[tex]r = 3sec( \alpha ) \\ r = \frac{3}{cos( \alpha )} [/tex]
[tex]x = rcos( \alpha ) \: \: \: \: \: \: \: cos( \alpha ) = \frac{x}{r} [/tex]
[tex]r = \frac{3}{ \frac{x}{r} } \\ r = \frac{3r}{x} \: \: \: \: \: \: x = 3 \\ line[/tex]
A mail carrier can deliver mail to 36 houses in 30 minutes. Mark wants to determine how many houses the carrier can deliver mail to in 7.5 minutes at this rate. He thinks that to find the answer, he should do the following.
1. First divide 36 houses by 30 minutes to find a unit rate of 1.2 houses per minute.
2. Then multiply 1.2 houses per minute by 7.5 minutes to get 9 houses.
Mark's method is correct, because even though it is impossible to deliver mail to 1.2 houses in minute, it represents the unit rate of houses per minute .
Is Mark's method correct?The first step is to determine the unit rate of houses per minute. This can be done by dividing 36 houses by 30 minutes.
36/30 = 1.2 houses per minute
The second step is to multiply 1.2 by 7.5: 1.2 x 7.5 = 9 houses
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Mary’s rectangular garden is 27 units long and 49 units wide. What is the perimeter?
Answer:
152 units
Step-by-step explanation:
Two sides of the rectangle are 27 units long and the other two sides are 49 units wide. You just add all the numbers up (27+27+49+49). When you do that, you get 152. I hope this helps!
i need the answer to this.
Answer:
56:49 = 8.7 36:48 = 3:448:42 = 8:724:36 = 2:320:30 = 2:324:32 = 3:418:27 = 2:316:14 = 8:79:12 = 3:4hope this helps
A body and tackle with a velocity ratio of 5 is used to raise a mass of 50kg through a vertical distance of 20n at a steady rate if the effort is equal to 80n. Determine (a) distance moved by effort (b)the workdone by the effort in lifting the load (c)the losses in energy involve the operating in machine
A. The distance moved by the effort is 100 m
B. The workdone by the effort in lifting the load is 8000 J
C. The losses in energy involve the operating in machine 1800 J
A. How to determine the distance moved by the effortVelocity ratio = 5Load distance = 20 mEffort distance =?Velocity ratio = Effort distance / Load distance
5 = Effort distance / 20
Cross multiply
Effort distance = 5 × 20
Effort distance = 100 m
B. How to determine the work done by the effortEffort distance = 100Effort = 80 NWorkdone by effort =?Workdone = force × distance
Workdone by effort = 80 × 100
Workdone by effort = 8000 J
C. How to determine the losses in the energyWe'll begin by calculating the workdone in lifting the load. This is illustrated below:
Mass (m) = 50 KgAcceleration due to gravity (g) = 9.8 m/s²Height (h) = 20 mWorkdone =?Workdone = mgh
Workdone = 50 × 9.8 × 20
Workdone = 9800 J
Now, we can determine the energy lost as follow:
Workdone = 9800 JWorkdone by effort = 8000 JEnergy lost =?Energy lost = 9800 - 8000
Energy lost = 1800 J
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f Tanisha has $ 1,000 to invest at 5 % per annum compounded , how long will it be before she has $1,400 ? If the compounding is continuous, how long will it be?
Question content area bottom
Part 1
Compounding , it will be about
enter your response here years before Tanisha has $1,400.
With annual compounding, the number of years for 1000 to become 1400 is 6.7 years
With continous compounding, the number of years for 1000 to become 1400 is 1.35 years
How long would it take $1000 to become $1,400?With annual compounding, the formula that would be used is:
(In FV / PV) / r
Where:
FV = future value PV = present value r = interest rate(In 1400 / 1000) / 0.05 = 6.7 years
With continous compounding, the formula that would be used is:
(In 1400 / 1000) / (In e^r)
Where r = interest rate
((In 1400 / 1000) / (In e^0.05) = 1.35 years
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(1/2)(-27Divided by 1/3) 2/3
The value of the quotient is - 27
How to determine the quotientTo determine the quotient, first, we have
(1/2)(-27Divided by 1/3) 2/3
[tex] \frac{1}{2} \times \frac{ - 27 \times 3}{1} \times \frac{2}{3} [/tex]Multiply the numerator and denominator
=
[tex] \frac{ - 162}{6} [/tex]
Then divide the numerator by the denominator, we get
= - 27
Thus, the value of the quotient is - 27
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Jeremiah is a salesperson who sells computers at an electronics store. He makes a base pay amount each day and then is paid a commission as a percentage of the total dollar amount the company makes from his sales that day. Let PP represent Jeremiah's total pay on a day on which he sells xx dollars worth of computers. The table below has select values showing the linear relationship between xx and P.P. Determine how many dollars worth of computers Jeremiah would have to sell in order to get paid $130 on a given day.
Jeremiah has to sell 5000 dollars worth of computers to get paid $130 on a given day. Using the linear equation, the required value is calculated.
What is a linear equation?An equation in which if the highest degree of the variable is 1(one), then that equation is said to be a linear equation.
General form: ax + b = c; where the power of the variable x is 1.
Calculation:It is given that,
Jeremiah makes a base pay amount each day and then is paid a commission as a percentage of the total dollar amount the company makes from his sales that day.
Consider,
P - as total pay on a day, x - as the number of dollars worth of computers, B - as basic pay, and C - as commission percentage.
So, the linear equation that relates x and P is,
P = Cx + B ...(i)
On substituting the values from the given table we get,
122.5 = C(4500) + B ...(ii)
160 = C(7000) + B ...(iii)
175 = C(8000) + B ...(iv)
By solving equations (iii) and (iv), we get
C = 15/1000 = 0.015
B = 55
Finding x value when P = $130:
We have P = Cx + B. Then for P = 130,
130 = Cx + B
We know C = 0.015 and B = 55
On substituting these values,
130 = (0.015) x + 55
⇒ 0.015x = 130 - 55 = 75
∴ x = 75/0.015 = 5000
Therefore, the required computers are 5000 dollars worth.
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Disclaimer: The given question on the portal was incomplete. Here is the complete question.
Question: Jeremiah is a salesperson who sells computers at an electronics store. He makes a base pay amount each day and then is paid a commission as a percentage of the total dollar amount the company makes from his sales that day. Let P represent Jeremiah's total payments on a day on which he sells x dollars worth of computers. The table below has select values showing the linear relationship between x and P. Determine how many dollars worth of computers Jeremiah would have to sell to get paid $130 on a given day.
Table:
x: 4500, 7000, 8000
P: 122.5, 160, 175
respectively.
Find the measure of Angle E if Arc AB = 80 degrees and Arc CD = 38. Round to the nearest tenth.
The measure of angle E in the secant intersection is 21 degrees.
How to find the angle of intersected secant?When two secants intersect outside a circle, the circle divides the secants into segments that are proportional with each other
Therefore,
m∠E = 1 / 2 (∠AB - ∠CD)
m∠E = 1 / 2 (80 - 38)
m∠E = 1 / 2 (42)
m∠E = 42 / 2
m∠E = 21 degrees.
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[tex]\int_{1}^{7} \frac{1}{x^{8}} d x[/tex]
\int_{1}^{7} \frac{1}{x^{8}} d x
Use the power rule,
[tex]\displaystyle \int x^n \, dx = \frac{x^{n+1}}{n+1} + C[/tex]
with [tex]n=-8[/tex]. It follows by the fundamental theorem of calculus that
[tex]\displaystyle \int_1^7 \frac{dx}{x^8} = -\frac1{7x^7} \bigg|_{x=1}^{x=7} = -\frac17 \left(\frac1{7^7} - \frac1{1^7}\right) = \boxed{\frac17 - \frac1{7^8}}[/tex]
An employee at a fireworks company is designing a rocket. The rocket will consist of a cardboard circular cylinder with a height that is seven times as large as the radius. On top of the cylinder will be a cone with a height of 5 in. and a radius equal to the radius of the base as shown in the figure. If the company wants to fill the cone and the cylinder with a total of 204 in.^3 of powder, then what should be the radius of the cylinder? Note that the volume of a right circular cylinder with radius r and height h is and the volume of a cone with a base of radius r and height h is .
The radius of the cylinder should be approximately 2.040 inches long.
How to calculate the radius of a rocket to contain a required quantity of powder
The volume required to store the powder is the sum of the volumes of the cylinder and the cone, whose expression is in this case:
204 in³ = (π/3) · r² · (4 in) + π · r² · h
204 in³ = (4/3 + h) · π · r²
204 in³ = (4/3 + 7 · r) · π · r²
204 = (4π/3) · r² + 7π · r³
7π · r³ + (4π/3) · r² - 204 = 0
The positive roots of the cubic equation are:
r ≈ 2.040 in
The radius of the cylinder should be approximately 2.040 inches long.
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Find the area of the smaller sector. Round to the nearest tenth. 130 8.02
Answer:
73.0 m²
Step-by-step explanation:
[tex] A = \dfrac{n}{360^\circ}\pi r^2 [/tex]
[tex] A = \dfrac{130^\circ}{360^\circ}\pi (8.02~m)^2 [/tex]
[tex] A = 73.0~m^2 [/tex]
What can you say about the y-values of the two functions f(x) = 3x² -3 and
g(x) = 2* - 3?
A. g(x) has the smallest possible y-value.
B. The minimum y-value of g(x) approaches -3.
C. f(x) and g(x) have equivalent minimum y-values.
D. f(x) has the smallest possible y-value.
The y-values of the two functions f(x) = 3x² -3 and g(x) = 2* - 3 has the minimum y-value of g(x) approaches -3 and f(x) contains the smallest possible y-value.
What is a function?It exists described as a special kind of relationship and they contain a predefined domain and range according to the function every value in the domain exists connected to just one value in the range.
Given: f(x) = 3x² -3
As we can see in the graph the first term exists 3x² and exists still positive for all x.
The range for f(x) ∈ [-3, ∞)
When x = 0 then f(x) = -3
The above value exists as the smallest possible value on the y-axis.
Given: [tex]g(x) = 2^x - 3[/tex]
[tex]2^x[/tex] exists also a positive quantity and it exists as an exponential function.
The range for the g(x) ∈ (-3, ∞)
It signifies that g(x) never touches the y-axis at -3.
We can express the minimum value of g(x) approaches -3.
Therefore, the correct answer is option B. The minimum y-value of g(x) approaches -3 and option D. f(x) has the smallest possible y-value.
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An international company has 21,700 employees in one country. If this represents 17.7% of the company's employees, how many employees does
it have in total?
Round your answer to the nearest whole number.
Answer:
122,599
Step-by-step explanation:
In words, what I am is asking is 17.7% of what number is 21,700. I will need to change 17.7% to a decimal. To do that, I move the decimal 2 places to the left. Then solve.
.177 x w = 21700 Divide both sides by .177
w = 122,599
How much money is borrowed if the interest rate is 9.25% simple interest and the loan is made for 3.5 years and has 904.88 interest
The amount borrowed is 2795
What is Principal?Principal is the amount loaned or invested in a bank or a financial institution that gives a certain interest on a specific rate over a period of time.
Analysis:
P = principal = unknown
R = rate = 9.25%
T = time = 3.5 years
I = interest = 904.88
simple interest(I) = PRT/100
P = 100I/RT
P = 100 x 904.88/3.5 x 9.25 = 2795
In conclusion, the amount borrowed is 2795.
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What is the slope of the line that contains the points (9,-4) and (1,-5)?
OA. 1
OB.1/5
O C.-1/8
O D. -1
Answer:
Step-by-step explanation:
hello .....
note : the slope of the line (AB) is :
m = (YB -YA)/(XB - XA)
given : A(9,-4) and B (1,-5)
m= ((-5)-(-4))/(1-9)
m= 1/8
Solve for x.
BC = 2
CD =2x-6
BD X+2
Answer:
6
Step-by-step explanation:
Assuming C lies on segment BD, we know that by the segment addition postulate,
[tex]BC+CD=BD \\ \\ 2+2x-6=x+2 \\ \\ 2x-4=x+2 \\ \\ x=6[/tex]
The values of BC = 2, CD = 2x - 6 and BD = x + 2 then the value of x = 6.
How to find the value of x?The algebraic expression should be any one of the conditions such as addition, subtraction, multiplication, and division.
In mathematics, an algebraic expression exists as an expression built up from integer constants, variables, and algebraic operations. For example, 3x² − 2xy + c exists as an algebraic expression.
To estimate the value of x, bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to estimate the result.
Given: BC = 2, CD = 2x - 6 and BD = x + 2 then
BC+CD= BD
2+2x-6=x+2
Simplifying,
2x-4=x+2
Thus,
x=6
Therefore, the value of x = 6.
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sec^2x-2secx.cosx+cos^2x=tan^2x-sin^2x
Prove the identity
Hello.
sin²x + cos²x = 1
cos²x = 1 - sin²x
secx = 1/cosx
sec²x = tan²x + 1
In a game of chance, two fair dice are thrown. If the sum of the two dice is seven, you get paid out $90. If the sum of two dice is a six or an eight, you must pay $90(No money is exchanged for all other sums). How much money would you expect to win or lose, on average, per game?
You are expected to lose $ 10 on an average per game
How to determine the amount of money you would winTotal outcome = 36Event of sum of 7 = 6Amount per sum of 7 = $ 90Amount won per game =?Probability of sum of 7 = 6 / 36
Probability of sum of 7 = 1 / 6
Amount won per game = (1 / 6) × 90
Amount won per game = $ 15
How to determine the amount of money you would loseTotal outcome = 36Event of sum of 6 = 5Event of sum of 8 = 5Event of sum of 6 or 8 = 5 + 5 = 10Amount per sum 6 or 8 = $ 90Amount lose per game =?Probability of sum 6 or 8 = 10 / 36
Probability of sum 6 or 8 = 5 / 18
Amount lose per game = (5 / 18) × 90
Amount lose per game = $ 25
How to determine your expect earning on an avarge per gameAmount won per game = $ 15Amount lose per game = $ 25Expected earnings =?Expected earnings = Amount won per game - Amount lose per game
Expected earnings = 15 - 25
Expected earnings = -$ 10
Thus, you are expected to lose $ 10 on an average per game
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find the y intercept of 2x - 5y + 7 = 0
the function f(x)=-x^2-x+15 is shown on the graph. what are donain and range of the function? t
Answer:
Domain: All real numbersRange: [tex]y \leq 61/4[/tex]Step-by-step explanation:
The domain is the set of x values.
The range is the set of y values.
About % of the area under the curve of the standard normal distribution is between z = − 0.9 z = - 0.9 and z = 0.9 z = 0.9 (or within 0.9 standard deviations of the mean).
Using the normal distribution, it is found that 63.18% of the area under the curve of the standard normal distribution is between z = − 0.9 z = - 0.9.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The area within 0.9 standard deviations of the mean is the p-value of Z = 0.9(0.8159) subtracted by the p-value of Z = -0.9(0.1841), hence:
0.8159 - 0.1841 = 0.6318 = 63.18%.
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If f(x)=x/4-3 and g(x)= 4x²+2x-4, find (f+g)(x).
OA. 4x²+x-7
OB.x²-12
O C. 4x²+2x+1
O D. 4x²+2x-7
Answer:
hello :
f(x)=x/4-3 and g(x)= 4x²+2x-4,
(f+g)(x).=f(x)+g(x)=x/4-3 + 4x²+2x-4,
(f+g)(x).= 4x²+(2x+x/4)-7
(f+g)(x).= 4x²+x(3+1/4) - 7......continu
Help me please!!!!!!!!
Answer:
The ratios are not equal, so this is not a dilation.
Step-by-step explanation:
4/3 is the first ratio
3/4 is the second ratio
Since these ratios are not equal there is not a dilation.
What is the y-intercept of the function f(x) = -2/9x + 1/3?
Answer: (0,1/3)
Step-by-step explanation:
Answer:
The y-intercept of the function f(x) = -2/9x + 1/3 is 1/3.
Step-by-step explanation:
Given, function is
f(x) = -2/9x + 1/3.
The y-intercept is the point where the graph intersects the y-axis.
The y-intercept of a graph is (are) the point(s) where the graph intersects the y-axis.
We know that the x-coordinate of any point on the y-axis is 0.
So the x-coordinate of a y-intercept is 0.
To find the y - intercept set x = 0.
f(0) = (2/9 . 0) + 1/3
f(0) = 0 + 1/3
f(0) = 1/3.
(02.04 LC)
Determine the equation of the line shown in the graph:
graph of a vertical line with an x intercept of negative 1
y = −1
y = 0
x = −1
x = 0
Answer:
x = - 1
Step-by-step explanation:
the equation of a vertical line is
x = c
where c is the value of the x- coordinates the line passes through
the line passes through the x- intercept of - 1 , then
x = - 1 ← equation of vertical line
Imagine the center of the London Eye Ferris Wheel is located at (0, 0) on a coordinate grid, and the radius lies on the x-axis. Write an equation of a circle for the ferris wheel, and sketch an image of what the ferris wheel would look like on the grid. Now graph a circle that is similar to the Ferris Wheel. Discuss the transformations needed to show that both circles on your graph are similar.
answer
symbolic materials ?
Which of the following is not a step in finding the area of an unknown figure?
- Calculate the areas of the smaller figures.
- Plug all dimensions into the formula: SA=Ixwxh.
- Divide the figure into smaller, known figures.
- Add up the areas of the smaller figures.
The answer choice which is not a step in finding the area of the unknown figure is; Plug all dimensions into the formula: SA=Ixwxh. option B
Which is not a step in finding the area of an unknown figure?It follows from the task content that all other steps except Plugging all dimensions into the formula; SA = l×w×h are correct steps.
This is due to the fact that, the formula does not work for all shapes and hence, it can't be generalized for all situations.
The step which is not involved in finding the area of an unknown figure is; Plug all dimensions into the formula: SA=Ixwxh.
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Answer:
B) Plug all dimensions into the formula: SA=Ixwxh.
Step-by-step explanation:
Simplify the trigonometric expression (sin^2(x/2)) (1 + cos(x)) using Half-Angle Identities.
Answer:
B
Step-by-step explanation:
1-cos2x=2sin²(x/2)
[tex]sin^2(\frac{x}{2} )=\frac{(1-cos(2x))}{2}\\(sin^2(\frac{x}{2} ))(1+cos(x))= \frac{(1-cos(2x))(1+cos(x))}{2}[/tex]
What are the fourth roots of -3+3√3i?
Enter your answer by filling in the boxes. Enter the roots in order of increasing angle measure in simplest form.
By De Moivre's formula, we have the following four roots: [tex]z_{1} = 1.565 \cdot \left(\cos \frac{\pi}{6} + i\,\sin \frac{\pi}{6} \right)[/tex], [tex]z_{2} = 1.565\cdot \left(\cos \frac{2\pi}{3} + i\,\sin \frac{2\pi}{3} \right)[/tex], [tex]z_{3} = 1.565\cdot \left(\cos \frac{7\pi}{6}+i\,\sin \frac{7\pi}{6} \right)[/tex] and [tex]z_{4} = 1.565\cdot \left(\cos \frac{5\pi}{3} + i\,\sin \frac{5\pi}{3} \right)[/tex].
How to determine a fourth root of a complex numberAccording to complex analysis, the fourth roots of a complex number can be found by De Moivre's formula:
[tex]\sqrt[n]{z} = \sqrt[n]{r}\cdot \left[\cos \left(\frac{\theta + 2\pi\cdot i}{n} \right)+ i\,\sin \left(\frac{\theta + 2\pi\cdot i}{n} \right)\right][/tex], for [tex]i = \{0, 1, ..., n - 1\}[/tex] (1)
Where:
r - Magnitude of the complex number.θ - Direction of the complex number, in radians.First, we find the magnitude and direction of the complex number:
[tex]r = \sqrt{(-3)^{2}+(3\sqrt{3})^{2}}[/tex]
r = 6
[tex]\theta = \tan^{-1} \left(\frac{3\sqrt{3}}{-3} \right)[/tex]
[tex]\theta = \frac{2\pi}{3} \,rad[/tex]
Now we find the four quartic roots of the complex number:
[tex]z_{1} = 1.565 \cdot \left(\cos \frac{\pi}{6} + i\,\sin \frac{\pi}{6} \right)[/tex]
[tex]z_{2} = 1.565\cdot \left(\cos \frac{2\pi}{3} + i\,\sin \frac{2\pi}{3} \right)[/tex]
[tex]z_{3} = 1.565\cdot \left(\cos \frac{7\pi}{6}+i\,\sin \frac{7\pi}{6} \right)[/tex]
[tex]z_{4} = 1.565\cdot \left(\cos \frac{5\pi}{3} + i\,\sin \frac{5\pi}{3} \right)[/tex]
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100 POINTS
Construct a horizontal line that passes through the intersection of lines AC and BC at point C. Add a vertical line segment connecting the horizontal line to line AC called FG and another vertical line connecting the horizontal line to line BC called DE.
Complete the proof.
LOOK AT IMAGE PLEASE
The blanks are as follows:
Angle addition postulateSubtraction property of equalityCorresponding sides of similar triangles are proportionalMultiplication property of equality