What do i have to look up to learn how to do this kind of trig. I went through kahn academy for trig but this stuff never came up
Answers
Answer:
(e) √(x² -1)
Step-by-step explanation:
You can look up the Pythagorean theorem, and SOH CAH TOA.
__
Pythagorean theoremThis tells you the relations between the sides of a right triangle. For the purpose of finding tan(θ), you need to know the length of the side that is not marked on the diagram. It is found using the Pythagorean theorem.
The sum of squares of the legs is equal to the square of the hypotenuse. If we call the unknown leg "o", then ...
1² +o² = x² . . . . . the Pythagorean relation
o² = x² -1 . . . . . . subtract 1
o = √(x² -1) . . . . take the square root
__
SOH CAH TOAThis mnemonic reminds you of the relationship between trig functions and side lengths of a right triangle.
Sin = Opposite/HypotenuseCos = Adjacent/HypotenuseTan = Opposite/AdjacentThis tells you that tan(θ) is the ratio of the side opposite θ to the side adjacent:
tan(θ) = o/1 = o
From the previous section, o = √(x²-1), so ...
tan(θ) = √(x² -1) . . . . . . . matches choice (e)
_____
Additional comment
Another way to think about this is in terms of the trig identities you have learned:
sec(θ) = 1/cos(θ) = 1/(1/x) = x
sec²(θ) = tan²(θ) +1 ⇒ tan(θ) = √(sec²(θ) -1) = √(x² -1)
Related Questions
A survey is planned to estimate the proportion of voters who support a proposed gun control law. The estimate should be within a margin of error of with 90% confidence, and we do not have any prior knowledge about the proportion who might support the law. How many people need to be included in the sample
Answers
Complete Question
A survey is planned to estimate the proportion of voters who support a proposed gun control law. The estimate should be within a margin of error of ±5% with 90% confidence, and we do not have any prior knowledge about the proportion who might support the law. How many people need to be included in the sample?
Round your answer up to the nearest integer.
sample size = _____
Answer:
The sample size is \(n = 271 \)
Step-by-step explanation:
From the question we are told that
The margin of error is E = 5% = 0.05
Generally given that there was no prior knowledge about the proportion of who might support the law, we will assume the sample proportion to be
\(\^ p = 0.5\)
From the question we are told the confidence level is 90% , hence the level of significance is
\(\alpha = (100 - 90 ) \%\)
=> \(\alpha = 0.05\)
Generally from the normal distribution table the critical value of \(\frac{\alpha }{2}\) is
\(Z_{\frac{\alpha }{2} } = 1.645\)
Generally the sample size is mathematically represented as
\(n = [\frac{Z_{\frac{\alpha }{2} }}{E} ]^2 * \^ p (1 - \^ p ) \)
=> \(n = [\frac{1.645 }{0.05} ]^2 * 0.5 (1 - 0.5 ) \)
=> \(n = 271 \)
If you monthly salary is 5,167 and 28% is withheld for taxes and social security. How much money will be withheld from your check?
Answers
Answer:
jjjjjjj
Step-by-step explanation:
nnnnnnn
It's in the picture !
Answers
The position of √17 between 4 and 5, which is nearer 5, and the location of 6, which is between 2 and 3, which is nearer 2.
What is Number line?A visual representation of real numbers in a linear manner is a number line. It is a straight line that is divided into intervals or segments, each of which stands for a distinct real number value.
Number lines can be vertical or horizontally oriented, and they can also have a positive or negative orientation. Positive numbers often extend to the right or up, whereas negative numbers typically extend to the left or down. The origin of the number line, or zero, is typically situated in the middle of the line.
The number line is a crucial tool in mathematics since it offers a means of representing numerical relationships visually and carrying out fundamental arithmetic operations. For instance, positive and negative motions along a number line can be used to depict addition and subtraction, respectively, with positive movements denoting addition and negative movements denoting subtraction. On a number line, multiplication and division can alternatively be shown as repeated addition or subtraction.
If we have a number line with the proper markings, we may indicate where the square roots of 17 and 6 are located as follows:
To begin, determine the approximate square root values:
√17 is between 4 and 5, since 4² = 16 and 5² = 25.
√6 is between 2 and 3, since 2² = 4 and 3² = 9.
Place the number √17 closer to 5, between 4 and 5.
Place the number √6 between the numbers 2 and 3, closer to 2.
Since 6 and 17 are not integers and their values are not evenly spaced, it should be noted that their markings will not be evenly spaced on the number line.
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Number line attached below,
-) Find the equation of the line that passes through (1,0) and (3,6).
Answers
The equation of the line that passes through the points (1, 0) and (3, 6) is y = 3x - 3.
To find the equation of a line passing through two points, we can use the slope-intercept form of a linear equation: y = mx + b, where m is the slope of the line and b is the y-intercept.
Given points:
Point 1: (1, 0)
Point 2: (3, 6)
Step 1: Calculate the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
Substituting the coordinates:
m = (6 - 0) / (3 - 1)
m = 6 / 2
m = 3
Step 2: Substitute one of the given points and the slope into the equation y = mx + b to find the y-intercept (b).
Using Point 1 (1, 0):
0 = 3(1) + b
0 = 3 + b
b = -3
Step 3: Write the equation of the line using the slope (m) and the y-intercept (b):
y = 3x - 3
Therefore, the equation of the line that passes through the points (1, 0) and (3, 6) is y = 3x - 3.
This equation represents a line with a slope of 3, indicating that for every increase of 1 unit in the x-coordinate, the y-coordinate increases by 3 units. The y-intercept of -3 means that the line crosses the y-axis at the point (0, -3). By substituting any x-value into the equation, we can determine the corresponding y-value on the line.
Hence, the equation of the line passing through (1, 0) and (3, 6) is y = 3x - 3.
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The July bank statement sent by the bank to ABC company shows a balance of cash on deposit at July 31 of Br.4,964.47 Assume that on July 31, assume the on July 31, ABCs ledger shows a bank balance of Br. 4 173. 83. 1. A deposit of Br 410. 90 made after banking hours and doesnt appear in the bank statement2. A check drawn for Br. 79 had been erroneously charged by the bank Br.973. For checks issued in July have not yet been paid by the bank (outstanding checks). : Theses checks are;- Check No date amount 801 June 15 ---Br.100,00 888 July 24 ----Br. 10.25 890 July 27--- Br. 294.50 891 July 30 ---Br. 205.004. A check written for birr 210 had been incorrectly charged by the bank as birr 120 5. Proceeds from collection of a interest bearing note receivable from David. ABC Company had left this note with the banks collection department. The face amount of the note was birr 500 6. Br. 24.75 interest earned on average account balance during July7. A check for Br. 10 returned with the statement had been recorded in the check register as Br. 100. The check was for the payment of an obligation to Davis Equipment Company for the purchase of office supplies on account 8. Br. 5,00 fee charged by bank for handling collection of note receivable 9. Br. 50.25 check from customer John deposited by ABC company charged bank as Non sufficient fund (NSF) 10. Br. 12.70 service charged by bank for the month of July. 11. Check number 875 was issued July 20 in the amount of Br 85 but was erroneously recorded in the cash payment Journal as Br 58 for payment of telephone expense prepare bank reconcilation and journal entry
Answers
The bank reconciliation shows an adjusted bank balance of Br.5,301.42 and an adjusted ledger balance of Br.4,173.83.
To prepare the bank reconciliation and journal entry for ABC Company based on the given information, we need to compare the transactions recorded in ABC's ledger with the transactions shown in the bank statement. Here's the bank reconciliation:
1. Bank Statement Balance:
Cash on deposit at July 31: Br.4,964.47
2. Adjusted Bank Balance:
Bank Statement Balance: Br.4,964.47
3. Deposit not on the statement: + Br.410.90
(Adjusted Bank Balance: Br.5,375.37)
Erroneously charged check: + Br.79
(Adjusted Bank Balance: Br.5,454.37)
Outstanding checks:
Check 801: - Br.100.00
Check 888: - Br.10.25
Check 890: - Br.294.50
Check 891: - Br.205.00
(Adjusted Bank Balance: Br.4,844.62)
4. Incorrectly charged check: + Br.90
(Adjusted Bank Balance: Br.4,934.62)
5. Collection of interest-bearing note: + Br.500
(Adjusted Bank Balance: Br.5,434.62)
6. Interest earned: + Br.24.75
(Adjusted Bank Balance: Br.5,459.37)
7. Incorrectly recorded check: - Br.90
(Adjusted Bank Balance: Br.5,369.37)
8. Collection fee: - Br.5.00
(Adjusted Bank Balance: Br.5,364.37)
9. NSF check: - Br.50.25
(Adjusted Bank Balance: Br.5,314.12)
10. Service charge: - Br.12.70
(Adjusted Bank Balance: Br.5,301.42)
Adjusted Ledger Balance:
Bank Balance in ABC's Ledger: Br.4,173.83
Reconciled Bank Balance: Br.5,301.42
Reconciled Ledger Balance: Br.4,173.83
Journal Entry:
To record the bank reconciliation, we make the following journal entry:
Debit: Cash (Ledger Balance adjustment) - Br.5,301.42
Credit: Cash (Bank Statement Balance adjustment) - Br.4,964.47
Credit: Miscellaneous Income/Expense - Br.336.95 (the difference between the two balances)
This journal entry ensures that the ledger balance matches the reconciled bank balance by adjusting for the discrepancies identified during the reconciliation process.
The journal entry reflects the necessary adjustments to reconcile the two balances, with a debit to Cash (Ledger Balance adjustment), a credit to Cash (Bank Statement Balance adjustment), and a credit to Miscellaneous Income/Expense to account for the difference.
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Please I need help badly I also have stuff on my account
Answers
Answer:
Alternate Interior Angles Theorem
Step-by-step explanation:
A lens used to observe a solar eclipse will filter 69% of the sunlight entering the lens for each 10 millimeters in thickness. Find an exponential function for the percentage of sunlight S passing through the lens as a function of the thickness t (in mm) of the lens.
S=
Answers
hmmm let's reword it
what is the Decay equation for sunlight, decaying at 69% at every interval of 10 mm of thickness for "t"?
\(\textit{Periodic/Cyclical Exponential Decay} \\\\ A=(1 - r)^{\frac{t}{c}}\qquad \begin{cases} A=\textit{current amount}\\ r=rate\to 69\%\to \frac{69}{100}\dotfill &0.69\\ t=thickness\\ c=period\dotfill &10 \end{cases} \\\\\\ A=(1 - 0.69)^{\frac{t}{10}}\implies A=0.31^{\frac{t}{10}}\hspace{5em}\boxed{S=0.31^{\frac{t}{10}}}\)
You are in charge of monitoring the pressure of a compressed air tank in a processing plant. After repeating the pressure measurement a large number of times, you found that the pressure values have Gaussian distribution with a mean value of 69 psi and a standard deviation of 10 psi. If it is important that the pressure stays below 86 psi, what is the probability (in percent) that the pressure will exceed this value? (Provide your answer as a percentage using two decimal places. Do not include the % symbol in your answer)
Answers
Answer:
4.46% probability that the pressure will exceed this value.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:
\(Z = \frac{X - \mu}{\sigma}\)
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Gaussian distribution with a mean value of 69 psi and a standard deviation of 10 psi.
Gaussian distribution = normal.
This means that \(\mu = 69, \sigma = 10\)
If it is important that the pressure stays below 86 psi, what is the probability (in percent) that the pressure will exceed this value?
As a proportion, this probability is 1 subtracted by the pvalue of Z when X = 86. So
\(Z = \frac{X - \mu}{\sigma}\)
\(Z = \frac{86 - 69}{10}\)
\(Z = 1.7\)
\(Z = 1.7\) has a pvalue of 0.9554
1 - 0.9554 = 0.0446
0.0446*100 = 4.46%
4.46% probability that the pressure will exceed this value.
Evaluate 10 - (x + 3) when 2 = 2.
Answers
Answer:
5
Step-by-step explanation:
Im asuming you meant " x = 2 ".
According to PEMDAS, parenthese come first so...
10 - ( 2 + 3 )
= 10 - 5
= 5
Answer:
its 50
Step-by-step explanation:
10 times (x+3) x=2
2 plus 3 is 5
10 time 5
=50
a billboard designer has decided that a sign should have 5-ft margins at the top and bottom and 2-ft margins on the left and right sides. furthermore, the billboard should have a total area of 150 ft2 (including the margins). if x denotes the width (in feet) of the billboard, find a function in the variable x giving the area of the printed region of the billboard.
Answers
If x denotes the width (in feet) of the billboard, find a function in the variable x giving the area of the printed region of the billboard as a function of x is (150/x - 10)(x - 4).
A billboard designer has decided that a sign should have 5-ft margins at the top and bottom and 2-ft margins on the left and right sides.
x = width of the billboard designer
Total Area including margin = 150 ft^2
Height of the billboard = Area/width
Height of the billboard = 150/x
Before the height of the billboard = (150/x - 5 × 2)
Before the height of the billboard = (150/x - 10) ft
The width of the printed region billboard = (x - 2 × 2)
The width of the printed region billboard = (x - 4) ft
The area of the printed region of the billboard = The width of the printed region billboard × The height of the printed region billboard
The area of the printed region of the billboard = (150/x - 10)(x - 4)
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The complete question is:
A billboard designer has decided that a sign should have 5-ft margins at the top and bottom and 2-ft margins on the left and right sides. Furthermore, the billboard should have a total area of 150 ft^2 (including the margins).
If x denotes the width (in feet) of the billboard, find a function in the variable x giving the area of the printed region of the billboard.
Area as a function of x =
Can the two triangles be proven congruent by SAS? Explain.Question 9 options:A) No, because the two triangles share a side.B) Yes, because ≅ , ∠B ≅ ∠D, and and are parallel.C) No, there's only one pair of congruent angles, ∠B ≅ ∠D, and one pair of congruent sides, ≅ .D) Yes, because ≅ , ∠B ≅ ∠D, and and are parallel.
Answers
From the given figure,
We can observe that,
\(\begin{gathered} \angle B\cong\angle D(\text{Given)} \\ AB\cong CD(Since,\text{ it is a parallelogram)} \\ BC\cong DA(Since,\text{ it is a parallelogram)} \\ \Delta ABC\cong\Delta CDA \end{gathered}\)Hence, yes, the two triangles can be proven congruent by SAS.
Write an equation that helps D'angela determine the amount of money she must save each month to 500$ in her saving account
Answers
The equation that helps her is $65 + 5m = $500. D'angela must save $87 each month for the next 5 months to reach her goal of having $500 in her savings account.
What is system of equation?A group of equations that must be solved simultaneously is referred to as a system of equations. The variables in the equations are interconnected, and the set of values for the variables that satisfy all of the system's equations is the solution. Depending on whether the equations feature linear or nonlinear interactions between the variables, a system of equations can be either linear or nonlinear. A vast range of phenomena, including physical systems, economic systems, and social systems, are modelled using systems of equations, which appear in many branches of mathematics and science.
Let us suppose the amount of money saved by her = m.
The, for 5 months the amount saved is = 5m.
Given an initial deposit of $65, we have the equation of total amount as:
T = $65 + 5m
Now, she needs to save $500 thus,
$65 + 5m = $500
5m = $500 - $65
5m = $435
m = $87
Hence, D'angela must save $87 each month for the next 5 months to reach her goal of having $500 in her savings account.
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The complete question is:
A political scientist surveys 20 of the current 136 representatives in a state's legislature. What is the size of the sample : what is the size of population
Answers
Answer:
The size of the sample is 20.
The size of population is 136.
Step-by-step explanation:
In statistics, a sample is a portion or subset of a larger population. In this case, the political scientist has surveyed 20 of the 136 representatives in the state's legislature, so the size of the sample is 20.
The population is the complete set of individuals or items under consideration. In this case, the population is the entire set of 136 representatives in the state's legislature, so the size of the population is 136.
By surveying a sample of representatives, the political scientist can make inferences or draw conclusions about the population as a whole. However, the sample size will affect the precision and accuracy of these inferences. The larger the sample size, the more likely it is that the sample represents the population well.
I would greatly appreciate Brainliest.
Have a nice day.
Find the volume of a right rectangular prism that has a base area of 112 square feet and a height of 4 1/2
Answers
The volume of the right rectangular prism is 504 cubic feet.
To find the volume of a right rectangular prism with a base area of 112 square feet and a height of 4½ feet, we can use the formula:
Volume = Base Area x Height
First, we need to convert the height to feet and inches or decimal feet:
4½ feet = 4.5 feet
Now we can substitute the given values into the formula and calculate the volume:
Volume = 112 square feet x 4.5 feet
Volume = 504 cubic feet
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For the question of total area of the cuboid is 200cm^.
I understand where we divide 150 by 4.
But why do I need to multiply by 5, when there are 6 faces.
Answers
You need to multiply by 5 instead of 6 because each pair of opposite faces on a cuboid has the same area, so by considering one face from each pair, you ensure that you don't count any face twice.
When calculating the total surface area of a cuboid, you need to understand the concept of face pairs.
A cuboid has six faces, but each face has a pair that is identical in size and shape.
Let's break down the reasoning behind multiplying by 5 instead of 6 in the given scenario.
To find the surface area of a cuboid, you can add up the areas of all its faces.
However, each pair of opposite faces has the same area, so you avoid double-counting by only considering one face from each pair. In this case, you have five pairs of faces:
(1) top and bottom, (2) front and back, (3) left and right, (4) left and back, and (5) right and front.
By multiplying the average area of a pair of faces by 5, you account for all the distinct face pairs.
Essentially, you are considering one face from each pair and then summing their areas.
Since all the pairs have the same area, multiplying the average area by 5 gives you the total surface area.
When dividing 150 by 4 (to find the average area of a pair of faces), you are essentially finding the area of a single face.
Then, by multiplying this average area by 5, you ensure that you account for all five pairs of faces, providing the total surface area of the cuboid.
Thus, multiplying by 5 is necessary to correctly calculate the total surface area of the cuboid by accounting for the face pairs while avoiding double-counting.
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HELPPPP PLZ
Savannah drew a map of Texas for her Geography class. According to Savannah’s map scale, one-half inch on the map represents approximately 77.5 kilometers. If the actual distance from Austin to El Paso is approximately 930 kilometers, what is the approximate distance between Austin and El Paso on Savannah’s map?
A.24 inches
B.2 inches
C.6 inches
D.12 inches
Answers
Answer:
A
Step-by-step explanation:
Newton and Descartes have a 70-day summer vacation. They go to camp for 23/70 of their vacation, and they travel for 6/35 of their vacation. They stay home the rest of their vacation. How many weeks do Newton and Descartes spend at home?
Answers
5 weeks do Newton and Descartes spend at home. This can be solved using the concept of fractions.
What is fractions?In mathematics, the portion or component of the complete item is represented by a fraction. It stands for the equal components of the whole. Both the numerator and denominator are components of a fraction. The top number is referred to as the numerator, while the bottom number is referred to as the denominator.
Given that,
Newton and Descartes have a 70-day summer vacation
They go to camp for 23/70 of their vacation
= 70 × (23/70)
= 23
Next, they travel for 6/35 of their vacation
= 70 × (6/35)
= 12
So, they stay home the rest of their vacation
= 70 - 23 - 12
= 35
Now, they stay home (35 ÷ 7) = 5 weeks.
Therefore, 5 weeks do Newton and Descartes spend at home.
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A) Find an equation for the line perpendicular to the tangent line to the curve y=x^3-4x+6 at the point (2,6)
-The equation is y=
b) What is the smallest slope on the curve? At what point on the curve does the curve have this slope?
-The smallest slope on the curve is
-The curve has the smallest slope at the point
c) Find equations for the tangent lines to the curve at the points where the slope of the curve is 8.
Answers
Answer:
f(x) = x³ - 4x + 6
f'(x) = 3x² - 4
a) f'(2) = 3(2²) - 4 = 12 - 4 = 8
6 = 8(2) + b
6 = 16 + b
b = -10
y = 8x - 10
b) 3x² - 4 = 0
3x² = 4, so x = ±2/√3 = ±(2/3)√3
= ±1.1547
f(-(2/3)√3) = 9.0792
f((2/3)√3) = 2.9208
c) 3x² - 4 = 8
3x² = 12
x² = 4, so x = ±2
f(-2) = (-2)³ - 4(-2) + 6 = -8 + 8 + 6 = 6
6 = -2(8) + b
6 = -16 + b
b = 22
y = 8x + 22
f(2) = 6
y = 8x - 10
The equation perpendicular to the tangent is y = -1/8x + 25/4
-The smallest slope on the curve is 2.92
The curve has the smallest slope at the point (1.15, 2.92)
The equations at tangent points are y = 8x + 16 and y = 8x - 16
Finding the equation perpendicular to the tangentFrom the question, we have the following parameters that can be used in our computation:
y = x³ - 4x + 6
Differentiate
So, we have
f'(x) = 3x² - 4
The point is (2, 6)
So, we have
f'(2) = 3(2)² - 4
f'(2) = 8
The slope of the perpendicular line is
Slope = -1/8
So, we have
y = -1/8(x - 2) + 6
y = -1/8x + 25/4
The smallest slope on the curveWe have
f'(x) = 3x² - 4
Set to 0
3x² - 4 = 0
Solve for x
x = √[4/3]
x = 1.15
So, we have
Smallest slope = (√[4/3])³ - 4(√[4/3]) + 6
Smallest slope = 2.92
So, the smallest slope is 2.92 at (1.15, 2.92)
The equation of the tangent lineHere, we set f'(x) to 8
3x² - 4 = 8
Solve for x
x = ±2
Calculate y at x = ±2
y = (-2)³ - 4(-2) + 6 = 6: (-2, 0)
y = (2)³ - 4(2) + 6 = 6: (2, 0)
The equations at these points are
y = 8x + 16
y = 8x - 16
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which is the graph of y= 3^x + 1 - 2 HELP PLEASE
Answers
Answer:
Step-by-step explanation:
A customer asks for two money orders. The first is for the amount of $637.24 and the second
is for $25.76. If there is a $1.00 charge for each money order, what is the total amount the
customer would owe you?
Answers
Answer:
A customer asks for two money orders. The first is for the amount of $637.24 and the second
is for $25.76. If there is a $1.00 charge for each money order, what is the total amount the
customer would owe you?
A customer asks for two money orders. The first is for the amount of $637.24 and the second
is for $25.76. If there is a $1.00 charge for each money order, what is the total amount the
customer would owe you?
find f(2) PLEASE HELP SOLVE!! MATH!!!
Answers
The numeric value of the function f(x) = 14/[3 + ae^(kx)] at x = 2 is given as follows:
f(2) = 0.172.
How to obtain the numeric value of the function?The function for this problem is defined as follows:
f(x) = 14/[3 + ae^(kx)]
When x = 0, y = 2, hence we can obtain the coefficient a as follows:
2 = 14/(3 + a)
6 + a = 14
a = 8.
Hence:
f(x) = 14/[3 + 8e^(kx)]
When x = 1, y = 1/2, hence the coefficient k is given as follows:
0.5 = 14/(3 + 8e^k)
1.5 + 4e^k = 14
4e^k = 12.5
e^k = 12.5/4
k = ln(12.5/4)
k = 1.14.
Hence:
f(x) = 14/[3 + 8e^(1.14x)]
Then the numeric value of the function at x = 2 is given as follows:
f(2) = 14/[3 + 8e^(1.14(2))]
f(2) = 0.172.
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Sarah's after-school club has
5 groups of 9 students. Which
of these is a way to find the
total number of students?
A 10 X 4 - 5
B 10 X 5 + 9
C 10 X 5 - 5
D 10 X 5 - 9
Answers
Answer:
Definitely D good luck
A parabola has its vertex at (-6, 5) and focus at (-6.25, 5). Which of the following is an equation for this parabola?
Answers
Answer:
Step-by-step explanation:
vertex and focus are horizontally aligned, so parabola is horizontal.
focal length p = distance between focus and vertex = 0.25
focus lies to the left of vertex, so the parabola opens to the left.
x = a(y-k)² + h,
vertex (h,k)
a = -1/(4p)
vertex (-6,5)
h = -6
k = 5
p = 0.25
a = -1/(4·0.25) = -1
x = -(y-5)² - 6
SUPER DUPER EASY! LOTS OF POINTS! WILL MARK BRAINLIEST!
Write all numbers in the 900s that are factors of 4.
Answers
Answer:
900 904 908 912 916 920 924 928 932 936 940 944 948 952 956 960 964 968 972 976 980 984 988 992 996 (not 1000)
Step-by-step explanation:
Answer:
900
904
908
912
916
920
924
928
932
936
940
944
948
952
956
960
964
968
972
976
980
984
988
992
996
The function F is given in 3 equivalent forms.
Which form most quickly reveals the y intercept?
Look at image below
Part 2: what is the y intercept?
Answers
The form that most quickly reveals the y intercept is
B f(x) = 1/2 x² - 5x + 21/2The y intercept is (0, 21/2)
What is y-intercept?The y-intercept is the point where a function or a curve intersects the y-axis. In other words, it is the value of the dependent variable (y) when the independent variable (x) is equal to zero.
In the form, f(x) = 1/2 x² - 5x + 21/2 it is easier to see that eliminating x by plugging in 0 leaves 21/2 which is the y intercept
hence we can easily say that the y intercept is (0, 21/2)
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Help please ill mark brainliest tysm for helping if you do
Answers
Answer:
GFBH
Step-by-step explanation:
1 (- 3, - 2 ) ⇒ G
2 (3, 4 ) ⇒ F
3 (2, 0 ) ⇒ B
4 (1, - 3 ) ⇒ H
The code is GFBH
The distance between two towns is 120 kilometers. There are approximately 8 kilometers in 5 miles. How many miles are between the two towns?
Answers
Answer:
15 miles
Step-by-step explanation:
You know that there are 8 kilometres in 5 miles, so:
120/8=15
PLS SOMEONE HELP ASAP IT'S DUE TONIGHT TY AND ILYSM <3
if the trends in yearly median earnings continues for both men and women. how many years after 1960 will women have a median yearly eating that is greater than the men's? In what year will this occur?
Answers
Step-by-step explanation:
yes because women where making the food for the men so they where eating the most foodone number is 2 less than another. their sum is 16
Answers
7 and 9
7 is 2 less than 9
And 7+9=16
Hope this helps :)
State where in the ty-plane the hypotheses of the Existence and Uniqueness Theorem are satisfied for the equation y'=(ycot(2t))/(t^2+y^2+1)
Answers
We can conclude that the hypotheses of the Existence and Uniqueness Theorem are satisfied in any rectangular region in the ty-plane that does not contain the curve t² + y² = -1.
Where in the ty-plane the hypotheses of the existence and uniqueness theorem are satisfiedThe Existence and Uniqueness Theorem for first-order ordinary differential equations states that if a differential equation of the form y' = f(t, y) satisfies the following conditions in some rectangular region in the ty-plane:
1. f(t, y) is continuous in the region.
2. f(t, y) satisfies a Lipschitz condition in y in the region, i.e., there exists a constant L > 0 such that |f(t, y₁) - f(t, y₂)| ≤ L|y₁ - y₂| for all t and y₁, y₂ in the region.
then there exists a unique solution to the differential equation that passes through any point in the region.
In the case of the differential equation y' = (y cot(2t)) / (t² + y² + 1), we have:
f(t, y) = (y cot(2t)) / (t² + y² + 1)
This function is continuous everywhere except at the points where t² + y² + 1 = 0, which is the curve t² + y² = -1 in the ty-plane. Since this curve is not included in any rectangular region, we can say that f(t, y) is continuous in any rectangular region in the ty-plane.
To check if f(t, y) satisfies a Lipschitz condition in y, we can take the partial derivative of f with respect to y and check if it is bounded in any rectangular region. We have:
∂f/∂y = cot(2t) / (t² + y² + 1) - (2y² cot(2t)) / (t² + y² + 1)²
Taking the absolute value and simplifying, we get:
|∂f/∂y| = |cot(2t) / (t² + y² + 1) - (2y² cot(2t)) / (t² + y² + 1)²|
= |cot(2t) / (t² + y² + 1)| * |1 - (2y² / (t² + y² + 1)))|
Since 0 ≤ (2y² / (t² + y² + 1)) ≤ 1 for all t and y, we have:
1/2 ≤ |1 - (2y² / (t² + y² + 1)))| ≤ 1
Also, cot(2t) is bounded in any rectangular region that does not contain the points where cot(2t) is undefined (i.e., where t = (k + 1/2)π for some integer k). Therefore, we can find a constant L > 0 such that |∂f/∂y| ≤ L for all t and y in any rectangular region that does not contain the curve t² + y² = -1.
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