Answer:
20
Step-by-step explanation:
Given that the triangles are similar, we know that the corresponding side lengths should all have similar ratios.
This means that ab/ef = bc/fg = ca/ge as they're corresponding.
We know that ge = 8, ca = 4, ab = 10 and we want to find ef
Remember ab/ef = ca/ge so 10/ef = 4/8
4/8 = 10/ef
==> cross multiply
80 = 4ef
==> divide both sides by 4
20 = ef
We can test our answer by seeing if the ratios are the same
ab/ef = 4/8 = 1/2
ca/ge = 10/20 = 1/2
The ratios are the same, therefore our answer is correct.
Explain why∣2x+5∣=−7 has no solutions.
Absolute value represents how far you are from zero on the number line.
Examples:
-27 is 27 units from zero, so |-27| = 2734 is 34 units from zero, so |34| = 34The output of an absolute value function is never negative. Negative distance does not make sense. Therefore, we have no way to reach an output of -7. This is why we have no solutions here.
Add or subtract. 1/x^3+y^3 see image for the whole problem
Answer:
[tex] \frac{1}x{} [/tex]
[WILL GIVE BRAINLIEST HELPPP!!]
Determine the value of x.
Answer: 14.46
Step-by-step explanation:
sin 56 = 12/x
0.83 = 12/x
0.83x = 12
x = 12/0.83
x = 14.46
Answer: 14.475
Step-by-step explanation:
Since we are given the angle 56°, this means that the other angle is 34°. We are given the side 12 this means that x, or the hypotenuse, is 14.475.
The hypotenuse is c, b is 12, and a is the side with the 90° angle.
What we do is c = a/sin(a) = b / sin(56°)
Justin and Daniel work at a dry cleaners
ironing shirts. Justin can iron 40 shirts per
hour, and Daniel can iron 20 shirts per hour.
Daniel worked 6 more hours than Justin and
they ironed 360 shirts between them.
Graphically solve a system of equations in
order to determine the number of hours
Justin worked, x, and the number hours
Daniel worked, y.
On solving the provided question, we can say that the linear equation formed will be y = -2x+18
What is a linear equation?A linear equation is one that has the form y=mx+b in algebra. B is the slope, and m is the y-intercept. It's usual to refer to the previous clause as a "linear equation with two variables" because y and x are variables. The two-variable linear equations known as bivariate linear equations. There are several instances of linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. It is referred to as being linear when an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept.When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.
In xx hours, Justin can iron 40x40x shirts since he can iron 40 shirts every hour. Daniel can iron 20 shirts each hour, or 20y20y shirts, in y hours. There were 360 shirts ironed in all (40x+20y):
[tex]40x+20y=360\\40x+20y=360\\x+y=14\\40x+20y= 360\\x+y=14\\40x+20y = 360 x+y = 14 20y = -40x+360 \\y = -2x+18[/tex]
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Maureen bought a new car worth $26,525 one year ago. She knows that her car's value will depreciate each year. She uses an online calculator to find that her car is worth $24,403 today. Write an exponential equation in the form y = a(b) that can model the value, y, of Maureen's car x years after purchase. Use whole numbers, decimals, or simplified fractions for the values of a and b.
The equation to model the value of Maureen's car x years after purchase can be written in the form of y = a(b)^x , where y is the value of the car, x is the number of years after purchase, and a and b are constants.
Using the information given, we can find the values of a and b.
We know that the value of the car one year after purchase is $24,403.
So, we can substitute this value into the equation:
24403 = a(b)^1
We also know that the car's original value is $26,525
So we can substitute this value into the equation:
26525 = a
Now we can use these two equations to find the value of b
24403 = 26525 (b)^1
b = 24403 / 26525
b = 0.9153
So the final equation is:
y = 26525 (0.9153)^x
where y is the value of the car, x is the number of years after purchase, and a = 26525 and b = 0.9153
Let f(x)=√x with f:R→R. Discuss the properties of f. Is it injective, surjective, bijective, is it a function? Why or why not? Under what conditions change this?Explain using examples.I'm having some trouble figuring out this equation.
The function f(x)=√x with f:R→R is injective and surjective but not bijective.
Injective (or one-to-one): f(x) is injective, which means that if f(x1) = f(x2), then x1 = x2. In other words, if the square root of x1 is equal to the square root of x2, then x1 and x2 are equal.
Surjective (or onto): f(x) is surjective, which means that for every y in the codomain (R), there exists an x in the domain (R) such that f(x) = y. In other words, the square root of any real number can always be expressed as a real number.
Bijective: f(x) is not bijective. The square root function is not bijective because it is not defined for negative values of x.
Function: A function f is a function if for every x in the domain of f, there is exactly one y in the codomain of f such that f(x) = y. In other words, each x in the domain is mapped to exactly one y in the codomain.
In the case of f(x) = √x, it is a function. For every x in the domain of f, which is [0,∞), there is exactly one y in the codomain of f, which is [0,∞), such that f(x) = y.
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How can you show that the set of number of the form a + b√2 , where a and b are sizable rational numbers is a field with respect to addition and multiplication?
We have to show that the set of numbers of the form a + b√2, where a and b are rational numbers, forms a field with respect to addition and multiplication.
To start, we need to show that the set of numbers is closed under addition and multiplication. This means that if we add or multiply two numbers in the set, the result must also be in the set.
For addition, let's take two numbers in the set, say (a1 + b1√2) and (a2 + b2√2). When we add them, we get (a1 + a2) + (b1 + b2)√2. Since a1, a2, b1, and b2 are all rational numbers, their sum is also a rational number. So, the result of adding two numbers in the set is always another number in the set, which means that the set is closed under addition.
For multiplication, let's take two numbers in the set, say (a1 + b1√2) and (a2 + b2√2). When we multiply them, we get (a1a2 + 2b1b2) + (a1b2 + a2b1)√2. Again, since all the numbers involved are rational, the result is also a rational number. This means that the set is closed under multiplication as well.
Next, we need to show that the set satisfies the commutative, associative, and distributive laws for both addition and multiplication. This means that the order in which we add or multiply numbers in the set does not matter, and that addition and multiplication can be combined in a predictable way.
The commutative, associative, and distributive laws for addition and multiplication are well-known for rational numbers, and it can be easily verified that they hold for this set as well.
Finally, we need to show that the set has additive and multiplicative inverses. This means that for each number in the set, there exists another number in the set such that when added (or multiplied) to the original number, the result is 0 (or 1).
It can be shown that for any number of the form a + b√2, its additive inverse is -a - b√2, and its multiplicative inverse is (a / (a^2 + 2b^2)) - (b / (a^2 + 2b^2))√2, assuming that a^2 + 2b^2 is not equal to 0. Both of these are also rational numbers, since they are obtained by dividing rational numbers.
So, we have shown that the set of numbers of the form a + b√2, where a and b are rational numbers, is closed under addition and multiplication, satisfies the commutative, associative, and distributive laws, and has additive and multiplicative inverses. This means that the set of numbers forms a field with respect to addition and multiplication.
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Reflect the point (13, 8). across the y-axis. What is the result?
The image of the point after the reflection across the y-axis is:
(-13, 8)
What is the image of the point after the reflection?Remember that for a general point (x, y), a reflection across the y-axis just changes the sign of the x-component, so the new point will be:
(-x, y)
Here we want to apply this reflection to (13, 8), using the rule above, we can see that the new coordinates after the reflection are:
(-13, 8)
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Use the long division method to find the result when x³ + 3x² + 5x + 6 is divided
by x + 2.
i hate deltamath.
[tex](x + 2)x( {x }^{2} + x + 3)[/tex]
Part 1 of 2
All the workers in a company were asked a survey question. The two-way frequency table shows the responses
from the workers in the day shift and night shift. Complete parts a and b.
The column cells are similarly filled by dividing the column cells by the corresponding column totals.
What is meant by frequency table?A table that displays the distribution of a characteristic's occurrence frequency in accordance with a specific set of class intervals.
Two sorts of data, or data in two categories, one pertaining to the columns and the other to the rows, make up a two-way relative frequency table.
Response
Shift Yes No Total
Day 67% 33% 100%
Night 23% 77% 100%
Total 45% 55% 200%
This table contains information about two categories, day/night and yes/no.
The day/night data percentages are computed along the rows.
The percentages of the yes/no values are calculated along the columns.
Shift Response
Yes No Total
Day 67/100 × 100 33/100 ×100 100
= 67% =33% 100%
Night 23/100×100 77/100×100 100
= 23% =77% 100%
Total 90/200×100 110/200×100 200
= 45% = 55% 200%
To make these computations, divide the row cells by the corresponding row totals.
The column cells are similarly filled by dividing the column cells by the corresponding column totals.
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suppose that an average person has a heartbeat of 71.2 beats per minute. how many heartbeats will the person have in 2.000 years?
Answer:
Step-by-step explanation:
if you meant just 2 years the answer is 74,845,440 if you meant 2,000 its 74,845,440,000
The number of heartbeats for a person with an average heartbeat of 71.2 BPM for 2,000 years is 86,567,520,000 heartbeats.
The formula to calculate the number of heartbeats in a given period of time is:
Number of heartbeats = Beats per minute (BPM) x Minutes in the period
In this case, the given information is the BPM (71.2) and the period of time is 2,000 years, which is equal to 1,209,600,000 minutes.
Therefore, the number of heartbeats for a person with an average heartbeat of 71.2 BPM for 2,000 years is:
Number of heartbeats = 71.2 BPM x 1,209,600,000 minutes
Number of heartbeats = 86,567,520,000 heartbeats.
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Match each expression to its equivalent standard form.
x2 + 2x + 2
x2 - 4x - 4
x2 + 4
x2 + x + 2
x2 - 4x + 8
x2 + 16
(x + 2i)(x − 2i)
arrowBoth
(x + 1 + i)(x + 1 − i)
arrowBoth
(x − 2 + 2i)(x − 2 − 2i)
arrowBoth
The requried match to the expression is given as,
x²+ 2x + 2 (x + 1 + i ) (x + 1 − i)
x² - 4x + 8 (x − 2 + 2i)(x − 2 − 2i)
x² + 4 (x + 2i)(x − 2i)
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
here,
1. expression,
= x²+ 2x + 2
Simplifying the above expression,
= x²+ 2x + 2
We know that,
x = -b ± √{b² - 4ac} / 2a
x = -2 ± √(4 - 8)/2
x = -1 ± i (i = √-1)
So,
The factored form of the given expression is given as,
= (x + 1 + i ) (x + 1 − i)
Similarly,
x² - 4x + 8 = (x − 2 + 2i)(x − 2 − 2i)
x² + 4 = (x + 2i)(x − 2i)
Thus, following the pattern of each expression to its equivalent standard form can be determined.
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can you please help me
Lexi's reasoning is correct because the theoretical probability of picking a yellow golf ball is 1 out of 2, or 1/2. This is because there are two yellow golf balls in the bag and one ball is being selected.
Determine whether Lexi's reasoning is correct?Theoretical probability is the ratio of the number of outcomes for a certain event to the total number of possible outcomes.
In this case, Lexi found the ratio of one yellow golf ball to the total number of balls in her bag (two balls: one yellow and one green).
This equals a theoretical probability of 1/2 or 0.5, meaning there is a 50% chance of picking a yellow golf ball.
This is the correct way to calculate theoretical probability.
Lexi's reasoning is correct in this situation. The theoretical probability of picking a yellow golf ball is 1 out of 2, or 1/2. This is because there are two yellow golf balls in the bag and one ball is being selected.
This ratio of 1/2 is the same as the theoretical probability of picking a yellow golf ball. Theoretical probability is based on the ratio of the outcomes being considered to the total number of possible outcomes.
In this case, the two yellow golf balls represent the possible outcomes, and the total number of golf balls in the bag is two. Therefore, the theoretical probability of picking a yellow golf ball is 1/2.
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Hello what is -5/9 divided (- 1/3) as a simplest form?
The answer to the question 5/9 divided (- 1/3) as a simplest form is 5/3
What is quotient of a number?
The number we obtain when we divide one number by another is the quotient. For example, in 8 ÷ 4 = 2; here, the result of the division is 2, so it is the quotient. 8 is the dividend and 4 is the divisor.
The question -5/9 divided (- 1/3) can be re-written as
-5/9 ÷ -1/3
-5/9 x -3/1
=15/9
=5/3
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Please help I have a learning disablity and need help.
What is the coefficient in the expression?
10 – 6 + 5n
5
6
10
5n
-6
What is a test statistic example?
The test statistic for a Z-test is the Z-statistic, which has the standard normal distribution under the null hypothesis
In statistics, what is a test statistic?A test statistic shows how closely your data’s distribution fits the distribution anticipated by the statistical test’s null hypothesis. The frequency with which each observation happens is defined by the distribution of data, which may be represented by its central tendency and variance around that central tendency.
Z= (x – y)/(x2/n1 + y2/n2) is the formula for calculating the test statistic when comparing two population means. To compute the statistic, we must first compute the sample means (x and y) and standard deviations (x and y) for each sample independently. In statistics, there are many different types of tests, such as the t-test, Z-test, chi-square test, anova test, binomial test, one sample median test, and so on. If parametric tests are applied,
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what does the slope mean for the relationship between the number of practices and the number of performances?
The values of the slope and y-intercept provide details on the relationship between the two variables, x and y. The slope shows how quickly y changes for every unit change in x. When the x-value is 0, the y-intercept shows the y-value.
The rate of change between two variables is shown by the slope of the line in a scatter plot. The slope would show how much the number of performances varies with a change of one unit in the number of practises in the connection between the two numbers.
If the slope is upward, then as the number of practises rises, so do the number of performances. If the slope is negative, then fewer performances will occur as the number of practises rises.
The slope's magnitude tells us how steep the line is, which tells us how strongly the two variables are related.
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Find the value of k
Thanks
Step-by-step explanation:
the picture is so fuzzy, I can hardly read the details.
I suspect the orange line is
f(x) = 6^x
the black line is
g(x) = 6^x + k⁵
to find k we simply create
(g - f)(x) = 6^x + k⁵ - 6^x = k⁵
as we can see, the difference (up/down distance) between both functions is a constant k⁵.
the best and most reliably we can see and calculate that difference at x = 0 :
2
k⁵ = 2
[tex]k = \sqrt[5]{2} [/tex]
which is 1.148698355...
but I see, I might have misunderstood the 5 of the coordinate axis as exponent of k.
so, the function might be
g(x) = 6^x + k
and then
the difference is simply k, and
k = 2
the area under the standard normal probability density function from negative infinity to z is interpreted as the probability that the random variable is:
The area under the standard normal probability density function from negative infinity to z is interpreted as the probability that the random variable takes a value less than or equal to z.
In order to model continuous phenomena or quantities that depend on chance, such as time, length, and mass, continuous random variables are utilized.
The likelihood that the random variable takes a value inside that interval is defined as the area under the density function over an interval. Therefore, the probability that the random variable will have a value less than or equal to z is given by the area under the normal curve from negative infinity to z.
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HELP ME PLSS!?!?
In the mall you receive a coupon for $5 off of a pair of jeans when you arrive at the store you find that all jeans are 25% off
.let x represent the original cost of the jeans
.the function f(x)=x-5 represents the cost of the jeans if you use the coupon
.the function g(x)=0.25x represents the cost of the jeans if you apply the store discount of 25% first
Write a function: H(x) that represents how much you would pay if you use the mall coupon that followed by applying the discount from the store??
The price of the jeans will be $27 if you apply the function composition h(x). The price of the jeans will be $30 if you apply the composition j(x). Because it is less expensive.
what is function?The subject of mathematics includes quantities and their variations, equations and related structures, shapes and their locations, and places where they can be found.
If you first use the coupon and then utilize the shop discount, the price of the jeans is represented by the function h(x). The combination of the functions f(x) and g may be used to calculate the function h(x) (x). If you first apply the shop discount and then utilize the coupon, the cost of the jeans is represented by the function j(x). The combination of the functions g(x) and f may be used to calculate the function j(x) (x).
The price of the jeans will be $27 if you apply the composition h(x). The price of the jeans will be $30 if you apply the composition j(x). Because it is less expensive, the composition h(x) will provide you a bigger discount.
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an f1,v random variable can be thought of as the square of what kind of random variable
The type of random variable is continuous
The term called variable in math is known as a quantity that may change within the context of a mathematical problem or experiment.
Here we know that the f1,v random variable can be thought of as the square.
Here the term random variable is known as a set of possible values from a random experiment and the domain of a random variable is called sample space
As we all know that random variables are classified into discrete and continuous variables.
Here the main difference between the two categories is the type of possible values that each variable can take.
The value of the function is continuous one.
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What is the answer to -7(x-2)+4=46
Answer:
x= -4
Step-by-step explanation:
-7(x-2)+4=46
-7x+14+4=46
-7x=46-18
-7x=28
x=28/-7
x= -4
Answer:
-4
Step-by-step explanation:
Hope it helps! =D
Given (x – 7)2 = 36, select the values of x.
a. x = 13
b. x = 1
c. x = –29
d. x = 42
The value of x for the expression (x – 7)² = 36 is 13. The correct option is A.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the expression is (x – 7)² = 36. The value of x will be calculated as:-
(x – 7)² = 36
(x – 7) = √36
(x - 7) = 6
x = 13
Hence, the value of x for the expression (x – 7)² = 36 is 13. The correct option is A.
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b) The average of 9 numbers is 23. If the average of first five numbers is 20 and
that of last five numbers is 25, what is the fifth number?
NEXT QUESTION:
c) The average age of a husband and wife was 23 years at the time of their
marriage. After 10 years, they have now a daughter of 6 years, what is he
average age of the family at present?
Answer:
b)
Step-by-step explanation:
As here it's stated that average of first 9 numbers is 23
so,
sum of 9 numbers = 9×23 = 207
Average of first 5 numbers is 20
so,
Sum of first 5 numbers = 5×20 = 100
Sum of remaining numbers = 207-100 = 107
Average of last five numbers = 25
So,
Sum of last five numbers = 5×25 = 125
Fifth Number = Sum of last five numbers- Sum of remaining numbers
= 125 - 107 = 18
Complete each comparison by entering the correct inequality symbol, < or >, in the box .
For the expressions (32 - 13) (54 -45) and (23.1 - 17)/(3.2 - 13), the inequality will be (32 - 13) (54 - 45) > (23.1 - 17)/(3.2 - 13).
For the expressions -(14/5) - 19.7 and (19.7)⁴, the inequality will be -(14/5) - 19.7 < (19.7)⁴.
What is an inequality?
In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa.
The first two expressions are -
(32 - 13) (54 -45) and (23.1 - 17)/(3.2 - 13)
Solve the expression (32 - 13) (54 -45) first.
(32 - 13) (54 - 45)
Use the arithmetic operation of subtraction -
(19)(9)
Use the arithmetic operation of multiplication -
171
Now solve the expression (23.1 - 17)/(3.2 - 13).
(23.1 - 17)/(3.2 - 13)
Use the arithmetic operation of subtraction -
6.1/-9.8
Use the arithmetic operation of division -
-0.622
Now, it can be seen that -0.622 is less than 171.
Therefore, the inequality symbol > will be used.
The second two expressions are -
-(14/5) - 19.7 and (-19.7)⁴
Solve the expression -(14/5) - 19.7 first.
-(14/5) - 19.7
Use the arithmetic operation of division -
-2.8 - 19.7
- 22.5
Now solve the expression (-19.7)⁴.
(-19.7)⁴
Expand using the powers rule -
150613.848
Now, it can be seen that - 22.5 is less than 150613.848.
Therefore, the inequality symbol < will be used.
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A triangle having area of √135 square meter and perimeter 18 meter has a side 4 meter. Find the measurement of remaining two sides.
The required measurement of the remaining two sides of the given triangle are 8 and 6 meters.
What is the Heron's formula?Heron's formula is a formula for calculating the area of a triangle in terms of the lengths of its sides that is credited to Heron of Alexandria.
Given that, a triangle having area of √135 square meter and perimeter 18 meter has a side 4 meter.
Let other two sides be x and y,
Therefore,
x + y + 4 = 18
x + y = 14.....(i)
Now, according to Heron's formula,
Area of a triangle = √s(s - a)(s - b)(s - c) where s is half the perimeter, or (a + b + c) / 2.
Therefore,
√9(9 - 4)(9 - x)(9 - y) = √135
Squaring both sides
45(9-x)(9-y) = 135
(9-x)(9-y) = 3
81 -9y - 9x + xy = 3
9(x+y)-xy = 78
Put x+y = 14 from eq(i)
9×14-xy = 78
xy = 48
Now finding the factors of 48
48 = (6, 8), (12, 4), (24, 2), (16, 3), (48, 1)
If we consider (6, 8) this is satisfying eq(i)
6+8 = 14
Therefore, we can say the other two sides of the triangle are 8 and 6.
Hence, the required measurement of remaining two sides of the given triangle are 8 and 6 meters.
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A 1800 kg car with the brakes applied comes to a stop in 7.90 s. During these 7.90s the force of friction slowing down the car is 2800 N. What is the change in momentum of the car?
The change in momentum is 22120Ns
What is change in momentum ?The change in momentum (Δp ) is defined as the change in the product of an object's mass and velocity. A force is required to change the momentum of an object. This applied force can increase or decrease the momentum or even change the object's direction.
Therefore the change in momentum = Final momentum - initial momentum
i.e mv -mu
where m is the mass
v is the final velocity
u is the initial velocity
The change of momentum is also called impulse. impulse is the product of the force and the time in applying it.
Change in momentum = force × time
= 2800× 7.90
= 22120 Ns
Therefore the change in momentum of the car is 22120Ns
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if o b pi and the area under the curve y=sinx from x=b to x=pi is 0.4, what is the value of b
The value of b is 0.927. Therefore, the correct answer is option A.
To find b, we need to substitute the given values into a formula for computing the area under a curve. The formula for the area under the curve y=sinx from x=b to x=π is:
Area = ∫πb sinxdx
We do this by splitting the integral into the following two parts:
Area = ∫πbg+∫bg sinxdx
We can evaluate the first integral easily, since bg is a constant:
∫πbg=bg∫π=bgπ
For the second integral, we use integration by substitution:
Let u=x −b, so du=dx. Then the integral can be rewritten as:
∫bg sinx dx=∫bg sin(u+b)du
Where u varies from 0 to π−b. Now that the integral is in a form we can easily integrate:
∫bg sin(u+b)du=∫π−b0 sin(u+b)du
And using the Pythagorean identity:
sin(u+b)=sinubcosb+cosubsinb
We can rewrite the integrand as:
sin(u+b)=sinucosb−cosusinb
And then using integration by parts:
∫π−b0 sin(u+b)du=−cosubcosb|π−b0+∫π−b0 cosusinbdu
And the second integral can be simplified the same way we did the first one.
∫π−b0 cosusinbdu=−sinubsinb|π−b0+∫π−b0 sinubcosbdu
Which can be easily calculated as:
∫π−b0 cosusinbdu=π−b2sinbcosb
Now that both integrals are solved, we can substitute them back into the formula for the area and then solve for b:
Area=bgπ+π−b2sinbcosb
Substituting the value for the Area, we get:
0.4=bgπ+π−b2sinbcosb
Which can be simplified to:
b(π−b)=(π−0.4)/sinbcosb
Solving for b, we get:
b=0.927
Therefore, the correct answer is option A.
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"Your question is incomplete, probably the complete question/missing part is:"
If 0≤b≤π and the area under the curve y=sinx from x=b to x=π is 0.4, what is the value of b?
A) 0.927
B) 1.159
C) 1.982
D) 2.214
(a) estimate the area under the graph of f(x)=55−x2 from x=−2 to x=4 using three approximating rectangles and right endpoints.
By splitting the range into three equal pieces and approximating the area under the graph using rectangles with right endpoints, the area under the graph of f(x) from x=-2 to x=4 is calculated.
Area = (55 - (-2)^2) + (55 - (1)^2) + (55 - (4)^2) = 55 + 9 + 1 = 65
By splitting the interval into three equal pieces and approximating the area under the graph using rectangles with right endpoints, the area under the graph of
f(x)=55x2 from x=2 to x=4
is calculated. We begin by calculating the area of the rectangle whose right endpoint is at
x = -2. F(-2)
provides the height of this rectangle, which is equal to
55 - (-2)2 = 55 + 4 = 59.
The rectangle's width is
(4 - (-2))/3 = 6/3 = 2.
The area of this rectangle is therefore 59 x 2 = 118. The area of the rectangle with x = 1 as its right terminus can also be determined in a similar manner. This rectangle has a height of f(1), which equals
55 - (1)2 = 55 - 1 = 54.
The rectangle's width is
(4 - (-2))/3 = 6/3 = 2
The area of this rectangle is therefore 54 x 2 = 108. f(4), which equals 55 - (4)2 = 55 - 16 = 39, gives the area of the rectangle with x = 4 as the right endpoint. The rectangle's width is
(4 - (-2))/3 = 6/3 = 2.
The area of this rectangle is therefore 39 x 2 = 78. The sum of the areas of the three rectangles, which equals 118 + 108 + 78 = 304, represents the total area under the graph.
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Compare the rates of change of the following items
y = 0.25 +2
a line with y-intercept (0, 2) which
passes through the point (2.6)
A The rate of change of item I is greater than the rate of change of item I
B. The rate of change of item I is equal to the rate of change of item I
C. The rate of change of item ill is greater than the rate of change of item
Answer:
The rate of change of a linear function is its slope, which is the coefficient of the x-term in the equation.
Item I: y = 0.25x + 2
The slope of this line is 0.25.
Item II: y = 2
This is a horizontal line with zero slope, so it has a rate of change of 0.
The slope of Item I is greater than the slope of Item II, therefore option C is correct: "The rate of change of item I is greater than the rate of change of item II".
Step-by-step explanation: