A base must be raised to a certain exponent or power, or logarithm, in order to produce a specific number.
How do you explain logarithm?
The exponent or power that must be added to a base to produce a particular number is called the logarithm. If bx = n, then the mathematical expression for x is x = logb n, where x is the logarithm of n to the base b. For instance, since 23 = 8, 3 is the logarithm of 8 in base 2, or 3 = log2 8.
The opposite of exponentiation in mathematics is the logarithm. The exponent to which b must be raised in order to obtain a number x is hence the logarithm of a number x to the base b. For instance, since 1000 = 103, log10 of 1000 is 3, or log10 = 3.
Common logarithms, with a base of 10, binary logarithms, with a base of 2, and natural logarithms, with a base of e 2.71828, are the four most popular varieties of logarithms.
Say you have n=4 and k=2. (Next, we might look at n=8 and k=3). Let f[(x-list_),y] be the expected value of the number of random trials needed to get from a list of thus and so many hits already, to completion with y or more hits in every slot. We want f[(0,0,0,0),2].
Note that f[anylist,0]=0, and that f[(0),1]=1.
Now f[0000,2]=1+f[0001,2], because the first random number has to go somewhere and whichever one it lands on is symmetric to the case where it lands on 4.
Next, f[0001,2]=1+(1/4)f[0002,2]+(3/4) f[0011,2]=1+(1/3)f[000,2]+(3/4)f[0011,2], the second step because once one slot is filled, it just takes 4/3 times as long to finish because 1/4 of your shots will be wasted on the saturated target.
By and by, you’ll encounter f[1111,2] among other situations, and this will be equal to f[0000,1].
It’s a finite calculation, it can be written up as a recursive program, and you’ll be able to get an exact answer for any f[(however many zeros), (whatever value counts as saturation)]. The calculation will, unfortunately, run into geometric expansion of time and space as there are going to be a lot of subcases to consider even for f[00000000,3]. Still, it’s nice to have the actual exact answer for a number of representative small cases.
As to the long term situation, once you’ve fired, say, n log n shots, you theoretically might be done, having `wasted no shots’. But consider the number of hits that “1” has got. This is a binomial distribution, with the probability of k hits out of n log n shots each at odds 1/n of hitting being Binomial[n log n, k](1/n)^k((n-1)/n)^(n log n-k). This should work out to roughly a Poisson distribution, with density something like (x/log n)e^{-x/log n} being the probability that you got x hits. The saturated targets would be the ones with x greater than log n, and you’d expect a typical target would need ( log n - x ) e x / log n dx further hits.
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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
What is the algebraic expression that represents the perimeter of the figure below?
A. 3x+31
b. 3x+43
c. 4x+31
d.4x+43
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].
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%
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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Three softball players discussed their batting averages after a game.
Probability
Player 1 six tenths
Player 2 five ninths
Player 3 four sevenths
Compare the probabilities and interpret the likelihood. Which statement is true?
.
.
A. Player 1 is more likely to hit the ball than Player 2 because P(Player 1) > P(Player 2)
B. Player 2 is more likely to hit the ball than Player 1 because P(Player 2) > P(Player 1)
C. Player 3 is more likely to hit the ball than Player 1 because P(Player 3) > P(Player 1)
D. Player 2 is more likely to hit the ball than Player 3 because P(Player 2) > P(Player 3)
Comparibg the probabilities and interpreting the likelihood, the true statement is that:
A. Player 1 is more likely to hit the ball than Player 2 because P(Player 1) > P(Player 2)
How to calculate the probability?Probability simply means the chance that a particular thing or event will happen. It is the occurence of likely events. It is simply the area of mathematics that deals with the numerical estimates of the chance that an event will occur.
Player 1 = six tenths = 0.6
Player 2 = five ninths = 0.56
Player 3 four sevenths = 0.57
This shows that player 2 has the highest probability. The correct option is A.
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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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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 :)
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 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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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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Find a vector (u ) with magnitude 4 in the opposite direction as v =⟨−2,3⟩ Give EXACT answer. You do NOT have to simplify your radicals!
u =
A vector (u) with magnitude 4 in the opposite direction as v =⟨−2,3⟩ is u = ⟨-2/√13, 3/√13⟩.
A vector in the opposite direction of a given vector can be found by multiplying that vector by -1. The magnitude of a vector is the length of the vector and it can be found by using the Pythagorean theorem on the coordinates of the vector.
The magnitude of the vector v = ⟨-2,3⟩ is:
|v| = √(-2)^2 + 3^2 = √4 + 9 = √13
To find a vector with magnitude 4 in the opposite direction as v, we can first normalize the vector v by dividing it by its magnitude,
then multiply it by 4:
u = (-1) * (1/|v|) * v
= (-1) * (1/√13) * ⟨-2,3⟩
= ⟨2/√13, -3/√13⟩
So, a vector (u) with magnitude 4 in the opposite direction as v =⟨−2,3⟩ is u = ⟨2/√13, -3/√13⟩
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A trapezium ABCD is inscribed into a semi-circle of radius l so that the base AD of the trapezium is diameter and the vertices B and C lie on the circumference. Then the value of base angle θ (in degree) of the trapezium ABCD which has the greatest perimeter, is
The value of base angle θ (in degree) of the trapezium ABCD which has the greatest perimeter, is 60°
Given, AD = 2I
From ΔABD,
cos∅=[tex]\frac{AB}{AD}[/tex]
⇒ AB = AD cos∅
⇒ AB = 2I cos∅
and x = ABcos∅ = 2I [tex]cos^{2}[/tex]∅
Now perimeter,
P = 2I+ 2I - 2x + 2AB
P = 4I - 4I [tex]cos^{2}[/tex]∅ + 4Icos∅
P = 4I (1 - cos²∅ + cos∅)
Differentiating with respect to ∅, we get
dP/d∅= 4I(2 cos∅ sin∅ - sin∅)
For max/min,
dP/d∅ = O
2 cos∅ sin∅ - sin∅ = 0
⇒ cos∅ = [tex]\frac{1}{2}[/tex] (∅ [tex]\neq[/tex] 0)
= 60°
[tex]d^{2}[/tex]P/d∅ = 4i(2 cos2∅ - cos∅)
[tex]d^{2}[/tex]P/d∅ < 0
∅ = 60°
Therefore, Perimeter is maximum when ∅ = 60°
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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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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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PLEASE HELPPPP
An equilateral triangle has sides of length (3x+7). Find the perimeter of triangle.
Answer:
9x + 21
Step-by-step explanation:
An equilateral triangle is a triangle with three equal sides. If we know the length of one side, we can find the perimeter by multiplying by three.
3(3x + 7) = 9x + 21
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]
Based on the information provided, what are the constraints on the mining problem? Let x represent the bins of Metalite and y represent the bins of Helotite.
The constraints on the mining problem are 8.3x + 7.2y = 180
and 4x + 3y = 24
How to determine the constraints on the mining problem?From the question, we have the following parameters that can be used in our computation:
x represent the bins of Metalitey represent the bins of Helotite.This means that
Weight: 8.3x + 7.2y
Number of bins: 4x + 3y
From the question, we have
Capacity = 180 tons ot 24 bins
So, the constraints are
8.3x + 7.2y = 180
4x + 3y = 24
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Caitlyn needs to mail a USB drive to a friend. She uses 42 -cent stamps and 5 -cent stamps to pay $1.71 in postage. How many of each stamp did Caitlyn use?
Solving an equation we will see that Caitlyn used 3 of the 42-cent stamps and 9 of the 5-cent ones.
How many of each stamp does she use?Let's define the variables that we will be using:
x = number of 42-cent stapms.y = number of 5-cent stamps.Then the total value of the stamps, in dollars, is:
x*0.42 + y*0.5
And we know that the value must be $1.71, then we can write the equation:
x*0.42 + y*0.05 = 1.71
y = (1.71 - x*0.42)/0.05
To find the values of x and y, we can just evaluate in different whole values of x, until we get a whole value of y.
using x = 1 we get:
y = (1.71 - 0.42)/0.05 = 2.58
This is not a solution.
if x = 3
y = (1.71 - 0.42*3)/0.05 = 9
This is the solution, she used 3 of the 42-cent and 9 of the 5-cent.
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The pre-image, quadrilateral ABCD was dilated to produce the image, quadrilateral A'B'C'D'. The length of the side between the vertices A and B is 5 inches. What is the length of the side between the vertices A' and B', when vertices B'C' is 9 inches and vertices BC is 12 inches?
The length of the side between the vertices A' and B' is 3.75 inches
How to find the length of the side between the vertices A' and B'?In order to find the length of the side between the vertices A' and B', we need to use the fact that the ratio of corresponding side lengths between the pre-image and the image is the same as the ratio of the scale factor used in the dilation.
The ratio of the side length between the vertices B'C' and BC is 9/12. If we call this ratio k, then the ratio of the side length between the vertices A'B' and AB is also k.
So we can use the side length between AB = 5 inches and k = 9/12 to find the side length between A'B'
A'B' /AB = k
A'B' = k × AB
A'B' = (9/12) × 5
A'B' = 3.75 inches
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4x-3y<9 x-3y>6 .... how does it look on a graph
A graph of the solution to this system of inequalities on a coordinate plane is shown in the image attached below.
How to graph the solution to this system of inequalities?In order to to graph the solution to the given system of inequalities on a coordinate plane, we would use an online graphing calculator to plot the given system of inequalities and then take note of the point of intersection;
4x - 3 < 9
x - 3y > 6
Based on the graph (see attachment), we can logically deduce that the solution to the given system of inequalities is the shaded region and the point of intersection of the lines on the graph representing each, which is given by the ordered pair (3, -1).
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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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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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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.
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 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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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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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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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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