After answering the provided question, we can conclude that Therefore, derivatives the function f(x, y) = ycos(x) has no local minimum or maximum points, only two saddle points at (π/2, 0) and (3π/2, 0).
what is derivative?In mathematics, the derivative of a function with real variables measures how sensitively the function's value varies in reaction to changes in its parameters. Derivatives are the fundamental tools of calculus. Differentiation (the rate of change of a function with respect to a variable in mathematics) (in mathematics, the rate of change of a function with respect to a variable). The use of derivatives is essential in the solution of calculus and differential equation problems. The definition of "derivative" or "taking a derivative" in calculus is finding the "slope" of a certain function. Because it is frequently the slope of a straight line, it should be enclosed in quotation marks. Derivatives are rate of change metrics that apply to almost any function.
∂f/∂x = -ysin(x)
∂f/∂y = cos(x)
-ysin(x) = 0 (Equation 1)
cos(x) = 0 (Equation 2)
Therefore, the critical points are:
(π/2, 0) (saddle point)
(3π/2, 0) (saddle point)
∂²f/∂x² = -ycos(x)
∂²f/∂y² = 0
∂²f/∂x∂y = cos(x)
At the point (π/2, 0), ∂²f/∂x² = 0 and ∂²f/∂x∂y = 1, so it is a saddle point.
At the point (3π/2, 0), ∂²f/∂x² = 0 and ∂²f/∂x∂y = -1, so it is also a saddle point.
Therefore, the function f(x, y) = ycos(x) has no local minimum or maximum points, only two saddle points at (π/2, 0) and (3π/2, 0).
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MARKING AS BRAINLIST PLEASE HELP!!
Answer:
b = 62°
Step-by-step explanation:
We Know
A triangle sum is 180°
We know two angles, one is 68.5° and the other is 49.5°.
Find angle b
We Take
180 - (68.5 + 49.5) = 62°
So, b = 62°
Find the arc length of the semicircle. Either enter an exact answer in terms of � πpi or use 3.14 3.143, point, 14 for � πpi and enter your answer as a decimal. units
The radius as 5, so the arc length of the semicircle is s = π(5) = 5π ≈ 15.71.
What is radius?Radius is a line segment that extends from the center of a circle or sphere to its circumference. It is the distance from the center to the edge of the circle or sphere. It is also used to measure the length of an arc of a circle. Radius is a necessary measure when calculating the area of a circle or sphere, as well as the volume of a sphere.
The arc length of a semicircle is given by the formula s = πr,
where r is the radius of the semicircle. In this case,
we are given the radius as 5, so the arc length of the semicircle is s = π(5) = 5π ≈ 15.71.
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The arc length of a semicircle with radius 'r' is equal to rπ or approximately 3.14r units.
What is an arc?
An arc is part of a circle's circumference. It is a segment of a curved line that is formed when a straight line intersects a circle or a curved shape. Arcs can be measured in length, angle, or radius, depending on the context.
To find the arc length of a semicircle, we need to know the radius of the circle and the angle subtended by the arc at the center of the circle.
Let's assume the radius of the semicircle is 'r'. Since it is a semicircle, the angle subtended by the arc at the center of the circle is 180 degrees or π radians.
The formula for arc length is given by:
arc length = radius x angle in radians
In this case, the angle is π radians and the radius is 'r'. Therefore, the arc length of the semicircle is:
arc length = r x π
We can leave the answer in terms of π or substitute the value of π to get a numerical answer. For example, if the radius of the semicircle is 4 units, the arc length will be:
arc length = 4 x π
arc length ≈ 12.57 units (using π ≈ 3.14)
Therefore, the arc length of a semicircle with radius 'r' is equal to rπ or approximately 3.14r units.
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Omar recorded the number of hours he worked each week for a year. Below is a random sample that he took from
data.
13, 17, 9, 21
What is the standard deviation for the data?
Answer:
Approx. 4.47
Step-by-step explanation:
To calculate the standard deviation for the data, we need to follow these steps:
1. Calculate the mean (average) of the data:
mean = (13 + 17 + 9 + 21) / 4 = 15
2. Calculate the difference between each data point and the mean:
13 - 15 = -2
17 - 15 = 2
9 - 15 = -6
21 - 15 = 6
3. Square each difference:
(-2)^2 = 4
2^2 = 4
(-6)^2 = 36
6^2 = 36
4. Calculate the variance by taking the average of the squared differences:
variance = (4 + 4 + 36 + 36) / 4 = 20
5. Calculate the standard deviation by taking the square root of the variance:
standard deviation = sqrt(variance) = sqrt(20) ≈ 4.47
Therefore, the standard deviation for the data is approximately 4.47.
4: The radius of a cylinder is 3x-2 cm. The height of the cylinder is x + 3 cm. What is the
surface area of the cylinder? Use the formula A = 2²²² +2arh.
02 (3x²+10x-8)
O 27(12x² +7x-2)
O27(12x² - 2x+13)
O 27 (12x²-5x-2)
The surface area (A) of a cylinder is given by the formula A = 2πr² + 2πrh, where r is the radius of the cylinder and h is its height.
In this case, the radius of the cylinder is 3x - 2 cm, and its height is x + 3 cm. Substituting these values into the formula, we get:
A = 2π(3x - 2)² + 2π(3x - 2)(x + 3)
Simplifying this expression, we get:
A = 2π(9x² - 12x + 4) + 2π(3x² + 7x - 6)
A = 18πx² - 24πx + 8π + 6πx² + 14πx - 12π
A = 24πx² - 10πx - 12π
So the surface area of the cylinder is 24πx² - 10πx - 12π.
URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
Theodore invests $15,000 into an account at an annual rate of 0.55% simple interest for 36 months.
1) What is the Principal in this scenario?
1) 0.0055
2) 0.55 %
3) $15,000
4) 3
2) What is the interest rate for this account?
1) 0.55 %
2) $15,000
3) 3
4) 0.0055
3) What number do you use to represent the interest rate in the simple interest formula?
1) 0.55 %
2) 3
3) $15,000
4) 0.0055
4) What is the length of time of this investment, in years?
1) 0.55 %
2) 3
3) $15,000
4)0.0055
5) Calculate the simple interest earned on this account.
Answer:
1)$15000
2)0.55%
3)0.55
4)3
5)24.75
Step-by-step explanation:
5)1500×0.55×3/100
The Dodd-Frank Wall Street Reform and Consumer Protection Act of 2010 established the Consumer Financial Protection Bureau (CFPB). The purpose of the CFPB is to ensure that consumer finance markets work effectively. It provides a forum for consumers to submit their complaints about the services received from financial providers. It also educates consumers about financial matters to help them make sound financial decisions.
Use this consumer credit card market report, published by the CFPB in 2017, to answer the following questions.
Refer to section 1.3.2, Credit scores, on page 22 of the report.
For which two purposes do credit card issuers use credit scores?
Select all the correct answers.
Oto determine the consumer's age and gender
Oto set pricing for rewards programs
O to determine the consumer's eligibility for credit
O to set pricing for late fees
to set pricing for credit lines
to determine the number of credit cards to be issued by a lending company
The correct answers are: To determine the consumer's eligibility for credit and To set pricing for credit lines.
what is pricing?
"Pricing" refers to the process of determining the value or cost of a product or service and setting a specific price for it. Pricing decisions involve taking into account various factors such as production costs, market demand, competition, and profit margins, among others. Pricing can also involve setting
In the given question,
Based on section 1.3.2, Credit scores, on page 22 of the report, the two purposes for which credit card issuers use credit scores are:
To determine the consumer's eligibility for credit.
To set pricing for credit lines.
Therefore, the correct answers are:
To determine the consumer's eligibility for credit
To set pricing for credit lines
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G 11. A The figure below is made up of 2 squares and triangle EDH. BC = CD and 25% of square CDEF is shaded. The ratio of the shaded area to the unshaded area in triangle EDH is 1:5. Find the ratio of the shaded area to the unshaded area in the figure. F E 75% B C D 5 H
The ratio of the shaded area to the unshaded area in the figure is 1 : 5.5 which can be calculated by adding the areas of the two squares and triangle EDH.
What is area?Area is the amount of two-dimensional space taken up by a shape or object. It is measured in square units, such as square centimeters, square meters, or square miles.
The ratio of the shaded area to the unshaded area in the figure can be calculated by adding the areas of the two squares and triangle EDH, and then subtracting the shaded area.
First, calculate the total area of the figure:
Area of the two squares = (BC)²
= (CD)²
= (4)²
= 16
Area of triangle EDH = ½ x BC x DH
= ½ x 4 x 5
= 10
Total area = 16 + 10
= 26
Next, calculate the shaded area:
Shaded area of square CDEF = 25% x 16
= 4
Total shaded area = 4
Finally, calculate the ratio of the shaded area to the unshaded area in the figure:
Unshaded area = 26 - 4
= 22
Ratio of the shaded area to the unshaded area = 4 : 22
= 1 : 5.5
Therefore, the ratio of the shaded area to the unshaded area in the figure is 1 : 5.5.
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Question:
A The figure below is made up of 2 squares and triangle EDH. BC = CD and 25% of square CDEF is shaded. The ratio of the shaded area to the unshaded area in triangle EDH is 1:5. Find the ratio of the shaded area to the unshaded area in the figure.
In the figure, the proportion of shaded to unshaded region is 1:5.5.
What is the Area of the Shaded Region?The area of the shaded region is the difference between the area of the entire polygon as well as the area of the polygon's unshaded part. In polygons, the area of the shaded portion can occur in two ways. The shaded area can be found in the centre of a polygon or on its sides.
As previously stated, the area of the shaded region is determined by subtracting the area of a complete polygon from the area of the unshaded region.
outer shape region – area of the interior unshaded shape = The shaded area
To begin, compute the entire area of the figure:
Area of the two squares [tex]=(BC)^2[/tex]
[tex]=(CD)^2\\\\=(4)^2\\\\=16[/tex]
Area of the EDH triangular [tex]=\frac{1}{2} \times BC\times DH[/tex]
Substitute values in the above equation
[tex]=\frac{1}{2} \times 4\times 5\\\\=10[/tex]
Total area = 16 + 10
= 26
The shaded region is then calculated as follows:
CDEF square shaded region = 25% x 16
= 4
Total shaded area = 4
Finally, compute the shaded-to-unshaded area ratio in the figure:
Unshaded area = 26 - 4
= 22
Shaded to unshaded region ratio = 4 : 22
= 1 : 5.5
As a result, the shaded area to unshaded area ratio in the image is 1: 5.5.
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The complete question is,
A The figure below is made up of 2 squares and triangle EDH. BC = CD and 25% of square CDEF is shaded. The ratio of the shaded area to the unshaded area in triangle EDH is 1:5. Find the ratio of the shaded area to the unshaded area in the figure.
please answer as SOON AS POSSIBLE
An exponential expression with base 25 and a single, simplified exponent is [tex](25)^{-28}[/tex]
What is an exponent?In Mathematics, an exponent simply refers to a mathematical operation that is typically used in conjunction with an algebraic expression in order to raise a quantity to the power of another.
Generally speaking, an exponent is represented by the following mathematical expression;
bⁿ
Where:
the variables b and n are numerical values (numbers) or an algebraic expression.n is referred to as a superscript or power.By applying the law of indices for powers of the same base number, we have the following:
[tex](25^7)^{-4}=(25)^{7 \times -4}\\(25)^{7 \times -4}=(25)^{-28}[/tex]
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Let p and q be prime numbers satisfying
p^3-pq^2=42024
Find the sum of the digits of the product pq.
The sum of the digits of the product p×q is 8
Define the prime numbers?A positive integer bigger than one that can be divided only by itself and by one is referred to as a prime number.
Given that: p³ - pq² = 42024
p (p² - q²) = 42024
Since factors, 42024 = 2³ x 3 x 17 x 103, and p and q are prime numbers, we can see that p must be 3, 17 or 103, We can try each case:
If p = 3 then we have:
3 (9 - q²) = 42024
q² = -13,999
This equation has no real solutions for q, so p cannot be 3.
If p = 17, then we have:
17 (289 - q²) = 42024
q² = -2183
This equation also has no real solutions for q, so p cannot be 17 either.
If p = 103, then we have:
103 (10609 - q²) = 42024
10609 - q² = 408
q² = 10201
q = 101
This equation also has a solution for q = 101, so p = 103
Product of pq = 103×101 = 10403
So, the sum of the digits of the product pq = 1+0+4+0+3 = 8
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drag numbers to the table so it shows a porpotinal relationship between x and y
The complete table that shows the proportional relationship is:
x y
0.8 4
3.2 16
12.8 64
How to find the proportional relationship?The ratio of the given y-value and x-value is calculated as:
y/x = 4/0.8 = 5
Thus, the ratio of the next terms must all be 5.
The second x coordinate is 3.2. Thus:
y/3.2 = 5
y = 3.2 * 5
y = 16
Difference of the first 2 x-values = 3.2 - 0.8 = 2.4
Thus, the third value of x will be:
3.2 + 2.4 = 5.6
Thus, the third y-coordinate = 5.6 * 5 = 28
Similarly, the fourth value of x will be:
5.6 + 2.4 = 8.0
Thus, the fourth y-coordinate = 8 * 5 = 40
The sixth value of x will be:
8 + 2.4 + 2.4 = 12.8
Sixth value of y = 12.8 * 5 = 64
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Complete question is:
Drag numbers to the table so it shows a proportional relationship between x and y.
Tiles : 8.8 , 12.8 , 5.6 , 64 , 6.4 , 16
X axis Y axis
0.8. 4
3.2 ?
? ?
The box plot above summarizes the resting heart rates, in beats per minute, of the members at a gym.
Which of the following could be the range of resting heart rates, in beats per minute ?
The range of resting heart rates is 70 beats per minute. Subtracting the lowest value from the highest value will give us the range.
What is range?It is a set of data which is the difference between the highest and lowest values.
The range of resting heart rates, in beats per minute, is calculated by subtracting the minimum value of the data set from the maximum value. In this case, the minimum value = 35
and the maximum value = 105,
so the range of resting heart rates = 105 - 35
= 70 beats per minute
The other answers cannot be the range of the resting heart rates because they are not calculated correctly.
The answer 16 beats per minute (105 - 89 = 16) is the difference between the maximum and the 90th percentile, and the answer 31 beats per minute (85 - 54 = 31) is the difference between the 85th percentile and the median.
The answer 62 beats per minute (95 - 33 = 62) is the difference between the 95th percentile and the minimum.
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Question:
The units of an item available for sale during the year were as follows:
Jan. 1 Inventory 10 units at $26 $260
Aug. 13 Purchase 6 units at $29 174
Nov. 30 Purchase 7 units at $30 210
Available for sale 23 units $644
There are 11 units of the item in the physical inventory at December 31. The periodic inventory system is used. Determine the inventory cost using the (a) first-in, first-out (FIFO) method; (b) last-in, first-out (LIFO) method; and (c) weighted average cost method (round per-unit cost to two decimal places and your final answer to the nearest whole dollar).
a. First-in, first-out (FIFO) $326
b. Last-in, first-out (LIFO) $289
c. Weighted average cost $
The inventory cost under:
a. First-in, first-out (FIFO) - $326.
b. Last-in, first-out (LIFO) - $289.
c. Weighted average cost - $308.
How to solvea. Calculation of inventory cost using the First-in, First-out (FIFO) method:
There are 11 units of the item in the physical inventory on December 31. Under FIF7 units will be from items purchased on Nov 30 and 4 units will be from items purchased on Aug 13.
( 7 units * 30) + (4 units *29)
= 210 + 116 = $326
b. Calculation of inventory cost using the Last-in, First-out (LIFO) method:
There are 11 units of the item in the physical inventory on December 31. Under LIFO Method, 10 units will be from items purchased on Jan 1 and 1 unit will be from items purchased on Aug 13.
10 units * 26 + (1 unit * 29)
= $289
c. Calculation of Weighted Average cost per unit:
$644/23 units
=$28 per unit
Calculation of inventory cost using the Weighted Average Cost method:
11 units * 28
= $308
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18. Find the 21st term if a₁ = 3/5 and
d = -1/3
(a) -6.07
(b) 11.67
Answer:
a
Step-by-step explanation:
the nth term of an arithmetic sequence is
[tex]a_{n[/tex] a₁ + (n - 1)d
here a₁ = [tex]\frac{3}{5}[/tex] and d = - [tex]\frac{1}{3}[/tex] , then
a₂₁ = [tex]\frac{3}{5}[/tex] + (20 × - [tex]\frac{1}{3}[/tex] )
= [tex]\frac{3}{5}[/tex] - [tex]\frac{20}{3}[/tex]
= 0.6 - 6.67
= - 6.07 ( to 2 decimal places )
at an amusement park 25 people ride the cras every 30 mins and 20 people rid the spinning swings which one will have more rides how many more
Answer:
Spinning Swings
10 more riders
Step-by-step explanation:
To find which ride will have more riders each hour, we need to first convert an hour into minutes.
[tex]\text{1 hour = 60 minutes}[/tex]
Now we let's first find how many riders there will be in the race cars.
So there are 25 riders every 30 minutes.
in 60 minutes there will be:
[tex]25 \times 2 = 50 \ \text{Riders}[/tex]
Now for the spinning swings there are 20 riders every 20 minutes.
In 60 minutes there will be:
[tex]20 \times 3 = 60 \ \text{Riders}[/tex]
Therefore, the spinning swings will have more riders as [tex]60 > 50[/tex].
Now to find how many more riders there will be in the spinning swings.
We simply subtract the total number of riders of each ride from each other.
[tex]\text{Race Cars = 50}[/tex]
[tex]\text{Spinning Swings = 60}[/tex]
[tex]60 - 50 = 10[/tex]
There will be 10 more riders in the spinning cups than the race cars.
Given 2^a = 16 find the value of a.
Please explain thanks.
Step-by-step explanation:
[tex]2 {}^{a} = 16[/tex]
Since our variable is in the exponent, we take the logarithm of both sides in order to solve for a.
The log base is 2 In order to cancel out base 2,
[tex]a = log_{2}(16) [/tex]
[tex]a = 4[/tex]
The gradient of the line joining (-2, K) and (K₁-14) Calculate the value of k the points
The value of k for this line is equal to -6.
How to calculate the gradient of a line?In Mathematics and Geometry, the gradient of any straight line is also referred to as slope and it can be determined by using the following mathematical equation;
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = rise/run
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Substituting the given data points into the slope formula, we have the following;
2 = (-14 - k)/(k + 2)
-14 - k = 2(k + 2)
-14 - k = 2k + 4
-14 - 4= 2k + k
3k = -18
k= -18/3
k = -6
In this context, we can reasonably infer and logically deduce that the value of k is equal to -6.
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Complete Question:
The gradient of the line joining the points (-2,k) and (k, -14) is 2 . Calculate the value of k.
find 3 consecutive even integers if three times the first integer is two times the third
Step-by-step explanation:
First = x
second = x + 2
third = x + 4
3 * x = 2 ( x+4)
3x = 2x+ 8
x = 8 8 10 and 12
Need help I can’t answer them
The triangles that translate to triangle X are A and F.
Triangle ABC is translated to triangle A'B'C', 5 square(s) to the right and 4 square(s) down.
How are triangles translated?Triangles can be translated by moving each of their vertices a certain distance in a certain direction. The distance and direction of the translation can be described using vector notation.
For example, a translation of a triangle by the vector <a, b> would move each vertex of the triangle a units to the right and b units up. The resulting translated triangle would have the same shape and size as the original triangle, but would be located in a different position in the plane.
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Image transcribed:
Select all of the triangles below which are translations of triangle X.
Triangle ABC is translated to triangle A'B'C'.
Fill in the gaps below to describe the translation.
Triangle ABC is translated to triangle A'B'C'.
Fill in the gaps below to describe the translation.
___ square(s) to the left/right and ___ square(s) up/down
A
B
C
A'
B'
C'
PLEASE HELP!!
x^2=7y-4+9x^2
ALGEBRA 1 HW!! I WILL GIVE BRAINLYEST
The average rate of change of P between t = 3 and t = 5 is -18 people/hour.
A possible value of people in line at t = 6, given the average rate of change would be 50.
How to find the average rate of change ?To find the average rate of change of P between t = 3 and t = 5, we can use the formula:
Average rate of change = (P(5) - P(3)) / (5 - 3)
From the table, we know P(3) = 85 and P(5) = 49.
Average rate of change = (49 - 85) / (5 - 3) = (-36) / 2 = -18 people/hour
To find the possible number of people at t = 6, Let P(6) = x. First, we will find the average rate of change between t = 3 and t = 6:
(P(6) - P(3)) / (6 - 3) = (x - 85) / 3
This value must be negative. Now, we will find the average rate of change between t = 5 and t = 6:
(P(6) - P(5)) / (6 - 5) = (x - 49) / 1
This value must be positive. Since (x - 49) is positive, we know that x > 49. Now we need to find a value for x that also satisfies the condition that the average rate of change between t = 3 and t = 6 is negative. Since (x - 85) / 3 is negative, we know that x < 85.
So, a possible value for P(6) is between 49 and 85. For example, we could choose P(6) = 50, which satisfies both conditions.
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if someone knows the answer please tell me
Answer:
Step-by-step explanation:
first graph
y = 5x + 2
2 = y-intercept
5 = slope
the first graph is y = 5x+2 because the y-intercept is 2 and it rises 5 and goes over 1
second graph:
y = 2x + 3
third graph:
y = 3x + 3
I could not for the life of me figure this out.
The area of the shaded region under the standard normal curve with z = 0.49 is 1.
The area of the shaded region under the standard normal curve with z = 0.49 is 1.
What is curve?
In mathematics, a curve is a continuous and smooth (i.e., differentiable) mathematical object that represents a path or a trajectory. Curves can be defined in different ways, depending on the context in which they are used.
What is area of curve?
The area of a curve refers to the amount of space enclosed by a curve on a two-dimensional plane. Finding the area of a curve can be a challenging problem, especially when the curve is not a standard geometric shape such as a circle or rectangle.
According to given minformation:To find the area of the shaded region under the standard normal curve with z = 0.49, we need to use a standard normal distribution table or a calculator with a normal distribution function.
Using a standard normal distribution table, we find that the area to the left of z = 0.49 is 0.6864. This means that the area to the right of z = 0.49 is 1 - 0.6864 = 0.3136.
Since the normal curve is symmetric about the mean (z = 0), the area to the left of z = -0.49 is also 0.6864. Therefore, the area between z = -0.49 and z = 0.49 is:
0.6864 (area to the left of z = 0.49) + 0.3136 (area to the right of z = 0.49) = 1
So the area of the shaded region under the standard normal curve with z = 0.49 is 1.
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Equations with fractions
Can someone please show me step by step how to answer this question.
now, if we take a looksie at the denominators on all sides, hmmm 2 and 3, so we can get an LCD of 6, so let's multiply both sides by 6 to do away with the denominators.
[tex]4-\cfrac{x-2}{2}=x+\cfrac{1-2x}{3}\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{6}}{6\left( 4-\cfrac{x-2}{2} \right)~~ = ~~6\left( x+\cfrac{1-2x}{3} \right)} \\\\\\ 24-3(x-2)~~ = ~~6x+2(1-2x)\implies 24-3x+6~~ = ~~6x+2-4x \\\\\\ 30-3x=2x+2\implies 30=5x+2\implies 28=5x\implies \cfrac{28}{5}=x\implies 5\frac{3}{5}=x[/tex]
The perimeter of a rectangle is
360cm. find the breadth if its
length is 80cm.
Answer:
4.5 cm.
Step-by-step explanation:
Divide the length by the width to get the perimeter: 360 / 80 = 4.5 cm.
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An account pays 2.4% compounded monthly. Suppose you invest $150 a month for 8 years, then leave the money in the account, without making additional payments, for another 12 years. a. How much will you have at the end of the 20 years? b. How much interest did you earn?
If yοu invest $150 a mοnth fοr 8 years, then leave the mοney in the accοunt, withοut making additiοnal payments, fοr anοther 12 years.
a) Yοu will have yοu will have apprοximately $59,073.95 at the end οf 20 years.$59,073.95 at the end οf 20 years.
b) Earned apprοximately $26,673.95 in interest οver the 20-year periοd.
What Is the Future Value οf an Annuity?The wοrth οf a series οf recurrent payments at a specific future date, assuming a specific rate οf return, οr discοunt rate, is the future value οf annuity.
Let's first calculate the tοtal number οf mοnths in 20 years:
20 years x 12 mοnths/year = 240 mοnths
a. we can use the fοrmula fοr the future value οf an annuity:
[tex]FV = PMT x (((1 + r/n)^(n*t) - 1) / (r/n))[/tex]
where:
PMT = the mοnthly payment ($150)
r = the annual interest rate (2.4% οr 0.024)
n = the number οf times the interest is cοmpοunded per year (12)
t = the tοtal number οf years (20)
FV = 150 x (((1 + 0.024/12)^(12*20) - 1) / (0.024/12))
FV ≈ $59,073.95
Therefοre, yοu will have apprοximately $59,073.95 at the end οf 20 years.
b. Tο calculate the amοunt οf interest yοu earned, we can subtract the tοtal amοunt οf mοney yοu invested frοm the future value:
Interest = FV - Tοtal amοunt invested
Interest = $59,073.95 - ($150 x 12 x 8 x 12)
Interest ≈ $26,673.95
Therefοre, yοu earned apprοximately $26,673.95 in interest οver the 20-year periοd.
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A corporation creates a sinking fund in order to have $900,000 to replace some machinery in 10 years. How much should be placed in this account at the end of each month if the annual interest rate is 3.8% compounded monthly? (Round your answers to the nearest cent.) How much interest was earned during the third month of the 7th year?
The interest earned during the third month of the 7th year is $3,613.55.
What is interest rate?
The amount of interest due each period expressed as a percentage of the amount lent, deposited, or borrowed is known as an interest rate.
Let PMT be the monthly payment, r be the monthly interest rate, and n be the total number of payments. Then:
FV = PMT × [(1 + r)n - 1]/r
In this case, we want to find PMT, given that FV = $900,000, r = 0.038/12, and n = 10 × 12 = 120:
[tex]$900,000 = PMT * {[(1 + 0.038/12)}^{120} - 1]/(0.038/12)[/tex]
Solving for PMT, we get:
PMT = $682.48
[tex]FV = $682.48 * [(1 + 0.038/12)^87 - 1]/(0.038/12)\\\\ = $89,324.47\\\\PV = $682.48 * [(1 + 0.038/12)^83 - 1]/(0.038/12) \\\\= $85,710.92[/tex]
The interest earned during the third month of the 7th year is:
$89,324.47 - $85,710.92 = $3,613.55
Therefore, the interest earned during the third month of the 7th year is $3,613.55.
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ssume there is a certain population of fish in a pond whose growth is described by the logistic equation. It is estimated that the carrying capacity for the pond is 1800 fish. Absent constraints, the population would grow by 180% per year.
If the starting population is given by
p
0
=
100
, then after one breeding season the population of the pond is given by
p
1
=
After two breeding seasons the population of the pond is given by
p
2
=
he is literally hitting the gritty
hi i dont understand this question for some reason
Answer: y = x + 6
Step-by-step explanation: "y = m x + b" is the format used to find the equation of a line on a graph.
Y and X remain the same in the equation, however you replace "m" with the value of the slope. In this problem, the slope is "1" because the rise is 1 and the run is 1, making it 1/1 or 1. Because the slope is "1", we do not need to include the number "1" in our equation.
Finally, "b" is the y-intercept (in other words, the place where the line crosses the y-axis). In this problem, the line crosses at "6"; therefore, 6 will replace b in the equation completing it.
An observer views a rocket take off from a distance of N miles from the launch pad, and tracks the angle of elevation.
a) Express the height of the rocket as a function of the angle of elevation, Θ.
b) Express the angle of elevation as a function of the height, h, of the rocket.
c) When the angle of elevation is A degrees, find the height of the rocket.
N=Any given number
A=Any given angle
(My Open Math question)
Short Answers:
a)N*tan(Θ)
b)arctan(h/N)
c)N*tan(A)
Let * stand for multiplication
Hope this is helpful to someone:)