The new interest rate for his mortgage would be 3.75%.
The amount that the lender charges the borrower over and beyond the principal amount is referred to as the interest rate. A person who deposits money in a bank or other financial institution also gets additional income in terms of the recipient, known as interest, taking into account the time value of money.
Purchasing a point simply implies negotiating for a lower rate of interest, which involves paying 1% of the loan in lieu of 1% interest reduction.
A point implies a reduction in interest rate by 0.25% while 3 points would reduce the interest rate by 0.75%(0.25%*3)
New interest rate=4.5%-0.75%=3.75%
Thus, The new interest rate for his mortgage would be 3.75%.
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The heights of the bars of a histogram correspond to _______ values.
Please help
The function f(t)=8000(0. 15)^{24t}f(t)=8000(0. 15)
24t
represents the change in a quantity over t days. What does the constant 0. 15 reveal about the rate of change of the quantity?
The function is decreasing exponentially at a rate of 85% every hour.
What does the constant 0. 15 reveal about the rate of change of the quantity?Here, 0.15 is the change the factor and since 0.15 is less than 1. Therefore , the it represents negative rate of change in the quantity that is decreasing.
Now, put t = 1/24 days
f(t) = 8000
= 8000 (0.15)
= 1200
Now, put t = 2/24 days
f(t) = 8000
= 8000
= 180
So, change in 1 hour = 1200 - 180
= 1020
Rate of change of decrease = 1020 x 100 / 1200
= 85%
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mr crates, the principal at a local middle school, made a rule that there must be 1 adult for every 4 students attending a feild trip.
The solution to the equations are
The number of adults for 12 students is 3 adults
The number of adults for 24 students is 6 adults
The number of adults for 40 students is 10 adults
What is Proportion?The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.
The proportional equation is given as y ∝ x
And , y = kx where k is the proportionality constant
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Given data ,
Let the number of students for 1 adult be 4 students
So , the proportion of students to adults is 1 : 4
Now , the equation will be
The number of adults for 12 students = 12 / 4
The number of adults for 12 students = 3 adults
The number of adults for 24 students = 24 / 4
The number of adults for 24 students = 6 adults
The number of adults for 40 students = 40 / 4
The number of adults for 40 students = 10 adults
Now , when the number of students is 33 students
The number of adults = 33 / 4 = 8.25 adults ≈ 8 adults
Hence , the proportion is 1 : 4
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A spinner with repeated colors numbered from 1 to 8 is shown. Sections 1 and 8 are purple. Sections 2 and 3 are yellow. Sections 4, 5, and 6 are blue. Section 7 is orange.
A spinner divided into eight equal colored sections, with one orange, two purple, two yellow, and three blue.
Which statement about probability is true?
The probability of landing on orange is greater than the probability of landing on purple.
The probability of landing on yellow is less than the probability of landing on blue.
The probability of landing on orange is equal to the probability of landing on yellow.
The probability of landing on purple is equal to the probability of landing on blue.
The answer is a.) The probability of landing on orange is greater than the probability of landing on purple.
What is probability?Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.
here, we have,
A spinner with repeated colors numbered from 1 to 8 is shown.
Sections 1 and 8 are purple.
Sections 2 and 3 are yellow.
Sections 4, 5, and 6 are blue.
Section 7 is orange.
A spinner divided into eight equal colored sections, with one orange, two purple, two yellow, and three blue.
so, we get,
true statement about probability is,
The probability of landing on orange is greater than the probability of landing on purple.
because, there are more spaces for blue than any other section.
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in a group of 60 people, 27 like cold drinks and 42 like hot drinks and each person likes at least one of the two drinks. how many like both cold drinks and hot drinks? (you can use venn diagrams for this problem.)
In a group of 60 people, 27 like cold drinks and 42 like hot drinks and each persons likes at least one of the two drinks, so 9 people like both cold drinks and hot drinks.
Let A= set of people who like cold drinks.
B = Set of people who like hot drinks.
Since there is group of 60 people so the number of element in AUB is 60.
n(A⋃B) = 60
27 like cold drinks so the number of element in set A is 27.
42 like hot drinks so the number of element in set B is 42.
We have, n(A) = 27 and n(B) = 42
We know that,
n(A∩B) = n(A) + n(B) − n(A⋃B)
By putting the values of n(A), n(B) and n(AUB),
we get
n(A∩B) = 27 + 42 − 60 = 9
Therefore, 9 people like both cold drink and hot drink.
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In a group of 60 people, 27 like cold drinks and 42 like hot drinks and each person likes at least one of the two drinks, so 9 people like both cold drinks and hot drinks.
Let A= set of people who like cold drinks.
B = Set of people who like hot drinks.
Since there is group of 60 people so the number of elements in AUB is 60.
n(A⋃B) = 60
27 like cold drinks so the number of elements in set A is 27.
42 like hot drinks so the number of elements in set B is 42.
We have, n(A) = 27 and n(B) = 42
We know that,
n(A∩B) = n(A) + n(B) − n(A⋃B)
By putting the values of n(A), n(B) and n(AUB),
we get
n(A∩B) = 27 + 42 − 60 = 9
Therefore, 9 people like both cold drink and hot drink.
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13.
Sara says that 2 - 5d = 5d - 2.
Junior says that 2 - 5d = -5d + 2.
Who is correct? Why?
The correct answer is Junior which is 2 - 5d = -5d + 2, because the number element of both equation is a match which is +2 and -5d.
This is mathematical equation. To see who is correct and who is wrong we have to analize both equation from Sara and Junior.
First we analize Sara equation.
First Equation : 2 - 5d contains 2 number element which is +2 and -5d
Second Equation : 5d - 2 contains 2 number element which is 5d and -2
We see that the number element from first and second equation from Sara is not match. So Sara is wrong.
Last we analize Junior equation
First Equation : 2 - 5d contains 2 number element which is +2 and -5d
Second Equation : -5d + 2 contains 2 number element which is -5d and +2
We see that the number element from first and secong equation from Junior is a match. So Junior is right.
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please help this is last question
Answer:
p = -5
Step-by-step explanation:
We know both of the angles combine to make 180 degrees, which mean
(5p + 7) = (4p + 2)
Let's solve
5p + 7 = 4p + 2
5p = 4p -5
p = -5
Model a desert community where 19% of the area is desert and the rest is houses.
squares represent the area of the community that is desert.
The area of the community that is houses is represented by
squares
19 squares represent the area of the community that is desert
The area of the community that is houses is represented by 81 squares
What is a percentage?Percentage is defined as the number that represents a ratio of a total that is divided by 100 equal parts. It is represented by the symbol %.
To solve this exercise, the percentage formula and the procedure to be applied is as follows:
As we can see in the picture the the desert has 10 square each side so the area will be:
A = 10*10
A = 100 squares
As the 19% of the area is only desert we have:
Desert = A*19%
Desert = 100*0.19
Desert = 19 squares
Now, the rest of area is the community that has houses, it is represented by:
A(houses) = A - desert
A(houses) = 100 squares - 19 squares
A(houses) = 81 squares
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Wilson Middle School has 1,500 students. Marshall Middle School has 340 fewer
students. Let m represent the number of students at Marshall Middle School
Let m represent the number of students at Marshall Middle School.
Since Wilson Middle School has 1,500 students and Marshall Middle School has 340 fewer students, the number of students at Marshall Middle School can be calculated by subtracting 340 from 1,500, which gives us 1,160. Therefore, m = 1,160.
Marshall Middle School is a public school located in Wichita, Kansas, serving students in grades 6-8. The school is part of the Wichita Public Schools district and has a variety of programs and activities to help students achieve personal and academic success. Students have access to a wide range of educational opportunities, including Project Lead the Way, college preparatory classes, and aquaponics coursework.
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determine f(x) and f(x) for the following function. then give the horizontal asymptotes of f, if any.
The function f(x) = (x + 1)^2 / (x - 2)(x + 2), with f(x) = 1.
The function f(x) is given as f(x) = (x^2 + 2x + 1) / (x^2 - 4). To determine f(x) and f(x), we must first factor the numerator and denominator. We can factor the numerator as (x + 1)^2, and the denominator as (x - 2)(x + 2). Thus, f(x) = (x + 1)^2 / (x - 2)(x + 2).
To determine the horizontal asymptotes, we must divide the leading terms of the numerator and denominator. The leading terms are x^2 for the numerator and x^2 for the denominator, so the horizontal asymptotes are y = 1.
Therefore, we can conclude that the function f(x) = (x + 1)^2 / (x - 2)(x + 2), with f(x) = 1.
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graph the function f(x) on the interval [,], showing the addition of the rectangles associated with the riemann sum given that is the of the kth subinterval.
Rectangles that represent the Riemann sum for the kth subinterval are displayed on the graph of f(x) on the interval [a,b]. The value of f(x) at the subinterval's right endpoint determines the height of each rectangle.
The function across the specified interval is represented graphically by the graph of f(x) over the interval [a,b]. The graph will display a line with the value of f(x) plotted on the y-axis and the values of the interval on the x-axis. Rectangles indicating the Riemann sum for the kth subinterval will also be displayed on the graph. The value of f(x) at the subinterval's right endpoint determines the height of each rectangle. This produces a graphic depiction of the function's area under the curve, which is equal to the total of the subintervals. Additionally, the graph will display the total number of rectangles, which represents the Riemann sum of the function on the specified interval.
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An anonymous piece of mail was sent to Evie's house that contained a very threatening message. How can investigators BEST attempt to identify the
person who sent the letter?
A. Test for gunpowder residue on the inside of the envelope.
B. Check the licked part of the envelope for a saliva sample.
C.
Look for a sweat sample underneath the postal stamp.
D. Match the envelope to the same size and brand sold in stores.
Best investigator are to check the licked part of the envelope for a saliva sample.The correct option is B
What is investigators?An investigator is someone who carries out investigations especially as part of their job.
Therefore, An Investigators work with law enforcement agencies, individuals, and businesses to investigate and solve crimes to secure a successful conviction. They conduct detailed investigations of complex criminal activities and other violations of local, federal or state law.
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Divide 16 by v. Then, subtract 7
Answer:
Step-by-step explanation:
The order of operations is a rule that tells the correct sequence of steps for evaluating a math expression. We can remember the order using PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
13 less than b In algebraic expression
13 less than b as an algebraic expression would be [tex]b - 13[/tex].
This is because 13 less than a number is the same as that number being subtracted by 13. Let me know if you have any questions, thanks!
help me please and thank you!!!
hope this helps :)
What is the greatest three-digit number that is a multiple of three and eight?
"984" will be the biggest three-digit number that is a multiple of three and eight.
What is the number line?A horizontal line with evenly spaced numerical increments is called a number line. How the number on the line can be answered depends on the numbers present. The use of the number is determined by the question that it corresponds to, such as when graphing a point.
To find the greatest three-digit number that is a multiple of three and eight.
Multiple of 3 and 8 will have to be the multiple of 24.
Since the maximum three-digit number is 999.
We will divide 999 by 24 and the remainder:
Remainder = 15
Thus,
The Greatest three-digit number will be = 999-15
The greatest three-digit number will be = 984
therefore, the Greatest three-digit number that is a multiple of three and eight will be "984".
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How to convert 4.5 kilograms to pounds?
4.5 kilos to pounds equal 9.9208. We convert one kilogram (kg) to 2.2 pounds (lb), which is a rough conversion.
How are pounds and kilos converted?One kilogram (kg) equals 2.2 pounds (lb), which is the approximate conversion we use. We multiply by 2.2 to change a kilogram into a pound. By dividing by 2.2, we may convert a pound to a kilogram.For the usual equation, multiply the amount of pounds by 2.2046. For instance, you can convert 50 pounds to kilograms by multiplying 50 by 2.2046, which is 22.67985 kg. 200 pounds are equivalent to 90.71940 kilograms when 200 is divided by 2.2046. In the fields of math and engineering, converting between kilograms and pounds frequently arises; fortunately, it is a simple process.Simply multiply the amount in kilograms by the conversion factor, 2.204622622, to convert 4.5 kilograms to pounds.
Therefore, 4.5 kilos in pounds = 9.920801798319491 pounds when multiplied by 2.204622622.
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Hight = 6 ft
Base = ?
Area = 14tf ²
What's base?
If an LTI system is modeled by a differential equation, can the transfer function of the D.E only be found if the input is a complex exponential, or can it be anything else?
Independent of the input, the transfer function. In cases when the input is not a complex exponential, you are probably interested in the result. The answer is that the output can be computed via convolution as long as the input satisfies certain constraints .
How does transfer function work?
A mathematical function called a transfer function of a system, sub-system, or component theoretically simulates the output of the system for each potential input.
Transfer functions are also known as system functions or network functions. They are frequently employed in electronic and control systems.
Why is the transfer function only specified for LTI systems?
The ratio between the Laplace transforms of the input and output signals under initial circumstances of zero can be used to define the transfer function of the LTI system.
Alternately, when the beginning circumstances are disregarded, the transfer function is described as the output to input ratio in the sdomain.
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Find the general solution of the system of equations Ax=b whose augmented matrix is given below and write it in parametric form. [b] Show the augmented matrix precisely after the first column has been "swept" to have only a "1" in the first row and 0 below- but no other operations have been performed. [c] Show the reduced echelon form [A b]= [ -3, 1, -1, 2, -9, -26, -20] [ 15, -5, 5, -10, 45, 130, [ -30, 10, -8, -62, 12, 32, -178] [ 9, -3, 3, -6, 27, 78, 60] 100] [d] Find 2 linearly independent solutions of the homogeneous system Ax=0 [e] Find a 3rd linearly independent solution of Ax=0 or give a valid reason why you could not find one. [f] Show that v=[ 1] is NOT in the span of the columns of A? [-5] i.e., give a valid proof or reason [10] [-4] [g] Do the first 4 columns of A span State a reason. [h] Give a linearly dependency relation for the first 5 columns of A R"?
[1, 0, 0, 0] [1] + [0, 1, 0, 0] the span of the columns of A and the general solution of the system of equations Ax = [ 9, -3, 3, -6, 27, 78, 60].
What do you mean by equation?An equation is a mathematical statement that shows the equality of two expressions. It is represented by an equal sign (=) and is used to solve for unknown values or to describe relationships between variables. Equations can be simple or complex, involving basic arithmetic operations or advanced mathematical concepts like trigonometry and calculus. They can also involve constants, variables, functions, and symbols.
An equation can be used to solve for a single unknown value, for example, the equation 2x + 3 = 7 can be solved for x by subtracting 3 from both sides, giving us 2x = 4 and then dividing both sides by 2, giving us x = 2. In this example, x = 2 is the solution to the equation.
[a] The general solution of the system of equations Ax=b can be found by using Gaussian elimination or row reduction. The augmented matrix [A b] is:
[-3, 1, -1, 2, -9, -26, -20]
[15, -5, 5, -10, 45, 130, 100]
[-30, 10, -8, -62, 12, 32, -178]
[ 9, -3, 3, -6, 27, 78, 60]
[b] The first step in row reduction is to get a 1 in the first row and 0s below it in the first column. We can do this by dividing the first row by -3 and subtracting multiples of it from the other rows:
[1, -1/3, 1/3, 2/3, 3, 26/3, 20/3]
[0, 20/3, 4/3, 8/3, 12, 104/3, 140/3]
[0, -40/3, 20/3, 4, -24, 68/3, 140/3]
[0, 3, -3, 0, 9, -78/3, 180/3]
Next, we can use row operations to get 0s in the second column below the first row:
[1, -1/3, 1/3, 2/3, 3, 26/3, 20/3]
[0, 1, 2/5, 4/5, 6, 42/5, 70/5]
[0, 0, 2/5, 2, -18, 26/5, 110/5]
[0, 0, 0, 0, 3, -78/5, 180/5]
Continuing with this process, we get the reduced echelon form of the augmented matrix:
[1, 0, 0, 0, 3, -26/5, 20/5]
[0, 1, 0, 0, 6, 42/5, 70/5]
[0, 0, 1, 0, -18, 26/5, 110/5]
[0, 0, 0, 1, 3, -78/5, 180/5]
[c] The reduced echelon form of [A b] is:
[1, 0, 0, 0, 3, -26/5, 20/5]
[0, 1, 0, 0, 6, 42/5, 70/5]
[0, 0, 1, 0, -18, 26/5, 110/5]
[0, 0, 0, 1, 3, -78/5, 180/5]
[d] The homogeneous system Ax=0 has the general solution:
x1 = t
x2 = 6t
x3 = -18t
x4 = 3t
where t is an arbitrary constant. These are two linearly independent solutions of the homogeneous system.
[e] Since the rank of A is 4, there are no more linearly independent solutions of the homogeneous system Ax=0.
[f] To show that v = [1, -5, 10, -4] is not in the span of the columns of A, we can check if it satisfies the homogeneous system Ax=0. Plugging in the values, we have:
[1, 0, 0, 0] [1] + [0, 1, 0, 0]
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The general solution of the system of equations Ax=b is [ 9, -3, 3, -6, 27, 78, 60], the augmented matrix precisely after the first column has been "swept" is [0, 0, 0, 1, 3, -78/5, 180/5], the reduced echelon form is [0, 0, 0, 1, 3, -78/5, 180/5], the rank of A is 4, there are no more linearly independent solutions of the homogeneous system Ax=0.
What do you mean by equation?An equation is a mathematical statement that shows the equality of two expressions. It is represented by an equal sign (=) and is used to solve for unknown values or to describe relationships between variables. Equations can be simple or complex, involving basic arithmetic operations or advanced mathematical concepts like trigonometry and calculus. They can also involve constants, variables, functions, and symbols.
An equation can be used to solve for a single unknown value, for example, the equation 2x + 3 = 7 can be solved for x by subtracting 3 from both sides, giving us 2x = 4 and then dividing both sides by 2, giving us x = 2. In this example, x = 2 is the solution to the equation.
[a] The general solution of the system of equations Ax=b can be found by using Gaussian elimination or row reduction. The augmented matrix [A b] is:
[-3, 1, -1, 2, -9, -26, -20]
[15, -5, 5, -10, 45, 130, 100]
[-30, 10, -8, -62, 12, 32, -178]
[ 9, -3, 3, -6, 27, 78, 60]
[b] The first step in row reduction is to get a 1 in the first row and 0s below it in the first column. We can do this by dividing the first row by -3 and subtracting multiples of it from the other rows:
[1, -1/3, 1/3, 2/3, 3, 26/3, 20/3]
[0, 20/3, 4/3, 8/3, 12, 104/3, 140/3]
[0, -40/3, 20/3, 4, -24, 68/3, 140/3]
[0, 3, -3, 0, 9, -78/3, 180/3]
Next, we can use row operations to get 0s in the second column below the first row:
[1, -1/3, 1/3, 2/3, 3, 26/3, 20/3]
[0, 1, 2/5, 4/5, 6, 42/5, 70/5]
[0, 0, 2/5, 2, -18, 26/5, 110/5]
[0, 0, 0, 0, 3, -78/5, 180/5]
Continuing with this process, we get the reduced echelon form of the augmented matrix:
[1, 0, 0, 0, 3, -26/5, 20/5]
[0, 1, 0, 0, 6, 42/5, 70/5]
[0, 0, 1, 0, -18, 26/5, 110/5]
[0, 0, 0, 1, 3, -78/5, 180/5]
[c] The reduced echelon form of [A b] is:
[1, 0, 0, 0, 3, -26/5, 20/5]
[0, 1, 0, 0, 6, 42/5, 70/5]
[0, 0, 1, 0, -18, 26/5, 110/5]
[0, 0, 0, 1, 3, -78/5, 180/5]
[d] The homogeneous system Ax=0 has the general solution:
x1 = t
x2 = 6t
x3 = -18t
x4 = 3t
where t is an arbitrary constant. These are two linearly independent solutions of the homogeneous system.
[e] Since the rank of A is 4, there are no more linearly independent solutions of the homogeneous system Ax=0.
[f] To show that v = [1, -5, 10, -4] is not in the span of the columns of A, we can check if it satisfies the homogeneous system Ax=0. Plugging in the values, we have:
[1, 0, 0, 0] [1] + [0, 1, 0, 0]
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Shelley has a piece of yellow ribbon that is 7.7 inches long and a piece of purple ribbon that is 6.99 inches long. How much longer is the yellow ribbon?
HELPPpp
Answer:
0.71
Step-by-step explanation:
To find how much longer the 1st one is, subtract: 7.7-6.99=0.71
the quadrilateral EFGH has vertices E (-3,2) F(3,2), G(3,-2), and H(-3,-2) which statement is correct
The statement that is correct on Quadrilateral EFGH is B. Quadrilateral EFGH is a rectangle.
What kind of shape is Quadrilateral EFGH ?To find out the type of shape that Quadrilateral EFGH is, you need to find the dimensions of the sides of the shape.
This can be found by the formula :
d=√(( x2 – x1 ) ² + ( y2 – y1 ) ² )
Using the formula, Side EF is 6 units
Side FG = 4 units
Side GH = 6 units
Side EH = 4 units
Two sides are therefore the same which means that this is a rectangle.
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Options for this question include:
A. Quadrilateral EFGH is a square.
B. Quadnlateral EFGH is a rectangle.
C. Quadrilateral EFGH is a rhombus
D. Quadriateral EFGH is a trapezium.
The equation 9t = 27.99 models a constant rate situation.
What is 1t?
The value of t from the given equation is 3.11.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The given equation is 9t=27.99
The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.
Now, t=27.99/9
t=3.11
Therefore, the value of t is 3.11.
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A student randomly draws a card from a standard deck of 52 cards. He records the type of card drawn and places it back in the deck. This is repeated 20 times. The table below shows the frequency of each outcome.
Outcome Frequency
Heart 7
Spade 3
Club 6
Diamond 4
Determine the experimental probability of drawing a spade.
0.15
0.25
0.35
0.50
The experimental probability of drawing a spade is 0.15.
What is probability?The probability that an event will occur is equal to the ratio of positive outcomes to all outcomes, according to the probability formula. The proportion of positive outcomes to overall outcomes, or P(E), determines the likelihood that an event will occur.
Given A student randomly draws a card from a standard deck of 52 cards, this is repeated 20 times.
total outcome = 20
The table below shows the frequency of each outcome.
Outcome Frequency
Heart 7
Spade 3
Club 6
Diamond 4
to find the probability of drawing a spade,
a favorable outcome for spade = 3
probability = favorable outcome/total outcome
P(spade) = 3/20
P(spade) = 0.15
Hence option A is correct.
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Answer:
Step-by-step explanation: .15 because there are 20 in total, and there are 3 spade.
3/20=.15
Hope this helps!
What is the answer to 1+5s≤ – 4?
Answer:
This is what I found, but not sure if it's right.
Simplify the expression by combining like
terms:
b+3b²+ b-b²
Enter the number that goes in the green box.
[?]b² + [ ]b
Enter
We can simplify the expression to get:
2*(b + b²)
How to simplify the expression?Here we want to simplify the following expression:
b + 3b² + b - b²
We can reorder that expression in the following way.
b + b + 3b² - b²
And now group like terms, we will get:
b + b + 3b² - b²
2b + (3 - 1)* b²
2b + 2b²
Now we can take 2 as a common factor to get:
2*(b + b²)
That is the expresion simplfied.
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Find the equation of the line that is tangent to the curve y = 3xcosx at the point (π,−3π). The equation of this tangent line can be written in the form y = mx+b. Compute m and b.
As the equation of tangent line is y = -3x, the value of slope, m is -3 and value of b is 0.
To find the equation of the tangent line at the point (π, -3π), we need to find the derivative of the function y = 3xcos(x), which is
y' = 3cos(x) - 3xsin(x)
and then evaluate the derivative at x = π to find the slope of the tangent line.
The slope at x = π is
m = 3cos(π) - 3πsin(π) = -3
So, the equation of the tangent line is y = -3x + b.
To find the value of b, we use the point (π, -3π) and the slope -3:
-3π = -3 * π + b
b = 0
So, the equation of the line tangent to the curve y = 3xcos(x) at the point (π, -3π) is y = -3x + 0 or simply y = -3x.
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The graph of y = tan x is concave up on which of the following intervals?A. (0,π/2)B. (-π/2,0)C. (-π/4, π/4) D. (0,π)E.(-π,0)
The graph of y = tan x is concave up on the interval (0,π/2).
The graph of y = tan x is concave up on the interval (0,π/2). This can be shown by studying the second derivative of the tangent function. The second derivative of the tangent function is d2y/dx2 = 2sec2(x)(tan(x)) > 0, which means that the tangent function is concave up for all values of x. This implies that the graph of y = tan x is concave up on the interval (0,π/2). To show this, we can take a few points on the interval (0,π/2) and calculate the values of the second derivative of tan x at those points. For example, for x = π/4, the second derivative of tan x is 2sec2(π/4)(tan(π/4)) = 2(1.1547)(1.7321) = 4.9289 which is positive. This shows that the graph of y = tan x is concave up on the interval (0,π/2).
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15 POINTS PLEASE HELP
a women made a deposit of $218. if her deposit consisted of 62 bills, some of them one-dollar bills and the rest being five-dollar bills, how many one-dollar bills did she deposit?
F = quantity of five dollar bills
S = quantity of single dollar bills
so she deposited 62 bills, that means that whatever F and S are, we know that F + S = 62.
we also know that all those amount to $218, so the fives are really 5*F or 5F from those $218, and the singles are just 1*S of the same $218, so we can also say that 5F + S = 218.
[tex]F+S=62\implies F=62-S \\\\\\ 5F+S=218\implies \stackrel{\textit{substituting from above}}{5(62-S) +S=218}\implies 310-5S+S=218 \\\\\\ 310-4S=218\implies 310=4S+218\implies 92=4S\implies \cfrac{92}{4}=S\implies 23=S[/tex]