For the first question, to get the limit of the function lim (In V 4x2 + 6 - In x), we can use the property of logarithms that says ln(a) - ln(b) = ln(a/b). Applying this property to the given function, we get ln[(4x^2 + 6)/x]. Now we can simplify the expression by dividing both the numerator and the denominator by x. So we get ln(4x + 6/x), which can be rewritten as ln(4 + 6/x). Now we can take the limit as x approaches infinity. As x gets larger and larger, the 6/x term becomes smaller and smaller and approaches zero. So ln(4 + 6/x) approaches ln(4), and the final answer is A. In 2.
For the second question, to get the horizontal asymptote(s) of the function f(x) = 37€*, we can take the limit as x approaches infinity. As x gets larger and larger, the exponential term €* becomes larger and larger, approaching infinity. So the function approaches 37 times infinity, which is infinity. Therefore, there is no horizontal asymptote and the answer is D. none.
For the third question, the statement is false. The limit as x approaches infinity of 2^(ln(a)/ln(x)) is equal to infinity if a > 1 and is equal to zero if 0 < a < 1.
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3. (3 points) For ordinary differential equation
X =1- ƛx³6
with ƛ > 0, compute the update Ax= x(t+h) - x(t) using
⚫ Euler's method
⚫ the implicit Euler method
⚫ the midpoint method.
The following are the updates for the given ordinary differential equation using Euler's method, the implicit Euler method, and the midpoint method.
To compute the update Ax for the given ordinary differential equation using Euler's method, we first need to discretize the time domain. Let t0 be the initial time and tn = t0 + nh be the time after n steps of size h. Then, using Euler's method, we have:
xn+1 = xn + hf(xn, tn)
where f(xn, tn) = 1 - ƛxn³/6. Therefore,
Ax = xn+1 - xn = h(1 - ƛxn³/6)
Using the implicit Euler method, we have:
xn+1 = xn + hf(xn+1, tn+1)
where f(xn+1, tn+1) = 1 - ƛxn+1³/6. Solving for xn+1, we get:
xn+1 = (xn + h)/[1 + ƛh/6(xn+1)²]
which is a nonlinear equation that needs to be solved iteratively at each step. Therefore, the update Ax becomes:
Ax = xn+1 - xn
Using the midpoint method, we have:
xn+1 = xn + hf(xn+½h, tn+½h)
where f(xn+½h, tn+½h) = 1 - ƛ(xn+½h)³/6. Therefore,
xn+1 = xn + h(1 - ƛxn³/6 + 3ƛx²n h/4)
and the update Ax becomes:
Ax = xn+1 - xn = h(1 - ƛxn³/6 + 3ƛx²n h/4)
These are the updates for the given ordinary differential equation using Euler's method, the implicit Euler method, and the midpoint method.
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Research on the major types of businesses in your province. Based from the data you have gathered, create 1 revenue problem involving quadratic functions.
The top industries are agriculture, mining, tourism, and manufacturing.
The quadratic equations are as given.A manufacturing company in my fiefdom produces and sells ceramic pots.
The company has fixed costs of$ 10,000 per month and variable costs of$ 5 per pot. The company's profit is given by the quadratic function R( x) = -0.2 x2 50x, where x is the number of pots produced and vended in a month.
What's the maximum profit that the company can induce in a month: To break this problem, we can use the formula for chancing the maximum value of a quadratic function, which is given by x = - b/ 2a. In this case, the measure of the x2 term is-0.2, and the measure of the x term is 50. Plugging these values into the formula, we get x = -50/( 2 *(-0.2)) = 125 Hence we obtain the quadratic equation.
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solve by completing the square x^2-14x+49=16
ANSWER:
(x+7)^2=16
Step-by-step explanation:
x^2-14x+49=16
x^2-14x+49-16=0
x^2-14x+33=0
subtract -33 on both sides
x^2-14x+33-33=-33
x^2-14x=-33
Add 49 on both sides
x^2-14x+49=-33+49
x^2-14x+49=16
x^2-7x-7x+49=16
x(x-7)-7(x-7)=16
(x-7)(x-7)=16
(x-7)^2=16
Find the measure of angle D.
The measure of angle D is 25°
What is exterior angle theorem?Exterior angle theorem states that the measure of an exterior angle of a triangle is greater than either of the measures of the opposite interior angles.
Angle D and angle C are the two opposite angles.
Therefore;
40+9x-2 = 20x +5
38+9x = 20x +5
38-5 = 20-9x
11x = 33
divide both sides by 11
x = 33/11
x = 3
Therefore since angle D = 9x-2
substitute 3 for x
D = 9(3) - 2
D = 27 -2
D = 25°
Therefore the measure of angle D is 25°
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Create trig ratios for sin, cos, and tan
Sin(z) = 4/5, Cos(z) = 3/5, tan(z) = 4/3
We know that
sin(z) = perpendicular/hypotenuse
cos(z) = base/hypotenuse
tan(z) = perpendicular/base
Now putting we get,
Sin(z) = 4/5
Cos(z) = 3/5
tan(z) = 4/3
Two days after he bought a speedometer for his bicycle; Lance brought it back (0 the Yellow Jersey Bike Shop. FThele problemn with this speedomeler;' Ba Lance complained to the clerk "Yesterday [ cycled the 22-mile Rogadzo Road Trail in 70 minutes and nOt once did the speedometer read above [5 miles per hour"" Yeah?" responded the clerk " What' $ the problem?" To explain Lance's complaint, first compute his average velocity: (Use decimal notation. Give your answer tO two decimal places ) average velocity: DNE mileshcur Incorrecr
Therefore, Lance's average velocity was 15.43 miles per hour.
What is equation?An equation is a mathematical statement that shows that two expressions are equal. It consists of two sides, left-hand side (LHS) and right-hand side (RHS), connected by an equal sign (=). The LHS and RHS can contain numbers, variables, operators, and functions, and the equal sign indicates that the value of the expression on the LHS is equal to the value of the expression on the RHS.
Here,
We can compute Lance's average velocity by dividing the total distance he cycled by the time it took him, and then converting the units to miles per hour.
Total distance: 22 miles
Time: 70 minutes = 70/60 hours
= 7/6 hours
Average velocity = Total distance / Time
= 22 / (7/6)
= 15.43 miles per hour (rounded to two decimal places)
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Question 6 < - Find the linear approximation of f(x) = In x at x = 1 and use it to estimate In(1.16). L(x) = In(1.16) Question Help: Video Message instructor Submit Question Question 5 Use linear ap
The linear approximation of f(x) = ln(x) at x = 1 is L(x) = x - 1. Using this approximation, we can estimate ln(1.16) to be approximately 0.16.
The formula for the linear approximation of a function f(x) at a point x = a is given by L(x) = f(a) + f'(a)(x - a), where f'(a) is the derivative of f(x) evaluated at x = a.
In this case, f(x) = ln(x), so f'(x) = 1/x by the derivative of natural logarithm.
We are asked to find the linear approximation of f(x) = ln(x) at x = 1, so a = 1 in the formula.
Plugging in the values, we get L(x) = ln(1) + 1( x - 1) = x - 1.
Now, we can use this linear approximation L(x) = x - 1 to estimate ln(1.16) by plugging in x = 1.16, as given in the question.
L(1.16) = 1.16 - 1 = 0.16, which is our estimated value for ln(1.16) using the linear approximation.
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y=1.5 In(et.t+5) for t=1; round your answer to the whole number (exponent "t.t" read (means) t square)
when t=1, y is approximately equal to 5.
To solve for y when t=1 in the equation y=1.5 In(et.t+5), we first need to plug in t=1:
y=1.5 In(e(1)(1)+5)
We simplify the exponent e(1)(1) to just e:
y=1.5 In(e+5)
Using the properties of natural logarithms, we can simplify this further:
y=1.5(1+ln(5+e))
We can use a calculator to evaluate ln(5+e) to be approximately 2.063, so we can plug that in and simplify:
y=1.5(1+2.063)
y=1.5(3.063)
y=4.5945
Rounding this answer to the nearest whole number, we get:
y=5
Therefore, when t=1, y is approximately equal to 5.
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Which correctly compares the numbers? 158,364 > 158,379 > 158,397 158,364 > 158,379 > 158,397 518,317 > 518,246 > 518,197 518,317 > 518,246 > 518,197 290,061 > 289,937 > 290,324 290,061 > 289,937 > 290,324 678,200 > 678,194 > 678,227
The correct comparison of the numbers is:
678,200 > 678,194 > 678,227
Therefore, the answer is the last option, "678,200 > 678,194 > 678,227".
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Find the radius of an eyebrow window with width 62.8 inches and height 18.5 inches
The radius of an eyebrow window with a width of 62.8 inches and a height of 18.5 inches is approximately 36.7 inches.
To find the radius of an eyebrow window, we first need to understand its shape. An eyebrow window is a type of arched window that has a curved shape similar to that of an eyebrow. The shape of an eyebrow window is created by a combination of a circular arc and a straight line.
To find the radius of an eyebrow window with a width of 62.8 inches and a height of 18.5 inches, we need to use some geometry formulas. The height of the eyebrow window represents the height of the circular arc, and the width represents the diameter of the circle.
The formula for the radius of a circle is r = d/2, where r is the radius and d is the diameter. To find the diameter, we divide the width by pi (3.14). So, the diameter is 62.8/3.14 = 20 inches.
The height of the circular arc is half of the width, which is 18.5/2 = 9.25 inches. To find the radius, we use the formula for the height of a circular arc, h = r(1-cos(a/2)), where h is the height, r is the radius, and a is the angle of the arc.
The angle of the arc can be found using trigonometry. The sine of half the angle is equal to the height divided by the radius. So, sin(a/2) = h/r. Solving for a, we get a = 2arcsin(h/r).
Plugging in the values, we get a = 2arcsin(9.25/r). To find the radius, we solve for r using a calculator or algebra. The radius is approximately 36.7 inches.
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Find the indicated probability using the two/way table: p(drive to school | senior)
The probability that a senior drives to school is 0.3 or 30%.
To find the indicated probability using the two-way table, we need to locate the row for "senior" and the column for "drive to school" and then find the corresponding cell.
Let's assume that the two-way table shows the number of students who either drive or take the bus to school based on their grade level. We are interested in finding the probability that a student drives to school given that they are a senior.
So, we locate the row for "senior" and the column for "drive to school". Let's say that the cell in the intersection of these two is labeled "30". This means that there are 30 seniors who drive to school.
Next, we need to find the total number of seniors in the sample. Let's say that the total number of seniors in the sample is 100.
To find the probability that a senior drives to school, we divide the number of seniors who drive to school by the total number of seniors in the sample:
P(drive to school | senior) = 30/100 = 0.3 or 30%
Therefore, the probability that a senior drives to school is 0.3 or 30%.
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Nicole has 28 nickels and dimes that amount to $1. 85 how many of each coin does she have
Answer:
Nicole has 9 dimes and 19 nickels.
LA and LB are vertical angles. If mLA=(x+21)° and mLB=(4x-30)°, the find then measure of LB
Answer:
38 degrees
Step-by-step explanation:
Vertical angles are congruent(equal measures), so mLA = mLB
STEP 1:
Let's use some simple substitution.
mLA = mLB
mLA = x+21, mLB = 4x-30
You plug these two in and get:
x+21 = 4x-30
This is your equation.
STEP 2:
Let's solve our equation!
x+21 = 4x-30
(add 30 to both sides)
x+51 = 4x
(subtract x from both sides)
51 = 3x
(switch order for comprehension)
3x = 51
(divide both sides by 3)
x = 17
Ta-da! You get the measure of x = 17 degrees.
STEP 3:
Let's plug in our value of x to get the value of LB.
mLB = 4x - 30
mLB = 4(17) - 30
mLB = 68 - 30
mLB = 38
This is your answer.
6 Moses makes a school spirit flag. He has as many yards of red fabric as blue
fabric. He buys 2 yards more red fabric. Now he has equal amounts of red and
blue fabric. Use x to represent the amount of blue fabric. Which equations could
you use to find the amount of red fabric Moses has? Select all that apply.
A X =
B x= x + 2?
x = 2
1/x + 273
x= 1/3x - 223
E x + 2 2 2 = 1/3 x + 2 2 3
C X=
D x- 27 28 = 1/3 x
F * = }}x+ 2
2 2 3
The equations to find the amount of red fabric Moses has are X = x + 2 and X + 222 = 1/3x + 223. These equations are obtained by using x as the amount of blue fabric and setting up equations based on the given information. So, the correct answer is A) and E).
There are two equations that can be used to find the amount of red fabric Moses has
X = x + 2, This equation represents the fact that Moses bought 2 more yards of red fabric than he originally had of blue fabric. So, the amount of red fabric (X) is equal to the amount of blue fabric (x) plus 2.
X + 222 = 1/3x + 223, This equation represents the fact that after buying 2 more yards of red fabric, Moses has equal amounts of red and blue fabric.
So, the amount of red fabric (X) plus 222 (the additional 2 yards he bought) is equal to one-third of the amount of blue fabric (1/3x) plus 223 (the original 2 yards of red fabric he had).
Therefore, the equations that could be used to find the amount of red fabric Moses has are A) and E).
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--The given question is incomplete, the complete question is given
" 6 Moses makes a school spirit flag. He has as many yards of red fabric as blue fabric. He buys 2 yards more red fabric. Now he has equal amounts of red and blue fabric. Use x to represent the amount of blue fabric. Which equations could you use to find the amount of red fabric Moses has? Select all that apply.
A X = x + 2
B x = 2
C 1/x + 273
D x= 1/3x - 223
E x + 2 2 2 = 1/3 x + 2 2 3
F x- 27 28 = 1/3 x
G = x+ {{22}*2}^3 "--
how much money do winners go home with from the television quiz show jeopardy? to determine an answer, a random sample of winners was drawn and the amount of money each won was recorded and listed below. estimate with 98% confidence the mean winning's for all the show's players. 256592886121164159762297615479276802828316105181371690216879240102008815149
The mean winnings for all of the show's contestants can be estimated with 92% certainty. 35014.48385 is the lower bound, while 40669.38281 is the upper bound.
Lower Bound = [tex]X - t(\alpha/2) * s / \sqrt{(n)[/tex]
Upper Bound = [tex]X + t(\alpha/2) * s / \sqrt{(n)[/tex]
where
[tex]\alpha/2 = (1 - confidence\: level)/2 = 0.04 \\ X = sample\: mean = 37841.93333 \\ t(\alpha/2) = critical\: t \:for \:the\: confidence\: interval = 1.887496145 \\ s = sample\: standard\: deviation = 5801.688541 n = sample\: size = 15 \\ df = n - 1 = 14[/tex]
Thus,
Lower bound = 35014.48385
Upper bound = 40669.38281
A lower bound refers to the smallest possible value or limit that a given quantity or parameter can take. In various fields of mathematics and computer science, lower bounds are used to establish limits on the performance of algorithms, the complexity of computational problems, and the amount of resources required to solve a problem. This information can be useful in developing more efficient algorithms or determining the practicality of a given approach.
Lower bounds are useful for understanding the fundamental limits of a system or process. By establishing a lower bound, researchers and practitioners can better understand the potential of a given technology or approach, and can work to optimize it within the constraints imposed by the lower bound.
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Complete Question:-
How much money do winners go home with from the television quiz show Jeopardy? To determine an answer, a random sample of winners was drawn and the amount of money each won was recorded and listed below. Estimate with 92% confidence the mean winning's for all the show's players.
30692 43231 48269 28592 28453
36309 45318 36362 42871 39592
35456 40775 36466 36287 38956
Lower confidence level (LCL) = ?
Upper confidence level (UCL) = ?
HELP PLEASE BRAINLIEST + POINTS
Answer:
CD = 34 units--------------------------
Since CD is diameter, therefore the angle CAD opposite to it is a right angle.
We are given the lengths of two legs, AD = 16 and AC = 30.
Use Pythagorean theorem to find the length of the hypotenuse CD:
CD² = AD² + AC²CD² = 16² + 30²CD² = 1156CD = √1156CD = 34The number of coyotes found in certain state counties is decreasing at a rate of 4. 5% per year. A wildlife biologist recently counted 100 coyotes in one tri-county area. The biologist uses a function to model the population over time and then uses this model to predict the coyote population. Which function model did the biologist correctly use to predict when the population would be fewer than 50 in this tri-county area?
The biologist predicts that the population would be fewer than 50 in approximately 30 years from the initial count.
The biologist likely used the exponential decay function to model the coyote population over time. This function takes the form:
P(t) = P0 * (1 - r)^t
Where:
P(t) is the population at time t,
P0 is the initial population (100 coyotes),
r is the rate of decrease (0.045 or 4.5%),
t is the time in years.
To predict when the population would be fewer than 50, the biologist would solve the equation:
50 = 100 * (1 - 0.045)^t
t = 30
This equation can be used to find the value of t, which represents the number of years it takes for the population to decrease to fewer than 50 coyotes in the tri-county area, which is 30 years.
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CD is a perpendicular bisector of chord AB and a chord through CD passes through the center of a circle. Find the diameter of the wheel.
The figure shows a circle. Points A, C, B, E lie on the circle. Chords A B and C E intersect at point D. The length of segment A B is 12 inches. The length of segment C D is 4 inches.
715 in.
10 in.
1425 in.
1215 in.
Need Help ASAP please!!!
We know that the diameter of the wheel is 1215 inches
Since CD is a perpendicular bisector of AB, it means that CD passes through the center of the circle. Let O be the center of the circle. Then OD is the radius of the circle.
Since chord CE passes through the center O, it is a diameter of the circle. Therefore, CE = 2OD.
Let's use the intersecting chords theorem to find OD.
According to the intersecting chords theorem,
AC * CB = EC * CD
We know that AC = CB (since they are radii of the same circle) and CD = 4 inches. We also know that AB = 12 inches. Let's call the length of segment AE x. Then the length of segment EB is 12 - x.
So we have:
x * (12 - x) = EC * 4
Simplifying:
12x - x^2 = 4EC
Rearranging:
EC = 3x - x^2/4
Now let's use the intersecting chords theorem again, but this time for chords AB and CD:
AC * CB = AD * DB
We know that AC = CB and AB = 12 inches. Let's call the length of segment AD y. Then the length of segment DB is 12 - y.
So we have:
x^2 = y * (12 - y)
Simplifying:
y^2 - 12y + x^2 = 0
Using the quadratic formula:
y = (12 ± sqrt(144 - 4x^2))/2
We can discard the negative solution (since y is the length of a segment, it cannot be negative), so:
y = 6 + sqrt(36 - x^2)
Now let's use the fact that CD is a perpendicular bisector of AB to find x.
Since CD is a perpendicular bisector of AB, it divides AB into two segments of equal length. Therefore,
AD = DB = 6
Using the Pythagorean theorem in triangle ACD:
AC^2 + CD^2 = AD^2
Substituting the values we know:
x^2 + 4^2 = 6^2
Solving for x:
x = sqrt(20)
Now we can find EC:
EC = 3x - x^2/4
Substituting x:
EC = 3sqrt(20) - 5
Finally, we can find OD:
AC * CB = EC * CD
Substituting the values we know:
(2OD)^2 = (3sqrt(20) - 5) * 4
Simplifying:
OD^2 = 12sqrt(20) - 20
OD = sqrt(12sqrt(20) - 20)
We are asked to find the diameter of the circle, which is twice the radius:
Diameter = 2OD = 2sqrt(12sqrt(20) - 20)
This is approximately equal to 1215 inches.
So the answer is:
The diameter of the wheel is 1215 inches.
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roger purchased a pair of pants for 34.50 and a new a new for 12.00 he had a 10% discount on his total purchased and paid 8.5% sales tax what was the total for rogers purchased
After the discount and the tax, the amount that Roger pays is $45.41
How to find the final price?We know that Roger purchased a pair of pants for 34.50 and a new a new for 12.00 he had a 10% discount on his total purchased and paid 8.5% sales tax, then the total cost before the discount and tax is:
C = 12.00 + 34.50 = 46.50
Now we apply the discount and the tax (as factors in a product) to get:
C' = 46.50*(1 - 0.1)*(1 + 0.085) = 45.41
That is the amouint that Roger pays for the two items.
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The mean number of sit-ups
done by a group of students is
46 with a standard deviation
of 7. If Rylee's Z-score was
1. 8, how many sit ups did she
do?
Rylee did approximately 58.6 sit-ups.
We are given that the mean number of sit-ups is 46 and the standard deviation is 7. We are also given that Rylee's Z-score was 1.8, we can use the formula for Z-score to find how many sit-ups she did.
The formula for Z-score is [tex]Z = \frac{X-\mu}{\sigma}[/tex]
Z = Z-score
μ = mean
σ = standard deviation
X = ?
Substituting these values into the formula
1.8 = (X - 46)/7
1.8 × 7 = X - 46
X - 46 = 12.6
X = 12.6 + 46
X = 58.6
Therefore, Rylee did approximately 58.6 sit-ups.
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It is kinda hard but just try it
Answer:
we 1st can get the weight of rat by
1 rat and 1 cat + 1 dog and rat = 30
2 rat + 1 cat + 1 dog = 30
Then 1 rat and cat measure 24 so
2 rat + 24 =30
2 rat + 24 =30 1 rat = 3 kg
2 rat + 24 =30 1 rat = 3 kg 1 cat + 1 rat = 10
2 rat + 24 =30 1 rat = 3 kg 1 cat + 1 rat = 101 cat + 3kg = 10
2 rat + 24 =30 1 rat = 3 kg 1 cat + 1 rat = 101 cat + 3kg = 101 cat = 7kg and
2 rat + 24 =30 1 rat = 3 kg 1 cat + 1 rat = 101 cat + 3kg = 101 cat = 7kg and 1 dog + 1 rat = 20 kg
2 rat + 24 =30 1 rat = 3 kg 1 cat + 1 rat = 101 cat + 3kg = 101 cat = 7kg and 1 dog + 1 rat = 20 kg 1 dog + 3kg = 20 kg
2 rat + 24 =30 1 rat = 3 kg 1 cat + 1 rat = 101 cat + 3kg = 101 cat = 7kg and 1 dog + 1 rat = 20 kg 1 dog + 3kg = 20 kg 1 dog = 17kg
so we get the weight of each now we r going to sum them 1 rat + 1 cat + 1 dog = x
1 rat + 1 cat + 1 dog = x 3 kg + 7 kg + 17 kg = x
1 rat + 1 cat + 1 dog = x 3 kg + 7 kg + 17 kg = x 27 kg = x ..... is the mass of 3 of them
Issac wants to save up some money to buy a new smartphone, so he babysits on the weekends. There is a proportional relationship between the time Oscar spends babysitting(in hours) , z, and the amount of money he earns babysitting(in dollars) , y. What is the constant of proportionality? Write your answer as a whole number or decimal
The constant of proportionality represents the rate at which Issac earns money while babysitting and can be found by dividing the amount of money he earns by the time spent babysitting.
Let's say that Issac earns $10 per hour of babysitting. Then, the constant of proportionality would be:
$10 per hour = $10/1 hour = 10
Therefore, the constant of proportionality is 10, which means that Issac earns $10 for every hour of babysitting. This relationship is an example of proportionality because the amount of money earned is directly proportional to the time spent babysitting. As Issac spends more time babysitting, he will earn more money in a proportional relationship.
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If (arc)mEA=112* and m
If angle of arc EA is 112 degrees then value of arc IV is 36 degrees by outside angles theorem
Given that Arc EA measure is One hundred twelve degrees
By Outside Angles Theorem states that the measure of an angle formed by two secants, two tangents, or a secant and a tangent from a point outside the circle is half the difference of the measures of the intercepted arcs
(112-x)/2=38
112-x=38×2
112-x=76
112-76=x
36 degrees = angle IV or x
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what is the value of sin 45 but as a fraction?
The exact value of sin 45° is [tex]\dfrac{\sqrt{2} }{2}[/tex]
Since we have given that
[tex]\text{sin} \ 45^\circ[/tex]
We need to find the exact value of sin 45°.
From the trigonometric table,
[tex]\text{sin} \ 45^\circ=\dfrac{1}{\sqrt{2}}[/tex]
We need to write it as a simplified fraction,
So, for this, we will rationalize the denominator:
[tex]\dfrac{1}{\sqrt{2}}\times\dfrac{\sqrt{2} }{\sqrt{2}}[/tex]
[tex]=\dfrac{\sqrt{2} }{2}[/tex]
Hence, the exact value of sin 45° is [tex]\dfrac{\sqrt{2} }{2}[/tex]
Answer: 1 divided by the square root of 2
Step-by-step explanation:
Let's set up an example, if the angle is forty five degrees, and the opposite length is 1, we can solve this as sin to get to the hypotenuse,
1. sin(45) = 1/hyp
2. sin(45) times hyp = 1
3. hyp = sin(45)/1
If we take any answer and put it over the hypotenuse as sin, we can see that it is going to end up as 1/√2, or 0.707
I did 1 because you are just asking for sin(45).
Estimate the radius of the object. Round to the nearest hundredth if necessary.
C = 8. 9 mm
radius: about
mm
The estimated radius of the object is about 1.42 mm.
The given information is that the circumference( C) of the object is8.9 mm.
We know that the formula for the circumference of a circle is given by
C = 2πr
where r is the compass of the circle.
To estimate the compass, we can rearrange the formula as
r = C/ 2π
Substituting the given value of C, we get
r = 8.9/ 2π
we can estimate this expression to get
r ≈1.42 mm( rounded to two decimal places)
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Find the divergence of vector fields at all points where they are defined.
div ( (2x^2 - sin(x2)) i + 5] - (sin(X2)) k)
The divergence of the given vector field at all points where it's defined is div [tex]F = 4x - 2x × cos(x^2).[/tex]
To find the divergence of the given vector field at all points where it's defined, we will use the following terms:
divergence, vector field, and partial derivatives.
The given vector field is[tex]F = (2x^2 - sin(x^2)) i + 5j - sin(x^2) k.[/tex]
To find the divergence of F (div F), we need to take the partial derivatives of each component with respect to their
respective variables and then sum them up. So, div [tex]F = (∂(2x^2 - sin(x^2))/∂x) + (∂5/∂y) + (∂(-sin(x^2))/∂z)[/tex].
Find the partial derivative of the first component with respect to x:
[tex]∂(2x^2 - sin(x^2))/∂x = 4x - 2x × cos(x^2)[/tex] (applying chain rule).
Find the partial derivative of the second component with respect to y:
∂5/∂y = 0 (since 5 is a constant).
Find the partial derivative of the third component with respect to z:
[tex]∂(-sin(x^2))/∂z = 0[/tex] (since there is no z variable in the component).
Sum up the partial derivatives:
[tex]div F = (4x - 2x × cos(x^2)) + 0 + 0 = 4x - 2x × cos(x^2).[/tex]
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(My question has a part A and part B)
The salesperson earns a 5%
commission on the first $5000
she has in sales. • The salesperson earns a 7. 5%
commission on the amount of her sales that are greater than.
Part A
This month the salesperson had $1,375
in sales. What amount of commission, in dollars, did she earn?
A) The total commission she earned is $475
B) Total sales for commission of $1375 is $20000
How to calculate the amount of commission?A) Total Commission = Commission 1+ Commission 2
Where:
Commission 1 = 5% of first $5000
Commission 2 = 7.5% of the amount left after $5000 is subtracted
thus
Commission 1 = $5000 * 0.05 = $250
Commission 2= $3000 * 0.075 = $225
Commission total = $250 + $225 = $475
The total commission she earned is $475
B) Total sales = Sales with 5% commission + Sales with 7.5% commission
Sales with 5% commission = $5000
Commission At 7.5% = Total commission -Commission with 5% = $1375 - $250
Sales * 0.075 = $1125
Sales with 7.5% commission = $15000
Total sales = $5000+$15000
Total sales = $20000
Total sales for commission of $1375 is $20000
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Complete question is:
A salesperson earns commission on the sales that she makes each month. The salesperson earns a 5% commission on the first $5,000 she has in sales.
The salesperson earns a 7.5% commission on the amount on her sales that are greater than $5,000.
Part A:
This month the salesperson had $8,000 in sales. What amount of commission, in dollars, did she earn?
Part B:
The salesperson earned $1,375 in commission, last month. How much money, in dollars, did she have in sales last month?
Hunter needs 10 ounces of a snack mix that is made up of seeds and dried fruit. the
seeds cost $1.50 per ounce and dried fruit costs $2.50 per ounce. hunter has $22
to spend and plans to spend it all.
let x = the amount of seeds
let y = the amount of dried fruit
part 1: create a system of equations to represent the scenario. (2 points)
part 2: solve your system using any method. write your answer as an ordered pair. (2
points)
Hunter needs 3 ounces of seeds and 7 ounces of dried fruit, which will cost him $22 in total. The system of equations is 1.5x + 2.5y = 22 and x + y = 10. The solution is (x,y) = (3,7).
The total amount of snack mix required is 10 ounces. So, the sum of the amount of seeds and dried fruit should be 10.
x + y = 10 ---(Equation 1)
The cost of seeds is $1.50 per ounce and the cost of dried fruit is $2.50 per ounce. The total cost of snack mix should be $22.
1.50x + 2.50y = 22 ---(Equation 2)
To solve the system, we can use substitution method. Solving Equation 1 for y, we get
y = 10 - x
Substituting this value of y in Equation 2, we get
1.5x + 2.5(10 - x) = 22
Simplifying and solving for x, we get
1.5x + 25 - 2.5x = 22
-x = -3
x = 3
So, Hunter needs 3 ounces of seeds and 7 ounces of dried fruit to make 10 ounces of snack mix with a total cost of $22.
The ordered pair is (3, 7).
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4
Consider the inequalities -1/4a > 3 a and b – 12> -3. What values, if any, make
both inequalities true? Show your work.
To solve the inequality -1/4a > 3a, we need to first multiply both sides by -4 to get rid of the fraction:
-1a > 12a
Next, we can subtract 12a from both sides to get:
-13a > 0
Dividing both sides by -13 gives us:
a < 0
To solve the inequality b – 12 > -3, we can add 12 to both sides:
b > 9
Now we need to find values of a and b that satisfy both inequalities. Since a < 0, we can try any negative value of a. Let's try a = -1:
-1/4(-1) > 3(-1)
1/4 > -3
This inequality is true, so we can move on to the next inequality. Let's plug in a = -1 and see if it satisfies b > 9:
b – 12 > -3
b > 9
Since -1 satisfies both inequalities, the values that make both inequalities true are: a = -1 and any value of b greater than 9.
If f(x) = 3(5") + x and g(x) = 3cos(x), what is (f9)'()? O (3(5*) In(5) + 1)(3cos(x)) + (3(5") + x)(sin(x)) O (3(5") In(5) + 1)(3sin(x)) O (3(5") In(5) + 1)(-3sin(x)) O (3(5) In(5) + 1)(3cos(x)) + (3(5") + x)(-3sin(x))
The derivative of (f∘g)(x) can be found using the chain rule, which states that the derivative of (f∘g)(x) is (f'(g(x)))(g'(x)).
In this case, (f∘g)(x) = f(g(x)) = 3(5^x) + 3cos(x), so we need to find f'(g(x)) and g'(x) and then multiply them together. The derivative of f(x) is f'(x) = 15^x * ln(5) + 1, so the derivative of f(g(x)) with respect to g(x) is f'(g(x)) = 15^(g(x)) * ln(5) + 1. The derivative of g(x) is g'(x) = -3sin(x). Therefore, using the chain rule, we have:(f∘g)'(x) = f'(g(x)) * g'(x) = (15^(g(x)) * ln(5) + 1) * (-3sin(x))Substituting g(x) = 3cos(x), we get:(f∘g)'(x) = (15^(3cos(x)) * ln(5) + 1) * (-3sin(x))So the correct answer is: (3(5^3cos(x)) ln(5) + 1) * (-3sin(x))
For more similar questions on topic a) The intervals for which f(x) = -5.5sin(x) + 5.5cos(x) is concave up and concave down on [0,2π] can be found by analyzing the second derivative of the function. Taking the second derivative of f(x), we get:
f''(x) = -5.5cos(x) - 5.5sin(x)
To find the intervals of concavity, we need to determine where f''(x) is positive and negative.
When f''(x) > 0, the function is concave up. When f''(x) < 0, the function is concave down.
Setting f''(x) = 0, we get:
-5.5cos(x) - 5.5sin(x) = 0
Simplifying, we get:
cos(x) + sin(x) = 0
Solving for x, we get:
x = 3π/4, 7π/4
These are the possible points of inflection for the function.
Using test intervals, we can determine the intervals of concavity:
When 0 ≤ x < 3π/4 or 7π/4 < x ≤ 2π, f''(x) < 0, so f(x) is concave down.
When 3π/4 < x < 7π/4, f''(x) > 0, so f(x) is concave up.
b) The possible points of inflection for f(x) on [0,2π] are x = 3π/4 and x = 7π/4. To find the coordinates of these points, we can substitute each value of x into the original function f(x):
f(3π/4) = -5.5sin(3π/4) + 5.5cos(3π/4) = 5.5√2 - 5.5√2/2 = 5.5√2/2
So the coordinates of the point of inflection at x = 3π/4 are (3π/4, 5.5√2/2).
Similarly, we can find the coordinates of the point of inflection at x = 7π/4:
f(7π/4) = -5.5sin(7π/4) + 5.5cos(7π/4) = -5.5√2 - 5.5√2/2 = -5.5(3/2)√2
So the coordinates of the point of inflection at x = 7π/4 are (7π/4, -5.5(3/2)√2).
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