x = 19 and x = 25 make the inequality true.
What is inequality?
In mathematics, a relationship between two expressions or values that are not equal to each other is called 'inequality. ' So, a lack of balance results in inequality.
To use substitution to determine which value of x makes the inequality true, we can substitute each value from the set {8, 19, 25} into the inequality and see if it makes the inequality true or false.
For example, if the inequality is x < 10, we can substitute 8, 19 and 25 into the inequality to see which one makes it true:
8 < 10 is true
19 < 10 is false
25 < 10 is false
So, we can see that only 8 makes the inequality true. Therefore, x = 8 makes the inequality true.
If the inequality is x > 10, we can substitute 8, 19 and 25 into the inequality to see which one makes it true:
8 > 10 is false
19 > 10 is true
25 > 10 is true
Hence, x = 19 and x = 25 make the inequality true.
To learn more about inequality visit,
https://brainly.com/question/25275758
#SPJ1
i need the answer to number 9
Answer:
502.5
Step-by-step explanation:
C = 24(12) + 5.50(39)
C = 288 + 214.5
C = $502.5
What is the domain and range of each function?
FIRST PERSON TO ANSWER GETS BRAINLIEST OR 5 STARS :D
A) f(x) = −2x
Domain:
Range:
g(x) = ½x2 + 5
Domain:
Range:
Answer:
Greetings!A) Domain: x∈R or in interval notation (- ∞, ∞)
Range: x∈R or in interval notation (- ∞, ∞)
Thus, they both the domain & the range of the first function are the same.
B) Domain: x∈R or in interval notation (- ∞, ∞)
Range: [-5,∞)
Using it's concepts, the domain and the range of the functions are given as follows:
a) Both all real numbers.
b) Domain all real numbers, range [tex]y \geq 5[/tex].
What are the domain and the range of a function?The domain of a function is the set that contains all the values of the input.The range of a function is the set that contains all the values of the output.In this problem, neither function has any impediment, such as an even root or denominator, hence the domain is all real numbers. As for the range, a linear function assumes all real values, while a concave up quadratic function assumes values of the vertex, in this case y = 5, and greater, hence the range of the second function is [tex]y \geq 5[/tex].
More can be learned about the domain and the range of functions at https://brainly.com/question/10891721
#SPJ1
In a survey of 1002 people, 701 (which is 70%) said that they voted in the most recent presidentia l election (based on data from ICR Research Group). The margin of error for the survey was 3 percentage points. However, actual voting records show that only 61% of all eligible voters actually did vote. Does this necessarily imply
Based on the percentage of people who actually voted and the margin of error, the data implies that people lied when responding to the survey.
What is the evidence that people lied?The evidence that people lied about voting would bet be shown by the confidence interval. If the confidence interval of the survey does not have the actual percentage of people who voted in it, then people lied.
The confidence interval is:
= Average ± Margin of error
Solving:
= 70% + 3%
= 73%
= 70% - 3%
= 67%
Confidence interval is:
67% - 73%
The actual percentage of 61% who voted is not in this interval which means that some people lied about voting in the survey.
Find out more on the margin of error at https://brainly.com/question/10218601
#SPJ1
Can someone help me out on these geometry questions? ASAP!!!
Write formal proofs the LL Theorm.
Question 6
1) [tex]\overline{AB} \cong \overline{BD}[/tex], [tex]\overline{CD} \perp \overline{BD}[/tex], O is the midpoint of [tex]\overline{BD}[/tex], [tex]\overline{AB} \cong \overline{CD}[/tex] (given)
2) [tex]\angle ABO, \angle ODC[/tex] are right angles (perpendicular lines form right angles)
3) [tex]\triangle ABO, \triangle CDO[/tex] are right triangles (a triangle with a right angle is a right triangle)
4) [tex]\overline{BO} \cong \overline{OD}[/tex] (a midpoint splits a segment into two congruent parts)
5) [tex]\triangle ABO \cong \triangle CDO[/tex] (LL)
Question 7
1) [tex]\angle ADC, \angle BDC[/tex] are right angles), [tex]\overline{AD} \cong \overline{BD}[/tex]
2) [tex]\overline{CD} \cong \overline{CD}[/tex] (reflexive property)
3) [tex]\triangle CDA, \triangle CDB[/tex] are right triangles (a triangle with a right angle is a right triangle)
4) [tex]\triangle ADC \cong \triangle BDC[/tex] (LL)
5) [tex]\overline{AC} \cong \overline{BC}[/tex] (CPCTC)
Question 8
1) [tex]\overline{CD} \perp \overline{AB}[/tex], point D bisects [tex]\overline{AB}[/tex] (given)
2) [tex]\angle CDA, \angle CDB[/tex] are right angles (perpendicular lines form right angles)
3) [tex]\triangle CDA, \triangle CDB[/tex] are right triangles (a triangle with a right angle is a right triangle)
4) [tex]\overline{AD} \cong \overline{DB}[/tex] (definition of a bisector)
5) [tex]\overline{CD} \cong \overline{CD}[/tex] (reflexive property)
6) [tex]\triangle ADC \cong \triangle BDC[/tex] (LL)
7) [tex]\angle ACD \cong \angle BCD[/tex] (CPCTC)
For the graph y = 1 find the slope of a line that is perpendicular to it and the slope of a line parallel to it. Explain your answer with two or more sentences.
The slope of the parallel line is 0 and the slope of the perpendicular line is undefined
How to determine the slope?The equation is given as:
y = 1
A linear equation is represented as:
y = mx + c
Where:
m represents the slope
By comparison, we have:
m = 0
The slope of the parallel line is:
Slope = m
This gives
Slope = 0
The slope of the perpendicular line is:
Slope =-1/m
This gives
Slope = -1/0
Slope = undefined
Hence, the slope of the parallel line is 0 and the slope of the perpendicular line is undefined
Read more about slopes at:
https://brainly.com/question/3605446
#SPJ1
-8+(3x)
3
2
=
5834
729
Which of the x-values are solutions to the following inequality? x < 100
help pls i need now
Answer:
A and B
Step-by-step explanation:
x < 100 means x is less than 100. Therefore, pick any x-values that are less than 100 which are x = 54 and x = 89.
Hence, A and B are the answer.
For the graph y = 1 find the slope of a line that is perpendicular to it and the slope of a line parallel to it. Explain your answer with two or more sentences.
The slope of the parallel line is 0 and the slope of the perpendicular line is undefined
How to determine the slope?The equation is given as:
y = 1
A linear equation is represented as:
y = mx + c
Where:
m represents the slope
By comparison, we have:
m = 0
The slope of the parallel line is:
Slope = m
This gives
Slope = 0
The slope of the perpendicular line is:
Slope =-1/m
This gives
Slope = -1/0
Slope = undefined
Hence, the slope of the parallel line is 0 and the slope of the perpendicular line is undefined
Read more about slopes at:
https://brainly.com/question/3605446
#SPJ1
What is the equation of the line parallel to the given line with an x-intercept of 4? y = x
Calculate the area of triangle abc with altitude bd, given a (-6,0) b (0,0) c (o,6) and d (3,-3)
The area of the triangle abc in which bd is altitude and having coordinates a(-6,0),b(0,0),c(0,6),d(3,-3) is 18 square units.
Given the coordinates of abcd are a (-6,0) b (0,0) c (o,6) and d (3,-3).
We are required to find the area of the triangle when bd is the altitude of the triangle.
When we draw the triangle we will find that that the base is ac and altitude is given bd.
ac=[tex]\sqrt{(6-0)^{2} +(0+6)^{2} }[/tex]
=[tex]\sqrt{36+36}[/tex]
=[tex]\sqrt{72}[/tex]
=6[tex]\sqrt{2}[/tex]
bd=[tex]\sqrt{(-3-0)^{2} +(3-0)^{2} }[/tex]
=[tex]\sqrt{9+9}[/tex]
=[tex]\sqrt{18}[/tex]
=3[tex]\sqrt{2}[/tex]
Area=(Base*Height)/2
=(6[tex]\sqrt{2}[/tex]*3[tex]\sqrt{2}[/tex])/2
=(18*2)/2
=18 square units.
Hence the area of the triangle abc in which bd is altitude and having coordinates a(-6,0),b(0,0),c(0,6),d(3,-3) is 18 square units.
Learn more about area at https://brainly.com/question/25965491
#SPJ1
41. The Puuur Place builds customized cat trees for pet owners. The basic tree is $100 and each additional platform, perch, or toy costs $50. Meow Now also builds customized cat trees. Their basic cat tree starts at $50 and each additional piece costs $75.
[A] Write and solve a system of equations to represent the total cost, y, when x additional pieces are purchased with a basic cat tree at each store.
[B] Solve this system of equations and show your work.
[C] Reggie wants to purchase a cat tree for his pets. Based on your work, explain which store would be cheaper depending on how many add-ons he wants to purchase.
The system of equations to represent the total cost, y, when x additional pieces are purchased with a basic cat tree at each store are;
y = 50x + 100 ------(eq 1)
y = 75x + 50 ------(eq 2)
How to Solve Simultaneous Equations?A) Let the total cost of the cat tree be y
Let each additional piece added be x.
Since basic tree is $100 and each additional platform costs $50, then we can say that;
y = 50x + 100 ------(eq 1)
Now, their basic cat tree starts at $50 and each additional piece costs $75. Thus;
y = 75x + 50 ------(eq 2)
B) Subtract eq 1 from eq 2 to gte;
25x - 50 = 0
25x = 50
x = 50/25
x = 2
y = 75(2) - 50
y = $100
C) The Store that would be cheaper depending on the add - ons is Puuur Place because as x increases, it's y-value increases at a lesser rate than that of Meow.
Read more about Simultaneous Equations at; https://brainly.com/question/148035
#SPJ1
(1)[3 Pts] The probability of producing a high-quality color print is 0.10. How many prints do you have to produce so that the probability of producing at least one quality print is larger than 0.90
The number of prints that the probability of producing at least one quality print is 22.
Given that the probability of producing a high-quality color print is 0.10.
The binomial distribution summarizes the number of trials or observations when each trial has an equal chance of reaching a certain value. The binomial distribution determines the probability of observing a particular number of positive results in a defined number of tests.
Probability of high-quality color print (P) = 0.1
Probability of producing not high-quality color print (1-P) = 0.9
Assume the no. of prints to produce 'n' and these are produced independently say 'x' be the no. of producing quality prints, which follows a binomial distribution.
The probability function of binomial distribution is
[tex]P(X=x)\left(\begin{array}{l}n\\ x\end{array}\right)P^x(1-P)^{n-x},x=0,1,2,.....,n[/tex]
Given that
P(X≥1)≥0.90
1-P(X=0)≥0.90
1-(1-P)ⁿ≥0.90
1-(0.90)ⁿ≥0.90
(0.90)ⁿ≥0.10
Now, taking log of both sides, we get
nlog(0.90)≥log(0.10)
n(0.1053)≥2.3025
n≥21.86
n≈22
Hence, the probability of producing a high-quality color print is 0.10 and the number of prints to produce so that the probability of producing at least one quality print is larger than 0.90 is 22.
Learn more about binomial distribution from here brainly.com/question/23929786
#SPJ4
Find angle V
(2x +29)= (10x-27)
Answer:
137
Step-by-step explanation:
VYXW is a parallelogram.
The opposite angles of a parallelogram are congruent, meaning their angle measurements are equal.
Following this information we can write an equation to find the value of x:
10x - 27 = 2x + 29 transfer like terms to the same side of the equation
10x - 2x = 29 + 27 add/subtract
8x = 56 divide both sides by 8
x = 7 replace x with 7 to find the given angle measures
now, the consecutive angles in a parallelogram are supplementary meaning their sum is equal to 180
m<V + m<W = 180
m<V + 2*7 + 29 = 180
m<V + 43 = 180 subtract 43 from both sides
m<V = 137
Which graph represents the function p(x) = |x-1|?
-3
O
-2-
-3.
O
64-3
3.
2
2
3
O
5
Graph is in the attached image.
This map of china is 65inches from east to west and 68 from the north to south. if 1 inch is 50 miles, how large is the actual country?
The country is 3250 miles in distance from east to west, and 3400 miles from north to south.
Given Information
It is given that,
The distance of the country on map from east to west, l = 65 inches
The distance of the country on map from north to south, b = 68 inches
As per the given scaling of map, 1 inch = 50 miles
How large is the actual country?
Thus, the actual distance from east to west, L = l × 50 miles
L = 65 × 50 miles
L = 3250 miles
The actual distance from north to south, B = b × 50 miles
B = 68 × 50 miles
B = 3400 miles
Therefore, the actual size of the country is 3250 miles in distance from east to west, and 3400 miles in distance from north to south.
Learn more about distance here:
https://brainly.com/question/15172156
#SPJ4
True or
False?
A binary predictor variable is tested for significance using a different test statistic than used for a quantitative predictor variable.
Answer:
it is False
Step-by-step explanation:
A client has just inherited a property. the deed is quite old, but she knows where the front two corners of the property are and that the distance between them is 210 feet. the shape is an irregular quadrilateral and the other three sides have distances of 515 feet, 232 feet, and 542 feet in a clockwise direction from the front left corner. more importantly, it is known that the front left corner of the property is a right angle.
This exercise involves the construction of a blueprint. To do so, we need to solve for angles using the Cos Rule. See the step by steps procedure below.
What is a blueprint?A blueprint is a masterplan that highlights how a structure will be look like when it is completed.
What is the solution to the above blueprint?Let the dimensions of the property be labelled QRST.Recall that the distance between the two corners are QR = 210 ftOther sides are: 515ft, 232ft, and 542ft going in a clockwise direction.Recall that the front left corner of the property is a right angle.From the above, see attached the first simple quadrilateral QRST (Draft I) that is indicates the above information.
Next Step
We have to derive ∠T, ∠ S, and ∠R.
In order to achieve the above, we must split the quadrilateral into two triangles.
As noted in the image, the quadrilateral is bisected from R to T.
∠R and ∠T are also divided into R1 R2 and T1, T2 respectively.
Next step - Derive ∠T1 and ∠R1 .
To do the above, we must deploy the Pythagoras Theorem. (PT)
PT requires:
TR² = QT² + QR²
TR² = (210)² + (515)²
TR² = 44,100 + 265,225
TR² = 309,325
TR = √309,325
TR = 556.17
Next step, Derive T1
We can derive T1 using the cos rule:
Cos T1 = QR/QT
= 515/556.17
Cos T1 = 0.926
Therefore
T1 = Cos⁻¹(0.926)
T1 = 22.18°
Next we derive R1
R1 = 180° - (90° + 22.18°)
R1 = 67.82°
In ΔTRS, by using Cosine Rule,
Cos T2 = [TS² + QR² - RS²]/2(TS) * (TR)
Cos T2 = [(232)² + (556.16)² - (542)²]/ 2 * (232) x (556.16)
Cost T2 = 69,373.945/258,058
Cost T2 ≈ 0.269
Therefore,
T2 = Cos⁻¹(0.269)
T2 ≈ 74.4°
Applying the same process, we can derive R2
Cos R2 = TR² + RS² - TS²
Cos R2 = [(556.16)² + (542)² - (232)²] / 2 (556.16) * (542)
Cost R2 = 0.911
R2 = Cos ⁻1 (0.911)
R2 = 24.34°
From the above, we can execute the following iterations:
∠S = 180° - (R2 + T2)
= 180 ° - (24.34 + 74.4)
∠C = 81.26°
Likewise:
∠R = R1 + R2
= 67.82 + 24.34
∠B = 92.16°
Lastly:
∠T = T1 + T2
= 22.18 + 74.40
∠T = 96.48°
Learn more about cos rule at;
https://brainly.com/question/23720007
#SPJ1
Full Question:
A client has just inherited a property. The deed is quite old, but she knows where the front two corners of the property are and that the distance between them is 210 feet. The shape is an irregular quadrilateral and the other three sides have a distance of 515 feet, 232 feet, and 542 feet in a clockwise direction from the front left corner. More importantly, it is known that the front left corner of the property is a right angle.
-Construct a blueprint of the property labeling the measures of all sides and angle of the property.
If a union member does not pay their union dues, they will not be able to
Answer:
The ¨mandatory dues¨ asked by the unions are not much (practically none), since it´s a voluntary system implemented, normally all the members pay a ¨agency fee¨ but not more than that, this changes depending on the personal involvement with the union.
a natural person can refuse the membership at any moment, without issues, and this way avoid any kind of activity with the union, including contributing with money (dues) or duties.
However, when this happens, the person it´s restricted to certain activities like participate in union elections, general or important meetings, and the contribution in the bargain for the collective elections is banned as well, these as main aspects to highlight.
If one doesn't pay they union dues, they will not be able to participate in collective bargaining with owners.
Only the real representatives of the union could participate in collective bargaining with owner (in which they could negotiate the new term of the salary with the owner). Without paying their dues, they're still haven't been acknowledged as the member of union.
Hope this helps have a great day!
(2/3)(-9/8)(-4/5)(-1)
Answer: -0.6
Step-by-step explanation:
A rectangular pen has a length 4 feet greater than its width. Find the area
A. x+4
b. x^2+4x
c. 4x
d. x^2+8x+16
Answer:
b. x^2+4x
Step-by-step explanation:
So since you don't know the width, you can just represent it as a variable, and in this case that variable will be "x". Now using this variable we can use it to represent the length since there is a relationship between the width and length which is given. Since the length is 4 feet greater than the width, we can represent the length as (x+4). Now to find the area, we simply multiply the length * width, which is x * (x+4) = x^2 + 4x
find the mean of 3,2,4,6,5,6,1,7,9,8,10
Answer:
[tex]5\frac{6}{11}[/tex]
Step-by-step explanation:
Number of Values = 11.
Mean = Sum of values / Number of Values
= [tex]\frac{3+2+4+6+5+6+1+7+9+8+10}{11} \\=\frac{61}{11} \\= 5\frac{6}{11}[/tex]
The Leader of Zip decrees that the digit 0, since it represents nothing, will no longer be used in any counting number. Only counting numbers without 0 digits are allowed. So the counting numbers in Zip begin 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, . . . , where the tenth counting number is 11. When you write out the first one thousand allowable counting numbers in Zip, what are the last three digits of the final number?
The last three digits of the final number are 109.
A number is an arithmetic value that is used to calculate and represent a quantity.
The digit zero will no longer be utilized in any counting numbers, according to the Leader of Zip, since it stands for nothing. There can only be counting numbers with 1 digit.
From 1 to 11,
11 is the tenth counting number.
So for the case of first 1000 numbers,
Number of permutations =1000/10 =100
Since 101 to 109 contains a zero.
So, 100+9=109
So, 1000+109=1109
Thus, the last number is 1109, and its last three digits are 1,0,9.
Learn more about numbers here:
https://brainly.com/question/148825
#SPJ1
help
Solve for x in the diagram below.
Answer:
X=10
Step-by-step explanation:
You can subtract 180 by 110 to get 70. Then you can do 8x+30+70=180
Add 30+70 to get 100
Subtract 100 to 180 to get 80.
8x=80
You divide 8 from both sides which leaves you with x=10.
Answer:
x=10
Step-by-step explanation:
See attached image
Solve for x: 12x^2 – 6 (a^2 + b^2)x + 3a^2b^2 = 0
Step-by-step explanation:
[tex]12 {x}^{2} - 6( {a}^{2} + {b}^{2} )x + 3 {a}^{2} {b}^{2} = 0[/tex]
Using quadratic formula, we get
[tex]x = 6( {a}^{2} + {b}^{2} )± \frac{ \sqrt{( - 6) {}^{2}( {a}^{2} + {b}^{2}) {}^{2} - 4(12)(3 {a}^{2} {b}^{2} )} }{24} [/tex]
[tex]x = 6( {a}^{2} + {b}^{2} )± \frac{ \sqrt{36( {a}^{2} + {b}^{2} ) {}^{2} - 144 {a}^{2} {b}^{2} } }{24} [/tex]
[tex]x = 6( {a}^{2} + {b}^{2} )± \frac{ \sqrt{36( ({a}^{2} + {b}^{2}) {}^{2} - 4 {a}^{2} {b}^{2} }) }{24} [/tex]
[tex]x = 6( {a}^{2} + {b}^{2} )± \frac{6 \sqrt{ ({a}^{2} + {b}^{2} ) {}^{2} - 4 {a}^{2} {b}^{2} } }{24} [/tex]
[tex]x = 6( {a}^{2} + {b}^{2} )± \frac{ \sqrt{( {a}^{2} + {b}^{2} ) {}^{2} - 4 {a}^{2} {b}^{2} } }{4} [/tex]
Answer: x₁=6b², x₂=6a².
Step-by-step explanation:
[tex]12x^2-6*(a^2+b^2)+3a^2b^2=0\\D=(6*(a^2+b^2))^2-4*12*3a^2b^2\\D=6^2*(a^2+b^2)^2-144a^2b^2\\D=36*(a^4+2a^2b^2+b^4)-144a^2b^2\\D=36a^4+72a^2b^2+b^4-144a^2b^2\\D=36a^4-72a^2b^2+36b^4\\D=(6a^2)^2-2*6a^2*6b^2+(6b^2)^2\\D=(6a^2-6b^2)^2\\\sqrt{D}=\sqrt{(6a^2-6b^2)^2}=|6a^2-6b^2|=б(6a^2-6b^2).\\\displaystyle x_{1,2}=\frac{-(-6*(a^2+b^2))б(6a^2-6b^2)}{2} .\\x_1=\frac{6a^2+6b^2-6a^2+6b^2}{2} \\x_1=\frac{12b^2}{2} \\x_1=6b^2.\\x_2=\frac{6a^2+6b^2+6a^2-6b^2}{2} \\x_2=\frac{12a^2}{2} \\x_2=6a^2.[/tex]
Juan had 4 candy bars for his 3 friends to share after lunch. But then, three other friends joined them. If Juan wants each friend to get the same amount, what part of a candy bar will each friend get?
Using proportions, it is found that the fraction of each candy bar that each friend will get is:
[tex]\frac{2}{3}[/tex].
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
Considering the three friends that were there initially and the three that arrived later, 4 candy bars will be split between 6 friends, hence the fraction that each will get is:
[tex]\frac{4}{6} = \frac{2}{3}[/tex]
More can be learned about proportions at https://brainly.com/question/24372153
#SPJ1
The taxi fare for the first two miles is $5 and for each additional mile the fare increases by $ 2. What is the taxi fare for a journey of n miles in dollars?
The taxi fare for a journey of n miles in dollars is 1 + 2n
What are linear equations?Linear equations are equations that have constant average rates of change, slope or gradient
How to determine the equation of the system?The given parameters about the taxi fares are given as
First two miles = $5
Additional mile = Increment of $2
Let the number of miles be n
So, we have:
2 miles = $5
Additional miles = (n - 2) * 2
Add the above expressions
5 + (n - 2)* 2
Represent the value with f(n)
So, we have:
f(n) = 5 + (n - 2)* 2
Expand the bracket
f(n) = 5 + 2n - 4
Collect the like terms
f(n) = 5 - 4+ 2n
Evaluate the like terns
f(n) = 1 + 2n
Hence, the taxi fare for a journey of n miles in dollars is 1 + 2n
So, the complete parameters are:
First two miles = $5
Additional mile = Increment of $2
n miles 1 + 2n
Read more about linear equations at:
https://brainly.com/question/14323743
#SPJ1
An equilateral triangle has a median drawn from one angle to the opposite side. What is the measure of each angle formed by the place where the median meets the vertex?
(Step by step pls)
Worth 20 points
The measure of each angle formed by the place where the median meets the vertex is 30 degrees
How to determine the angle?The median of an equilateral triangle divides the side and the angle into equal parts.
If the angle at the vertex is, the new angle would be
Angle = x/2
The angle at the vertex of an equilateral triangle is 60.
So, we have:
Angle = 60/2
Evaluate
Angle = 30
Hence, the measure of each angle formed by the place where the median meets the vertex is 30 degrees
Read more about triangle median at:
https://brainly.com/question/2288141
#SPJ1
please answer asap with a clear answer
The permutations is computed below.
How to illustrate the permutations?1. Evaluate 9P4
9P4 = 9!/(9 - 4)
= 9!/5!
= (9 × 8 × 7 × 6)
= 3024
2. How many ways can 5 students sit on a row of 15 chairs for a photograph?
= 15!(15 - 5)
= 15!/10!
= (15 × 14 × 13 × 12 × 11)
= 360360
Learn more about permutations on:
brainly.com/question/28062699
#SPJ1
simplify the expression 2^m/n * 2^n/m
A balloon rises at the rate of 10 ft/sec from a point on the ground 100 feet from an observer. Find the rate of change of the angle of elevation of the balloon from the observer when the balloon is 100 feet above the ground.
When the balloon, rising at 10 ft/sec, rises to 100 feet, the rate of change of the angle of elevation is 0.05 rad/sec
How can the rate of change of the angle of elevation be found?The rate at which the balloon rises = 10 ft/sec
Horizontal distance of the balloon from the observer, d = 100 feet
Therefore;
[tex] \frac{dy}{dt} = 10[/tex]
The angle of elevation can be presented as follows;
[tex] tan(\theta) = \frac{y}{100} [/tex]
[tex] y = 100 \times tan(\theta) [/tex]
Therefore;
[tex] \frac{dy}{dt} = \mathbf{ 100\cdot sec^2 \frac{d \theta}{dt}} [/tex]
Which gives;
[tex] \frac{d \theta}{dt}= \frac{ \frac{d y}{dt}}{100} \times cos^2 \theta [/tex]
[tex] \mathbf{ \frac{d \theta}{dt}} = \frac{ 10}{100} \times cos^2 \theta [/tex]
When the balloon is 100 ft. from the ground, we have;
cos(theta) = 100/(√(100²+100²) = 1/(√2)Therefore;
[tex] \frac{d \theta}{dt}= \frac{ 10}{100} \times \left(\frac{1}{\sqrt{2}} \right)^2 [/tex]
[tex] \frac{ 10}{100} \times \left(\frac{1}{\sqrt{2}} \right)^2 = \frac{ 1}{20} [/tex]
Which gives;
[tex] \frac{d \theta}{dt}=\frac{ 1}{20} = 0.05 [/tex]
The rate of change of the angle of elevation when the balloon is 100 feet from the ground is 0.05 rad/secLearn more about finding the rate of change of a function here:
https://brainly.com/question/101533
https://brainly.com/question/8728504
#SPJ1