The magnitude of f3 is 6.403N and the coordinate direction angle is 247.9°
We can calculate the magnitude and coordinate direction angle of f3 using the vector triangle method.
We assume that the coordinate direction angle of f1 is 0° and the coordinate direction angle of f2 is 90°.
Using the law of cosines, we can determine the magnitude of f3, which is 6.403N:
f3^2 = f1^2 + f2^2 -2f1f2cos180°
f3^2 = 5^2 + 8^2 -2(5)(8)cos180°
f3^2 = 25 + 64 -80
f3^2 = 49
f3 = 6.403N
We can then use the law of sines to determine the coordinate direction angle of f3, which is 247.9°:
sinθ3 = f2sin180°/f3
sinθ3 = (8)(180°)/6.403
sinθ3 = 147.6°
θ3 = 247.9°
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Mason is going to invest in an account paying an interest rate of 5. 3% compounded
quarterly. How much would Mason need to invest, to the nearest hundred dollars,
for the value of the account to reach $205,000 in 14 years?
Rounding to the nearest hundred dollars, the amount Mason needs to invest is $144,000.
Compound Interest Investment CalculationTo determine the amount Mason needs to invest, you can use the formula for compound interest:
A = P * (1 + r/n)^(nt)
Where:
A = final amount
P = initial investment (principal)
r = annual interest rate (5.3%)
n = number of times interest is compounded per year (quarterly = 4 times)
t = number of years
Setting A = 205,000 and solving for P:
205,000 = P * (1 + 0.053/4)^(4 * 14)
P = 205,000 / (1 + 0.053/4)^(4 * 14)
Rounding to the nearest hundred dollars, the amount Mason needs to invest is $144,000.
The information provided is about calculating the initial investment (or principal) that Mason needs to make in an account paying an interest rate of 5.3% compounded quarterly, in order to reach a target amount of $205,000 in 14 years. The calculation uses the formula for compound interest, which takes into account the initial investment, the interest rate, the number of times the interest is compounded in a year, and the number of years the investment will grow.
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Moira is paid $891.60 each fortnight as a hairdresser. How much would she have been paid after working for 18 weeks?
Answer: To find out how much Moira would have been paid after working for 18 weeks, we need to multiply her fortnightly pay by the number of fortnights in 18 weeks.
Since there are 26 fortnights in a year, 18 weeks is equivalent to 18/26 = 9/13 of a year.
So, Moira's total pay after 18 weeks would be:
891.60 * 9/13 = $584.40
So, Moira would have been paid $584.40 after working for 18 weeks.
Step-by-step explanation:
In a blueprint, each square has a side of lenght of 1/4inch.
The cost of the tiles and carpet will be $1,600 and $640, respectively.
What is the area of the rectangle?Let W be the rectangle's width and L its length.
The area of the rectangle is the multiplication of the two different sides of the rectangle. Then the rectangle's area will be
Area of the rectangle = L × W square units
The area of the bedroom is given as,
A = (5 x 1/4 x 16) x (4 x 1/4 x 16)
A = 20 x 16
A = 320 square feet
A = 320 / 9
A = 35.56 square yards
Ceramic tile costs $5 per square foot. Then the cost of tiles is given as,
⇒ 320 x 5
⇒ $1,600
The carpet costs $18 per square yard. Then the cost of the carpet is given as,
⇒ 35.56 x 18
⇒ $640
The cost of the tiles and carpet will be $1,600 and $640, respectively.
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bella has 52$ and save 14$ every week how much will she have for the first 5 weeks?
Using a linear equation, since Bella currently has $52 and saves $14 weekly, for the first 5 weeks, she will have $122.
How is the total savings determined?We can use a linear equation to determine the total savings that Bella will have after x weeks.
A linear equation is an algebraic equation that can be modeled on a graph line and written in the form of y = mx + b, where m is the slope, x is a variable and the x-intercept, and b is the y-intercept.
The current savings = $52
The weekly savings = $14
The number of weeks = 5 weeks
The total savings in five weeks = $122 ($52 + 14(5)
Linear Equation:= 52 + 14x, where x is the number of weeks
Thus, we can conclude that Bella will have $122 in her savings after 5 weeks.
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find scalars 1 and 2 such that w = 1u 2v.
The scalars 1 and 2 in the equation w = 1u + 2v can be found by knowing the components of the vectors u and v.
Given the equation w = 1u + 2v, the scalars 1 and 2 can be found by knowing the components of the vectors u and v. Let's assume that u has the components (a, b) and v has the components (c, d). Then, the vector w can be written as (a + 2c, b + 2d).
Comparing the components of w with the equation w = 1u + 2v, we can see that 1 = 1 and 2 = 2. This means that the scalars 1 and 2 are simply equal to 1 and 2, respectively.
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p^2 + 2p - (q+1)(1-1)
Solving the provided question, we can say that The quadratic equation we have is - [tex]p^2 + 2p - (q+1)(1-1)[/tex] => p = [tex]\sqrt{-2p}[/tex]
What is quadratic equation?A quadratic equation is x ax2+bx+c=0, which is a quadratic polynomial in a single variable. a 0. The Fundamental Theorem of Algebra ensures that it has at least one solution since this polynomial is of second order. Solutions may be simple or complicated. An equation that is quadratic is a quadratic equation. This indicates that it has at least one word that has to be squared. The formula "ax2 + bx + c = 0" is one of the often used solutions for quadratic equations. where are numerical coefficients or constants a, b, and c. where the variable "X" is unidentified.
The quadratic equation we have is -
[tex]p^2 + 2p - (q+1)(1-1)[/tex]
[tex]p^2 + 2p - (q+1)*0[/tex]
[tex]p^2 + 2p = 0[/tex]
[tex]p^2 = -2p[/tex]
p = [tex]\sqrt{-2p}[/tex]
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In a survey of 135 adults, 85 were employed full time and the remainder were employed part time. Of those employed full time, 70 had been to a doctor in the last year. Of those employed part time, 25 had been to a doctor in the last year.
From the question, we can conclude that the survey produced the following results.
Employed Full Time, Yes doctor = 70
Employed Full Time, No doctor = 15
Employed Part Time, Yes doctor = 25
Employed Part-Time, No doctor = 25
The question states that there are:-
135 adults
85 fully employed, which also means that there are
135 - 85 = 50 part employed
Full employed, 70 = yes doctor
Part employed, 25 = yes doctor
From the above, we can subtract that
Full employed = 85
Yes doctor = 70
No doctor = 85 - 70 = 15
Part employed = 50
Yes doctor = 25
No doctor = 50 - 25 = 25
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What is the equation of the line, in slope-intercept form, that passes through (4, 2) and (-2, -3)?
A. 5 x - 6 y - 8 = 0
B. 3 y = -2x + 20
C. y=(5)/(6)x-(4)/(3)
The equation of the line in slope intercept form is A. 5x - 6y - 8 = 0.
What is Slope?Slope of a line is the ratio of the change in y coordinates to the change in the x coordinates of two points given.
Slope can also be defined as the tangent of the angle that the line is making with the positive X axis.
Equation of a line in slope intercept form is,
y = mx + d
m : slope
d : y intercept
y intercept is the y coordinate of the point where the line touches the Y axis.
Given are two points (4, 2) and (-2, -3).
Slope = (-3 - 2) / (-2 - 4) = -5 / -6 = 5/6
So the equation becomes,
y = 5/6 x + d
Substitute one of the points given in the above equation.
2 = (5/6) 4 + d
d = 2 - 10/3
d = -4/3
Equation is,
y = 5/6 x - 4/3
Multiplying throughout the equation with 6,
6y = 5x - 8
5x - 6y - 8 = 0
Hence the required equation is 5x - 6y - 8 = 0.
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!100 POINTS!!!
I need help with these geometry problems unit 1.14 circles
Answer:
Convert from degrees to radians using the ratio
π
180.001989675
radians
what is the change in t from 5.6 hours after the candle was lit to 10.2 hours after the candle was lit?
The change in time between 5.6 hours after the candle was lit and 10.2 hours after the candle was lit is 4.6 hours.
What is the change in t from 5.6 hours after the candle was lit to 10.2 hours?The change in time (Δt) between two given points can be calculated as the difference between the two values:
Δt = t2 - t1
Where t1 is the first time (5.6 hours after the candle was lit) and t2 is the second time (10.2 hours after the candle was lit).
So,
t1 = 5.6 hours
t2 = 10.2 hours
Δt = t2 - t1
Δt = 10.2 hours - 5.6 hours
Δt = 4.6 hours
Therefore, the change in time between 5.6 hours after the candle was lit and 10.2 hours after the candle was lit is 4.6 hours.
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suppose the caravan has 20 cars, and that the tollbooth services a car at a rate of one car per 5 seconds. car speed is 10 kilometers per second. how long does it take for the entire caravan to receive service at the first tollbooth, and line up before the second toll booth?
It takes 40 seconds (400 / 10) for the entire caravan to line up before the second toll booth.
It takes 100 seconds (20 * 5) for the entire caravan to receive service at the first toll booth.
Assuming that the cars line up at the second toll booth right after receiving service at the first toll booth, the time it takes for the entire caravan to line up before the second toll booth depends on the speed of the cars.
Since the speed of the cars is 10 kilometers per second, in the 100 seconds it takes for the entire caravan to receive service at the first toll booth, the entire caravan travels a distance of 1000 kilometers (100 * 10).
Since the distance between the first and second toll booths is 400 km, it takes 40 seconds (400 / 10) for the entire caravan to line up before the second toll booth.
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It takes 40 seconds (400 / 10) for the entire caravan to line up before the second toll booth.
It takes 100 seconds (20 * 5) for the entire caravan to receive service at the first toll booth.
Assuming that the cars line up at the second toll booth right after receiving service at the first toll booth, the time it takes for the entire caravan to line up before the second toll booth depends on the speed of the cars.
Since the speed of the cars is 10 kilometers per second, in the 100 seconds it takes for the entire caravan to receive service at the first toll booth, the entire caravan travels a distance of 1000 kilometers (100 * 10).
Since the distance between the first and second toll booths is 400 km, it takes 40 seconds (400 / 10) for the entire caravan to line up before the second toll booth.
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Use the image below to determine what relationship exists between AGC and FGD
A: supplementary angles
B: vertical angles
C: adjacent angles that form EGA
D: complementary angles
Answer: Your mom?
Step-by-step explanation: Your mom?
Given the function [tex]f(x)=\left \{ {{x^2+a, for x\leq 1} \atop {-2ax+7, for x\ \textgreater \ 1}} \right.[/tex] , what must the value of [tex]a[/tex] be so that [tex]y=f(x)[/tex] is continuous at [tex]x=1[/tex]? (i.e., you can draw it without lifting your pencil.)
The value of a such that f(x) is continuous at x = 1 is given as follows:
a = 2.
What is the continuity concept?A function f(x) is continuous at x = a if it is defined at x = a, and the lateral limits are equal, that is:
[tex]\lim_{x \rightarrow a^-} f(x) = \lim_{x \rightarrow a^+} f(x) = f(a)[/tex]
To the left of x = 1, the lateral limit is given as follows:
lim x -> 1^- f(x) = lim x -> 1^- x² + a = 1² + a = a + 1.
To the right of x = 1, the lateral limit is given as follows:
lim x -> 1^+ f(x) = lim x -> 1^+ -2ax + 7 = -2a + 7.
The function f(x) is only continuous at x = 1 if the lateral limits are equal, hence the value of x is obtained as follows:
a + 1 = -2a + 7
3a = 6
a = 6/3
a = 2.
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what is the most appropriate measure of center for this data, and why? group of answer choices mean, because the histogram is normal. mean, because the histogram is skewed to the right. median, because the histogram is normal. median, because the histogram is skewed to the right.
The correct answer is "median, because the histogram is skewed to the right."
It depends on the shape of the histogram and the specific characteristics of the data set.
If the histogram is roughly symmetrical and resembles a bell-shaped curve, it is considered normal or approximately normal, and the mean and median are appropriate measures of center. In this case, both the mean and median would give similar values and could be used to describe the center of the data.
If the histogram is skewed to the right, with a longer tail on the right side, the mean will be larger than the median. In this case, the median is considered the most appropriate measure of center because it is not influenced by outliers or extreme values, which can have a significant impact on the mean.
Therefore, the correct answer is "median, because the histogram is skewed to the right."
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The correct answer is "median, because the histogram is skewed to the right."
It depends on the shape of the histogram and the specific characteristics of the data set.
If the histogram is roughly symmetrical and resembles a bell-shaped curve, it is considered normal or approximately normal, and the mean and median are appropriate measures of center. In this case, both the mean and median would give similar values and could be used to describe the center of the data.
If the histogram is skewed to the right, with a longer tail on the right side, the mean will be larger than the median. In this case, the median is considered the most appropriate measure of center because it is not influenced by outliers or extreme values, which can have a significant impact on the mean.
Therefore, the correct answer is "median, because the histogram is skewed to the right."
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What is the number outside of the radical called (ex: the K in the photo attached)
The number outside of the radical symbol is called the index or the radicand.
In your photo, the letter "K" appears to be a variable and is not commonly referred to as a specific term. However, in some contexts, the letter "K" may represent a constant value.
The phrase "x radical n" or "the nth root of x" used to denote that a root is known as a radical.The horizontal line of the radical symbol is referred to as the vinculum, the quantity underneath it as the radicand, and the number n written to the left as the index.
A square root is written with a radical symbol √ and the number or expression inside the radical symbol, below denoted a, is called the radicand.The term "radical" is used to represent the square root or nth roots.
Radicand: A value or phrase included within the radical symbol.
Therefore, the number outside of the radical symbol is called the index or the radicand
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find a second-degree polynomial p such that p(2) = 14, p'(2) = 14, and p''(2) = 8.
The required second-degree polynomial in the given situation is f(x)=14x²+14x+8.
What is a polynomial?An expression that consists of variables, constants, and exponents that are combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable).
Sums of terms of the form k-xⁿ, where k is any number and n is a positive integer, make up polynomials.
For instance, the polynomial 3x+2x-5. a description of polynomials.
So, we have:
p(2) = 14, p'(2) = 14, and p''(2) = 8
So, the equation would be in the form:
f(x) = ax² + bx + x
Now, insert values as follows:
f(x) = ax² + bx + x
f(x) = 14x² + 14x + 8
Therefore, the required second-degree polynomial in the given situation is f(x) = 14x² + 14x + 8.
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a survey of a number of large corporations gave the following probability table for events related to the offering of a promotion involving a transfer two career marriage one career marriage unmarried total rejected promotion 0.184 0.0555 0.0170 0.2565 accepted promotion 0.276 0.3145 0.1530 0.7435 total 0.46 0.37 0.17 what is the probability that a professional (selected at random) would accept the promotion? report your answer as a decimal with no more than two places.
The probability that a professional would accept the promotion is 0.7435.
The total row represents the sum of the probabilities of each event for all the categories, and in this case, the probability of accepting the promotion is the sum of the probabilities of accepting the promotion for each category, which is 0.276 + 0.3145 + 0.1530 = 0.7435.
This means that if we randomly select a professional, there is a 0.7435, or 74.35%, chance that they would accept the promotion. The probability is calculated by taking the sum of the probabilities for each category that corresponds to accepting the promotion and dividing it by the total number of professionals surveyed.
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At a shoe store shoes are one third of their original price the sale price of a pair of gym shoes is $ 15. 50 write and solve an equation that could be used to find the original cost of the shoes
The original cost of the shoes is $0.31. A pair of workout sneakers is being sold for $15.50 at a shoe retailer, which is one third of its original cost.
How can you determine the original price based on the sale price?
The original cost, for instance $90, should be located. Obtain the discounted amount, say 20%. Create a savings estimate: 20% of $90 = $18. Get the sale price by deducting the savings from the original cost: $90 - $18 = $72. Finally, revenue = cost + cost * markup / 100 should work if you need the selling price. This is perhaps the most frequent scenario: you know the purchase price of an item, along with the intended markup, thus you're trying to determine the sale price.
Enter several numbers into the markup calculator if you want to. $15.50 + $15.50 =$ 31/100 =$0.31.
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A.N.'s burns are being treated by the open method with topical application of silver sulfadiazine (Silvadene). In caring for A.N., which interventions will you perform?
a. Shave all hair within the wound beds
b. Maintain the room temperature at 85 degree F (29.4 degree C)
c. Use clean technique when changing A.N.'s dressings
d. Monitor the CBC and WBC with differential frequently
e. Do not allow her to bathe for the initial 72 hours after injury
f. Apply a 1/16-inch film of medication, covering entire burn
In caring for A.N., we will perform a number of interventions. The first is to shave all hair within the wound beds, to minimize the risk of infection and reduce the amount of bacteria around the wound.
We will also maintain the room temperature at 85 degrees Fahrenheit (29.4 degrees Celsius) to ensure a warm and comfortable environment for A.N. when she is receiving treatment. We will also use clean technique when changing A.N.'s dressings to reduce the risk of infection. Additionally, we will monitor the CBC and WBC with differential frequently to ensure A.N. is receiving adequate treatment.
Furthermore, we will not allow her to bathe for the initial 72 hours after injury to reduce the chances of infection. Lastly, we will apply a 1/16-inch film of medication, covering the entire burn, to help aid in the healing process and reduce the risk of infection.
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an environmental engineer tracking replacements of pump rotors has noticed that of the newest batch of rotors purchased by her company, 12% of the rotors have failed after 235 hours of operation. assuming a constant failure rate, what is the mean time to failure (mttf) of the new rotors?
Mean time to failure (MTTF) of new rotors is 1952 hours, calculated as reciprocal of failure rate (12% per 235 hours).
What is rate ?
Rate is a measure of the change of a quantity per unit of time or per unit of another quantity. It can refer to various physical or abstract quantities, such as speed, velocity, frequency, interest rate, growth rate, etc. It is often expressed as a ratio or a fraction and has units specific to the quantity being measured.
The mean time to failure (MTTF) can be calculated as the reciprocal of the failure rate. The failure rate can be calculated as the number of failures per unit of operating time.
In this case, the failure rate is 12% per 235 hours, or 0.12 / 235 = 0.00051 failures per hour.
So, the MTTF would be:
MTTF = 1 / failure rate = 1 / 0.00051 = 1952 hours.
Mean time to failure (MTTF) of new rotors is 1952 hours, calculated as reciprocal of failure rate (12% per 235 hours).
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Mean time to failure (MTTF) of new rotors is 1952 hours, calculated as reciprocal of failure rate (12% per 235 hours).
Rate is a measure of the change of a quantity per unit of time or per unit of another quantity. It can refer to various physical or abstract quantities, such as speed, velocity, frequency, interest rate, growth rate, etc. It is often expressed as a ratio or a fraction and has units specific to the quantity being measured.
The mean time to failure (MTTF) can be calculated as the reciprocal of the failure rate. The failure rate can be calculated as the number of failures per unit of operating time.
In this case, the failure rate is 12% per 235 hours, or 0.12 / 235 = 0.00051 failures per hour.
So, the MTTF would be:
MTTF = 1 / failure rate = 1 / 0.00051 = 1952 hours.
Mean time to failure (MTTF) of new rotors is 1952 hours, calculated as reciprocal of failure rate (12% per 235 hours).
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Roses are selling for $5 for 3 roses . How much will bradley payfor a dozen roses
F $15
G $60
H $20
J $25
Answer:
H
Step-by-step explanation:
if its 5$ for 3 roses and a dozen is 12 you would just times it by 4 to get 20$ for 12 roses
Pls answer these for me
The simplification of the given terms is 32√a¹⁰b⁷.
What is simplification?
In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler. Calculations and problem-solving techniques simplify the issue. When an expression is simplified, it is reduced to a simpler form utilizing a variety of processes. While not completely accurate, the approximation is the process of reducing a complex mathematical expression to its nearest value.
Here, we have
Given: Expression 2√32a³b⁵√8a⁷b²
We have to simplify this given expression
= 2√32a³b⁵√8a⁷b²
= 2 √256a¹⁰b⁷
= 2×16√a¹⁰b⁷
= 32√a¹⁰b⁷
Hence, the simplification of the given terms is 32√a¹⁰b⁷.
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Consider the following quadratic function: f(x) = 3x^2 - 8x + 2. Find the x-intercept
For the quadratic function f(x) = 3x² - 8x + 2, the x-intercepts are x1 = (4 + √10) / 3 and x2 = (4 - √10) / 3.
What is a quadratic function?
A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. It is also known as the polynomial of degree 2 since the greatest degree term in a quadratic function is of second degree.
The given quadratic function is - f(x) = 3x² - 8x + 2.
The quadratic function is in the standard form ax² + bx + c = 0.
Here, a = 3, b = -8 and c = 2.
The x-intercepts can be found using the formula -
x1 = (-b + √Δ) / (2a)
x2 = (- b - √Δ) / (2a)
Here, Δ = b² - 4ac.
Substitute the values in the above equation -
Δ = b² - 4ac
Δ = (-8)² - 4(3)(2)
Δ = 64 - 24
Δ = 40
Now, substitute the value of Δ in the x-intercepts formula -
x1 = [-(-8) + √40) / [2(3)] x2 = [-(-8) - √40) / [2(3)]
Open the brackets and use arithmetic operation of multiplication -
x1 = (8 + √40) / 6 x2 = (8 - √40) / 6
Take out the common value -
x1 = (8 + 4√10) / 6 x2 = (8 - 4√10) / 6
Use arithmetic operation of division -
x1 = (4 + √10) / 3 x2 = (4 - √10) / 3
Therefore, the x-intercepts are x1 = (4 + √10) / 3 and x2 = (4 - √10) / 3.
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Solve the system of linear equations using substitution. X= 7y-6 x+7y=2
Answer:
(-2, 4/7)
Step-by-step explanation:
Ahh the wonderful world of substitution:
x = 7y - 6
x + 7y = 2
So, we need to find what x and y are. Since we know what x is equal to because of the first equation, we can plug that into the second equation:
7y - 6 + 7y = 2
Now let's solve this
14y - 6 = 2
+6 +6
14y = 8
/14 /14
y = 4/7
Now that we know what y is equal to, we can plug this into the equation. I'll choose the first one, since it is much easier:
x = 7(4/7) - 6
x = 4 - 6
x = -2
Therefore, x is equal to -2 and y is equal to 4/7, final answer.
Hope this helps :D
find a formula for a function that has vertical asymptotes x = 2 and x = 4 and horizontal asymptote y = 2.
The function with the asymptotes as x = 2 , x = 4 and y = 2 is given by the relation f(x) = 2 / [(x - 2)(x - 4)]
Given data,
To find a function that has vertical asymptotes at x = 2 and x = 4, and a horizontal asymptote at y = 2, we can start by considering the basic form of a rational function:
f(x) = (ax + b) / (cx + d)
To satisfy the given conditions, we need the denominator of the rational function to have factors of (x - 2) and (x - 4) since these will create the vertical asymptotes at x = 2 and x = 4.
So, f(x) = (ax + b) / [(x - 2)(x - 4)]
Now, let's consider the horizontal asymptote at y = 2. For a rational function, the horizontal asymptote occurs when the degree of the numerator is less than or equal to the degree of the denominator. Since we want a horizontal asymptote at y = 2, which is a horizontal line, the numerator needs to be a constant, and the denominator needs to be linear.
Let's choose a = 0 and b = 2 so that the numerator is a constant equal to 2.
f(x) = 2 / [(x - 2)(x - 4)]
Hence , a formula for the function that satisfies the given conditions is given by f(x) = 2 / [(x - 2)(x - 4)].
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what is the missing length? 16km area=224km
The missing length, considering a rectangle with dimensions 16 km and x km, with an area of 224 km, is given as follows:
x = 14 km.
How to obtain the area of a rectangle?The area of a rectangle is given by the multiplication of the width and the length of the triangle, as follows:
A = lw.
The parameters for this problem are given as follows:
Width of 16 km.Length of x km.Area of 224 km.Hence the length is obtained as follows:
16x = 224
x = 224/16
x = 14 km.
Missing InformationThe problem asks for the missing length, considering a rectangle with dimensions 16 km and x km, with an area of 224 km.
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Tamela compared the rates of three cable companies.
TV Watchers—$63.00 for 140 channels
Tel-EVision—$53.75 for 125 channels
Channels Galore—$41.80 for 110 channels
Which cable company has the best rate of price per channel?
Channels Galore has the best rate for price per channel.
Tel-EVision has the best rate for price per channel.
TV Watchers has the best rate for price per channel.
All of the companies have the same rate.
Answer:y = 4x-5.
Step-by-step explanation:
A wheel on a tractor has a 28-inch diameter. How many full revolutions does the wheel make if the tractor travels 5 miles?
4706 revolutions are made by the wheel over the course of 7 miles.
How many complete wheel revolutions does the wheel make?The wheel is a circular, therefore one revolution covers its entire circumference.
So, circumference C = d, where d is the wheel's diameter in inches, which is 30.
So, C = πd
= π × 30 in
= 30π in
= 94.25 in
Now that the tractor has traveled D = 7 miles, we need to determine how many revolutions the wheel completes.
As 1 mile equals 63360 inches,
D = 7 miles when converting miles to inches
= 7 × 1 mile
= 7 × 63360 in
= 443520 in
N = D/C is the number of revolutions the wheel completes in 7 kilometers.
= 443520 in/94.25
= 4705.89
To the nearest whole number, enter 4706.
Therefore, 4706 revolutions are made by the wheel over the course of 7 miles.
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Rosalyn's company, Snack Attack Inc., owns a few vending machine. Lasy night she collected $82.50 in dimes and quarters. If she collected 50 more quarters than dimes
Solving a system of equations we will see that she has 250 quarters and 200 dimes.
How many quarters and dimes does she has?
Let's define the variables:
d = number of dimes.
q = number of quarters.
We know that:
q = 50 + d
And:
0.25*q + 0.10*d = 82.50
Then we can write the system of equations:
q = 50 + d
0.25*q + 0.10*d = 82.50
Replacing the first equtaion into the second one we will get:
0.25*(50 + d) + 0.10*d = 82.50
12.5 + 0.35*d = 82.5
0.35*d = 82.5 - 12.5
0.35*d = 70
d = 70/0.35 = 200
And:
q = 50 + d
q = 50 + 200 = 250
So she has 250 quarters and 200 dimes.
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sketch the region enclosed by the graphs of the given functions. y = sec2(x), y = 8 cos(x), − 3 ≤ x ≤ 3
The region graph enclosed by the given functions y = sec2(x) and y = 8 cos(x) for -3 ≤ x ≤ 3 can be sketched as follows.
1. Plot the graphs of the given functions:
y = sec2(x) and y = 8 cos(x) for -3 ≤ x ≤ 3.
2. Shade the area enclosed the two graphs.
3. The region enclosed by the given functions is shown below.
The region enclosed by the given functions y = sec2(x) and y = 8 cos(x) for -3 ≤ x ≤ 3 can be sketched as follows. Firstly, plot the graphs of the two functions on the same coordinate plane. Then, shade the area enclosed by the two graphs. The resulting region is a curved area that starts from the point (-3, 8 cos(-3)) on the left, curves up until it reaches the point (3, 8 cos(3)) on the right and then curves down until it reaches the point (-3, 8 cos(-3)). The enclosed region is a continuous, curved area that lies between the two graphs.
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