The point that partitions the line in the ratio of 1:3 is (1.333, 3.333).
Given two points P1(x1,y1) and P2(x2,y2), the point that partitions the directed line between these two points in a given ratio r can be calculated using the following formula:
P(x,y) = (x1 + r(x2-x1), y1 + r(y2-y1))
For example, if we have P1(1,2) and P2(4,6) and we want to partition the line in a ratio of 1:3, the point P(x,y) can be calculated as follows:
P(x,y) = (1 + 1/3(4-1), 2 + 1/3(6-2)) = (1.333,3.333)
Therefore, the point that partitions the line in the ratio of 1:3 is (1.333, 3.333).
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1
10 points
(x + 2)(3x + 4)
3x²-2x-8
3x²+2x-8
3x² +8
3x² +10x+8
(x + 2)(3x + 4) on simplification we get 3x² + 10x + 8.
How can I tell if something is a function or not?To ascertain whether a graph accurately depicts a function, use the vertical line test. The graph is a function if a vertical line drawn across it is moved and touches it only once at any given time. If there are multiple points where the vertical line touches the graph, the graph is not a function.
Given,
(x + 2)(3x + 4)
x (3x + 4) + 2(3x +4)
3x² + 4x + 6x + 8
3x² + 10x + 8.
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find derivative
f'(x) =
Answer:
[tex]\displaystyle{f'(x)=\dfrac{9}{4}x\left(8x^4+x^2-1\right)^{\frac{1}{8}}(16x^2+1)}[/tex]
Step-by-step explanation:
Given the function [tex]\displaystyle{f(x)=\sqrt[8]{\left(8x^4+x^2-1\right)^9}}[/tex]. We can rewrite the function in exponential form as [tex]\displaystyle{f(x)=\left(8x^4+x^2-1\right)^{\frac{9}{8}}}[/tex]. Here, we have to know the power rules and the chain rule:
[tex]\displaystyle{f(x) = u^n \to f'(x) = nu^{n-1} \cdot \dfrac{du}{dx}}[/tex]
Therefore, from the above formula, we will have:
[tex]\displaystyle{f'(x)=\dfrac{9}{8}\left(8x^4+x^2-1\right)^{\frac{9}{8}-1} \cdot \dfrac{d}{dx}\left(8x^4+x^2-1\right)}\\\\\displaystyle{f'(x)=\dfrac{9}{8}\left(8x^4+x^2-1\right)^{\frac{9}{8}-\frac{8}{8}} \cdot \dfrac{d}{dx}\left(8x^4+x^2-1\right)}\\\\\displaystyle{f'(x)=\dfrac{9}{8}\left(8x^4+x^2-1\right)^{\frac{1}{8}} \cdot \dfrac{d}{dx}\left(8x^4+x^2-1\right)}[/tex]
Next, we derive the function 8x⁴ + x² - 1 by applying the power rules:
[tex]\displaystyle{f(x) = x^n \to f'(x) = nx^{n-1} \cdot \dfrac{dx}{dx} \to f'(x)=nx^{n-1}}[/tex]
Also, deriving any constants will result in 0 always.
Therefore:
[tex]\displaystyle{\dfrac{d}{dx}\left(8x^4+x^2-1\right)} = 4\cdot 8 x^{4-1} + 2\cdot x^{2-1} - 0}\\\\\displaystyle{\dfrac{d}{dx}\left(8x^4+x^2-1\right)} = 32x^3 + 2x}[/tex]
Thus, we will have:
[tex]\displaystyle{f'(x)=\dfrac{9}{8}\left(8x^4+x^2-1\right)^{\frac{1}{8}} \cdot (32x^3+2x)}\\\\\displaystyle{f'(x)=\dfrac{9}{8}\left(8x^4+x^2-1\right)^{\frac{1}{8}} \cdot 2x(16x^2+1)}\\\\\displaystyle{f'(x)=\dfrac{9}{4}x\left(8x^4+x^2-1\right)^{\frac{1}{8}}(16x^2+1)}[/tex]
Therefore, the derivative is:
[tex]\displaystyle{f'(x)=\dfrac{9}{4}x\left(8x^4+x^2-1\right)^{\frac{1}{8}}(16x^2+1)}[/tex]
or you can rewrite in the form of surd as:
[tex]\displaystyle{f'(x)=\dfrac{9}{4}x(16x^2+1)\sqrt[8]{8x^4+x^2-1}}[/tex]
Drag each item to the container that best describes it.
Answer:
Rate : 1 page for every 4 students.
Unit Rate: 500 pages per ream.40 pages for every blooket.15 pages for evry blooket
Neighter: 25 pages
Step-by-step explanation:
I hope this helps :)
The diffrence between unit rate and rate is the unit rate refers to those rates in which the numerator is 1. Rate would be like there is 1 person per car. Unit rate would mean There are 3 cars for each person.
one gallon of paint covers 400 squars feet. what is the least amount of paint needed to paint the walls of s room in the shape of a rectangular prism with a length of 20 feet, a width of 18 feet. and a height of 12 feet?
The minimum amount of paint needed to paint the walls of the room would be 2,2 gallon.
How to calculate the amount of paint we need?To calculate the amount of paint we need to paint the walls of the room we must calculate the area of each of the walls, in this case it would be 4 rectangles with the following dimensions:
(12ft x 18ft)*2(20ft x 12ft)*2According to the above, the area of the walls would be:
12*18=216cm²20*12=240cm²216cm² * 2 = 432cm² 240cm² * 2 = 880cm²880cm² + 432cm² = 1312cm²Based on the above, it can be inferred that 2.2 gallons of paint are needed to paint all the walls.
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Listed below are the systolic blood pressures for a sample of six men aged 20-29 and for a sample of six men aged 60-69 Men aged 20-29: 117 122 129 118 131 123
Men aged 60-69: 130 153 141 125 164 139
Find the variance for each of the two sets of data then compare the variance. Round results to one decimal place.
A) Men aged 20-29: 4.8% Men aged 60-69: 10.6%
There is substantially more variation in blood pressures of the men aged 60-69.
B) Men aged 20-29: 4.6% Men aged 60-69: 10.2 %
There is substantially more variation in blood pressures of the men aged 60-69.
C) Men aged 20-29: 7.6% Men aged 60-69: 4.7%
There is more variation in blood pressures of the men aged 20 -29.
D) Men aged 20-29: 4.4% Men aged 60-69: 8.3%
There is substantially more variation in blood pressures of the men aged 60-69.
The obtained Z score for the following blood pressures =-2
Enter data in Excel work sheet and use the formulae
=VAR(A1:A6) and =VAR(B1:B6) to get the variance
Variance for
Men aged 20-29=42.97
Men aged 60-69=211.77
The variance is substantiaaly larger for the set of blood pressures of men aged 60-69
Enter the data in Excel worksheet and use =AVERAGE(A1:A15) to find mean and calculate is the mean
Mean=15833.33 and is to calculated for finding relative position
Z=38-(27*10)=-232Z=262.7-(200*57)=-11,137.3
Hence 262.7 has higher relative position
=[48-70]/11=-2
Z score=-2
The calculated Z score for the subsequent blood pressures is therefore = -2.
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Alec buys a refrigerator priced at $820.33 . If the sales taxi s 10%,how much tax will Alec pay?
Answer:
$902.36
Step-by-step explanation:
820.33 times 10% = 82.033
add 82.033 to 820.33
820.33 + 82.033 = 902.363
If a and b denote the vectors OA and OB, indicate on the same diagram the vectors OC and OD denoted by a + b and a − b. Draw on another diagram the vector OE denoted by a + 2b.
A vector diagram showing the vector OE denoted by a + 2b is as attached.
How to draw vector diagram?Vector diagrams can be used to improve visualization and understanding of the magnitude and direction of vectors, and more importantly how multiple vectors interact.
For example, if Peter is pushing a heavy container towards the west, while John is pulling it in the northwest direction, in what direction does the container actually move?
A vector diagram is what will be useful in finding the answer.
Now, we see the vectors OC and OD denoted by a + b and a − b in the attached diagram. Now, if we want to find a + 2b, we know that a + b will be a resultant but by use of vector analysis, we can plot a + 2b as seen in the first vector diagram attached.
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Cameron determined that an ordered pair made a true statement when substituted into one of the equations but not in the other equation. Is her ordered pair a solution to the system of equations? If not, explain.
The ordered pair is not solution to the system of equations.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
Cameron determined that an ordered pair made a true statement when substituted into one of the equations but not in the other equation.
As, we know we enter the values of the variables into each equation to see if an ordered pair is a solution to the system of two equation. The system has a solution if the ordered pair proves both of the equations.
So, the ordered pair is not solution..
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the annual expenditure of the us federal government is approximately 444 trillion dollars. if a one dollar bill is 0.00010.00010, point, 0001 meters thick, how many meters tall would a stack of 444 trillion one dollar bills be? write your answer in scientific notation. for reference: 111 trillion
the annual expenditure of the US federal government is 4 trillion dollars and dollar bill is 0.001m then, the length of four trillion dollars would be 4×[tex]10^{9}[/tex] m
Government spending or expenditure includes all government
consumption, investment, and transfer payments. In national income accounting, the acquisition by governments of goods and services for current use, to directly satisfy the individual or collective needs of the community, is classed as government final consumption expenditure.
Since we have given that annual expenditure = 4 trillion dollars,
1 dollar bill = 0.0001m
so, the thickness would be.
[tex]4*10^{12} *0.001\\\\=4*10^{12}*10^{-3}\\\\=4*10^{9}[/tex]
the length of 4 trillion dollars would be. 4×[tex]10^{9}[/tex]
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Which of the following is a measure of air filter efficiency?
A-Total volume of dirt collected.
B-Total weight of dirt collected.
C-Size of the largest particle that can be removed.
D-Total weight of the particles that can be removed.
C-Size of the largest particle that can be removed is a measure of air filter efficiency.
Air filter efficiency is a measure of how effectively a filter removes particles from the air. It can be measured in various ways, depending on the type of filter and the particles it is designed to remove.
A-Total volume of dirt collected - This measure does not provide information about the efficiency of the air filter, it could be a measure of how long the filter has been in use.
B-Total weight of dirt collected - This measure does not provide information about the efficiency of the air filter, it could be a measure of how long the filter has been in use.
C-Size of the largest particle that can be removed - This measure provides information about the efficiency of the air filter, because it tells us the size of the largest particle that the filter can remove. The smaller the particle size, the more efficient the filter is.
D-Total weight of the particles that can be removed - This measure does not provide information about the efficiency of the air filter, it could be a measure of how long the filter has been in use.
Air filter efficiency is usually measured by the Minimum Efficiency Reporting Value (MERV) rating, which is a standard measurement scale that ranges from 1 to 16, the higher the MERV rating, the more efficient the filter is at capturing small particles.
Determine the median for each of thefollowing sit of data 3,5,2,5,5,3,7,8,5
Answer:
5
Step-by-step explanation:
To find the median in a set of data, we first need to arrange the numbers in ascending order.
2,3,3,5,5,5,5,7,8
The median is the middle value of the set. Since there is an even number of data points in this set, the median is the average of the two middle values, which are 5 and 5.
So the median = (5+5)/2 = 5.
Solve for x
(B) and (c) please
Step-by-step explanation:
(b)
logx . logx = 2log x
logx = 2
so x = 100
(c)
2x + 3x= 10
5x = 10
so ×=2
Tarush is a landscape architect. For his first public project he is asked to create a small scale drawing of a garden to be placed in the corner of a city park. The garden is a right triangle with base
10
m
10 m10, start text, space, m, end text and height
15
m
15 m15, start text, space, m, end text.
The Area and perimeter of the triangle is given by 75m² and 33.02 m respectively.
What is the Pythagoras theorem?Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, a² + b² = c².
Given here: A right triangular garden with base 10m and height 15 m
We know the area of a triangle is given by A=1/2×b×h where b=base and h=height. And the perimeter of a triangle is given by sum of all sides.
Thus Area of triangular Garden =1/2×10×15
=75 m²
And the perimeter the triangle is given by=10+15+[tex]\sqrt{10^2+15^2}[/tex]
=10+15+18.02
=33.02 m
Hence, The Area and perimeter of the triangle is given by 75m² and 33.02 m respectively.
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The police department in your city was asked by the mayor’s office to estimate the cost of crime. The police began their study with burglary records, taking a random sample of 500 files. If the average dollar loss in a burglary, for this sample size 500 is $678, with a standard deviation of $560, construct the 95% confidence interval for the true average dollar loss in burglaries rounded to the nearest dollar amount.
The 95% confidence interval for the true average dollar loss in burglaries rounded to the nearest dollar amount is 629 to 727
What are variance and standard deviation?
The variance of a variate X is the arithmetic mean of the squares of all the deviations of X from the arithmetic mean of the observations and it is denoted by Var(X) or σ². The spread of statistical data is measured by the standard deviation. Distribution measures the deviation of data from its mean or average position. The positive square root of the variance of a variate X is known as the standard deviation.
Given here: Sample mean x=678, Sample size n=500, Standard deviation σ=560
Standard error=σ.x=σ/√n
=560/√500
=25.044
Now for a 95% Class interval the value of z=1.960
The margin of error, E=Z×standard error
=49.08624
Lower bound=628.9147
upper bound=728.0854
∴ The 95% interval for population mean = 629 to 727
Hence, The 95% confidence interval for the true average dollar loss in burglaries rounded to the nearest dollar amount is 629 to 727
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glenn bought 3 pounds of tomatoes. he used 5-eighths of them to make sauce. questionmake an equation that shows the number of pounds of tomatoes glenn used for the sauce. move numbers and symbols to the blanks to complete the equation. if there is no whole number in the answer, put a 0 in the first box after the equals sign.
He used [tex]$=1 \frac{7}{8} \mathrm{lb}$[/tex] . An algebraic equation, often known as a polynomial equation
What are mathematical equations?An algebraic equation, often known as a polynomial equation, is a mathematical equation of the kind P=0 where P is a polynomial with coefficients in some field, typically the field of the rational numbers. Transcendental equations are what they are known as. The phrase "is not solvable by radicals" is used to describe a polynomial problem that you are unable to solve. A nontrivial differential-algebraic equation called a universal differential equation (UDE) has the feature that every continuous function on any interval of the real line can be approximated to arbitrary accuracy by one of its solutions.Determine the number of pounds used
To solve this, we simply multiply the fraction of tomato used by the total;
[tex]Used $=$ Fraction $*$ Total[/tex]
Used[tex]=\frac{5}{8} * 3 l b$[/tex]
Used[tex]=\frac{5 * 3}{8} l b$[/tex]
Used = 15/8 lb
Convert to mixed number
Used [tex]$=1 \frac{7}{8} \mathrm{lb}$[/tex]
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Mark u as brainliest
Answer:
-9 -6
Step-by-step explanation:
in 1973, braley and nelson studied the effect of price increases on school lunch participation in the city of pittsburgh. the revenue function for the program was given by: r ( q )
The new revenue can be calculated as R = q*p = 2,000*4 = $8,000.
R(q) is the revenue function for the school lunch program, which is given by the equation q*p, where q is the quantity and p is the price. According to Braley and Nelson's study, the city of Pittsburgh had an increase in price of school lunches. The revenue can be calculated by multiplying the quantity (q) of school lunches with the new price (p) after the increase. Therefore, the new revenue (R) can be calculated by R = q*p. As an example, if the quantity of school lunches is 2,000 and the price is increased to $4, then the new revenue can be calculated as R = q*p = 2,000*4 = $8,000.
R(q) is the revenue function for the school lunch program, which is given by the equation q*p, where q is the quantity and p is the price. According to Braley and Nelson's study, the city of Pittsburgh had an increase in price of school lunches. The revenue can be calculated by multiplying the quantity (q) of school lunches with the new price (p) after the increase. Therefore, the new revenue (R) can be calculated by R = q*p. As an example, if the quantity of school lunches is 2,000 and the price is increased to $4, then the new revenue can be calculated as R = q*p = 2,000*4 = $8,000.
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Help is greatly appreciated!
The largest possible value for the probability of A4 is 0.2000
How to determine the probabilitySince A1, A2, A3, and A4 are events from a common sample space, the sum of their probabilities must be less than or equal to 1.
So, the sum of the probabilities of the events can be expressed as:
P(A1) + P(A2) + P(A3) + P(A4) = 1
From the question, we have
P(A1) = P(A2) = P(A3) = 0.3
Also, we have that
Al and A2 occur simultaneously with a probability of 0.1
This means that the initial equation becomes
P(A1) + P(A2) - P(A1 and A2) + P(A3) + P(A4) = 1
Where
P(A1 and A2) = 0.2
So, we have
0.3 + 0.3 - 0.1 + 0.3 + P(A4) = 1
Evaluate the like terms
P(A4) = 0.2
Hence, the probability is 0.2
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023 at
11:00 am
1. A person plans to make equal annual deposits into a retirement account for 25
years in order and then make 20 equal annual withdrawals of TShs.25,000,000
reducing the balance in the amount to zero. Assume the account offers a
nominal annual rate of 6.5% compounded annually.
(a) How much must be deposited annually to accumulate sufficient funds to
provide for these payments?
(b) How much total interest is earned during thi
Before any lease payments, the lease liabilities on January 1, 2021, is Liability $1,282,994.04 and Annual Deposit = $92,633.22.
What liabilities mean?Liability is a general term that describes the condition of being accountable for a good or service that is owed to another person.
For instance, a homeowner's tax responsibility may be related to the property taxes he must pay to the civil government or the income taxes he must pay to the external government.
leasing fee:A lease payment is a type of annual rent that is technically required by a contract between two parties and gives one party the right to use the other party's fixed assets, such as computers, manufacturing equipment, software, or other real estate impacts, for a predetermined period of time.
Evaluation:FVAD of $1 table or calculator function
$530,000 in future worth
n = 5
I = 5.00%
divided by 6.1533, the FV factor
Deposit each year: $92,633.22
Check out the FVAD table.
PVAD of $1 in a table or calculator function
the sum of $133,000
n = 20
I = 10.00%
9.36492 PV factor multiplied
Amount Owed $1,282,994.04
Check out the PVAD table.
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Ishi bought a $6.95 canvas and 8 tubes of paint. She spent a total of $24.95 on the canvas and paints. Determine the cost of each tube of paint.
Answer:
1 tube of paint is $2.25.
Step-by-step explanation:
We can set this as an equation first. Since we know that the canvas is $6.95 and the total is $24.95, those are the values that we will work with to determine the tube price. We can set the tube price as 8x, x being the tube price, and 8 being the number of tubes Ishi plans to buy. Now, we can set an equation:
6.95 + 8x = 24.95
8x = 18
x = 18/8 (simplified is 9/4, or 2.25)
Answer:
$ 2.25
Step-by-step explanation:
A= $6.95
B= (Cost of each tube) x 8
C= $24.95
A+B = C
the lengths of the sides of a triangle are b and c let S be the length of the angle bisector of the angel between the two given sides . the length of the third side of the triangle is
The length of the third side of the triangle is given by 2 (b + c) S /2bc2 - 1 (b + c)
To determine: the triangle's third side's length.
Since b and c are the lengths of a triangle's sides, let S be the length of the angle that bisects the given sides.
Suppose that angle A is 2α.
ABC's area is equal to (1/2) bcsin2α.
ADC's area is (1/2) bSsinα.
ADB = (1/2) cSsinα Area
Area of ABC is equal to Area of ADC plus Area of ADB.
The equation is (1/2) bcsin2α = (1/2) bSsinα + (1/2) cSsinα.
=> bcsin2α = (b + c) Ssinα
=> bc2sinαcosα = (b + c) Ssinα
=> cosα = (b + c) S /2bc
cos2α = 2cos²α - 1
=> cos2α = 2 {(b + c) S /2bc}² - 1
also cos2α = (b² + c² - a²)/2bc
Both being equal:
(b2 + c2 - a2)/2bc = 2 (b + c) S /2bc2 - 1 (b + c)
Simplify to discover an in relation to b.
or, if available, substitute the values of b, c, and S to find a ( this side of triangle )
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Find the least common denominator of 1/2x-6 and 2x/7x-21.
The least common denominator or LCD of the given fractions 1/2x-6 and 2x/7x-21 is (2x-6)(7x-21)
What is a fraction?A fraction can simply be defined in mathematics as the part of a whole variable or number.
Some types of fractions in mathematics are;
Proper fractionsImproper fractionsMixed fractionsComplex fractionsSimple fractionsWhat is the least common denominator?The least common denominator of a fraction is seen as the lowest or smallest number in all the common multiples of the denominator given.
Given the information, the fractions are;
1/2x-6 and 2x/7x-21
It is crucial to identify that the denominator of the two fractions are;
(2x-6)(7x-21)
They are in form of algebraic expressions, thus, the least common denominator is the product of the expression.
Hence, the lowest common denominator is (2x-6)(7x-21)
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Find the product of (3n-8)²
9n²+64
9n²-48n+64
9n²-64
16n² + 16n +4
The answer is 9n²-48n+64
Students have received the marks for their Mathematics quiz. Ali found out that Ahmad's marks is five more than double of his marks. If the total of their marks is 125, what is Ali's marks and what is Ahmad's marks?
Answer:
Ali's mark= 40
Ahmad's mark= 85
Step-by-step explanation:
Let x be Ali's mark and y be Ahmad's mark.
y=2x+5
x+y=125
x+2x+5=125
3x=120
x=40
y=85
Please having a hard time these 3
1) y-coordinate of the vertex of y = x^2 + 2x - 1 is -1.
2) The statement "the vertex of quadratic function f is (-b/2a, f(-b/2a))" is true.
3) The equation y = -2x^2 - 12x - 17 has a maximum.
What is Quadratic Equation?
A quadratic equation is any equation in algebra that can be rearranged in standard form as where x represents an unknown value and a, b, and c represent known numbers.
1) y = x^2 + 2x - 1 is the equation of a parabola in vertex form.
In vertex form, the equation of a parabola is y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola.
So, to find the y-coordinate of the vertex, we can substitute the values of a, h and k into the equation and get the y-coordinate.
For the equation y = x^2 + 2x - 1, the vertex is (-1, -1), where -1 is the y-coordinate.
So, the y-coordinate of the vertex of y = x^2 + 2x - 1 is -1.
2) True.
The vertex of a quadratic function f(x) = ax^2 + bx + c is the point on the parabola that represents the graph of the function where the parabola changes direction from opening upward to opening downward or vice versa.
The x-coordinate of the vertex is given by (-b/2a), and the y-coordinate is given by f(-b/2a), where a, b, and c are constants.
So, the statement "the vertex of quadratic function f is (-b/2a, f(-b/2a))" is true.
3) maximum
The equation y = -2x^2 - 12x - 17 is a quadratic function, and it is in vertex form.
The leading coefficient is -2 which is negative, so the parabola opens downward, which means the vertex of the parabola represents the maximum point of the function. Therefore, the equation y = -2x^2 - 12x - 17 has a maximum.
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Obtain an estimate for the computation shown below by rounding the numbers so that the resulting arithmetic can easily be performed by hand or in your head.
0.87 x 310
The estimation of the numbers given as 0.87 × 310 will give 270.
Howw to calculate the estimation?You must approximate (eliminate or round off) the decimals to obtain whole numbers before you can use the whole numbers to find the product of two decimals using estimation.
A figure is discovered through estimation.
A value, amount, or size that rounds off to the nearest whole number is said to be approximating.
The estimation of the numbers given as 0.87 × 310 will give:
= 0.9 × 300
= 270.
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Which of the following tables represents a linear relationship that is also proportional?
x y
0 2
4 4
8 6
x y
0 0
2 1
4 2
x y
0 1
5 3
10 5
x y
0 3
3 7
6 11
The option second correctly represents a linear relationship that is also proportional.
Define the term proportional relationship?Relationships between two variables that are proportional occur when their ratios are equal. Another way to consider them is that in a proportionate relationship, 1 variable is consistently equal to the other's constant value.For the stated table:
Option 1:
x y
0 2
4 4
8 6
y/x = 4/4 = 1
y/x = 6/8 = 3/4 (NOT proportionate).
Option 2:
x y
0 0
2 1
4 2
y/x = 1/2
y/x = 2/4 = 1/2 (proportionate).
Option 3:
x y
0 1
5 3
10 5
y/x = 3/5
y/x = 5/10 = 1/2 (NOT proportionate).
Option 4:
x y
0 3
3 7
6 11
y/x = 7/3
y/x = 11/6 (NOT proportionate).
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A 14-foot ladder is leaning against a building. The ladder makes a 50° angle with the ground as shown in the diagram.
14 ft,
50ft
Which expression can be used to find the height, h, in feet that the ladder reaches on the building?
The height that the ladder reaches on the building is 10.7 feet
What is an equation?An equation is an expression that uses mathematical operations to show the relationship between numbers and variables. Types of equations are linear, quadratic, cubic and so on.
Trigonometric ratio is used to show the relationship between the sides and angles of a right angled triangle.
A 14-foot ladder is leaning against a building. The ladder makes a 50° angle with the ground. Let h represent the height of the building. Using trigonometric ratio:
sin(50) = h/14
h = 14 * sin(50)
h = 10.7 feet
The height is 10.7 feet
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60.9% 3.7 million 20.4% source: philippines statistics authority the cultural composition of the philippines and its constituent islands affects the political stability of the country. which of the following patterns is best explained by the data in the tables?
A concentration of the majority of Muslim population of the country is on one island, leading to ethnic separatism.
What is ethnic separatism?Ethnic Separatism is the process by which a nation or ethnic group makes efforts to become more autonomous from the central government of a state, or even secedes, when it is unhappy with any combination of social, economic, and political conditions in the nation in which it is located.
When an ethnic group actively works to assert its rights and importance, ethnic nationalism is the result. When it serves the interests of the state, governments may support ethnic nationalism as a project; however, for a variety of reasons, ethnic nationalism may also pose a threat to the state. Separatism based on ethnicity is one of these causes. Find out what ethnic separatism is, some examples of it, and more by continuing to read.
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Full question:
THE PHILIPPINES, 2010
Total Population
Roman Catholic Population
Percent Roman Catholic
Muslim Population
Percent Muslim
92 million74 million
80.6%
5.1 million
5.6%
THE PHILIPPINE ISLAND OF MINDANAO, 2010
Total Population
Roman Catholic Population
Percent Roman Catholic
Muslim Population
Percent Muslim
18 million
10.9 million
60.9%3.7 million
20.4%Source: Philippines Statistics Authority
The cultural composition of the Philippines and its constituent islands affects the political stability of the country. Which of the following patterns is best explained by the data in the tables?
A. An even dispersal of Muslims around the country, leading to assimilation
B.An even dispersal of Muslims around the country, leading to ethnic separatism
C. An even dispersal of Muslims around the country, leading to irredentism
D. A concentration of the majority of the country’s Muslim population on one island, leading to assimilation
E. A concentration of the majority of the country’s Muslim population on one island, leading to ethnic separatism
2 What is the derivative of the function f(x) = 3x² + 2√x - 4x at x=1?
Answer:
The derivative of the function f(x) = 3x² + 2√x - 4x at x=1 is
[tex]\boxed{f'(1) = 3}[/tex]
Step-by-step explanation:
We have f(x) = 3x² + 2√x - 4x
[tex]f'(x) = \dfrac{d}{dx}\left(3x^2+2\sqrt{x}-4x\right)\\\\=\dfrac{d}{dx}\left(3x^2\right)+\dfrac{d}{dx}\left(2\sqrt{x}\right)-\dfrac{d}{dx}\left(4x\right)\\\\[/tex]
[tex]\dfrac{d}{dx}\left(3x^2\right) = 6x\\\\[/tex]
[tex]\dfrac{d}{dx}\left(2\sqrt{x}\right) = 2\dfrac{d}{dx}\left(\sqrt{x}\right)\\\\=2\dfrac{d}{dx}\left(x^{\frac{1}{2}}\right)\\\\= =2\cdot \dfrac{1}{2}x^{\frac{1}{2}-1}\\\\\\=\dfrac{1}{\sqrt{x}}\\\\[/tex]
[tex]\dfrac{d}{dx}\left(4x\right)=4[/tex]
Therefore
[tex]f'(x) = 6x+\dfrac{1}{\sqrt{x}}-4\\\\f'(1) = 6(1) + \dfrac{1}{\sqrt{1}} - 4\\\\f'(x) = 6 + 1 - 4\\\\f'(x) = 3\\\\[/tex]
