The derivative of the function cos(xº) in radians is y' = -sin(xπ/180)
Finding the derivative of the functionFrom the question, we have the following function definition that can be used in our computation:
cos(xº)
Changing the degree into radian, we have
cos(xπ/180)
Express as a function
So, we have
y = cos(xπ/180)
When the cosine function is differentiated, we have
y' = -sin(xπ/180)
Hence, the differentiated function is y' = -sin(xπ/180)
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A music store marks up the instruments it sells by 30%.
If the price tag on a trumpet says $104, how much did the store pay for it?
CAN SOMEONE HELP WITH THIS question?✨
The summation ∑₁¹²⁴(29a₁ - 13b₁) = -30
How to find the given summation?Suppose that ∑₁¹²⁴a₁ = -10 and ∑₁¹²⁴b₁ = -20. We desire to compute the following ∑₁¹²⁴(29a₁ - 13b₁), we proceed as follows.
So, the summation ∑₁¹²⁴(29a₁ - 13b₁)
Expanding the brackets, we have that
∑₁¹²⁴(29a₁ - 13b₁) = ∑₁¹²⁴29a₁ - ∑₁¹²⁴13b₁)
= 29∑₁¹²⁴a₁ - 13∑₁¹²⁴b₁
Given that ∑₁¹²⁴a₁ = -10 and ∑₁¹²⁴b₁ = -20.
So, substituting the values of the variables into the equation, we have that
∑₁¹²⁴(29a₁ - 13b₁) = 29∑₁¹²⁴a₁ - 13∑₁¹²⁴b₁
= 29(-10) - 13(-20)
= -290 + 260
= -30
So, ∑₁¹²⁴(29a₁ - 13b₁) = -30
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2y−3x=6 Into slope-intercept form, simplifying all fractions.
Answer:
y = 3/2x + 3
Step-by-step explanation:
The slope-intercept form is y = mx + b
2y − 3x = 6
2y = 3x + 6
y = 3/2x + 3
So, the answer is y = 3/2x + 3
Tarea de rendimiento
12
La señora Ericson preparó sándwiches para sus 4 hijos. Todos los sándwiches tenían
el mismo tamaño. Después del almuerzo, a cada niño le quedaba una fracción
diferente de su sándwich. Matt tenía, Elisa tenía
7
3, Carl tenía 2, y Riley tenía 8
8
4
A Usa esta información para escribir un problema en que se comparen dos fracciones
con el mismo numerador.
The word problem is given thus: Given this gridlock, which child between Matt and Riley still had more proportionate remaining sandwich contents provided they both possess a shared 4/8 numerator?
How to solveFour sandwiches were prepared by Mrs. Ericson, each identical in size, for her offspring: Matt, Elisa, Carl, and Riley.
The children consumed varying portions of their respective sandwiches during the shared midday meal.
Post-lunch investigations denoted different fractions residual from each child's original sandwich quantity.
Matt kept 7/8 of his portion while Elisa held on to 3/4 of hers. Meanwhile, two halves (2/4) constitute what remained of Carl's sandwich with Riley retaining 4/8 for himself.
Given this gridlock, which child between Matt and Riley still had more proportionate remaining sandwich contents provided they both possess a shared 4/8 numerator?
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The question in English is:
Mrs. Ericson made sandwiches for her 4 children. All the sandwiches had
The same size. After lunch, each child had a fraction left.
different from your sandwich. Matt had, Elisa had
7
3, Carl was 2, and Riley was 8
8
4
Use this information to write a problem comparing two fractions
with the same numerator.
A contractor can by two types of wood. she got 45 expensive wood and 60 cheap wood for the same total price. if the 45 expensive wood cost $3.00 more than the 60 cheap wood, then which equation below shows the correct relationship between the 2 types of wood that she purchased. Also (x =price of the 60 cheap wood)
A.45(x+3)=60x
B.45(x-3)=60x
C.60(x-3)=45x
D.60(x+3)=45x
The correct answer is,
C. 60(x - 3) = 45x.
This equation is based on the information that the 45 expensive wood costs $3.00 more than the 60 cheap wood. In other words, if the price of the 60 cheap wood is x, the price of the 45 expensive wood is x + 3.
Since, Algebra involves working with numbers, equations, and variables to solve real-world problems and understand abstract relationships.
Now, To solve this equation, we must use algebra and solve for x.
First, we multiply both sides of the equation by 4/5. This gives us:
48x + 36 = 45x
-36 = 3x
Finally, we divide left side of the equation by 3, giving us the final solution:
x = -12
Therefore, the price of the 60 cheap wood is $12, and the price of the 45 expensive wood is $15.
that is, 60 (x - 3) = 45x
This equation shows the correct relationship between the two types of wood that the contractor purchased.
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Find the maximum value of C=4x+2y subject to the following restraints x>2 x<5 y>1 y<6
The required maximum value of C is 16, and it occurs when x = 3 and y = 2.
To find the maximum value of C = 4x + 2y subject to the restraints x > 2, x < 5, y > 1, and y < 6, we can use the method of Lagrange multipliers.
First, we set up the Lagrangian function L as follows:
L = 4x + 2y - λ₁(x - 2) - λ₂(x - 5) - λ₃(y - 1) - λ₄(y - 6)
where λ1, λ2, λ3, and λ4 are Lagrange multipliers.
Next, we take the partial derivatives of L with respect to x, y, λ1, λ2, λ3, and λ4, and set them equal to zero:
∂L/∂x = 4 - λ₁ - λ₂ = 0
∂L/∂y = 2 - λ₃ - λ = 0
∂L/∂λ₁ = x - 2 = 0
∂L/∂λ₁ = 5 - x = 0
∂L/∂λ₃ = y - 1 = 0
∂L/∂λ₄ = 6 - y = 0
Solving these equations simultaneously, we get:
λ₁ = 1, λ₂ = 3, λ₃ = 1, λ₄ = 1, x = 3, y = 2
Therefore, the maximum value of C is:
C = 4x + 2y = 4(3) + 2(2) = 16
So, the maximum value of C is 16, and it occurs when x = 3 and y = 2.
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Need help with this please
The area of the original figure is 1/9 times the area of the new figure
The perimeter of the original figure is 1/2 times the perimeter of the new figure
Estimating the areas of the figuresFrom the question, we have the following parameters that can be used in our computation:
The figures
The areas of the new figures is calculated as
Area = Old area * scale factor
So, we have
Area Figure 1 = (1 * 3) * 3
Area Figure 1 = 9
The perimeter of the new figures is calculated as
Perimeter = Old Perimeter * scale factor
So, we have
Perimeter Figure 2 = (4 * 4 + 4 * (2 + 3)) * 1/2
Perimeter Figure 2 = 18
See attachment for the dilates figures
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What is the length of the unknown leg of the triangle?5 ft 8 ft
Let f(g(x)) = 3sin (pi/4(x − 1)) and g(f(x)) = pi/4(3 sin(x) − 1). Find a single formula for f and a single formula for g so that both compositions hold true.
Assume that g(x) does not equal x and f(x) does not equal x.
The single formulas for f and g so that both compositions hold true are f(x) = 3sin(x) and g(x) = π/4(x − 1)
Calculating the functions f(x) and g(x)From the question, we have the following parameters that can be used in our computation:
f(g(x)) = 3sin (pi/4(x − 1))
g(f(x)) = pi/4(3 sin(x) − 1)
Express pi as π
So, we have
f(g(x)) = 3sin (π/4(x − 1))
g(f(x)) = π/4(3 sin(x) − 1)
In f(g(x)) = 3sin (π/4(x − 1)), replace the expression in bracket with g(x)
So, we have
f(g(x)) = 3sin (g(x))
This means that
f(x) = 3sin(x) and also, it means
g(x) = π/4(x − 1)
Hence, the single formulas that both compositions hold true are f(x) = 3sin(x) and g(x) = π/4(x − 1)
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CAN SOMEONE HELP WITH THIS QUESTION?
The value of the given summation is:
[tex]\sum (29a_i - 13b_i) ]= -30[/tex]
How to find the sum?Here we know that the sums are:
[tex]\sum a_i = -10\\\\\sum b_i = -20[/tex]
And we want to find the value of the sum:
[tex]\sum (29a_i - 13b_i)[/tex]
First we can distribute the sum to get:
[tex]\sum 29a_i + \sum - 13b_i[/tex]
And take the coefficients out of the sum:
[tex]29\sum a_i -13\sum b_i[/tex]
Now replace the known values:
[tex]29\sum a_i -13\sum b_i = 29*-10 - 13*-20 = -290 + 260 = -30[/tex]
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Find the volume of a right circular cone that has a height of 11.9 ft and a base with a radius of 16.3 ft. Round your answer to the nearest tenth of a cubic foot.
The volume of a right circular cone which has a height of 11.9 ft and a base with a radius of 16.3 ft as required is;
What is the volume of the right circular cone?As evident in the task content; the volume of a right circular cone a height of 11.9 ft and a base with a radius of 16.3 ft is to be determined.
Recall, the volume of the cone is;
V = (1/3) × πr²h
V = (1/3) × π × 16.3² × 11.9
V = 3310.9 ft³.
Ultimately, the volume of the right circular cone is; 3310.9 ft³.
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Answer:
3310.9
Step-by-step explanation:
if you are asked to find the value of the 100th term of a sequence, would you use the explicit formula for that sequence or the recursive formula?
An arithmetic sequence is a sequence of integers with its adjacent terms differing with one common difference.
We know that,
An arithmetic sequence is a sequence of integers with its adjacent terms differing with one common difference.
The explicit formula for any arithmetic series is given by the formula,
a_n = a_1 + (n-1)d
where d is the difference and a₁ is the first term of the sequence.
The major distinction between recursive and explicit formulas is that a recursive formula returns the value of a particular term depending on the preceding term, whereas an explicit formula returns the value of a given term based on its location.
When the value of the first term and the common difference is known then an explicit formula is used, while the recursive formula will be used when the value of the previous value is known and the value of the common difference is known.
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complete question:
what is the difference between the explicit formula and recursive formula for sequences when would you use one over the other
Solve the system.
x + 7y-z = 49
2x - 5y + 2z = -28
x-6y=-32
The values of x, y and z in the given simultaneous equation is:
x = 4
y = 6
z = -3
What is the solution to the simultaneous equation?The 3 simultaneous equations are given as:
x + 7y - z = 49
2x - 5y + 2z = -28
x - 6y=-32
Rearranging the first equation gives:
x = 49 - 7y + z
2x - 5y + 2z = -28
x - 6y = -32
Substitute 49 - 7y + z into equations 2 and 3 to get:
2(49 - 7y + z) - 5y + 2z = -28
49 - 7y + z - 6y = -32
Convert the equation in terms of u and solving simultaneously gives:
y = 6 and z = -3
Thus:
x = 49 - 7(6) + (-3)
x = 4
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solve (2x - 3) (x + 2) = 0
Answer:
x=3/2
x=-2
Step-by-step explanation:
One owl hoots every 3 hours, and a second owl hoots every 8 hours, and a third owl hoots every 12 hours. If they all hoot together at midnight of the first day, how many times on the hour in 3 days will at least two owls not give a hoot.
The number of times on the hour in 3 days at least two owls will not hoot obtained using number theory are 69 times.
What is number theory?Number theory is the study of integers and functions of arithmetic.
The number of hours in 3 days = 72 hours
Number theory indicates that the multiples of the periods of hooting are;
The multiples of 8 are; 8, 16, 24, 32, 40, 48, 56, 64, 72
The multiples of 3 are; 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 66, 69, 72
The multiples of 12 are; 12, 24, 36, 48, 60, 72
The common multiples of 3 and 8 are 24, 48, 72
The common multiples of 8 and 12 are 24, 48, 72
The number of times in 72 hours when at least 2 owls are hooting are therefore;
The times when only one owl is hooting are
8, 16, 32, 40, 56, 64, = 6 times only the second owl is hooting
3, 6, 9, 12, 15, 18, 21, 27, 30, 33, 36, 39, 42, 45, 51, 54, 57, 60, 63, 66, 69 = 21 times when only the first owl hoots
The times when non of the owls hoot are;
72 - 24 - 6 = 42 times
The number of times when at least two owls don't give a hoot = 42 + 6 + 21 = 69 timesLearn more on number theory here: https://brainly.com/question/4301692
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Find the equation (in terms of x) of the line through the points (-4,-6) and (3,8).
y=
Answer: y = 2x + 2
Step-by-step explanation: First, you find slope between the points with point slope form. (8-(-6))/(3-(-4) = 2.
2 is the slope.
Now we have y = 2x + b.
To find b, we pick a coordinate and insert the values.
8 = 2(3) + b
8 = 6 + b
8 - 6 = b
b = 2
Put it together, you have y = 2x + 2
Carla loves her coffee...she visits the Kind Bean every weekday morning and
about three days per week she stops in for an afternoon pick-me-up. With
tax and tip, she usually spends about $5 per visit. Brianna figures this is just
a little indulgence. Is she right?
Find out how much she spends per year on coffee.
Answer:
$2080
Step-by-step explanation:
You want to know the annual cost of coffee purchased 5 mornings and 3 afternoons per week when each purchase amounts to $5.
Weekly costFive morning visits and three afternoon visits to the coffee shop will be a total of 8 visits per week. At $5 each, the cost per week is ...
8 × $5 = $40
Annual costThe cost for a year will be the cost for 52 weeks:
52 × $40 = $2080
Carla spends $2080 per year on coffee.
Whether this is a "little indulgence" or not will depend on Carla's budget.
Find each angle and arc measure.
m∡RST = ______ degrees
m∡RUT = ______ degrees
(50 POINTs will give BRAINIEST FOR EFFORT)
m∡RST angle is 146 degrees and m∡RUT is 157 degrees are the arc measures.
Let us find angle RVT
The sum of four angles should be 360 degrees
∠RVS +∠SVU+∠UVT+∠RVT=360
64+139+75+x= 360
278+x=360
x=360-278
x=82 degrees
Arc measure m∡RST =64+82
m∡RST = 146 degrees
m∡RUT = 82+75
m∡RUT = 157 degrees
Hence, m∡RST is 146 degrees and m∡RUT is 157 degrees are the arc measures.
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I WILL GIVE 35 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS PLEASE
Answer:
F1 8,-2 F2 -5,-3
Step-by-step explanation:
What is the answer.
Answer:106
Step-by-step explanation:
The elevations of four locations are shown in the table. Which statement is true?
Location
New Orleans
Death Valley
Salton Trough
Rio Bravo
Elevation
(meters)
-2
-86
-69
95
New Orleans is closer to sea level than Salton
Trough.
Rio Bravo has a lower elevation than Salton
Trough.
New Orleans has a lower elevation than Death
Valley.
Rio Bravo is closer to sea level than Death
Valley.
The elevations of four locations.
Hence, the correct option is C.
Based on the elevation
New Orleans has an elevation of -2 meters, which means it is below sea level.Death Valley has an elevation of -86 meters, which means it is also below sea level, but at a lower elevation than New Orleans.Salton Trough has an elevation of -69 meters, which means it is also below sea level, but at a higher elevation than New Orleans.Rio Bravo has an elevation of 95 meters, which means it is above sea level, and thus cannot be closer to sea level than any of the other three locations.Therefore, New Orleans has a lower elevation than Death Valley.
Hence, the correct option is C.
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What is the inverse relation of f(x)=15x−45?
The inverse of the function f(x) = 15x - 45 is g(x) = x + 45 / 15
What is the inverse of the functionAn inverse function or an anti function is defined as a function, which can reverse into another function. In simple words, if any function “f” takes x to y then, the inverse of “f” will take y to x. If the function is denoted by ‘f’ or ‘F’, then the inverse function is denoted by f-1 or F-1.
In this problem, f(x) = 15x - 45, we can find the inverse as;
To determine the inverse function, switch x and y and solve the resulting equation for x
If the initial function is not one-to-one, then there will be more than one inverse.
y = 15x - 45
x = 15y - 45
Let's solve for y
15y = x + 45
y = x + 45 / 15
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A rectangle has an area of 54 square inches and a length of 6 inches. What is the width, in inches, of the rectangle?
Answer:
width = 9 in
Step-by-step explanation:
Area = A = length x width = w x l
w = A/l = 54 in²/6 in = 9 in
PLS HURRY I AM GIVING BRAINLIEST!!!
the question is in the photo!!
In the above triangle,
1) the sum of side 1 and 2 is: 4x² + 3x + 4
2) the length of side 3 is: 5x³-6x²-12
1) To find the sum of side 1 and side 2, we simply need to add them together.
Side 1 = 3x² - x - 1
Side 2 = x² + 4x + 5
Side 1 + Side 2 = (3x² - x - 1) + (x² + 4x + 5)
= 3x² + x² - x + 4x - 1 + 5
= 4x² + 3x + 4
Therefore, the sum of side 1 and side 2 is = 4x² + 3x + 4
2) We can derive the expression of the thried side by removing the expression in (1) above form the perimeter.
That is;
(5x³-2x² + 3x - 8) - (4x² + 3x + 4)
First we distribute the negative sign
= 5x³-2x² + 3x - 8 + -1 (4x² + 3x + 4)
= 5x³-2x² + 3x - 8 + -1 (4x²) -1( 3x) -1( 4)
= 5x³-2x² + 3x - 8 + -4x² - 3x - 4
Combining like terms we have
= (5x³) (-2x²+-4x²) + (3x +- 3x) + (-8 + - 4)
= 5x³-6x²-12
Hence the missing side (thrid side is) 5x³-6x²-12
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Breanna and Qasim plan to send their daughter to university. To pay for this they will contribute 8 equal yearly payments to an account bearing interest at the APR of 4%, compounded annually. Five years after their last contribution, they will begin the first of five, yearly, withdrawals of $51,100 to pay the university's bills. How large must their yearly contributions be?
Breanna and Qasim must contribute $22,583.39 per year for eight years to have enough money to pay for their daughter's university education.
To determine the yearly contribution required for Breanna and Qasim, we need to use the present value formula for an annuity.
The formula is:
PV = C * ((1 - (1 + r)⁻ⁿ) / r)
Where PV is the present value of the annuity, C is the annual contribution, r is the annual interest rate, and n is the number of years.
First, we need to calculate the present value of the contributions that Breanna and Qasim make for the first eight years. We can use the formula:
PV = C * ((1 - (1 + r)⁻ⁿ) / r)
Where C is the annual contribution, r is the annual interest rate, n is the number of years, and PV is the present value of the contributions.
We know that the annual contribution is the same for each of the eight years, so we can simplify the formula to:
PV = C * (((1 - (1 + r)⁻ⁿ) / r))
The present value of the contributions is equal to the future value of the withdrawals five years after the last contribution. We can use the future value formula for an annuity to calculate this:
FV = R * ((1 + r)ⁿ - 1) / r
Where FV is the future value, R is the annual withdrawal, r is the annual interest rate, and n is the number of years.
We know that the future value of the withdrawals is $51,100 per year, the interest rate is 4%, and the number of years is 5.
FV = 51,100 * ((1 + 0.04)⁵ - 1) / 0.04 = $246,387.19
This is the present value of the contributions that Breanna and Qasim make over the first eight years. We can now solve for the annual contribution required using the present value formula:
PV = C * (((1 - (1 + r)⁻ⁿ) / r))
$246,387.19 = C * (((1 - (1 + 0.04)⁻⁸) / 0.04))
C = $22,583.39
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31, 92, 25, 69, 80, 31, 29
Median
Mode
Range
Answer:
Median: 31
Mode: 31
Range: 67
Step-by-step explanation:
Median: To find the median, we first need to arrange the numbers in order from smallest to largest:
25, 29, 31, 31, 69, 80, 92
The middle number is 31, so the median is 31.
Mode: The mode is the number that appears most frequently in the set. In this case, the number 31 appears twice, which is more than any other number. So, the mode is 31.
Range: The range is the difference between the largest and smallest numbers in the set. The smallest number is 25 and the largest number is 92, so the range is:
92 - 25 = 67.
Therefore, the median is 31, the mode is 31, and the range is 67.
Answer:
The median of the given set of numbers is 31, the mode is 31, and the range is 67.
Step-by-step explanation:
To find the median, we need to first arrange the numbers in order from smallest to largest:
25, 29, 31, 31, 69, 80, 92
There are seven numbers in the list, which means the middle number will be the fourth number: 31.
Therefore, the median is 31.
To find the mode, we need to determine which number appears most frequently in the list.
In this case, the number 31 appears twice, which is more than any other number in the list.
Therefore, the mode is 31.
To find the range, we need to subtract the smallest number from the largest number. The smallest number is 25 and the largest number is 92, so the range is:
92 - 25 = 67
Therefore, the range is 67.
You want to purchase a new car in 6 years and expect the car to cost $12,000. Your bank offers a plan with a guaranteed APR of 6.5% if you make regular monthly deposits. How
← much should you deposit each month to end up with $12,000 in 6 years?
T
You should invest $ each month
(Round the final answer to the nearest cent as needed. Round all intermediate values to seven decimal places as needed
Answer:
To calculate the monthly deposit required, we can use the formula for future value of an annuity, which is:
FV = Pmt x (((1 + r)^n - 1) / r)
where FV is the future value, Pmt is the monthly payment, r is the monthly interest rate, and n is the number of months.
In this case, we want to find the monthly payment required to achieve a future value of $12,000 in 6 years, or 72 months. The monthly interest rate is the annual percentage rate (APR) divided by 12, so:
r = 6.5% / 12 = 0.00541666667
Substituting these values into the formula, we get:
12,000 = Pmt x (((1 + 0.00541666667)^72 - 1) / 0.00541666667)
Solving for Pmt, we get:
Pmt = 12,000 / (((1 + 0.00541666667)^72 - 1) / 0.00541666667)
≈ $164.41
Therefore, you should deposit $164.41 each month to end up with $12,000 in 6 years
Grayson can text 70 words in 4 minutes. At this rate, how many minutes would it take him to text 140 words?
17. The diameter of a cylinder is 7 yards. The height
is 12 yards. What is the volume, in terms of and
to the nearest cubic yard, of the cylinder?.7.GR.2.3
The volume of the cylinder that has a diameter of 7 yards and a height of 12 yards is: 147π cubic yard.
What is the Volume of a Cylinder?The volume of a cylinder can be determined by applying the volume formula which is given as:
Volume (V) = πr²h,
where "r" is the radius of the cylinder
"h" is the height of the cylinder
π is a constant
Given the following:
Diameter of cylinder = 7 yards, thus, radius (r) = 7/2 = 3.5 yards
Height (h) = 12 yards
Plug in the values:
Volume of the cylinder = π * 3.5² * 12 = 147π cubic yard.
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please help, asap. for an assignment
The value of m in terms of other variables of the right angle triangle is: m = √(p² - n²)
How to use pythagoras theorem?Pythagoras Theorem is the way in which you can find the missing length of a right angled triangle.
The triangle has three sides, the hypotenuse (which is always the longest), Opposite (which doesn't touch the hypotenuse) and the adjacent (which is between the opposite and the hypotenuse).
Pythagoras is in the form of;
a² + b² = c²
However, it can also be written in the form of c² = a² + b²
From the given triangle, we can write as:
p² = m² + n²
m² = p² - n²
m = √(p² - n²)
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