Answers
Answer:
[tex]J' = (-2,-4)[/tex]
Step-by-step explanation:
Given
The attached figure
[tex]J = (-3,-6)[/tex]
[tex]D_{o,\frac{2}{3}}(x,y)[/tex]
Required: Determine J'
The given transformation: [tex]D_{o,\frac{2}{3}}(x,y)[/tex] means that the quadrilateral is dilated by a scale factor or 2/3.
So, J' is calculated as:
[tex]J' = \frac{2}{3} * J[/tex]
[tex]J' = \frac{2}{3} * (-3,-6)[/tex]
[tex]J' = (\frac{2}{3} * -3,\frac{2}{3} * -6)[/tex]
[tex]J' = (2*-1,2*-2)[/tex]
[tex]J' = (-2,-4)[/tex]
Hence, J' = (-2,-4)
Related Questions
Given this equation...
4x - 1 6
--------- = -----
3x + 7 5
What is the value of x in this proportion?
Answers
In this equation, the value of x in the ratio 4x-1/ 3x + 7 = 6/5 is 23.5. In algebra, an equation is a mathematical statement .
what is equation ?A mathematical formula known as an equation combines two assertions using the equal sign (=) to denote equivalence. An equation is a mathematical statement that proves the equality of two mathematical expressions, according to the definition of an equation in algebra. The terms 3x + 5 and 14 are separated by an equal sign in the equation 3x + 5 = 14, for example. Mathematical equations are used to express the relationship between two phrases on either side of a letter. In most cases, the symbol serves as the sole variable.
given
4x-1/ 3x + 7 = 6/5
20x - 5 = 18x + 42
x = 23.5
In this equation, the value of x in the ratio 4x-1/ 3x + 7 = 6/5 is 23.5.
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HELPPPPPPP i need hellpppp
Answers
The gradient of the line in the image will be -3.
What is a slope?Slope or the gradient is the number or the ratio which determines the direction or the steepness of the line. The slope of the line is defined as the ratio of the rise of the line to the run of the line.
Given that the line in the image is passing through the points ( 0,3) and (1,0). the gradient or slope of the line will be calculated as:-
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
Slope = ( 0 - 3 0 / 9 1 - 0 )
Slope = -3
Hence, the gradient will be -3.
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Solve the proportion
Answers
The value of the proportion x is 10. When determining if two ratios or fractions are equivalent, the proportion formula is utilized.
What is proportion formula?When determining if two ratios or fractions are equivalent, the proportion formula is utilized. By dividing the supplied numbers, we may determine the missing value. One way to express the percentage formula is as a: Whereas a and d are the extreme terms and b and c are the mean terms, b::c: d = a/b = c/d.
1)Cross, multiply, and spread
2) Be sure to alter the signs when you move the x to one side and the numbers without the x to the other.
3)solve
4)x=
x - 2 /4 = x + 4 /2
2x-4 = 4x+ 16
-20= 2x
x=10.
The value of the proportion x is 10.
The complete question is
Solve the proportion : x - 2 /4 = x + 4 /2
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Use the graphing tool to graph the function . Then identify the features of the graph.
Select the correct answer from each drop-down menu.
Function f has a horizontal asymptote of
.
The range of function f is
.
The y-intercept of function f occurs at the point
.
As x decreases toward negative infinity,
.
Answers
the function f(x)=10^x and ploted below.
What is a function?
A unique kind of relation called a function is one in which each input has precisely one output. In other words, the function produces exactly one value for each input value. The graphic above shows a relation rather than a function because one is mapped to two different values. The relation above would turn into a function, though, if one were instead mapped to a single value. Additionally, output values can be equal to input values.
The x-values are input into the function machine. The function machine then performs its operations and outputs the y-values. The function within can be any function.
function f(x)=10^x
Y = 0
Y greater than 0
(0,1)
Decreases toward 0
Hence, the function f(x)=10^x and plotted below.
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In this activity, you are investigating the financial viability of the martingale betting strategy that was introduced in class.
Recall how a martingale works. You place a bet on any "even money" event (that is, a wager where winning means gaining the money bet). If you win, you stop — you have won money. If you lose, you keep doubling the bet until you win, and then stop. Your winnings will cover the previous losses. Unfortunately, a long losing streak means that you run out of money and can no longer bet – hence losing a lot.
Balph Snerdwell has $31 in his wallet. He is going to be betting on red or black, at the roulette table. Recall that, in an American casino, there are 38 numbers — 18 red and 18 black (plus 0 and 00). So Balph has an 18/38 probability of winning, each time he bets.
a) Balph plays a martingale — doubling his bet after each loss. What’s the maximum number of times he can lose? Why?
b) Recall that Balph might win a dollar from playing a martingale … or he might lose all $31 in his wallet. What’s the probability that he wins a dollar? That he loses everything?
c) And so, what is the expected value of Balph’s net winnings, from one martingale?
d) Sometimes Balph will bet only one dollar. But sometimes he will bet three dollars (if he loses, then wins). Or seven dollars (lose, lose, win). Or some other amount. What are the possible values for total amount wagered? Their probabilities? Therefore, what is the expected value of the numbers of dollars wagered?
e) In Part D you found how much money Balph won, on average. In Part E, you found how much money Balph bet, on average. How much did Balph win, per dollar bet? (Does this number look familiar?)
The answers are:
b) 0.9596, 0.0404
c) expected value of dollars won = -$0.29236
d) expected value of dollars wagered = $5.55475
Can someone please break it down and explain how they got the answers
Answers
Answer:
a) Balph can lose a maximum of 6 times in a row before running out of money and not being able to place any more bets. This is because if he loses 6 times in a row, he would have to bet $64 (1+2+4+8+16+32) which is more than the $31 he has in his wallet.
b) The probability that Balph wins a dollar is 0.9596 and the probability that he loses everything is 0.0404. These probabilities are calculated by assuming a 18/38 probability of winning each bet and using the martingale betting strategy.
c) The expected value of Balph's net winnings from one martingale is -$0.29236. This means that on average, Balph can expect to lose $0.29236 each time he plays the martingale betting strategy.
d) The possible values for the total amount wagered are $1, $3, $7, $15, $31, and $64. These values correspond to the amount wagered after losing 0, 1, 2, 3, 4 and 5 times in a row. The probability of each value depends on the probability of losing that many times in a row, calculated using the 18/38 probability of winning each bet. The expected value of the number of dollars wagered is $5.55475.
e) The amount Balph wins per dollar bet is -0.0527. This number is calculated by dividing the expected value of Balph's net winnings by the expected value of the number of dollars wagered. This number is less than zero, indicating that on average, Balph will lose money for every dollar he bets.
What are the slope and y-intercept of the equation 2x - 5y = -10?
Answers
Answer:
slope 2/5
y-intercept (0,2)
Step-by-step explanation:
8 = 3 a - 4
Nmbvcxzstyhvff
Answers
The value of a in the equation 8 = 3a - 4 is
What are linear equations?A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept. Occasionally, the above is called a "linear equation of two variables," where y and x are the variables.
The equation 8 = 3a -4 is an example of linear equation with only one variable. The variable here is a. And the value of this variable can be found using mathematics principle.
8 = 3a - 4
collect like terms
3a = 12
divide both sides by 3
a = 12/3
a = 4
therefore the value of a in 8 = 3a -4 is 4
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You want to invest some money. You do some research and find that 2
different financial institutions are suited to your investment needs.
Bank A offers an interest rate of 8.8% compounded quarterly.
Bank B offers an interest rate of 9.0% compounded annually.
Apply mathematic reasoning to state which bank will give you a better
return for your money.
Answers
Bank A will give better return for the money we invest. The solution has been obtained using the concept of compound interest.
What is compound interest?
The interest earned on savings that is computed using both the original principal and the interest accrued over time is known as compound interest.
It differs from simple interest in that simple interest does not take the principal into account when calculating the interest for the following month. In math, compound interest is typically represented by the letter C.I.
We have 2 different financial institutions which suit our investment needs.
1. Bank A offering an interest rate of 8.8% compounded quarterly.
2. Bank B offering an interest rate of 9.0% compounded annually.
In order to find that which bank will give better return of our money, we need to calculate the effective rate of interest for both the options.
1. 8.8% compounded quarterly
Effective interest= (1+(0.088/4))^4-1
= (1.022)^4-1
= 1.09094-1
= 0.09094
= 9.094%
2. 9.0% compounded annually
Effective interest= (1+(0.09/1))^1-1
= 1.09-1
= 0.09
= 9%
Hence, Bank A will give better return for the money we invest.
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y= 2x- 2
y = 2x - 2
How many solutions does the system of equations have?
• One solution
• Infinitely many solutions
• No solution
Answers
Answer:
Infinitely many solutions
System of EquationsA system of equations is solving for 2 or more lines. Solving it means finding the point where they intersect.
One solution means the lines only intersect once and have a different slope.
No solution means the lines never intersect and have the same slope but a different y-intercept.
Infinitely many solutions means the lines are always intersecting, meaning the lines have the same y-intercept and slope.
Q)y= 2x - 2
y = 2x - 2
They have the same slope and y-intercept, so there are infinitely many solutions.
Does x and y vary inversely for each ordered pair?
Mark yes or no please for each answer
Answers
Answer:
Step-by-step explanation:
yes
no
no
ye
A copper pipe has an inside diameter of 3.00 cm and an outside diameter of 5.00 cm (see the figure(Figure 1)) - Part A What is the resistance of 19.0 m of this pipe?
Answers
The resistance of 19.0m of the given copper pipe is 1.19 x [tex]10^{-6}[/tex] ohm.
The resistance of a pipe is given by the formula:
R = (p * L) / (A * n)
where R is the resistance, p is the resistivity of the material (in this case, copper), L is the length of the pipe, A is the cross-sectional area of the pipe, and n is the number of conductors (in this case, 1).
To find the cross-sectional area of the pipe, we first need to find the radius of the pipe. We can do this by taking the difference between the outside diameter and the inside diameter and dividing by 2:
r = (d_outside - d_inside) / 2
r = (5.00 cm - 3.00 cm) / 2
r = 1.00 cm
Now we can find the cross-sectional area of the pipe:
A = pi * [tex]r^2[/tex]
A = pi * [tex](1.00 cm)^2[/tex]
A = 3.14
Next, we can use the resistivity of copper, which is 1.68 x[tex]10^{-8}[/tex] ohm-cm. Now we have all the values required to find the resistance of the pipe:
R = (p * L) / (A * n)
R = (1.68 x [tex]10^{-8}[/tex] ohm-cm * 19.0 m) / (3.14 [tex]cm^2[/tex] * 1)
R = (1.68 x [tex]10^{-8}[/tex] ohm-cm * 19.0 m) / (3.14 [tex]cm^2[/tex])
R= 1.19 * [tex]10^{-6}[/tex] ohm
Therefore, the resistance of 19.0m of this pipe is 1.19 x [tex]10^{-6}[/tex] ohm.
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the table of ordered pairs (x y) gives an exponential function write an equation for the function
Answers
The equation of the function is found to be y = [tex]2^{2x+3}[/tex].
What is a function?
A unique kind of relation called a function is one in which each input has precisely one output. In other words, the function produces exactly one value for each input value. The graphic above shows a relation rather than a function because one is mapped to two different values. The relation above would turn into a function, though, if one were instead mapped to a single value. Additionally, output values can be equal to input values.
The x-values are input into the function machine. The function machine then performs its operations and outputs the y-values. The function within can be any function.
y = 2⁽ᵃˣ⁺ᵇ)
x = - 1 y = 2 = 2¹
=> ax + b = 1 => -a + b = 1
=> b -a = 1
x = 0 y = 8 = 2³
=> ax + b = 3 => 0 + b = 3
=> b = 3
b -a = 1
=> 3 - a = 1
=> a = 2
checking for others
x = 1 y = 32 = 2⁵
ax + b = 2(1) + 3 = 5
x = 2 y = 128 = 2⁷
ax + b = 2(2) + 3 = 7
The equation is y = [tex]2^{2x+3}[/tex]
Hence the equation of the function is found to be y = [tex]2^{2x+3}[/tex].
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Determine if the expression -a^{2}+b^{4}-7a^{3}−a
2+b 4 −7a^3
is a polynomial or not. If it is a polynomial, state the type and degree of the polynomial.
The given expression
represents
a polynomial. The polynomial is a
and has a degree of
.
Answers
The expression a² + b⁴ - 7a³ - a² + b⁴ - 7a³ is a binomial.
Degree of the binomial = 4.
What is Polynomial?A polynomial is defined as an expression which is composed of variables, constants and exponents, that are combined using mathematical operations such as addition, subtraction, multiplication and division (No division operation by a variable).
The degree of a polynomial is the highest power of the variable in a polynomial expression.
Given expression
a² + b⁴ - 7a³ - a² + b⁴ - 7a³
Combining like terms
2b⁴ - 14a³
above expression has where a and b as variables with power 4 and 3 and coefficients 2 and 14 respectively combined with subtraction operation.
So, it is a polynomial with two terms which means it is a binomial and its degree is 4.
Hence, the expression a² + b⁴ - 7a³ - a² + b⁴ - 7a³ is a binomial with degree 4.
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Coordinate grid shows from -2 to positive two on x-axis and -2 to positive two on y-axis. There are increments I have one over four for each grid line on each of the two axes. Only the whole numbers are labeled on either side of the axis. A point A is shown at the intersection of 5 grid lines to the right of the y-axis and 3 grid lines below the x-axis. What are the coordinates of point A?
Answers
The coordinates of point A are ( 5/4, -3/4)
What are coordinates?
A pair of numbers that use the separations between the two reference axes to define the location of a point on a coordinate plane. usually represented by the x- and y-values, respectively, (x, y).
The position of a point or a shape in a given space is determined by coordinates, which are numbers (a map or a graph ).
x - coordinate = 5 grid lines to the right of the y-axis
y - coordinate = 3 grid lines below the x-axis.
The point A is in the 4th quadrant
(x,y) = ( + 5 grid lines, -3 grid lines )
There are increments I have one over four for each grid line on each of the two axes
This means,
(x,y) = ( + 5 * 1/4, -3*1/4 ) = ( 5/4, -3/4)
So, the coordinates of point A are ( 5/4, -3/4)
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maths question worth lots of points
Answers
The bearing form the cliff to the island is 58.09 degrees
How to determine the bearing form the cliff to the islandInformation from the question
A puffin leaves a cliff and flies 33 km due east
and then 53 km due north
Work out the bearing form the cliff to the island = ?
The bearing form the cliff to the island is worked using SOH CAH TOA
Sin = opposite / hypotenuse - SOH
Cos = adjacent / hypotenuse - CAH
Tan = opposite / adjacent - TOA
The direction of movements describes a right triangle of
opposite = 53 km
adjacent = 33 km
The bearing is calculated using tan, TOA
let the angle be x
tan x = Opposite / Adjacent
tan x = 53 / 33
tan x = 1.60606
x = arc tan 1.60606
x = 58.09 degrees
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14. Damian is building a display case to hold
75 model cars. The case will have fewer
than 10 shelves, and each shelf will hold
no more than 15 cars. If Damian wants
each shelf to have the same number of
cars, how many shelves should he put in
the display case?
Answers
Damian should put 5 shelves in the display case to hold 75 model cars and ensure that each shelf has the same number of cars.
What is the unit value?
Unit value is a measure of the price of a single unit of a good or service. It is calculated by dividing the total cost of the good or service by the number of units purchased. It is also known as unit cost.
To determine how many shelves Damian should put in the display case, we can use the following steps:
Divide the total number of cars by the maximum number of cars per shelf. In this case, 75 model cars / 15 cars per shelf = 5
If the number of shelves is not a whole number, round up to the next whole number. In this case, 5 shelves is already a whole number, so we don't need to round up.
Check that the number of shelves is less than 10. In this case, 5 shelves are less than 10 shelves.
Hence, Damian should put 5 shelves in the display case to hold 75 model cars and ensure that each shelf has the same number of cars.
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Two motorcycles leave home at the same time, heading directly toward each other. They are a total of 300 miles apart. The first motorcycle travels at 65 miles per hour. The second motorcycle travels at 85 miles per hour. How long will it take for the two motorcycles to meet?
Answers
Answer:
150 miles
Step-by-step explanation:
Total miles by the two motorcycles
300 miles
The first motorcycle travel 65 miles per hour
The second motorcycle travel 85 miles per hour
Total miles the two motorcycles travels
65 mile + 85 miles
=150 miles
Long it will take for the two motorcycles to meet
= 300 miles + 150 miles
=150 miles.
Hence it will take 150 miles for the two motorcycles to meet.
3. BIRDS An ostrich can run at a rate of
50 miles in 60 minutes. At this rate,
how long would it take an ostrich to
run 15 miles?
Distance Run (mi)
Time (min)
50
60
x2
15
■
Answers
Answer: It would take the ostrich 4 minutes
Step-by-step explanation:
The time taken by the Ostrich running at a rate of 50 miles in 60 minutes to cover a distance of 15 miles is 18 minutes.
What is the time taken by the ostrich to cover 15 miles?Speed is simply referred to as distance traveled per unit time.
Mathematically, Speed = Distance ÷ time.
Given the data in the question;
An ostrich can run at a rate of 50 miles in 60 minutes.
First, we determine the speed of the ostrich.
Speed = Distance / time
Speed = 50 / 60
Speed = 5/6 miles per min
Now, time taken for the ostrich to run 15 miles will be;
Speed = Distance / time
Time = Distance ÷ Speed
Time = 15 ÷ 5/6
Time = 15 × 6/5
Time = 3 × 6
Time = 18 min
Therefore, the time taken by the Ostrich is 18 minutes.
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Trisha is twice as old as Mina. 10nyears from now, Trisha will be 4 years older than Mina. How old is Trisha and Mina?
Answers
Answer: Let's say Trisha is currently T years old and Mina is currently M years old.
We know from the problem statement that Trisha is twice as old as Mina:
T = 2M
We also know that 10 years from now, Trisha will be 4 years older than Mina:
T + 10 = M + 4
We can substitute the first equation into the second equation:
2M + 10 = M + 4
We can then solve for M:
M = 6
So, Mina is currently 6 years old.
We can use the first equation to find Trisha's current age:
T = 2M = 2 * 6 = 12
Therefore, Trisha is currently 12 years old and Mina is currently 6 years old.
Step-by-step explanation:
Hurry - Fill in the blanks
Answers
Answer:
The first value of a relation is an input value and the second value is the output value. A function is a specific type of relation in which each input value has one and only one output value.
An input is an independent value, and the output value is the dependent value, as it depends on the value of the input.
If a distribution has zero variance which of the following is true? The number of positive values and the number of negative values are equal OAll the values are positive 0 All the values are negative d) OAll the values are equal to each other
Answers
When asked which of the following is true in this situation, "if a distribution has zero variants," the response is "D."
Due to the variance's definition, which is the same for both continuous and discrete random variables, all of the values must be equal to one another. For all possible values of X, the variance is determined by measuring the excess distance from the mean.
If any one of these individual values deviates from the mean, it follows that the variations must also deviate from zero because the integration will result in the difference squared being represented as a positive number.
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0.1 | 0.4 | ? | 1.6 | 2.5
Answers
Answer:
? = 1
Step-by-step explanation:
You are trying to mind the MEDIAN of the given expression.
The MEDIAN is the middle number of a set of given values.
1. Arrange the terms in ascending order.
= 0.1 , 0.4 , 1.6 , 2.5
2. The median is the middle term in the arranged data set. In the case of an even number of terms, the median is the average of the two middle terms.
= (0.4 + 1.6)/2
Write as a fraction where (0.4 + 1.6) is the NUMERATOR & 2 is the DENOMINATOR. Include parentheses.
3. Remove parentheses.
= 0.4 + 1.6/2
Write as a fraction where 0.4 + 1.6 is the NUMERATOR & 2 is the DENOMINATOR.
4. Add 0.4 and 1.6.
= 2/2
5. Divide 2 by 2.
= 1
6. Convert the median 1 to decimal.
= 1
What is the slope of the line shown below? (6, 2); (- 2, - 3); 8/5; 5/8; - B/5 D. - 5/8
Answers
The slope of the line shown below is -5/8.
What is slope?Slope is the measure of the steepness or incline of a line or surface. It is calculated by measuring the ratio of the vertical change over the horizontal change between two points. It is a mathematical concept used in algebra, geometry, and calculus to measure the rate of change of a function or line. Slope is also used to identify the direction of a line or surface. It is represented by the variable ‘m’ and is calculated by dividing the vertical change by the horizontal change between any two points on a line or surface.
This can be determined by using the formula for slope, which is (y2 - y1)/(x2 - x1). In this equation,
(y2 - y1) = -3 - 2 = -5 and (x2 - x1) = -2 - 6 = -8. Thus, the slope of the line is -5/8.
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Which of the following is an example of a variable measured at the nominal level of measurement?
A. Location in which respondent was born
B. Religiosity measured as not religious, somewhat religious, and very religious
C. Time in seconds in which a subject completes a given task D. Number of respondents' first cousins
E. Level of education in years completed
Answers
Religion is an example of a variable measured at the nominal level of measurement. Thus, option B is correct.
Nominal values are those that cannot be quantified by numbers, such as when calculating age or tallying academic accomplishments. As opposed to the ordinal, interval, or ratio measurements, it is the level of measurement representing a variable that just has distinct properties.
Since the 'characteristic' or 'identity' we are interested in is just named, the nominal level of measurement is the least accurate and illuminating. In nominal variables, the numerical values just "label" the attribute in a distinctive way. The numerical value is just a label in this instance.
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please help! Kendra and Theo each collected data on the number of birds observed at a bird feeder each hour for eight hours.
Answers
Remaining two data of Theo's observation is 9 and 11.
What is mean, median and range in a data list?
Mean is the average of all data value. Range is the difference between the highest and lowest value of a data set. Median implies the middle value of a data set. If the number of data is even than median is calculated from average of two middle value. If the number of data is odd, then the median is the middle of all data.
What is the two-missing data for Theo's bird observation?
given, Kendra and Theo both collected data of bird observation.
Kendra data's summary are as following.
range = 6
median = 7
mean = 7
From the Theo's data
range = 6
median = 7
mean = 7.5
the question shows 6 data among the total 8 data of Theo's observation.
5,5,6,6,8,10 are 6 data of total 8 data.
let, the missing value are X and Y.
we know mean of a data list is calculated by adding all the value and divided the sum by total amount of data.
mean = 7.5 = (X + Y + 5+ 5+ 6+ 6+ 8+10) / 8
X + Y + 40 = 60
X+Y = 20
we know range is the difference between the highest and the lowest number of a data set.
let, the highest number is X and lowest number is assumed 5.
As range is 6, range = X - 5
X- 5 = 6
X = 11
highest number of data set = 11
now we get the other missing data from the equation, X + Y = 20
Y = 20 -11
Y = 9
now, the data set can be arranged as
5,5,6,6, 8,9, 10,11
we notice that the two middle value is 6 and 8.
median = (6+8) / 2 = 7
that is equal to given median by Theo.
hence, the determination is verified.
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this is factorizing by looking for the common factor i have no idea how to answer any of them and i need it for tomorrow please help (im in algebra 2)
Answers
Answer:keep dividing
Step-by-step explanation:
keep dividing till you get a common factor
Please help if you can what are the factors for 45 (math)
Answers
Answer:
Step-by-step explanation:
The number in consideration here is 45 and the integers that divide it evenly are known as the factors of 45. There are a total of six factors of the number 45: 1, 3, 5, 9, 15 and 45. The numbers that are multiplied in pairs to produce 45 are the factor pairs of 45.
(a) Your Mom has a sum of x. She spent 3,000 on grocery and 2,000 on milk.
Write the algebraic expression for the amount left with her.
Answers
Answer:
y=x-5000
Step-by-step explanation:
Given,
total sum of money mom has=x
money spent on grocery=Rs 3000
money spent on milk= Rs 2000
total money spent by mom=Rs 5000
Let the money left with the mom =y
then the algebric expression for the amount left with her is given by
y=x-5000
The function f is defined on the closed interval [-5,4]. The graph of f consists of three line segments and is above in the figure above. Let g be the function defined by g(x) = integral_2_-3 f(t) dt. a. Find g(3) b. On what open intervals contained in -5 lessthan x lessthan 4 is the graph of g both increasing and concave down? c. The function h is defined by h(x) = g(x)/5x. Find h'(3). d. The function p it defined by p(x) = f(x^2 - x). Find the slope of the line tangent to the graph of p at the point where x = -1.
Answers
a. g(3) = -2
b. g is increasing and concave down on the intervals (-3 <= x < 2) and (2 <= x <= 4).
c. h'(3) = 0
d. The slope of the tangent line to the graph of p at x = -1 is -3.
a. The function g is defined as the definite integral of f(t) with respect to t from -3 to 2. Therefore, g(3) = integral_2^3 f(t) dt. From the graph, we can see that:
f(t) = 2 for -5 <= t < -3f(t) = -t for -3 <= t < 2f(t) = 2t - 8 for 2 <= t <= 4.Therefore, g(3) = integral_2^3 (-t) dt + integral_2^3 (2t - 8) dt
= -1/2(3^2 - 2^2) + 1/2(3^2 - 2^2 - 8(3 - 2)) = -5/2 + 1/2 = -2.
b. The graph of g is increasing and concave down when the graph of f is concave down and when the definite integral of f is increasing. From the graph of f, we can see that f is concave down on the intervals (-5 <= t < -3) and (2 <= t <= 4). Therefore, g is increasing and concave down on the intervals (-3 <= x < 2) and (2 <= x <= 4).
c. The function h is defined by h(x) = g(x)/5x. To find h'(3), we need to use the quotient rule for derivatives. h'(x) = (5xg'(x) - g(x)5)/5x^2.
Since g(x) = integral_2_-3 f(t) dt, it is not a function of x, so g'(x) = 0. Therefore, h'(3) = (530 - 05)/53^2 = 0.
d. The function p is defined by p(x) = f(x^2 - x). To find the slope of the line tangent to the graph of p at the point where x = -1, we need to find the derivative of p at -1. Using chain rule: p'(x) = f'(x^2-x)(2x-1) so p'(-1) = f'(-1) * (2(-1)-1) = (2(-1) -1) = -3.
Therefore, the slope of the tangent line to the graph of p at x = -1 is -3.
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Part C
What is the length y of the remaining, vertical side of the 30-60 right triangle? (Figure 3)
Express your answer in centimeters to 3 significant figures
Answers
Y = 12.12 cm is determined by Pythagoras' Theorem, where the hypotenuse and one side of a right-angled triangle are specified as being 14 cm and 7 cm, respectively.
what is triangle ?Triangles are shapes with three sides and three vertices, making them polygons. It is one of geometry's fundamental forms. A triangle containing vertices A, B, and C is known as a triangle ABC. In Euclidean geometry, a singular plane and triangle are discovered when the three points are not collinear. A polygon with three sides and three corners is called a triangle. The corners of the triangle are the points where the three sides meet one another end to end.
given
by Pythagoras theorem
c2 = a2 + b2
14*14 = y2 + 7*7
196 - 49 = y2
y2 = 147
y = [tex]\sqrt{147}[/tex] = 12.12 cm
Y = 12.12 cm is determined by Pythagoras' Theorem, where the hypotenuse and one side of a right-angled triangle are specified as being 14 cm and 7 cm, respectively.
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