Answers
Answer:
1) Therefore, the height of the waterfall above the observer is approximately 688.62 feet.
2) Therefore, the length of the arc intercepted by a central angle of I radians in a sector of a circular patio with a diameter of 24 feet is 12I feet.
Step-by-step explanation:
1)
1. Draw the Triangle ABC
2. point A represents the top of the waterfall, point B represents the far side of the pool, and point C represents the observer's position. We want to find the value of x.We know that the angle of elevation from point C to point A is 75°, so we can use the tangent function to relate the angle to the opposite and adjacent sides of the triangle
tan(75*)= opposite/adjacent
3. In this case, the opposite side is x (the height of the waterfall above the observer), and the adjacent side is the distance from the observer to the far side of the pool, which is given as 185 feet. So we can write:
tan (75*)= x/185
4. To solve for x, we can multiply both sides by 185:
x= 185* tan(75*)
5. Using a calculator, we can evaluate tan(75°) to be approximately 3.732, so:
x=185*3,732
6. The solution is 688.62 Feet
2)
1. The length of the arc intercepted by a central angle is given by the formula
length of arc = (central angle / 2π) * circumference of circle
2. n this case, the circular patio has a diameter of 24 feet, which means the radius is 12 feet. So the circumference of the circle is:
circumference = 2π * radius
circumference = 2π * 12
circumference = 24π
3. Now we need to find the length of the arc intercepted by a central angle of I radians. We can substitute these values into the formula:
length of arc = (I / 2π) * 24π length of arc = I * 12
4.So the length of the arc intercepted by the central angle is 12 times the measure of the angle in radians.
5.Therefore, the length of the arc intercepted by a central angle of I radians in a sector of a circular patio with a diameter of 24 feet is 12I feet.
Related Questions
!!!PLEASE HELPPPP!!!! Select all options that are greater than 17. (the answer's are power)
2 to the power of 5
4 to the power of 2
2 to the power of 2 + 3 to the power of 2
3 to the power of 3 - 3 to the power of 2.
Answers
Answer:
it's 2 to the power of 5, 2 to the power of 2 + 3 to the power of 2 and the last one is 3 to the power of 3 - 3 to the power of 2
The length of a rectangle is 5 inches longer than the width. The perimeter of the rectangle is 40 inches. What is the width of the rectangle, in inches?
Answers
Answer:
23
Step-by-step explanation:
345 centimeters
A student ran out of time on a multiple-choice exam and randomly guessed the answers for two problems. Each problem had 4 answer choices –a,b,c,d – and only one correct answer. What is the probability that he answered both of the problems correctly?
Do not round your answer.
Answers
\({\huge{\fbox{\tt{\blue{ANSWER}}}}}\)
______________________________________
The probability of answering a single problem correctly by randomly guessing is 1/4, since there are 4 answer choices and only one correct answer. Since the student randomly guessed the answer to both problems, the probability of answering both problems correctly is:
(1/4) x (1/4) = 1/16
Therefore, the probability that the student answered both problems correctly is 1/16.
Find the solution of the system of equations.
-x+3y=9
-x-y=-3
Answers
Step-by-step explanation:
use the steps of simultaneous
elimination steps
A wet sock is stuck onto the inner wall of a washing machine drum as it rotates at a steady speed the graph shows the sock displacement y, in inches, from the center of the drum, for a given number of seconds, X what is the diameter of the washing machine drum?
Answers
The diameter of the washing machine which is equivalent to the wavelength using the graph above would be = 2.5in.
How to determine the diameter of the washing machine's drum?To calculate the diameter of the washing machine drum, the formula that should be used is given below as follows;
V = fλ
where
V = displacement/time
F = 1/T
But;
Displacement = 10 in
Time = 2 seconds
V = 10/2 = 5 in/s
F = 1/2 = 0.5
λ = 5/0.5 = 2.5in
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A store is having a 20% off sale. The sale price of an item with price p is p - 0.2p. What is an equivalent expression.
Answers
An equivalent expression would be the sale price of an item with price p is 0.8p
s(sale price) = 0.8p
a ball is kicked with an initial height of 0.75 meters and initial upward velocity of 22 meters/second. this inequality represents the time,t, in seconds, when the ball's height is greater than 10 meters. -4.9t^2+22t+0.75>10.
the ball's height is greater than 10 meters when t is approximately between blank and blank seconds
Answers
Answer:
t is between 0.47 seconds and 4.02 seconds
Step-by-step explanation:
Given
\(Inequality: -4.9t^2+22t+0.75>10\)
Required
Determine the values of t
\(-4.9t^2+22t+0.75>10\)
Subtract 10 from both sides
\(-4.9t^2+22t+0.75 - 10 >10 - 10\)
\(-4.9t^2+22t-9.25 >0\)
Multiply through y -1
\(4.9t^2-22t+9.25 <0\)
Solve t using quadratic formula:
\(t = \frac{-b \±\sqrt{b^2 - 4ac}}{2a}\)
Where
\(a = 4.9\)
\(b = -22\)
\(c = 9.25\)
So, we have:
\(t = \frac{-(-22) \±\sqrt{(-22)^2 - 4*4.9*9.25}}{2 * 4.9}\)
\(t = \frac{22 \±\sqrt{484 - 181.3}}{9.8}\)
\(t = \frac{22 \±\sqrt{302.7}}{9.8}\)
\(t = \frac{22 \±17.40}{9.8}\)
Split the equation
\(t = \frac{22 + 17.40}{9.8}\) or \(t = \frac{22 - 17.40}{9.8}\)
\(t = \frac{39.4}{9.8}\) or \(t = \frac{4.6}{9.8}\)
\(t = \frac{39.4}{9.8}\) or \(t = \frac{4.6}{9.8}\)
\(t = 4.02\) or \(t = 0.47\)
Hence; the range is
\(0.47 < t <4.02\)
3
Nora scored three-quarters of the maximum points on a video game level. She scored a total
of 105 points. Let the variable m stand for the maximum number of points possible.
(a) Use the tape diagram below to determine the maximum number of points possible.
(b) Now, find the maximum, m, two different ways using algebra by solving each of the
following equations. Show the work you use to solve the equations.
(1)
m=105
(ii)
105 3
m 4
5. Shaun is painting a fence. After finishing three-eighths of the length of the fence he finds that
he has painted 15 feet. Let / be the total length of the fence, set up an equation like one of
those in 4(b) and solve to find f. Use either of the two methods.
Answers
Answer:
105 times 4/3 equals 140
Step-by-step explanation:
Nora specifically states that she scored three quarters of the max points in the video game level.
use the reciprocal of 3/4 and multiply it by 105
105 times 4/3 equals 140 which represents the maximum amount of points
In ∆BCD if BC=BD, m<B=(13x-35)°, m<C=(5x-19)°, and m<D=(2x+14)°, find x and the measure of each angle
Answers
Answer:
Value of x = 11 ° , ∠B = 108° ,∠C = 36° ,∠D = 36°
Step-by-step explanation:
Given :
In ΔBCD , BC = BD And ∠B= (13x-35)° , ∠C= (5x-19)° ,∠D=(2x+14)°
To Find :
value of x and ∠D , ∠B and ∠C
Solution:
∵ BC=BD , So ∠C = ∠D
Therefore 5x-19 = 2x+14
3x = 33 , ∴ x=11°
So, ∠B = (13×11) - 35 = 108°
∠C = (5×11)-19 = 36°
∠D= (2×11) +14 =36°
PLEASE HELP! WILL GIVE YOU BRAINLEST
Alana is riding a Ferris Wheel with Brianna and either Lindsay, Emily, or Janelle.
Lindsay is at the movies.
Emily does not like caramel apples.
Janelle is afraid of heights and won't go on rides over 15 feet high.
.
.
Who is the third person riding the Ferris Wheel?
third person =
Answers
Answer:
Emily because Lindsay is at the movies so she can't ride the Ferris Wheel. Janelle is too afraid to go that high. Emily only doesn't like caramel apples so she can still go on the Ferris Wheel.
Answer:
Emily
Step-by-step explanation:
The third person riding on the ferris wheel is Emily. why? well Lindsey is at the movies so she can't be at the carnival riding the ferris weel, Janelle is afraid of heights so their is no way she would ride the ferris wheel, but Emily just doesn't like Carmel apples which would not stop her from riding the ferris wheel.
The radiuses of two intersecting circles are 17 and 39. The distance between their centers is 44. Find the length of their common chord
Answers
Answer:
If x is the distance from centre fo the circle, with radius 25cm, to its intersection point with the common chord, x²+24²=25² =>x=7cm.
Distance from this intersecting point to the centre of the other circle=39–7=32cm
Ratio of the sides of the right triangle thus formed is 24:32=3:4. Since 3:4:5 is the basic pythagorean triplet, the radius of the other circle=5*24/3=40cm.
Aliter: radius of the other circle=√32²+24²= 40cm.
please mark me as brainalistWhat is the factored form of this expression? 4x^2-12x+9
Answers
Answer:
(2x-3)^2
i hope its correct...
Step-by-step explanation:
Answer:
2x-3
Step-by-step explanation:
9.858/0.795 find quotient
Answers
Step by step
Quotient is the word for a division solution.
Since this is a decimal problem, we can use the calculator and type in
9.858 ÷ .795 = 12.4
Problem solved
4x^2=x+3
Solve by factoring
Show your work please!
Answers
Answer:
x = - \(\frac{3}{4}\) , x = 1
Step-by-step explanation:
4x² = x + 3 ← subtract x + 3 from both sides
4x² - x - 3 = 0 ← in standard form
consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.
product = 4 × - 3 = - 12 and sum = - 1
the factors are - 4 and + 3
use these factors to split the x- term
4x² - 4x + 3x - 3 = 0 ( factor the first/second and third/fourth terms )
4x(x - 1) + 3(x - 1) = 0 ← factor out (x - 1) from each term
(x - 1)(4x + 3) = 0 ← in factored form
equate each factor to zero and solve for x
4x + 3 = 0 ( subtract 3 from each side )
4x = - 3 ( divide both sides by 4 )
x = - \(\frac{3}{4}\)
x - 1 = 0 ( add 1 to both sides )
x = 1
solutions are x = - \(\frac{3}{4}\) , x = 1
The length of a rectangle is 5 centimeters longer than twice its width. If the perimeter of the rectangle is 88 centimeters, what is the width?
Answers
Answer:
The length of a rectangle is 5 centimetres longer than twice its width. If the perimeter of the rectangle is 88 centimetres, what is the width?
width=x
length=2x+5
perimeter=88=2L+2W
so half perimeter=44=L+W
x+2x+5=44
3x=39
x=13 cm width ANSWER
2x+5=31 cm length
The width of the rectangle is Width, W = 13 centimeters.
Let the length of the rectangle be L. Let the width of the rectangle be W.Given the following data:
Perimeter of rectangle = 88 centimetersTranslating the word problem into an algebraic equation, we have;
\(L = 2W + 5\)
To find the width of the rectangle;
Mathematically, the perimeter of a rectangle is given by the formula;
\(P = 2(L + W)\)
Substituting the values into the formula, we have;
\(88 = 2(2W + 5 + W)\\\\88 = 2(3W + 5)\\\\88 = 6W + 10\\\\6W = 88 - 10\\6W = 78\\\\W = \frac{78}{6}\)
Width, W = 13 centimeters.
Therefore, the width of the rectangle is Width, W = 13 centimeters.
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When graphing rational functions, we denote values for x that we cannot pick by sketching in what is known as a vertical asymptote (blue dashed line). This is not actually a part of the graph, but rather, a reminder of sorts. The blue dashed line tells us that we can pick values VERY, VERY close to 2, but we can never pick exactly 2 because x = 2 would make the denominator 0 and you can't divide by 0. However, in the box below describe what happens if you plug x = 2.01 and x = 1.99 into the equation . What are the y-values when x is very close to 2?
Answers
When x is very close to 2, the y-values of the function can become very large (or very small) because the denominator becomes very close to 0.
The concept used to solve this question is the definition of a vertical asymptote in a rational function, which indicates values of x that make the denominator equal to zero and are therefore not in the domain of the function. To find the behavior of the function near a vertical asymptote, we can evaluate the function for values of x very close to the asymptote on either side.
When plugging in x = 2.01 and x = 1.99 into the equation of a rational function with a vertical asymptote at x = 2, we can see what happens when x is very close to 2.
For example, let's say the rational function is:
\(f(x) = (x^2 - 4) / (x - 2)\)
When x = 2.01, we have:
\(f(2.01) = (2.01^2 - 4) / (2.01 - 2)\)
\(f(2.01) = (4.0401 - 4) / 0.01\)
\(f(2.01) = 0.0101 / 0.01\)
\(f(2.01) = 1.01\)
Similarly, when x = 1.99, we have:
\(f(1.99) = (1.99^2 - 4) / (1.99 - 2)\)
\(f(1.99) = (3.9601 - 4) / (-0.01)\)
\(f(1.99) = -0.0399 / (-0.01)\)
\(f(1.99) = 3.99\)
So, when x is very close to 2, the y-values of the function can become very large (or very small) because the denominator becomes very close to zero. The vertical asymptote reminds us that we cannot actually evaluate the function at x = 2, but we can see what happens as we approach this value from either side.
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Consider the polynomial
(4mn^2n - 2mn + 6) + (6mn^2 - 1) - (mn^2 - 2 + 9mn)
Combine all like terms and enter the coefficients for each term into the blanks below
Answers
The required coefficients are:4, -1, -11, and 7.
Coefficients refer to the numerical values that are assigned to variables in mathematical equations, models, or formulas. They indicate the relative importance or contribution of each variable in the equation. Coefficients are used to determine the relationship between variables and are often estimated through statistical analysis or optimization techniques.
In algebraic equations, coefficients are the numbers multiplied by variables. For example, in the equation 2x + 3y = 5, the coefficients are 2 and 3.
In statistical models, such as linear regression, coefficients represent the slopes or weights assigned to the predictor variables. These coefficients indicate how much the response variable is expected to change for a unit change in the corresponding predictor variable, assuming all other variables are held constant.
We need to consider the polynomial:
(4mn^2n - 2mn + 6) + (6mn^2 - 1) - (mn^2 - 2 + 9mn)
To combine the like terms and find the coefficients of each term, we can write the polynomial in the following form:
4mn^2n - 2mn + 6 + 6mn^2 - 1 - mn^2 + 2 - 9mn
Taking the coefficients of the terms with "mn^2"4mn^2n - mn^2
Taking the coefficients of the terms with "mn"-2mn - 9mn = -11mn
Taking the coefficients of the constant terms6 + 2 - 1 = 7
Therefore, the required coefficients are:4, -1, -11, and 7.
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What do y=|x-3|+4 look like on a graph
Answers
Answer:
I got my answer in desmos. Hope this graph helps!!!
Which of the following statements are not true regarding functions?
Check all that apply.
A. A sequence is a function whose domain is the set of natural
numbers
OB. A function is a relation in which each value of the input variable is
paired with at least one value of the output variable.
I c. The horizontal line test may be used to determine whether a
function is one-to-one.
O D. The vertical line test may be used to determine whether a function
is one-to-one.
Answers
Answer:
(A) A sequence is a function whose domain is the set of natural
numbers.
(C) The horizontal line test may be used to determine whether a
Step-by-step explanation:
Vertical and horizontal line test can be used to find out whether the function, not one-to-one. The test is done by making a horizontal line (for horizontal line test) or vertical line( for vertical line test). If there are no 2 or more points of the graph that touch the line in both tests, then the function would be one-to-one
1. Round 0.007492 to the nearest hundredth.
Answers
Answer:
The answer is 0.01
Step-by-step explanation:
so in order to round it you have to know after the decimal it goes: tenths, hundreds, thousands (0 tenths, 0 hundreds, 0 thousands)
So 0.007492, take the first 3 numbers after the decimal, 0.007, since it will be in the hundreds place, lets see if we can round the 0 up. If the number behind 0 is greater then or equal to 5 round up, if the number is less then 5 then it stays the same. Since 7>5 it rounds up, so the 0 becomes 1. So your new number will be 0.01
Hoped this helped :D
By rounding 0.007492 to the nearest hundredth, we get 0.01.
What is the method of rounding a number?The number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up.
Example: 0.3879 rounded to the nearest hundredth is 0.39.
If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down.
Example: 0.3823 rounded to the nearest hundredth is 0.38.
Given number is 0.007492.
Rounding to nearest hundredth, we get:
0.00749 ⇒ 0.01.
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Christie makes changes to her budget at the end of every month. What is her reason for doing this in terms of smart financial planning?
A.
She keeps changing her mind about her goals.
B.
She is reviewing her goals and aligning the budget to work toward them.
C.
Her needs keep changing, so she changes her monthly budget.
D.
She realizes that her budget is tightly aligned to her goals.
Answers
The most appropriate reason for Christie making changes to her budget at the end of every month in terms of smart financial planning is B. She is reviewing her goals and aligning the budget to work toward them.Option B is correct.
Smart financial planning involves regularly evaluating and adjusting one's budget to ensure that it reflects their financial goals and current circumstances. By reviewing her goals, Christie can assess if her budget is still aligned with those goals and make any necessary changes to stay on track.
Life circumstances, such as changes in income, expenses, or financial priorities, may warrant adjustments to the budget. Christie recognizes that her needs may change over time, and by modifying her monthly budget, she can ensure that her financial resources are allocated appropriately to meet her evolving goals.
Regularly revisiting and modifying the budget allows Christie to adapt her financial plans, optimize her spending, and make informed decisions to achieve her financial objectives. Option B is correct.
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Watch help video
Graph the line that passes through the points (-6, -8) and (3,-2) and determine
the equation of the line.
Answers
Answer : y=2/3x-4
. Pay close attention to the order operations to find the value of: 26 + (10-2) = 4 + 3 - 6 Show each step:
Answers
You buy a $75 ipod and get a 10% discount. What is the sale price?
Answers
Answer:
$67.50
Step-by-step explanation:
here you go
Write an explicit formula for an, the nth term of the sequence 30, 35, 40
Answers
Answer:
The sequence is increasing by 5 at each step. So, we can write:
a1 = 30
a2 = 30 + 5 = 35
a3 = 30 + 25 = 40
a4 = 30 + 35 = 45
a5 = 30 + 4*5 = 50
We notice that the nth term is given by:
an = 30 + (n-1)5
So, the explicit formula for the nth term is:
an = 25n + 5
Solve for x round to the nearest hundredth
27=(1/3)^x
Answers
The value of x is x = -3.
What is solving an equation?
Finding an equation's solutions, or the values that satisfy the condition given by the equation, is known as solving an equation in mathematics. Solutions often consist of two expressions connected by an equals sign. One or more variables are marked as unknowns in order to find a solution.
Consider the given equation,
27 = (1/3)^x
This equation can be written as,
\(27 = \frac{1^x}{3^x}\)
Here 1^x
1\(27 = \frac{1}{3^x}\)
Take 3^x on numerator.
\(27 = 3^-^x\)
Now 27 can be written as, \(27 = (3)(3)(3) = 3^3\)
⇒ \(3^3 = 3^-^x\)
Applying the exponent rule: \(a^b=a^c\) ⇒ b = c
So we get,
3 = -x
Multiply both sides by -1.
-3 = x
x = -3
Hence the value of x is x = 3.
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Suppose your total taxable income this year is $75,000 you are taxed a rate of 10 percent on the first 25,000 20 percent on the next 25,000 and 30 percent on the final 25,000 what is your total income tax
Answers
Refer to the table summarizing service times (seconds) of dinners at a fast food restaurant. How many individuals are included in the summary? Is it possible to identify the exact values of all of the original service times?
Time (sec) Frequency
60 to 119 7
120 to 179 24
180 to 239 14
240 to 299 1
300 to 359 4
Answers
Answer:
Based on the provided information, the table summarizes service times (in seconds) of dinners at a fast food restaurant. To determine the number of individuals included in the summary, we can sum up the frequencies listed in the table:
7 + 24 + 14 + 1 + 4 = 50
Therefore, there are 50 individuals included in the summary.
Regarding the exact values of all the original service times, it is not possible to determine them precisely based on the given information. The table only provides ranges of service times and their corresponding frequencies. We can determine the range within which each individual's service time falls, but we cannot determine the exact value within that range.
PLEASE HELP ME!
Simplify -2 1/9 - (-4 1/3)
A: 2 2/9
B: -6 4/9
C: 2 2/9
D: 6 4/9
Answers
Answer:
2 2/9
Step-by-step explanation:
Solve the system of equations.
5x - 4y = -10
y=2x-5
x=
y=
Answers
Answer:
x = 10
y = 15
Step-by-step explanation:
5x - 4y = -10
y = 2x - 5
5x - 4(2x - 5) = -10
5x - 8x + 20 = -10
-3x = -30
x = 10
y = 2x - 5
y = 2(10) - 5
y = 15