When the the light's angle is 20° from perpendicular to the wall, and the light is rotating at an angular speed of one rotation in 2 seconds the rate the light projected onto the wall is moving is approximately 60.48 feet/s
What is angular speed?Angular speed, ω, is the angle, θ, in radians rotated by a rotating object per second. The unit of angular speed is radians per second, rad/s.
Mathematically;
[tex]\omega = \dfrac{\Delta \theta}{\Delta t}[/tex]
Where;
Δt = The time the object rotates through an angle of Δθ
The distance of the light from the wall, x = 17 feet
Time it takes the light to complete one rotation = 2 seconds
Angle the light makes with the perpendicular wall = 20°
[tex]tan(\theta) = \dfrac{y}{x}[/tex]
The distance the light has moved along the wall, y = x × tan(θ)
Therefore;
The y = 17 × tan(θ)
The angular velocity of the light, ω = θ/t
Therefore, θ = ω × t = ω·t
Which gives; y = 17 × tan(ω·t)
[tex]\omega = \dfrac{2\cdot \pi}{2}\ rad/s = \pi \ rad/s[/tex]
Therefore; x = 17 × tan(·t)
[tex]\dfrac{dy}{dt} = \dfrac{d}{dt} \left(17\times tan(\omega\cdot t)\right) = 17\cdot \omega\cdot sec^2(\omega \cdot t)[/tex]
ω = π rad/s (constant)
ω·t = θ
Therefore;
[tex]\dfrac{dy}{dt}= 17\cdot \omega\cdot sec^2(\theta)[/tex]
Rate the light is moving along the wall, dy/dt when θ = 20°, is therefore;
[tex]\dfrac{dy}{dt}= 17\times \pi\cdot sec^2(20^{\circ}) \approx 60.48[/tex]
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NEED HELP ASAP
What is the value of y in the solution to this system of equations 6y+x= -59 x= -2y+9?
Answer:
y = - 17
Step-by-step explanation:
6y + x = - 59 → (1)
x = - 2y + 9 → (2)
substitute x = - 2y + 9 into (1)
6y - 2y + 9 = - 59
4y + 9 = - 59 ( subtract 9 from both sides )
4y = - 68 ( divide both sides by 4 )
y = - 17
Creating a Function from a Mapping
The mapping shows a relationship between input and
output values.
Input
Activity
-5
SAING
2
40 Intro
Output
T? 7 NO
-3
-2
2
Which ordered pair could be removed to make this
relation a function?
O (-5,0)
-O (-1, -3)
O (4,-2)
O (6,-1)
Done
The ordered pair could be removed to make this relation a function is (4,-2).
What is an ordered pair?
An ordered pair is made up of the ordinate and the abscissa of the x coordinate, with two values given in parenthesis in a certain sequence.
The numeric values in an ordered pair can be integers or fractions.
Here,
A function is when each input has one output. So, for every x there is one y. The x values can not repeat.
But in the given value x is repeating so the ordered pair (4, -2) can be removed.
Hence, the ordered pair could be removed to make this relation a function is (4,-2).
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Last year, Ivanna opened an investment account with $7500. At the end of the year, the amount in the account had decreased by 7.8%. How much is this
decrease in dollars? How much money was in her account at the end of last year?
0.065=x/5800
x=$377; that is the dollar value of the decrease
The account is now worth $5423.
use the figure below to solve for the missing value(s):
The missing values are:
m∠1 = 36°
m∠2 = 122°
m∠3 = 122°
m∠4 = 38°
What is a triangle?It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
We have,
The figure has two triangles.
58° and m∠3 is a straight angle.
58 + m∠3 = 180
m∠3 = 180 - 58
m∠3 = 122
Now,
m∠3 + m∠4 + 20 = 180
122 + m∠4 + 20 = 180
m∠4 = 180 - 122 - 20
m∠4 = 180 - 142
m∠4 = 38
m∠3 and m2 are opposite angles.
Opposite angles are equal.
m∠3 = m∠2 = 122
Now,
m∠1 + m∠2 + 22 = 180
m∠1 + 122 + 22 = 180
m∠1 = 180 - 144
m∠1 = 36
Thus,
The missing values are:
m∠1 = 36°
m∠2 = 122°
m∠3 = 122°
m∠4 = 38°
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PLEASE HELP ME !!!
x² + 12x -
2
8 can be written in the form
(x + a)² + b, where a and b are numbers.
Work out the values of a and b.
Answer:
a = 6 , b = - 44
Step-by-step explanation:
x² + 12x - 8
using the method of completing the square
add/subtract ( half the coefficient of the x- term)² from x² + 12x
x² + 2(6)x + 36 - 36 - 8
= (x + 6)² - 44 ← in the form (x + a)² + b
with a = 6 and b = - 44
At the end of an amusement park ride, a boat lands in a pool, splashing out a lot of water. Three inlet pipes, each working alone, can fill the pool in 8 seconds, 12 seconds, and 16 seconds, respectively. How long would it take to fill the pool if all three inlet pipes are used?
The three inlet pipes, each working alone can fill the pool in 8 seconds, 12 seconds, and 16 seconds, respectively. it will take them 3.69 seconds fill the pool
How to determine how long it takes it fill the poolThe problem requires to determine how long it takes to fill the pool when the three pipes are working simultaneously
let the time to fill the the pool when the three pipes are working simultaneously be y, such that
8 seconds pipe fills the pool in y/8 seconds
12 seconds pipe fills the pool in y/12 seconds
16 seconds pipe fills the pool in y/16 seconds
Adding the times together
y/8 + y/12 + y/16 = 1
13y/48 = 1
y = 48/13
y = 3.69 seconds
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Henry invested $1500 into an account that pays 2% interest compounded annually.
How much money will Henry have at the end of 3 years?
Enter your answer in the box. Round to the nearest hundredth.
The compound interest is obtained as $91.81, rounded off to the nearest hundredth.
How is compound interest estimated annually?In order to compute compound interest, multiply the principle of the original loan by the annual interest rate multiplied by the number of compound periods minus one. You will then be left with the principal amount of the loan plus compound interest. The entire compound interest is then obtained by deducting the initial principal.
The equation that results will look like this:
Compound Interest = [tex]P(\left(1+r\right)^{ t}-1)[/tex]
Amount, rate of interest and time is given as $1500, 2% and 3 years respectively.
First, change r as a percent to r as a decimal.
r = R/100
r = 2/100
r = 0.02 rate per year,
Then solve the equation for compound interest.
[tex]\text{Compound Interest}=1500(\left(1+0.02\right)^{3}-1)\\=1500(1.061208-1)\\=15000\cdot 0.061208\\\\=91.81[/tex]
So, the compound interest is obtained as $91.81, rounded off to the nearest hundredth.
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Answer: its 1591.81
Step-by-step explanation:
I took the test and tried with the answer on top and got it wrong.
Find the Surface Area for the following:
(Use 3.14 for . Do not round and do not type your units.)
Surface Area = ______ in²
The shape has a surface area of: Surface Area = 282.6 in²
How to determine the surface area?The given parameter is represented on the figure
In this case, the figure is a cone with the following parameters
Radius, r = 5 inches
Height, h = 12 inches
The surface area of the cone is then calculated as
A = πr * (r + √(h² + r²))
Substitute the known values in the above equation, so, we have the following representation
A = 3.14 * 5 * (5 + √(12² + 5²))
Evaluate the expression
A = 282.6
Hence, the surface area is 282.6 square inches
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(x2 + 3x –9) ÷ (x – 2).
Answer:
Step-by-step explanation:
Fill in the blanks below in order to justify whether or not the mapping shown represents a function.
It is a function because the mapping .
(A) Due to the fact that there are no two values in Set B that have only one value in Set A mapped to them, the mapping diagram above represents a function.
(B) A function's very special property is that it associates one output with each input.
(C) Set A represents the domain, whereas Set B represents the range. Therefore, there would be exactly one value in the range that was unique for each value in the domain and would be present for each value in the domain.
What are functions?In mathematics, a function from a set X to a set Y assigns each element of X exactly one element of Y. The subsets X and Y are referenced to as the function's domain and codomain, correspondingly. A function is described as a relationship between a group of inputs with one output each. A function is, to describe it simply, a connection between inputs in which each input is associated to exactly one output. Every function has a domain and a codomain, or range. A function is a type of rule that produces one output from one input. Y=X2 is a good illustration of this. Any input for x yields a single output for y.
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3.
A circular pool of oil grew so that its radius increased by 2 feet. The formula shown can
be used to determine the area of the circle.
A = π (r + 2)²
Which equation is equivalent to the formula solved for r in terms of A?
Or=√1-2
Or=√√√+2
Or=√√4+2
Or-√4-2
Equation which is equivalent to the formula solved for r in term of A is [tex]Or = \sqrt{\frac{A}{r}-2 }[/tex].
What is circle?
A circle is a special kind of ellipse in which the eccentricity is zero and the two foci are coincident.
A circle is also termed as the locus of the points drawn at an equidistant from the centre.
What is radius?
Radius of a circle is the distance from the center of the circle to any point on it's circumference. It is usually denoted by 'R' or 'r'.
What is circumference?
Circumference of the circle or perimeter of the circle is the measurement of the boundary of the circle. Whereas the area of circle defines the region occupied by it.
Given that;
[tex]A = \pi{({r+2})^{2}}[/tex]
[tex](r+2)^{2} =\frac{A}{\pi}[/tex] (equivalent transformation)
[tex]r + 2 = \sqrt{\frac{A}{\pi} }[/tex]
[tex]r = \sqrt{\frac{A}{\pi} -2}[/tex]
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Which of the following (x,y) coordinates are solutions to the inequality 2x+5y<1?
The solution to the inequality given as 2x+5y<1 has the coordinates of (-10, 4)
How to determine the coordinates of the solution of the inequality?From the question, we have the following inequality that can be used in our computation:
2x+5y<1
Solving further, we need to collect the like terms
Since there are no like terms in the expression, it remains unchanged
So, the inequality becomes
2x + 5y < 1
Subtract 5y from both sides of the inequality
This gives
2x < 1 - 5y
Divide both sides by 2
The expression becomes
x < 1/2 - 5/2y
Evaluate
x < 0.5 - 2.5y
At this point, we assume any value for y and then solve for x
Assume that the value of y is 4
So, we have the following representation
x < 0.5 - 2.5 * 4
Evaluate the products
x < -9.5
This means that x is less than -9.5 when y is 4
-10 is less than -9.5
So, we have
x = -10 and y = 4
Express as ordered pairs (i.e. coordinates)
(x, y) = (-10, 4)
Hence, the coordinates of the solution is (-10, 4)
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4/7
of a square is painted green.5/6 of the remainder is painted red. If the green
part is 36 cm² more than the red. find the area of the square.
Answer:
168
Step-by-step explanation:
Let the area of the square be [tex]x[/tex].
[tex]\frac{4}{7}x-\frac{5}{6}\left(\frac{3}{7}x \right)=36 \\ \\ \frac{4}{7}x-\frac{5}{14}x=36 \\ \\ \frac{8}{14}x-\frac{5}{14}x=36 \\ \\ \frac{3}{14}x=36 \\ \\ \frac{1}{14}x=12 \\ \\ x=168[/tex]
Convert the height of a person who is 5.2 feet tall to centimeters. Include the inches-centimeter conversion
factor. Use the table given to create conversion factors. Show all conversion factors needed.
Round final answer to 2 decimal places if needed. The setup below should look like the typical dimensional
analysis that you learned.
The height of a person is 5.2ft in centimeter: 158.49cm
What are the Factors?A factor is a number that completely divides another number. To put it another way, if adding two whole numbers results in a product, then the numbers we are adding are factors of the product because the product is divisible by them.So, the conversion of measurement from the unit feet to centimeters is provided by the feet-to-centimeter calculator.
The letters "ft" and "cm" stand for feet and centimeters, respectively. The centimeter is used in the International System of Units and is regarded as a component of the metric system. The US customary measurement system uses the unit foot.Approximately 30.48 cm makes up one foot.
1 ft = 30.48 cm
Now, the formula for 5.2 feet to centimeters is as follows:We are aware that 1 foot equals 30.48 centimeters.Therefore, 5.2 feet equals 5.2 x 30.48 centimeters.
5.2 ft = 158.49 cm.5.2 feet is therefore equal to 158.49 cm in centimeters.
Hence, the height of a person who is 5.2 feet tall to centimeters is 158.49cm.
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Select the correct answer from the drop-down menu.
A new park is adding two new walking paths, as indicated by and , which are measured in meters. The park resembles an isosceles trapezoid.
Figure shows a trapezium ABCD. AC and BD are diagonals. The length of BD is 14x plus 4, and AC is 11x plus 31.
Determine the length of each path.
A.
The length of each path is
130
meters.
B.
The length of each path is
140
meters.
C.
The length of each path is
120
meters.
D.
The length of each path is
150
meters.
A.The length of each path is 130 meters.
Given:
The park resembles an isosceles trapezoid.
Figure shows a trapezium . AC and BD are diagonals. The length of BD is 14x plus 4, and AC is 11x plus 31.
we know that:
Diagonals are equal in isosceles trapezoid.
14x + 4 = 11x + 31
14x - 11x = 31 - 4
3x = 27
divide by 3 on both sides
3x/3 = 27/3
x = 9
Diagonal length = 14x + 4.
= 14*9 + 4
= 126 + 4
= 130 meters.
Therefore The length of each path is 130 meters.
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what is (x+5)……………
……….:…………
Answer:
x+5
Step-by-step explanation:
there are no like terms
I need help asap thank you..
Step-by-step explanation:
the angle TSW is the total angle and is 73°.
from that total angle, we have one part : angle 1 = 36°.
as angle TSW = angle 1 + angle 2
we have
73 = 36 + angle 2
angle 2 = 73 - 36 = 37°
a recipe requires 3/4 cup of water. Nora has a 1 1/2 cup measuring cup. how much of the measuring cup is filled with water?
Answer:
i think it is 15/20
Step-by-step explanation:
because 6/8,9/12,12/16
1. A factory is testing a new machine on its production line that is intended to improve efficiency. Management randomly
selects 12 employees and measures the number of products they complete in one hour when using the new machine. Below
are the results.
Employee 1 2 3 4 5 6 7 8 9 10 11 12
# units 72 68 74 78 75 79 71 69 82 71 73 80
(a) Estimate at the 95% confidence level the average number of units an employee can produce in one hour using the
new machine.
(b) The manufacturer of the machine claims the typical efficiency for a factory worker should be 78 units per hour. What
does the interval suggest about the manufacturer’s claim
(c) An investigation at a similar factory estimates the standard deviation to be 3.91 units. Using this information, what
size sample should we select to estimate the mean number of units produced each hour to within 1.04 units at the
95% confidence level?
a) The confidence interval is given as follows: (71.43, 77.17).
b) The manufacturer's claim is not correct, as 78 is not a part of the interval.
c) A sample of 55 employees is needed to achieve the desired margin of error.
What is a t-distribution confidence interval?The bounds of the t-distribution confidence interval, used when only the standard deviation for the sample is known, are given by the equation presented as follows:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
The variables of the equation are presented as follows:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.The critical value, considering the 95% confidence level and 12 - 1 = 11 df, is of:
t = 2.201.
The remaining parameters, namely sample mean, sample standard deviation and sample size are given as follows:
[tex]\overline{x} = 74.3, s = 4.52, n = 12[/tex]
(obtained using a calculator from the sample given in this problem).
The bounds of the interval are given as follows:
Lower bound: 74.3 - 2.201 x 4.52/sqrt(12) = 71.43.Upper bound: 74.3 + 2.201 x 4.52/sqrt(12) = 77.17.The interval does not contain the number 78, hence it is not a good estimate for the mean amount.
For item c, the z-distribution is used, as the population standard deviation is used, hence the minimum sample size is obtained as follows:
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]1.04 = 1.96\frac{3.91}{\sqrt{n}}[/tex]
[tex]1.04\sqrt{n} = 1.96 \times 3.91[/tex]
[tex]\sqrt{n} = \frac{1.96 \times 3.91}{1.04}[/tex]
[tex](\sqrt{n})^2 = \left(\frac{1.96 \times 3.91}{1.04}\right)^2[/tex]
n = 55. (rounded up, as a sample size of 54 would mean that the margin of error would be slightly above 1.04).
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HEEELPPPPPPPP Rearrange the formula v = 2gh for h. A) h = v 2g B) h = 2v g C) h = v2 g D) h = v2 2g
Rearranging the equation, making h the subject of the formula, h = v² / 2g
How to rearrange formula?we rearrange equations and formulas by using inverse operations to make one variable the subject of the formula.
In order to change the subject of, or rearrange, a formula items in the formula need to be arranged so a different variable is the subject.
In our case the the formula needs to be rearrange to make h the subject of the formula.
Therefore,
v = √2gh
square both sides of the equation
v² = (√2gh)²
v² = 2gh
divide both sides by 2g
v² / 2g = 2gh / 2g
h = v² / 2g
Therefore,
h = v² / 2g
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Solve. 4x+2=(1/8)x-2
_______
In a geometric sequence, the difference between each pair of consecutive terms must be the same.
The given statement "In a geometric sequence, the difference between each pair of consecutive terms must be the same" is false.
What is a Sequence?Number sequence is a progression or an ordered list of numbers governed by a pattern or rule. For example -
3, 6, 9, 12, 15
x, x + 2, x + 4, x + 6
Given is the following statement -
"In a geometric sequence, the difference between each pair of consecutive terms must be the same"
The given statement is false as the statement mentioned above is the definition of a arithmetic sequence. In geometric sequence, the ratio of each pair of consecutive terms must be the same. Mathematically -
a[n + 1]/a[n] = r {constant}
Therefore, the given statement "In a geometric sequence, the difference between each pair of consecutive terms must be the same" is false.
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Solve the following system of equations.
Provide your answer below:
-3x+4y= 7
7x- 12y = -11
Answer:
x = -5
y = -2
Step-by-step explanation:
-3x + 4y = 7 ⇒ ( 1 )
7x - 12y = -11 ⇒ ( 2 )
Multiply the equation ( 1 ) by 3.
( 1 ) × 3
3( -3x + 4y = 7 )
-9x + 12y = 21 ⇒ ( 3 )
Let us find the value of x.
Add equations ( 2 ) & ( 3 ).
( 2 ) + ( 3 )
7x - 12y - 9x + 12y = - 11 + 21
Combine like terms.
-2x = 10
Divide both sides by -2.
x = -5
Let us find the value of y.
For that, let us use equation ( 1 ) and replace x with -5 and make y the subject.
- 3x + 4y = 7
-3 × -5 + 4y = 7
15 + 4y = 7
Subtract 15 from both sides.
4y = 7 - 15
4y = -8
Divide both sides by 4.
y = -2
Max wanted to test a new dishwasher detergent to see if it was less likely to leave residue on his dishes. What would be the null hypothesis in Max’s experiment
Given that Max wanted to test a new dishwasher detergent to see if it was less likely to leave residue on his dishes, the suitable null hypothesis in Max’s experiment will be "the new detergent will leave more residue than the old one".
What is a null hypothesis?In statistics, a null hypothesis means a typical theory which suggests that no statistical relationship and significance exists in a set of given single observed variable between the two sets of observed data and measured phenomena.
Therefore, the Option B is correct.
Missing options' The new detergent will leave less residue than the old one. The new detergent will leave more residue than the old one. O The new detergent is equally likely to leave residue compared to the old detergent. The old detergent will leave more residue than the new detergent."
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Help with this math problem
The value of the investment after 3.25 years is $434.93.
What is the interest rate?The amount a lender charges a borrower, expressed as a percentage of the principle, is known as the interest rate.
Given that, the initial investment is P₀ = $400, the interest rate is n = 2.6%, and the time is x = 3.25 years.
The formula for the future value in continuous compounding is:
P(x) = P₀eⁿˣ
Substitute P₀ = 400, n = 2.6%, and x = 3.25 into the equation:
[tex]P(3.25) = (400)e^{2.6\%(3.25)}\\[/tex]
= 434.93
Hence, the value of the investment after 3.25 years is $434.93.
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ASAP Write an equation of a quadratic formula with the given properties: f(3)=f(-5)=0;f(-6)=-36
The quadratic equation y = - 4 · x² - 8 · x + 60 contains the points (3, 0), (- 5, 0) and (- 6, - 36).
How to derive a quadratic equation that contains three points
In this question we find the coordinates of three points set on Cartesian plane and we are asked to find the quadratic equation that contains the these points. The standard form of the quadratic equation is shown below:
y = a · x² + b · x + c
Where:
x - Independent variable.y - Dependent variable.a, b, c - Real coefficients.We can determine the values of the three coefficients because the number of known points is equal to the number of coefficients. Then, we have the following system of linear equations by replacing x and y on each of the three points:
9 · a + 3 · b + c = 0
25 · a - 5 · b + c = 0
36 · a - 6 · b + c = - 36
Then, the solution to the system is found by numerical methods:
(a, b, c) = (- 4, - 8, 60)
The equation that contains the three points is y = - 4 · x² - 8 · x + 60.
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Find missing side length given two similar triangles
Answer: 49
Step-by-step explanation:
by using triangle ABC and the known values of triangle XYZ, we can divide side XY/AB, 28/4=7. By doing the same with YZ/BC, 56/8=7, we find that the scale factor is 7. With this information, we multiply side CA by the scale factor, 7x7=49.
Find the X-intercept for this please .
Answer: I believe both the x and y- intercepts are “(0,0)”
Step-by-step explanation: there is only one intercept and it is at the origin (0,0) making both the x and y - intercepts (0,0) :)
which is the correct answer ????
The correct way to replace equation 1 into equation 2 using the substitution method is 2x+(-5x+10) = 7.
According to the question,
We have the following two equations:
Equation 1: y = -5x+10
Equation 2: 2x+y = 7
Now, we will substitute the value of y from equation 1 in equation 2.
So, we have the following expression:
2x+(-5x+10) = 7
(More to know: we can also solve this equation to find the value of x and then the obtained value of x can be put in equation 1 to find the value of y.)
Hence, the correct option is B.
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Which value of x makes the following statement true? 1.4 - x = a positive number
Answer:1.4<x
math math math
Answer:daddy
Step-by-step explanation:gay