3, 0 ≤ t ≤ 11(a) Find the velocity at time t. 3 m/s (b) Find the distance traveled during the given time interval.
The distance traveled during the given time interval be 2024 m.
What is meant by acceleration function?An object's rate of change in velocity is referred to as its acceleration. The rate of change in velocity is known as acceleration. Acceleration typically signals a change in speed, though this is not always the case. Because of the shifting direction of its velocity, an item moving on a circular path at a constant speed is still accelerating.
By integrating the velocity v in terms of time t, v = gt, we can determine acceleration, which is the rate of change of velocity with respect to time.
Let the function be a(t) = t + 4
time = 11
substitute the value of t in the above equation, we get
a(11) = 11 + 6 = 17 m/s²
a = v/t, so v = at
finally v = (17 m/s²) (11s)
v = 187 m/s
b) Find the distance traveled during the given time interval
[tex]$$V_{total} = V_{final} - V_{ initial[/tex]
V final = 187 m/s, Vinitial = 3 m/s
V total = 187 - 3 = 184 m/s
Let the equation of velocity be
Velocity = distance/time
distance = velocity × time
distance = 184 m/s × 11 s
distance = 2024 m
Therefore, the distance traveled during the given time interval be 2024 m.
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