1. Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = 5x, y = 5x, x20; about the x-axis. 2. Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. x = 2 V 3y, x = 0, y = 5; about the y-axis 3. Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = x-1, y = 0, x = 4; about the x-axis. 4. Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = x + 1, y = 0, x=0, x= 5; about the x-axis
Answers
The volume V of the solid obtained by rotating the region bounded by the given curves about the specified line.
1. y = 5x, y = 5x, x20; about the x-axis is (8π/75) cubic units.
2. x = 2 V 3y, x = 0, y = 5; about the y-axis is (125π/48) units³
3. y = x-1, y = 0, x = 4; about the x-axis is (47π/3) cubic units.
4. y = x + 1, y = 0, x=0, x= 5; about the x-axis (200π/3) cubic units.
1. The given curves are y = 5x, y = 5x, x≥0. To rotate the region bounded by these curves about the x-axis, we need to integrate the area of the cross-sections perpendicular to the x-axis. The cross-sections are disks with radius y/5 and thickness dx. Thus, the volume of the solid is:
V = ∫(0 to 2) π(y/5)² dx
= π/25 ∫(0 to 2) x² dx
= π/25 [x³/3] from 0 to 2
= (8π/75) units³
Therefore, the volume of the solid is (8π/75) cubic units.
2. The given curves are x = 2V3y, x = 0, y = 5. To rotate the region bounded by these curves about the y-axis, we need to integrate the area of the cross-sections perpendicular to the y-axis. The cross-sections are disks with radius x/2V3 and thickness dy. Thus, the volume of the solid is:
V = ∫(0 to 5) π(x/2V3)² dy
= π/12 ∫(0 to 5) y³ dy
= π/12 [y⁴/4] from 0 to 5
= (125π/48) units³
Therefore, the volume of the solid is (125π/48) cubic units.
3. The given curves are y = x-1, y = 0, x = 4. To rotate the region bounded by these curves about the x-axis, we need to integrate the area of the cross-sections perpendicular to the x-axis. The cross-sections are disks with radius y and thickness dx. Thus, the volume of the solid is:
V = ∫(0 to 4) πy² dx
= π ∫(0 to 4) (x-1)² dx
= π ∫(0 to 4) (x²-2x+1) dx
= π [(x³/3)-x²+x] from 0 to 4
= (47π/3) units³
Therefore, the volume of the solid is (47π/3) cubic units.
4. The given curves are y = x + 1, y = 0, x=0, x= 5. To rotate the region bounded by these curves about the x-axis, we need to integrate the area of the cross-sections perpendicular to the x-axis. The cross-sections are disks with radius y and thickness dx. Thus, the volume of the solid is:
V = ∫(0 to 5) πy² dx
= π ∫(0 to 5) (x+1)² dx
= π [(x³/3)+x²+2x] from 0 to 5
= (200π/3) units³
Therefore, the volume of the solid is (200π/3) cubic units.
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Related Questions
Determine the number of sides for the 6th shape in this pattern?
A)
ON
B)
7
C)
8
D)
9
Answers
Each successive shape in the sequence has one more side than the preceding shape. Therefore, the 6th shape in the sequence, an octagon, has 8 sides,beginning with a triangle which has 3 sides
The 6th shape in this pattern is an octagon, which has 8 sides. This pattern follows a sequence of shapes, beginning with a triangle which has 3 sides, followed by a square which has 4 sides, then a pentagon which has 5 sides, and so on. Each successive shape in the sequence has one more side than the preceding shape. Therefore, the 6th shape in the sequence, an octagon, has 8 sides.
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find the distance traveled by a train averaging 50 miles per hour for4 hours.
Answers
Speed = 50 miles per hour
Time = 4 hours
Distance = D
Distance = speed x time
Replacing:
D = 50 mph x 4 h = 200 miles
suppose a sequence (xn) of positive real numbers converges to a positive number. show that the set fxngis bounded below by a positive number. g
Answers
Let (xn) be a sequence of positive real numbers that converges to a positive number. We aim to show that the set {x_n : n ∈ N} is bounded below by a positive number. Since the sequence converges to a positive number, we can choose an ε > 0 such that for all sufficiently large n, |x_n - L| < ε, where L is the limit of the sequence. By considering the inequality x_n > L - ε, we can see that all terms of the sequence are greater than or equal to a positive number, thereby establishing the boundedness from below.
Since the sequence (xn) converges to L, for any ε > 0, there exists a positive integer N such that for all n ≥ N, |x_n - L| < ε. This means that eventually, all terms of the sequence will be arbitrarily close to L.
Now, consider the inequality x_n > L - ε. For all n ≥ N, we have |x_n - L| < ε, which implies L - ε < x_n. Since L and ε are positive, we can rearrange the inequality to get x_n > L - ε.
Therefore, for all n ≥ N, we have x_n > L - ε, and since ε can be chosen to be any positive number, we can conclude that all terms of the sequence (xn) are greater than or equal to L - ε, which is a positive number.
Hence, the set {x_n : n ∈ N} is bounded below by a positive number, as desired.
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some people advised that it in very cold weather you should keep the gas taking your car more than half full. Irene’s car had 5.3 gallons in the 13 gallon tank on the coldest day of the year. Irene filled the tank with gas that cost $3.80 per gallon. How much did Irene spend on gas?
Answers
Answer:26.98
Step-by-step explanation:
Answer:
$29.26
Step-by-step explanation:
I subtracted 5.3 from 13 to get 7.7 and then multiplied 7.7 by 3.80 to get 29.26
rewrite this division expression as an equivalent multiplication expression. 9/4 divided by 7/5
Answers
Step-by-step explanation:
9/4 divided by 7/5
= 9/4 multiplied by 5/7
= 9/4 * 5/7.
Market value of bond : $7000
Por volue of bond : $10000
Time to maturity : 8 year Market rate : 15% ( semi annualy )
Q. What is the coupon payment to be every 6 month
Answers
The coupon payment to be paid every 6 months is $375.
The market value of a bond, the par value of a bond, the time to maturity of a bond, and the market rate of interest on a bond are all crucial aspects in determining the coupon payment of a bond.
As a result, to determine the coupon payment, we must first comprehend the terms and then perform calculations.M
The given details are as follows:Market value of bond (MV) = $7000Par value of bond (PV) = $10000Time to maturity (t) = 8 yearsMarket rate of interest (r) = 15% (semi-annually).
To begin, we must determine the amount of interest that will be paid on the bond over the course of a year. Because the market rate is a semi-annual rate, we must first divide it by two, which results in a semi-annual rate of 7.5%.
As a result, the semi-annual interest payment will be calculated using the following formula: Semi-annual interest payment = (Par value of bond × semi-annual interest rate) ÷ 2.
Plugging in the values, we have:Semi-annual interest payment = ($10000 × 7.5%) ÷ 2= ($10000 × 0.075) ÷ 2= $375.
Because interest is paid twice a year (semi-annually), we can see that each interest payment is $375. As a result, the coupon payment every six months would be $375.
Thus, the coupon payment to be paid every 6 months is $375.
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Suppose cone a is similar to cone b and the scale factor between the solids is 3:2, respectively. If the height of cone a is 15 inches, determine the height of cone b.
Answers
The height of cone is 10 inches.
What is cone?
A cone is indeed a three-dimensional geometric shape with a smooth transition from a flat base—often but not always circular—to the point at the top, also known as the apex or vertex. A cone is made up of a collection of line segments, half-lines, as well as lines that connect the apex—the common point—to every point on a base that is in a plane other than the apex. The base may only be a circle, any closed one-dimensional figure, any one-dimensional quadratic shape in the plane, or any combination of the above and furthermore all the enclosed points, depending on the author.
What is the formula for finding the height of a cone?
The cone height formula calculates the height of the cone. The height of the cone using cone height formulas are, h = 3V/πr 2 and h = √l2 - r2, where V = Volume of the cone, r = Radius of the cone, and l = Slant height of the cone.We know that
If two figures are similar, then the ratio of its corresponding sides is proportional
Let x----> the height of cone B
using proportionality
3/2 = 15/x
x = 2 * 15/3
x = 10 inches
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. Natalie works for a florist. She charges $32 per day to make 12 bouquets. For every additional bouquet that she makes, she charges $1.40. The equation below represents this situation, where E is her total earning in dollars, in a day when she makes b additional bouquets. = 32 + 1.40 How many additional bouquets will she have to make so that she earns at least $60 in a day?
Answers
Answer:
20
Step-by-step explanation:
E = 32 + 1.40b
Since E is earnings, set E equal to $60 and solve for b for bouquets.
60 = 32 + 1.40b
60 - 32 = (32 + 1.40b) - 32
28 = 1.40b
28/1.4 = (1.40b)/1.40
20 = b
Natalie needs to make 20 additional bouquets.
use the probability rules in this chapter to solve each of the following. (a) suppose in 2012, the probability that a randomly selected child in a country was living with his or her mother as the sole parent was 0.242 and with his or her father as the sole parent was 0.080. what was the probability that a child was living with just one parent?
Answers
The probability that a child was living with just one parent is 0.322
The probability that a randomly selected child in a country was living with his or her mother as the sole parent was 0.242
P(mother as sole parent) = 0.242
The probability that a randomly selected child in a country was living with his or her father as the sole parent was 0.080
P(father as sole parent) = 0.080
P(A U B) = P(A) + P(B) - P(A∩ B)
P(living with just one parent) = P(mother as sole parent) + P(father as sole parent)
P(living with just one parent) = 0.242 + 0.080 = 0.322
Therefore, the probability that a child was living with just one parent is 0.322
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A ray is 23 feet below sea level, what is its elevation?
Answers
The elevation of the ray is -23 feet below the sea level
How to determine the elevatin of the rayFrom the question, we have the following parameters that can be used in our computation:
Elevation = 23 feet below the sea level
The elevation of a location is its height above a certain reference point, typically sea level.
If a location is 23 feet below sea level, its elevation is -23 feet.
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find a basis of the subspace of that consists of all vectors perpendicular to both[1] [0][0] [1][-8] [-5][_]and[_][3] [-2][_] [_]
Answers
To find a basis of the subspace that consists of all vectors perpendicular to both [1] [0] [0] [1] [-8] [-5] and [_] [3] [-2] [_], we first need to find the cross product of the two given vectors.
[1] [0] [0]
[1] [-8] [-5]
[_] [3] [-2]
The cross product of these three vectors is:
[0] [0] [-3]
This vector represents the normal vector to the plane that contains the two given vectors. Any vector that is perpendicular to both of the given vectors will lie in this plane and be orthogonal to this normal vector.
Thus, we can set up the following equation:
[0] [0] [-3] • [x] [y] [z] = 0
Simplifying this equation gives: -3z = 0
This tells us that z can be any value, while x and y must be zero in order for the vector to be perpendicular to both of the given vectors. Therefore, a basis for the subspace of all vectors perpendicular to both [1] [0] [0] [1] [-8] [-5] and [_] [3] [-2] [_] is:[0] [0] [1]
or any scalar multiple of this vector.
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what is the inverse of y + 6 = 3x?
Answers
Greetings from Brasil...
To find the inverse of a function, just replace X for Y and vice versa
Y + 6 = 3X replacing X by Y
X + 6 = 3Y isolating y
(X + 6)/3 = Y⁻¹
Then the inverse of Y + 6 = 3X will be
Y⁻¹ = (X + 6)/3the lines represented by the equations 25y-10x=200 and 5y+2x=40 are
Answers
Answer:
The slope
Step-by-step explanation:
t. 5. find the extreme points of f : r 3 ! r, f (x; y; z) = xyz subject to the two conditions x y z = 1; x 2 y 2 z 2
Answers
Since x²+y²+z²=0, we must have x=y=z=0, which satisfies the first three equations as well. However, this point does not satisfy the condition x+y+z=1, so it cannot be an extreme point. Therefore, there are no extreme points for the given function subject to the given conditions.
To find the extreme points of the function f(x,y,z)=xyz subject to the two conditions x+y+z=1 and x²+y²+z²=0, we need to use the method of Lagrange multipliers. Let λ be the Lagrange multiplier, then we have the following system of equations:
y*z = λ + 2λ*x
x*z = λ + 2λ*y
x*y = λ + 2λ*z
x + y + z = 1
x² + y² + z² = 0
We can solve this system by eliminating λ and getting the following equations:
x(y²+z²) = -2xyz
y(x²+z²) = -2xyz
z(x²+y²) = -2xyz
x + y + z = 1
x² + y² + z² = 0
Since x²+y²+z²=0, we must have x=y=z=0, which satisfies the first three equations as well. However, this point does not satisfy the condition x+y+z=1, so it cannot be an extreme point. Therefore, there are no extreme points for the given function subject to the given conditions.
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Complete Question:
Find the extreme points of\(f: R^{3} \rightarrow R\)
f (x, y, z) = xyz
subject to the two conditions
\(\begin {aligned}x+y+z & = 1 \\x^{2} +y^{2} +z^{2} & = 0\\\end {aligned}\)
Workers in an office of 40 staff were asked their favourite type of take-away. The results are summarised in the table. Take-away Frequency Angle Pizza 3 a Curry 12 b Fish & chips 7 c Kebab 3 d Other 15 e Work out the size of each angle to draw a pie chart.
Answers
The measure of angles a, b, c, d and e are 54°, 18°, 108°, 81° and 99°.
What is the fraction?In Mathematics, fractions are represented as a numerical value, which defines a part of a whole. A fraction can be a portion or section of any quantity out of a whole, where the whole can be any number, a specific value, or a thing.
Given that, workers in an office of 40 staff were asked their favorite type of take-away.
Fraction of a person = 1 degree
Here, 360° = 40 people
So, 1 degree = 40/360 =1/9
Now, angle a =6/40 ×360
= 54°
Angle b= 2/40 ×360
= 18°
Angle c= 12/40 ×360
= 108°
Angle d = 9/40 ×360
= 81°
Angle e =11/40 ×360
= 99°
Therefore, the measure of angles a, b, c, d and e are 54°, 18°, 108°, 81° and 99°.
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Tri-County G\$T selis 150,000 MWh per yeat of electrical power to Boulder at $80 per MWh, has fixed costs of $80.1 milion per yoar, and has varistele costs of $20 por MWh. If Tri-County has 1,000,000MW h of demand from its customers (other than Boulder), what will Tri-County have to charge to break even? Tri-County wit have to charge? to break oven. (Enter your response rounded to the nearest penny.)
Answers
Tri-County will have to charge approximately $83.1 per MWh to break even.
To calculate the break-even price that Tri-County will have to charge to cover its costs, we need to consider both the fixed costs and the variable costs. The fixed costs are given as $80.1 million per year.
The variable costs are calculated by multiplying the quantity of electrical power sold (150,000 MWh per year to Boulder) by the variable cost per MWh ($20). Therefore, the variable costs amount to 150,000 MWh/year * $20/MWh = $3 million per year.
To cover both fixed and variable costs, Tri-County needs to charge a total amount that equals the sum of these costs. The total cost is $80.1 million + $3 million = $83.1 million per year.
Now, let's calculate the break-even price per MWh. Since Tri-County has a demand of 1,000,000 MWh from its customers (other than Boulder), we can divide the total cost by this quantity to find the break-even price.
Break-even price = Total cost / Quantity of electrical power demanded
Break-even price = $83.1 million / 1,000,000 MWh = $83.1/MWh
Therefore, Tri-County will have to charge approximately $83.1 per MWh to break even.
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Why is having a long credit history with a few blemishes that were corrected better than a short history that is clear?
Answers
Answer:
A long history with corrected blemishes exhibits that though mistakes were made, they were corrected which allows for those viewing your credit history to know that you've learned to fix mistakes making you trustworthy and experienced.
Step-by-step explanation:
edge 2022
a sample of 60 information system managers had an average hourly income of $45.80 with a standard deviation of $7.00. what is the lower limit for the 95% confidence interval estimate for the average hourly wage of all information system managers? round your answer to two decimal places.
Answers
The lower limit for the 95%confidence interval for the given mean and standard deviation is equal to 39.03.
As given in the question,
Sample size 'n' = 60
Mean 'μ' = $40.80
Standard deviation 'σ' = $7.00
Using z-score table of normal distribution
z-value for 95%confidence interval = 1.96
Formula used
Confidence interval
= μ ± ( z-value × σ ) /√n
= 40.80 ± (1.96 × 7)/√60
= 40.80 ± (13.72 /7.75)
= 40.80 ±1.770
Lower limit of the confidence interval is equal to :
40.80 - 1.770 = 39.03
Upper limit of the confidence interval is equal to :
40.80 + 1.770 = 42.57
Therefore, the lower limit for the 95% confidence interval is equal to 39.03.
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Ayuden por favor, no entiendo este problema
Answers
We will get that the angle theta is:
θ = β/2
How to find the value of theta?Remember that the sum of the interior angles of any triangle must be equal to 180°.
Now, looking at the triangle in the left, we can see that the top angle is equal to:
180 - 2α
The right angle is equal to:
180 - 2β
And the left angle is α
Then we can write:
α + (180 - 2α) + (180 - 2β) = 180
-α - 2β = -180
α = 180 - 2β
Now we can go to the other triangle, where theta is, and write:
α + β + 2θ = 180
Replacing what we found above, we get:
180 - 2β + β + 2θ = 180
-β + 2θ = 0
θ = β/2
That is the best simplification we can get with the given diagram.
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A manufacturer has determined that the total cost C of operating a factory is
Answers
We have the next cost given function:
\(C=2.5x^2+75x+25000\)The average cost function is given by:
\(A(x)=\frac{C(x)}{x}\)Replace:
\(A(x)=\frac{2.5x^2+75x+25000}{x}\)Simplify the expression:
\(\begin{gathered} A(x)=\frac{2.5x^2}{x}+\frac{75x}{x}+\frac{25000}{x} \\ \text{Then:} \\ A(x)=2.5x+75+\frac{25000}{x} \end{gathered}\)Derivate A(x)
\(A^{\prime}(x)=2.5(1)+0-\frac{25000}{x^2}\)Set A'(x)=0
\(0=2.5(1)+0-\frac{25000}{x^2}\)Solve for x:
\(\begin{gathered} 0=2.5-\frac{25000}{x^2} \\ -2.5=-\frac{25000}{x^2} \\ x^2=\frac{-25000}{-2.5} \\ x^2=10000 \\ \text{Take square root of both sides:} \\ \sqrt[]{x^2}=\sqrt[]{10000} \\ \text{Hence } \\ x=100 \end{gathered}\)Therefore, the average cost per unit will be minimized at 100 units of production level.
prime factorization of 52 using factor tree
Answers
Answer: 52 = 2, 4, 13, 52
Step-by-step explanation:
Three boxes each contain a different number of marbles. Box A has 70 marbles, box B has 88 marbles, and box C has 80 marbles. Marbles are to be transferred from box B to box A. What is the least number of marbles that can be transferred so box C has the most marbles?
Answers
it A
Step-by-step explanation:
if 25^x+1 = 125/5^x find the value of x
Answers
x =1/3
Step-by-step explanation:25ˣ⁺¹ = 125/5ˣ
5²⁽ˣ⁺¹⁾ = 5³/5ˣ
5²⁽ˣ⁺¹⁾ = 5³ : 5ˣ
5²⁽ˣ⁺¹⁾ = 5³⁻ˣ
2(x + 1) = 3 - x
2x + 2 = 3 - x
2x + x = 3 - 2
3x = 1
x = 1/3
What is the length of side JI
Answers
The value of the segment Ji is 6 units.
What is a line segment?A line segment in geometry is a section of a line that has two clearly defined endpoints and contains every point on the line that lies within its confines.
here, we have,
Given that there is a line segment whose4 length is KI and the segment KJ is 6 units and Ji is x units.
As J is the midpoint of the segment, the length of KJ is the same as the length of JI hence the length of JI is 6.
KI = 6 + x
KJ = 6
JI = x
Therefore, the value of the segment Ji is 6 units.
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Let X be a uniform random variable on the interval [O, 1] and Y a uniform random variable on the interval [8, 10]. Suppose that X and Y are independent. Find the density function fx+y of X +Y and sketch its graph. Check that your answer is a legitimate probability density function.
Answers
Since X and Y are independent, their joint density function is given by the product of their individual density functions:
fX,Y(x,y) = fX(x)fY(y) = 1 * 1/2 = 1/2, for 0 <= x <= 1 and 8 <= y <= 10
To find the density function of X+Y, we use the transformation method:
Let U = X+Y and V = Y, then we can solve for X and Y in terms of U and V:
X = U - V, and Y = V
The Jacobian of this transformation is 1, so we have:
fU,V(u,v) = fX,Y(u-v,v) * |J| = 1/2, for 0 <= u-v <= 1 and 8 <= v <= 10
Now we need to express this joint density function in terms of U and V:
fU,V(u,v) = 1/2, for u-1 <= v <= u and 8 <= v <= 10
To find the density function of U=X+Y, we integrate out V:
fU(u) = integral from 8 to 10 of fU,V(u,v) dv = integral from max(8,u-1) to min(10,u) of 1/2 dv
fU(u) = (min(10,u) - max(8,u-1))/2, for 0 <= u <= 11
This is the density function of U=X+Y. We can verify that it is a legitimate probability density function by checking that it integrates to 1 over its support:
integral from 0 to 11 of (min(10,u) - max(8,u-1))/2 du = 1
Here is a graph of the density function fU(u):
1/2
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| /
| /
| /
| /
| /
| /
| /
| /
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|/
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0 11
The density is a triangular function with vertices at (8,0), (10,0), and (11,1/2).
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\(( - \frac{3}{5} )( - \frac{10}{3} )( - \frac{2}{9} ) = \)
I need help please
Answers
\((-\frac{3}{5})(-\frac{10}{3})(-\frac{2}{9}) = (\frac{30}{15})(-\frac{2}{9}) = 2(-\frac{2}{9}) = -\frac{4}{9}\)
Please help there is no word problem.
5 − a + 4a =
Answers
5-a+4a
=5+3a
1. Consider the circle to the right,
Part A: Determine mzSBE.
Part B: Determine mob.
S
52
B
Answers
Answer:
m∠SBE = 26°, \(m\hat O B\) = 126°
Step-by-step explanation:
The arc of a circle is a portion of the circumference of the circle. For a circle, the degree measure of an arc is equal to the measure of the central angle that intercepts the arc.
Central angle is an angle whose vertex is on the center of the circle and endpoints on the circumference of the circle. If the endpoints of the central angle are are also the endpoints for the angle's intercepted arc, then both angles are congruent.
Also, the angle at the center is twice the angle at the circumference.
Angle at center = \(m\hat S E\) = 52° (central angle is congruent with angle that intercept the arc)
2 * m∠SBE = central angle (angle at the center is twice the angle at the circumference)
2 * m∠SBE = 52
m∠SBE = 26°
2 * m∠BEO = central angle (angle at the center is twice the angle at the circumference)
2 * 63 = central angle
central angle = 126°
Angle at center = \(m\hat O B\) = 126° (central angle is congruent with angle that intercept the arc)
Question 4 Given: csc 55° =, find tan 145° A. 514 B. - D. C. 2/ 314413 E. - / 6 pts
Answers
tan 145° is equal to csc 55°. Given that csc 55° is not provided in the options, none of the given options is correct. cotangent is the reciprocal of the sine function.
To find the value of tan 145°, we can use the relationship between tangent and cotangent:
tan x = 1 / cot x
Since cotangent is the reciprocal of the sine function, we can rewrite the given equation as:
csc 55° = 1 / sin 55°
To find the value of sin 55°, we can use the fact that sin x = cos (90° - x):
sin 55° = cos (90° - 55°)
= cos 35°
Now, we need to find the value of cos 35°. We can use a trigonometric identity:
cos (90° - θ) = sin θ
cos 35° = sin (90° - 35°)
= sin 55°
Substituting this value back into the equation, we have:
csc 55° = 1 / sin 55°
= 1 / cos 35°
Now, let's find the value of tan 145° using the relationship between tangent and cotangent:
tan 145° = 1 / cot 145°
Since cotangent is the reciprocal of the sine function, we can rewrite the equation as:
tan 145° = 1 / sin 145°
To find the value of sin 145°, we can use the fact that sin x = sin (180° - x):
sin 145° = sin (180° - 145°)
= sin 35°
Now, we have:
tan 145° = 1 / sin 145°
= 1 / sin 35°
Since we previously found that csc 55° = 1 / cos 35°, we can substitute this value into the equation:
tan 145° = 1 / sin 35°
= csc 55°
Therefore, tan 145° is equal to csc 55°. Given that csc 55° is not provided in the options, none of the given options is correct.
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Kim stands in a line of people. She is the 25th person counting from the front of the line. She is the 12th person counting from the rear. How many people are in the line
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Kim stands in a line of people, being the 25th person counting from the front and the 12th person counting from the rear, there are total 34 people in the line.
To find the total number of people in the line, we can add the number of people in front of Kim and the number of people behind Kim, then subtract one to account for Kim herself.
At the front of the line, there are 24 people in front of Kim (since she is the 25th person counting from the front). From the rear of the line, there are 11 people behind Kim (since she is the 12th person counting from the rear).
To find the total number of people in the line, we can add these two numbers:
24 (people in front of Kim) + 11 (people behind Kim) = 35
However, we need to subtract one to account for Kim herself. Therefore, the total number of people in the line is 35 - 1 = 34.
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