Answers
The vertices of the hyperbola are (±2√3, 0), foci of the hyperbola are (±2√7, 0) and asymptotes are y = 2x/√3 and y = -2x/√3
What is hyperbola?
It's a two-dimensional geometry curve with two components that are both symmetric. In other words, the number of points in two-dimensional geometry that have a constant difference between them and two fixed points in the plane can be defined.
We have an equation for the hyperbola:
[tex]16x^{2} - 12y^{2} = 192[/tex]
dividing each term by 192
[tex]\frac{x^{2} }{12} + \frac{y^{2} }{16} = 1[/tex]
[tex](\frac{x}{2\sqrt{3} } )^{2} + \frac{y^{2} }{4^{2} } = 1[/tex]
Here h = 0, k = 0, a = 2√3, and b = 4
c = √((2√3)²+4²) = 2√7
The first vertex is:
(h-a, k)
= (0 - 2√3, 0) = (-2√3, 0)
The second vertex is:
(h + a, k)
= (0 + 2√3, 0) = (2√3, 0)
The first focus is:
(h - c, k)
= (0 - 2√7, 0) = (-2√7, 0)
The second focus is:
(h + c, k)
= (0 + 2√7, 0) = (2√7, 0)
The asymptote is:
y = ± b/a(h - x) + k
y = [tex]\frac{2x}{\sqrt{3} }[/tex]
Thus, The vertices of the hyperbola are (±2√3, 0), foci of the hyperbola are (±2√7, 0) and asymptotes are y = 2x/√3 and y = -2x/√3
Learn more about the hyperbola here:
brainly.com/question/12919612
#SPJ1
Related Questions
Opens down with compression coefficient of 0.2. Shifted right 1 unit and down 6 unitshow do I right this as a parabola equation?
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
opens down
compression coefficient = 0.2
translated:
right 1
down 6
parabola equation = ?
Step 02:
opens down
(x - h)² = -4p (y - k)
compression coefficient = 0.2
0.2 (x - h)² = -4p (y - k)
translated:
right 1
down 6
0.2 (x - 1)² = -4p (y + 6)
The answer is:
0.2 (x - 1)² = -4p (y + 6)
find the difference between the mode and median of the distribution of data
Answers
Step 1: Rewrite the dot plot in tabular form
Step : Compute the mode
From the table, we can see that the numer appears most ( that is the number with the highest frequence, f) is 4.
Therefore,
mode = 4
Step 3: Find the median
First arrange the data in ascending order. In this case, the data is already in ascending order.
If ∑f is odd, the median is the middle value which is at position
[tex]\frac{\sum f+1}{2}[/tex]If ∑f is even, the median is the average of the two values at positions
[tex]\frac{\sum f}{2}\text{ and }\frac{\sum f}{2}+1[/tex]In this case, ∑f = 12 is even.
Therefore, the median is the average of the numbers at position 6 and 7
number at position 6 is 3
number at position 7 is 4
Hence, the median is given by
[tex]\frac{3+4}{2}=\frac{7}{2}=3.5[/tex]median = 3.5
Step 4: Find the difference between the median and mode
The difference is given by
[tex]4-3.5=0.5[/tex]Hence the difference is 0.5
Solve the inequality and express your answer in intervalvenation use decimal form for numeric values
Answers
Given:
[tex]\frac{20}{4}<\frac{z+7}{2}<\frac{25}{4}[/tex]Required :
To solve this
Explanation:
[tex]\begin{gathered} first\text{ of all separate compound inequalities into system of inequalities} \\ \\ \frac{z+7}{2}>\frac{20}{4}\text{ }\frac{z+7}{2}<\frac{25}{4} \\ \\ reduce\text{ the fraction} \\ \\ \frac{z+7}{2}>5\text{ or z+7>2}\times5 \\ \\ z+7>10 \\ \\ z>10-7 \\ \\ z>3 \end{gathered}[/tex][tex]\begin{gathered} \frac{z+7}{2}<\frac{25}{4} \\ \\ multiply\text{ both sides of the inequality by the least common denominator} \\ \\ 4\times\frac{z+7}{2}<4\times\frac{25}{4} \\ \\ reduce\text{ the expression to the lowest term} \\ \\ 2(z+7)<25 \\ \\ 2z+14<25 \\ \\ 2z<25-14 \\ \\ z<\frac{11}{2} \end{gathered}[/tex][tex]\begin{gathered} z>3\text{ and z <}\frac{11}{2} \\ \\ 3Required answer:3
Urgent!!! Long division
Answers
So, we know the bus can hold 20 people in 15 minutes, so the rate per hour is:
20/15m
60m/15m
4
20/15 x 4/4m
80/60m (80 per hour)
4/1 = 4
80/60m x 4/4
320/240m
320/4h
320 people could ride the bus in 4 hours.
I would like to this math sentence question that I will send a picture of
Answers
Let
x -----> number of hours
we have that
the inequality that represents this situation is
[tex]45-12t\ge9[/tex]solve for t
[tex]\begin{gathered} -12t\ge9-45 \\ -12t\ge-36 \\ t\leq3 \end{gathered}[/tex]that means
the bakery can sell bread for a timeless than or equal to 3 hours
identify which value is not in the domain of the piecewise function
Answers
From the graph we notice that the only value of x for which the fuction generating the graph it not defined is x=-3.
Answer: A).
Use the properties of logarithms to write the following expression as a single term that doesn't contain a logarithm.e6-8ln(x)+In(y)
Answers
Given:
The expression is,
[tex]e^{6-8\ln (x)+\ln (y)}[/tex]Explanation:
Simplify the expression by using logathimic properties.
[tex]\begin{gathered} e^{6-8\ln (x)+\ln (y)_{}}=e^{6-\ln (x^8)+\ln (y)} \\ =e^6\cdot e^{-\ln (x^8)}\cdot e^{\ln (y)} \end{gathered}[/tex]Simplify further.
[tex]\begin{gathered} e^6\cdot e^{-\ln (x^8)}\cdot e^{\ln (y)}=e^6\cdot\frac{1}{e^{\ln(x^8)}}\cdot e^{\ln (y)} \\ =e^6\cdot\frac{1}{x^8}\cdot y \\ =\frac{e^6y}{x^8} \end{gathered}[/tex]So answer is,
[tex]\frac{e^6y}{x^8}[/tex]Which of the following inequalities is false?
A: 10 < 9 incorrect answer
B: 9 < 10 incorrect answer
C: 10 > 9 incorrect answer
D: 9 (is less than or equal to)
Answers
The inequalities 9 < 10 incorrect answer and 10 > 9 incorrect answer are false. Option (B) and Option (C) are false.
Before we determine the false statement, we must understand that all negative values are less than positive values and all positive values are greater than negative values,
For the inequality 10 < 9 incorrect answer
Since, it is given that 10 is less than 9 is incorrect answer and we know that 10 is greater than 9 . Therefore, this inequality is true.
For the inequality 9 < 10 incorrect answer
Since, it is given that 9 is less than 10 is incorrect answer but we know that 9 is less than 10. Therefore, this inequality is false.
For the inequality 10 > 9 incorrect answer
Since, it is given that 10 is greater than 9 is incorrect answer but we know that 10 is greater than 9 . Therefore, this inequality is false.
For the inequality 9 (is less than or equal to) 10 incorrect answer
Since, it is given that 9 (is less than or equal to) 10 is incorrect answer and we know that 9 is less than 10. Therefore, this inequality is true.
Therefore, Option (B) and Option (C) are false.
Know more about Inequalities: -https://brainly.com/question/17448505
#SPJ1
Your company fireworks show is getting bigger, The boss has requested that the viewing area (which is 4 ft x 6 ft) be doubled; the parking area (which is 540 ft x 75 ft) be doubled; and the city ordinance requires the fireworks to be in the air less than 4 seconds and not go any higher than 600 feet.
Answer the following questions:
1. Determine the dimensions of the new viewing area. The existing area is 6 ft long by 4 ft wide.
2. Determine the dimensions of the new parking area. The existing area is 540 ft long by 75 feet wide.
3. Determine the height of the fireworks and how long they are in the air using the following equation:
ℎ= −500/9 t^2 + 1000/3 t + 10
Answers
The solution to the questions are
New viewing area dimension: 8 ft by 12 ftNew parking area dimension: 1080 ft by 150 ftHeight of fireworks: 510 unitsThe dimension of the new viewing areaFrom the question, we have the following parameters:
Initial dimension of the viewing area:
4 ft by 6 ft
The scale of dilation is given as
Scale = 2 (i.e. doubled)
Using the above as a guide, the new dimensions are calculated using
New = Old * Scale
So, we have
New = (4 ft by 6 ft) x 2
Evaluate
New = 8 ft by 12 ft
The dimension of the new parking areaThe given parameters are
Initial dimension of the parking area:
540 ft by 75 ft
We use the same scale factor as (a) i.e.
Scale = 2 (i.e. doubled)
Using the above as a guide, the new dimensions are calculated using
New = Old * Scale
So, we have
New = (540 ft by 75 ft) x 2
Evaluate
New = 1080 ft by 150 ft
The height of fireworksThe function is given as
ℎ= −500/9 t^2 + 1000/3 t + 10
Differentiate the function
So, we have
ℎ'= −1000/9 t + 1000/3
Set the differentiated function to 0
So, we have
−1000/9 t + 1000/3 = 0
This gives
1000/9 t = 1000/3
Multiply both sides by 9/1000
t = 3
Substitute 3 for t in ℎ= −500/9 t^2 + 1000/3 t + 10
ℎ = −500/9 x 3^2 + 1000/3 x 3 + 10
Evaluate
ℎ = 510
Hence, the height is 510 units
Read more about scaled drawings and height functions at
https://brainly.com/question/17031580
https://brainly.com/question/9094323
#SPJ1
a1.Find the equation for a polynomial f(x) that satisfies the following:Degree 5Root of multiplicity 1 at x = 3• Root of multiplicity 2 at x = 2• Root of multiplicity 2 at x = -3y-intercept of (0, -216)f(x) =
Answers
we have that
the polynomial is of the form
f(x)=a(x-3)(x-2)^2(x+3)^2
where
a is the leading coefficient
y-intercept -----> (0,-216)
For x=0
substitute and solve for a
-216=a(0-3)(0-2)^2)(0+3)^2
-216=a(-3)(-2)^2(3)^2
-216=a(-3)(4)(9)
-216=-108a
a=2
therefore
[tex]f(x)=2(x-3)(x-2)^2(x+3)^2[/tex]Find the minimum and maximum values of the function on the interval [11,27].
Answers
-4x + 0.4y = -0.8 6x + 0.4y = 4.2 The solution to the system is ( , ).
Answers
An equation is a mathematical statement created by joining two numerical or variable expressions with an equal sign, as in 3x+5=11. A number that may be entered for the variable to produce a true number statement is the answer to an equation.
Explain about the solution?An assignment of values to the unknown variables that establishes the equality in the equation is referred to as a solution. To put it another way, a solution is a value or set of values (one for each unknown) that, when used to replace the unknowns, cause the equation to equal itself.
Take into account the formula 7x - 35 = 0. If we solve, we get either x = 5 or 7x = 35. The following linear equation only has one solution, x = 5, because the above linear equation is only true if x = 5.
The solution to this system (x=0.5 y=3)
To learn more about solution refer to:
https://brainly.com/question/25896797
#SPJ9
Lisa received a 70 gift card for a coffee store. She used it in buying some coffee that cost 8.49 per pound. After buying the coffee, she had 36.04 left on her card. How many pounds of coffee did she buy?
Answers
Initially she had 70 pounds in her gift card.
After buying her coffee she was left with 36.04 pounds.
Amount she spent on coffee is 70-36.04=34.96
One pound of coffee costs 8.49
To calculate how many pounds of coffee Lisa bought ->
34.96/8.49= 4
So in total she bought 4 pounds of coffee.
To learn more about the pounds of coffee she purchased visit:https://brainly.com/question/22542162
Part A: At a fair, Derrick used a total of 16 tickets to ride the roller coaster 4 times and the bumper cars 2 times. Javier used a total of 12 tickets to ride the roller coaster 2 times and the bumper cars 3 times. Let x represent the number of tickets it takes to ride a roller coaster. Let y represent the number of tickets it takes to ride the bumper cars. Model Derrick and Javier's trip to the fair by creating linear equations to represent how Derrick and Javier each used their ride tickets. 4 X + y = Derrick: Javier: X + Blank 1: 4 Blank 2: Blank 3: Blank 4:
Answers
x: number of tickets it takes to ride a roller coaster
y: number of tickets it takes to ride the bumper cars
Derrick used a total of 16 tickets to ride the roller coaster 4 times and the bumper cars 2 times, that is,
4x + 2y = 16
Javier used a total of 12 tickets to ride the roller coaster 2 times and the bumper cars 3 times, that is,
2x + 3y = 12
Jackie had 2 part time jobs at Shoney's Restaurant. One week she earned a total $306, working 12 hours as a cashier and 10 hours as a cook. The next week, sheworked 14 hours as a cashier and 22 hours as a cook, earning $512. How much doesshe earn per hour as a cashier?
Answers
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Represent the terms with a variable
Let x be the amount she earns per hour as a cashier
Let y be the amount she earns per hour as a cook
STEP 2: Interpret the statements in the question as seen below:
[tex]\begin{gathered} 12x+10y=306 \\ 14x+22y=512 \end{gathered}[/tex]STEP 3: Solve the simultaneous equation using elimination to get x and y
[tex]\begin{gathered} 12x+10y=306---(1) \\ 14x+22y=512----(2) \\ \\ \text{ Multiply equation 1 by 14 and equation 2 by 12} \\ 14\lbrack12x+10y=306\rbrack\Rightarrow168x+140y=4284----(3) \\ 12\lbrack14x+22y=512\Rightarrow168x+264y=6144----(4) \\ \\ \text{Subtract equation 4 from equation 3} \\ 168x\text{ cancels 168x, we have;} \\ 140y-264y=4284-6144 \\ -124y=-1860 \\ \text{Divide both sides by -124} \\ \frac{-124y}{-124}=\frac{-18600}{-124} \\ y=15 \end{gathered}[/tex]STEP 4: Solve any of equation to get the value of x
[tex]\begin{gathered} \text{From equation 1} \\ 12x+10y=306 \\ y=15\text{, By substitution;} \\ 12x+10(15)=306 \\ 12x+150=306 \\ \text{Subtract 150 from both sides} \\ 12x+150-150=306-150 \\ 12x=156 \\ \text{Divide both sides by 12} \\ \frac{12x}{12}=\frac{156}{12} \\ x=13 \end{gathered}[/tex]Since x represents the amount she earns as a cashier, hence She earns $13 per hour as a cashier
what is 5.37 with 15% discount
Answers
Answer
5.37 with 15% discount = 4.5645
Explanation
5.37 with 15% discount
= 5.37 - (15% of 5.37)
= 5.37 - 0.15(5.37)
= 5.37 - 0.8055
= 4.5645
Hope this Helps!!!
Answer:
Step-by-step explanation:
15% off 5.37 is 4.56.
The difference is 0.81
Going to store for Quetion‘s 9X -7 equals -7
Answers
The polynomial 9x-7=-7. The value is x=0.
Given that,
The polynomial 9x-7=-7
Algebraic expressions called polynomials include coefficients and variables. Indeterminates are another name for variables. We are able to perform mathematical operations on polynomial expressions such addition, subtraction, multiplication, and positive integer exponents but not division by variables.
The terms Poly (meaning "many") and Nominal (meaning "terms") make form the word polynomial.
The highest exponent of a monomial contained within a polynomial is referred to as the polynomial's degree. So-called polynomial degrees are polynomial equations with one variable having the largest exponent.
9x-7=-7
9x=-7+7
9x=0
x=0
Therefore, The value is x=0
Complete question: The polynomial 9X -7 = -7. Find the value of x.
To learn more about polynomial visit: https://brainly.com/question/11536910
#SPJ1
use the ratio to solve , how can the table help me to solve ? how do I find part? please assist me
Answers
We have to determine te 30 percent of 50.
[tex]\frac{30}{100}\times50=15[/tex]Hence the answer is 15.
Rick and Chumlee buy and sell sports collectibles. Rick bought 14 rookie cards and 13 autographed baseballs
for a total of 263 dollars. Chumlee bought 17 cards and 4 baseballs for a total of 284 dollars. Let c be the cost
of each card and let b be the cost of an autographed baseball.
a) Write an equation relating the items bought by Rick:
b) Write an equation relating the items bought by Chumlee:
c) Solve the system above using substitution and interpret in context:
The cost of a card is
dollars.
dollars and the cost of a baseball is
Answers
a) equation relating the items bought by Rick is
14c + 13 b = 263
b)equation relating the items bought by Chumlee
17c + 4b = 284
C) The cost of a card is 16
The cost of a baseball is 3
What is basic algebra ?Algebra is a branch of mathematics that helps translate real-world problems or situations into mathematical truths. It takes variables like x, y, and z as well as mathematical operations like addition, subtraction, multiplication, and division to generate a meaningful mathematical statement. All branches of mathematics, including coordinate geometry, calculus, and trigonometry, employ algebra. A fundamental algebraic formula is 2x + 4 = 8. Algebraic expressions serve as the mathematical statement when operations like addition, subtraction, multiplication, division, etc. are done on variables and constants.
Rick and Chumlee buy and sell sports collectibles.
Let c be the cost of each card and let b be the cost of an autographed baseball.
Rick bought 14 rookie cards and 13 autographed baseballs
for a total of 263 dollars.
a) equation relating the items bought by Rick is
14c + 13 b = 263
Chumlee bought 17 cards and 4 baseballs for a total of 284 dollars.
b)equation relating the items bought by Chumlee
17c + 4b = 284
C)
14c + 13 b = 263 .....(i)
17c + 4b = 284......(ii)
[tex]b = \frac{284-17c}{4}[/tex]
put the value of b in equation 1 you will get
14c +13([tex]\frac{284 - 17c}{4}[/tex])=263
56c + 3692 - 221c = 1052
175c = 2640
c = 16
[tex]b = \frac{284-17c}{4}[/tex].....(iii)
put the value of c in equation 3
b = [tex]\frac{284 - 17(16)}{4}\\ = \frac{12}{4}[/tex]
= 3
The cost of a card is 16
The cost of a baseball is 3
To learn more about about basic algebra visit :
brainly.com/question/15167098
#SPJ13
please help
A bird flying over water drops a crab from a height of 10 feet. The distance
the crab is from the water as it falls can be represented by d in the equation
d equals negative t to the power of 2 end exponent plus 10, where t is time in seconds. To catch the crab as it falls, a different
bird flies along a path represented by the equation d equals 5 t plus 5. In how many
seconds will the second bird catch the crab before it hits the water?
Answers
Solving a quadratic equation we can see that the second bird catches the crab after 0.85 seconds.
In how many seconds the second bird catches the crab?
The equation that describes the height of the crab is:
d = -t^2 + 10
The equation that represents the path of the second bird is:
d' = 5t + 5
The bird will be able to catch the crab when both are at the same height, this happens when:
-t^2 + 10 = 5t + 5
We need to solve this for t.
-t^2 + 10 - 5t - 5 = 0
-t^2 - 5t + 5 = 0
Using the quadratic formula we will get:
t = (5 ± √( (-5)^2 - 4*(-1)*5))/(2*-1)
t = (5 ± 6.7)/(-2)
We only care for the positive solution, which is:
t = (5 - 6.7)/(-2) = 0.85
So the bird catches the crab after 0.85 seconds.
Learn more about quadratic eqations:
https://brainly.com/question/1214333
#SPJ1
Graph the image of the figure on the right under the given translation.T(3,2)(x,y)
Answers
To translate the triangle we will translate each vertex using the rule of translation given
The vertice of the triangle are
(-1, 4), (-5, -2), (-8, 2)
The translation rule is T (3, 2)
That means we will add the x-coordinate of each point by 3,
and the y-coordinates by 2
The image of point (-1, 4) = (-1 + 3, 4 + 2) = (2, 6)
The image of point (-5, -2) = (-5 + 3, -2 + 2) = (-2, 0)
The image of point (-8, 2) = (-8 + 3, 2 + 2) = (-5, 4)
That means the triangle will move 3 units right and 2 units up
The images of the vertices are (2, 6), (-2, 0), (-5, 4)
I need to show you a pic of the question
Answers
The y-intercept and the x-intercept are the various points on the y and x axes where the graph cuts through.
In this our graph, there are interceptions at y = 0.4 and x = 0.3.
Thus, y-intercept exists at (0, 0.4) and x intercept at (0.3, 0)
I need help with Slopes!
Answers
we know that
To find out the slope of the line, we use the formula
[tex]m=\frac{y2-y1}{x2-x1}[/tex]we need two points
Looking at the graph
we take the points
(1,3 ) and (2,5)
substitute in the formula above
[tex]\begin{gathered} m=\frac{5-3}{2-1} \\ m=\frac{2}{1} \\ m=2 \end{gathered}[/tex]therefore
the slope of the line is 2Question 2 of 5
Which of the following is not an expression?
A. + 1 = 4
B. 3 - 2x
C. 4x+7
D. x/3 - 1
Answers
Answer:
A.
Step-by-step explanation:
The answer is A, because an expression does not have an equal sign.
A line passes through (5,-4) and (-1,-4). Write the equation of the line in slope-intercept form.
Answers
Explanation:
The formula of the slope of a line that passes through points (x1, y1) and (x2, y2) is:
[tex]m=\frac{y_1-y_2}{x_1-x_2}[/tex]For this problem the slope is:
[tex]m=\frac{-4-(-4)}{5-(-1)}=\frac{-4+4}{5+1}=\frac{0}{6}=0[/tex]A slope of zero indicates that the line is horizontal. Therefore it is a constant.
The slope-intercept form of the equation of a line is:
[tex]y=mx+b[/tex]Where m is the slope and b is the y-intercept. In this case, the slope is zero so we just have:
[tex]y=b[/tex]b is the y-coordinate of the given points: b = -4
Answer:
y = -4
multiply the question
Answers
EXPLANATION:
In order to multiply correctly we must follow the following steps:
-Multiply the numbers that are not in power of 10 and finally add the powers of 10.
The exercise is as follows:
[tex]undefined[/tex]Can someone give examples of negative exponents in the world
Eg : seize of bacteria 1*10^-4
Answers
The example of negative exponent in the real world is the world's smallest bat, the bumblebee bat weighs of 7 × 10^-2 ounces
How to illustrate the information?An exponent's sign indicates how many times to multiply or divide a base number. A negative exponent indicates the opposite.
The multiplicative inverse of the base raised to a power with the opposite sign of the provided power is referred to as a negative exponent. In plain English, we write the number's reciprocal and solve it just like positive exponents. The bat has a negative exponent.
Learn more about exponents on:
https://brainly.com/question/13669161
#SPJ1
clasificar el siguiente polinomio2xy +9b -4z + 9
Answers
Los polinomios se clasifican según el número de términos que lo componen.
Los términos de una expresión están separados entre sí por los signos "+" y "-"
Se conoce como "monomio" a un polinomio con un solo término.
Son ejemplos de monomios:
6x²
2x
z
Un "binomio" es un polinomio de dos terminos.
Por ejemplo:
2x-3y
4x²+1
5y⁴z-2x²
Un "trinomio" es un polinomio con tres términos.
Por ejemplo:
2x+3y+z
y²-z+7
Un "cuadrimonio" es un polinomio de cuatro términos
Por ejemplo
xy+5y-9z+4
Los polinomios también pueden clasificarse según su grado. El grado del polinomio está dado por el valor del mayor exponente.
Un polinomio de grado cero es aquel que tiene coefficientes igual a cero.
Por ejemplo
0x²+0x
Un polinomio de primmer grado es aquel en el que la variable está elevada a la uno. En general este exponente no se escribe por lo que en un polinomio grado uno las variables no van a tener exponente.
Por ejemplo
x+2
x+y+4
Un polinomio de segundo grado es aquel cuyo mayor exponente es dos, es decir, tiene un termino elevado al cuadrado.
Por ejemplo:
x²
x+y²+3
x-9y+5z²-7
Un polinomio de tercer grado es aquel cuyo mayor exponente es tres, es decir, al menos una variable está elevada al cubo.
Por ejemplo:
x
x³+y²
2x-y³+25
Teniendo estas definiciones en cuenta, puedes clasificar el polinomio:
[tex]2xy+9b-4x+9[/tex]Este polinomio tiene 4 términos, "2xy", "9b", "4x" y "9" por lo que se lo puede clasificar como un cuadrimonio.
Como puedes ver, ninguna de las variables tiene exponente, es decir que, el exponente de mayor valor es 1, por lo que se puede clasificar como un polinomio de primer grado.
Entonces esta expresión es un cuadrimonio de primer grado
While visiting Yosemite National Forrest, Joe approximated the angle of elevation to the top of a hill to be 25 degrees. After walking 350 ft closer, he guessed that the angle of elevation had increased by 14 degrees. Approximately how tall is the hill?A. 475 feetB. 385 feetC. 608 feetD. 202 feet
Answers
The line sketch of the movement and positioning of Joe and the hill are shown below.
Brief description of the sketch made.
From the sketch, point A is where Joe started from heading towards the hill.
The hill is represented by BC and the height is h
25 degrees was the initial angle of elevation.
After moving 350 ft closer to the hill, the angle of elevation increased by 14 degrees to 25 + 14 = 39 degrees.
From triangle BCD,
Using the trigonometric function of tan,
[tex]\begin{gathered} \tan =\frac{opposite}{\text{adjacent}} \\ \tan 39=\frac{h}{x} \\ 0.8098=\frac{h}{x} \\ \text{Making h subject of the formula,} \\ h=0.8098x \end{gathered}[/tex]From triangle ABC,
Using the trigonometric function of tan,
[tex]\begin{gathered} \tan =\frac{opposite}{\text{adjacent}} \\ \tan 25=\frac{h}{350+x} \\ \text{Substituting the value of h gotten from the previous triangle,} \\ \tan 25=\frac{0.8098x}{350+x} \\ 0.4663=\frac{0.8098x}{350+x} \\ C\text{ ross multiplying,} \\ 0.4663(350+x)=0.8098x \\ 163.205+0.4663x=0.8098x \\ C\text{ ollecting the like terms,} \\ 163.205=0.8098x-0.4663x \\ 163.205=0.3435x \\ \text{Dividing both sides by 0.3435 to get x,} \\ x=\frac{163.205}{0.3435} \\ x=475.124ft \\ \\ \text{The height, h of the hill is;} \\ h=0.8098x \\ h=0.8098\times475.124 \\ h=384.755ft \\ h\approx385ft \end{gathered}[/tex]Therefore, the height of the hill is 385 feet
The correct answer is option B.
Innings in his latest game,
Answers
The equation for the expression is given by
[tex]x+6\frac{2}{3}>82\frac{1}{3}[/tex]To get the value for x
Step 1: Subtract
[tex]\begin{gathered} 6\frac{2}{3} \\ \text{from both sides} \end{gathered}[/tex][tex]x+6\frac{2}{3}-6\frac{2}{3}>82\frac{1}{3}-6\frac{2}{3}[/tex][tex]x>82\frac{1}{3}-6\frac{2}{3}[/tex][tex]\begin{gathered} 82\frac{1}{3}=\frac{247}{3} \\ \\ 6\frac{2}{3}=\frac{20}{3} \\ \\ x>\frac{247}{3}-\frac{20}{3} \end{gathered}[/tex]Simplifying further
[tex]\begin{gathered} x>\frac{247-20}{3} \\ \\ x>\frac{227}{3} \end{gathered}[/tex][tex]\begin{gathered} x>\frac{227}{3}\text{ } \\ or \\ x>75\frac{2}{3} \end{gathered}[/tex]