Answers
The most convenient way to capture [tex]D[/tex] is with the parameterization
[tex]D = \left\{(x,y) \mid -1 \le y \le 3 \text{ and } -\dfrac{y+1}2 \le x \le y+1\right\}[/tex]
so we only need one iterated integral.
[tex]\displaystyle \iint_D e^{x-y} \, dA = \int_{-1}^3 \int_{-(y+1)/2}^{y+1} e^{x-y} \, dx \, dy[/tex]
Compute the integral with respect to [tex]x[/tex].
[tex]\displaystyle \int_{-(y+1)/2}^{y+1} e^{x-y} \, dx = e^{x-y} \bigg|_{x=-(y+1)/2}^{x=y+1} = e^{(y+1)-y} - e^{-(y+1)/2-y} = e - e^{-(3y+1)/2}[/tex]
Compute the remaining integral.
[tex]\displaystyle \int_{-1}^3 \left(e - e^{-(3y+1)/2}\right) \, dy = \left(ey + \frac23 e^{-(3y+1)/2}\right)\bigg|_{y=-1}^{y=3} \\\\ ~~~~~~~~ = \left(3e + \frac23 e^{-(9+1)/2}\right) - \left(-e + \frac23 e^{-(-3+1)/2}\right) \\\\ ~~~~~~~~ = \boxed{\frac{10e}3 + \frac2{3e^5}}[/tex]
If we had chosen the opposite order of variables, we would have used
[tex]D = \left\{(x,y) \mid -2 \le x \le 4 \text{ and } \max\left(-2x-1,x-1\right)\le y\le3\right\}[/tex]
where
[tex]\max(-2x-1, x-1) = \begin{cases} -2x-1 & \text{when } x<0 \\ x-1 & \text{when } x\ge0\end{cases}[/tex]
so we would have needed two iterated integrals,
[tex]\displaystyle \iint_D e^{x-y} \, dA = \int_{-2}^0 \int_{-2x-1}^3 e^{x-y} \, dy \, dx + \int_0^4 \int_{x-1}^3 e^{x-y} \, dy \, dx[/tex]
Related Questions
What is the probability that the top-three finishers in the contest will
all be seniors?
Type in the correct answer in each box. Use numerals instead of
words. If necessary, round your answers to the nearest tenth.
Answers
Answer: Just guessing, try.. or dont.
Step-by-step explanation:
There are 3 seniors. To make up 100% we would have to do 33.33%. I would say that the probabilty is around 33.33, and don't know the different orders possible.
HELP!!! A,B,or C
Eric was rock climbing. At one point, he stopped and climbed straight down 2 1/2 meters. Then he climbed straight up 6 3/4 meters.Eric was wondering what his change in elevation was after these two moves.
Answers
Let’s think of his current location as 0
Since he climbed down 2 1/2 meters, u would think of it as 0 - 2 1/2 which equals - 2 1/2
Now his current location is - 2 1/2
Then he goes up 6 3/4 so to get his new location, we would simply add 6 3/4 to -2 1/2
So the answer would be -2 1/2 + 6 3/4 which would be B! Hope this helps!!
what the milk and and butter
Answers
Answer:
1/4 cups of milk and 1 1/3 Tbsp of butter.
Step-by-step explanation:
Milk : 3/4 multiplied by 1/3 = 3/12 = 1/4
Butter : 4 multiplied by 1/3 = 4/3 = 1 1/3
……hellppppppppp nowwwe
Answers
Answer:
18 miles
Step-by-step explanation:
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A binomial experiment is given. Decide whether you can use the normal distribution to approximate the binomial distribution. If you can, find the mean and standard
deviation. If you cannot, explain why.
A survey of adults found that 66% have used a multivitamin in the past 12 months. You randomly select 40 adults and ask them if they have used a multivitamin in the
past 12 months.
Select the correct answer below and, if necessary, fill in the answer boxes within your choice.
OA. No, because np < 5.
B. No, because nq <5.
OC. Yes, the mean is_______
(Round to two decimal places as needed.)
and the standard deviation is _____
Answers
Yes, the mean is 26.4 and the standard deviation is 3
How to find the mean in binomial experiment?We are given;
n = 40, p = 66% = 0.66, and q = 1 – 0.66 = 0.34
If np ≥ 5 and np ≥ 5, then the binomial random variable, x is approximately normally distributed, then;
Mean; µ = np
Standard deviation; σ = √npq
where;
n is the sample size.
p is the population proportion.
q = 1 – p.
Calculating np and nq gives;
np = (40)(0.66) = 26.4
nq = (40)(0.34) = 13.6
Both np and nq are greater than 5, the normal distribution can be used to approximate the binomial distribution.
Thus, µ = np
µ = 40(0.66) = 26.4
Standard deviation;
σ = √(40 * 0.66 * 0.34)
σ = 3
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Ramiro was on a 2-day road trip. On the first day he drive at an average speed 40 mph. On the second day he drove at an average speed of 60 mph. If he drove 2 hours. If he drove 2 hours longer and went 20 miles farther on the first day, find the total distance Ramiro traveled on his first road trip
Answers
Y = second day hours
x = y + 2
40x = 60y + 20
40(y + 2) = 60y + 20
40y + 80 = 60y + 20
60 = 20y
y = 3 hours on day 2
x = y + 2
x = 3 + 2
x = 5 hours on day 1
Miles = 40(5) + 60(3)
200 + 180
380 miles
The total distance Ramiro travelled is 380 miles.
What is equation?Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign. It shows the relationship of equality between the expression written on the left side with the expression written on the right side. In every equation in math, we have, L.H.S = R.H.S (left hand side = right hand side).
Parts of an EquationThere are different parts of an equation which include coefficients, variables, operators, constants, terms, expressions, and an equal to sign. When we write an equation, it is mandatory to have an "=" sign, and terms on both sides. Both sides should be equal to each other. An equation doesn't need to have multiple terms on either of the sides, having variables, and operators. An equation can be formed without these as well, for example, 5 + 10 = 15. This is an arithmetic equation with no variables. As opposed to this, an equation with variables is an algebraic equation.
let x be the first day hours
let y be the second day hours.
now,
x = y + 2
40x = 60y + 20
Putting x= y+2
40(y + 2) = 60y + 20
40y + 80 = 60y + 20
60 = 20y
y = 3 hours
For, first day
x = y + 2
x = 3 + 2
x = 5 hours
Thus,
Total distance = 40(5) + 60(3)
=200 + 180
=380 miles
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What is the range of the exponential function f(x) = 2*+25? Check all that
apply.
A. (2,+00)
B. (25,+00)
C. f(x) 22
D. f(x) > 25
Answers
points a,b, and c make the triangle ABC and are at the coordinates A(-2,9), B(-33,13) and c(-21,25) point D is the midpoint of BC and AD is a median of ABC, the equation of the median can be given by ax+by=c where A B and C
what is most simple way to answer this
Answers
Answer:
[tex]2x+5y=41[/tex]
Step-by-step explanation:
Median of a triangle: A line segment that connects a vertex of a triangle to the midpoint of the opposite side.
Vertex: The point where any two sides of a triangle meet.
Given vertices of a triangle:
A = (-2, 9)B = (-33, 13)C = (-21, 25)Step 1Find the midpoint of BC (Point D) by using the Midpoint formula.
Midpoint between two points
[tex]\textsf{Midpoint}=\left(\dfrac{x_2+x_1}{2},\dfrac{y_2+y_1}{2}\right)\quad \textsf{where}\:(x_1,y_1)\:\textsf{and}\:(x_2,y_2)\:\textsf{are the endpoints}}\right)[/tex]
Define the endpoints:
[tex]\text{Let }(x_1,y_1)=\sf B=(-33,13)[/tex][tex]\text{Let }(x_2,y_2)=\sf C=(-21,25)[/tex]Substitute the defined endpoints into the formula:
[tex]\textsf{Midpoint of BC}=\left(\dfrac{-21-33}{2},\dfrac{25+13}{2}\right)=(-27,19)[/tex]
Therefore, D = (-27, 19).
Step 2Find the slope of the median (line AD) using the Slope formula.
Define the points:
[tex]\textsf{let}\:(x_1,y_1)=\sf A=(-2,9)[/tex][tex]\textsf{let}\:(x_2,y_2)=\sf D=(-27,19)[/tex]Substitute the defined points into the Slope formula:
[tex]\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{19-9}{-27-(-2)}=-\dfrac{2}{5}[/tex]
Therefore, the slope of the median is -²/₅.
Step 3Substitute the found slope and one of the points into the Point-slope formula to create an equation for the median.
[tex]\implies y-y_1=m(x-x_1)[/tex]
[tex]\implies y-9=-\dfrac{2}{5}(x-(-2))[/tex]
Simplify and rearrange the equation so it is in standard form Ax+By=C:
[tex]\implies 5(y-9)=-2(x+2)[/tex]
[tex]\implies 5y-45=-2x-4[/tex]
[tex]\implies 2x+5y-45=-4[/tex]
[tex]\implies 2x+5y=41[/tex]
ConclusionTherefore, the equation of the median is:
2x + 5y = 41
Hey guys I need some help with #7 so if anyone could help that would be great THANK YOU!!
Answers
The average rate of change obtained from the ratio of change in y to the change in x is 27
The average rate of change can be obtained using the relation :
Rate of change = (y2 - y1) ÷ (x2 - x1)
at; x1 = -3
y1 can be calculated from the function ;
y1= 3(-3³)-1
y1=-82
At ; x2 = 3
y2 can be calculated from the function ;
y2 = 3(3³)-1
y2=80
The rate of change can be calculated thus : (y2 - y1) ÷ (x2 - x1)
[80-(-82)]/[3-(-6])
162/6
27
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Determine the point (x,y) ( x , y ) on the unit circle associated with the following real number s. Write the exact answer as an ordered pair. Do not round. s=−11π6
Answers
The required coordinates of the unit circle for s = -11π/6 is (√3/2, 1/2). Using trigonometric functions, the required answer is calculated.
What are the trigonometric functions?There are six trigonometric functions.
They are sin θ, cos θ, tan θ, sec θ, cosec θ, and cot θ.
Where θ - 0 to 360° or 0 to 2π
Calculation:For a unit circle, the coordinates are given in the form of trigonometric functions as below:
x = cos θ and y = sin θ
Here it is given that s = θ = -11π/6
So, on substituting,
x = cos θ = cos (-11π/6)
⇒ x = √3/2
y = sin θ = sin (-11π/6)
⇒ y = 1/2
Thus, the required coordinate pair is (√3/2, 1/2).
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Students were surveyed about their preference between dogs and cats. The following two-way table displays data for the sample of students who responded to the survey. Preference Male Female TOTAL Prefers dogs 36 20 56 Prefers cats 10 26 36 No preference 2 6 8 TOTAL 48 52 100 Of females in the sample, what fraction prefer cats? Choose 1 answer: 26 52 36 100 26 36 26 100
Answers
Based on the data presented, it can be concluded out of the 52 females 26 prefer cats.
How to read the graph?To read the graph we must take into account that the rows refer to the preference of men, preference of women and those who have no preference.
On the other hand, the columns refer to the number of students of both genders who prefer or do not prefer each animal. Additionally, adding all the students of each gender we have the total of the sample.
According to the above, the total sample of female students would be 52.
20 + 26 + 6 = 52According to the above, the fraction that expresses this relationship correctly is:
[tex]\frac{26}{52}[/tex]
Note: This question is incomplete because the graph is missing. Here is the graph.
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Graph the solution set of the system of inequalities. 2x - 6y≤ 12 4x-2y > 8 Use the graphing tool to graph the system. Click to enlarge graph.
Answers
The graph is shown in the attached image.
the difference between 2 numbers, a and b is 21. the difference of 5 times a and 2 times b is 18. What are the values of a and b?
Answers
Answer:
Step-by-step explanation:
a-b=21
5a-2b=18
Using elimination, we have
5a-5b=105
5a-2b=18
So:
3b=-87 so b=-29
Substituting, a=-8
(a,b)=(-8,-29)
Briana received a 10-year subsidized student loan of $26,000 at an annual interest rate of 4.125%. Determine her monthly payment (in dollars) on the loan after she graduates in 2 years. (Round your answer to the nearest cent.)
Answers
Answer:
$264.78
Step-by-step explanation:
The government pays the interest on Briana's loan while she is in school. Her monthly payments will be for a loan of $26,000. The amount of the payment can be found from the amortization formula, or using a calculator or spreadsheet.
Payment amountFor a loan of principal amount P at annual rate r for t years, the monthly payment is ...
A = P(r/12)/(1 -(1 +r/12)^(-12t)) = $26000(0.04125/12)/(1 -(1 +0.04125/12)^(-120)) = $264.78
Briana's monthly payment after she graduates is $264.78.
Use synthetic division to determine which of the following is a factor of [tex]2x^3-3x^2-5x+6\\[/tex]
Option A. x + 6
Option B. x - 2
Option C. x - 3
Option D. x + 2
Answers
The factor of the polynomial function 2x^3 - 3x^2 - 5x + 6 is (b) x -2
How to determine the factor using the synthetic division?The polynomial is given as:
2x^3 - 3x^2 - 5x + 6
Next, we test the factors
Option A. x + 6
Set the factor to 0
x + 6 = 0
Solve for x
x = -6
So, we set up the division as follows:
-6 l 2 - 3 -5 6
Bring down the leading coefficient
-6 l 2 - 3 -5 6
2
Multiply 2 and -6
-6 l 2 - 3 -5 6
-12
2
Add -3 and -12
-6 l 2 - 3 -5 6
-12
2 -15
Repeat this process
-6 l 2 - 3 -5 6
-12 72 -402
2 -15 67 -396
-396 is the remainder of the above division.
This means that x + 6 is not a factor of the polynomial
Option B. x - 2
Set the factor to 0
x - 2 = 0
Solve for x
x = 2
So, we set up the division as follows:
2 l 2 - 3 -5 6
Bring down the leading coefficient
2 l 2 - 3 -5 6
2
Multiply 2 and 2
2 l 2 - 3 -5 6
4
2
Add -3 and -12
2 l 2 - 3 -5 6
4
2 1
Repeat this process
2 l 2 - 3 -5 6
4 2 -6
2 1 -3 0
0 is the remainder of the above division.
This means that x - 2 is a factor of the polynomial
There is no need to check for the remaining options
Hence, the factor of the polynomial function 2x^3 - 3x^2 - 5x + 6 is (b) x -2
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domain of f(x)=(1/4)^x
What is the domain of f(x)
O A. x>0
OB. All real numbers
O C. y>0
O D. x<0
? Need help asap
Answers
Answer: B. All real numbers
Step-by-step explanation:
See attached image.
Solve for x. PLEASE HELP ASAP
Answers
Answer:
x = 6
Step-by-step explanation:
the tangent- tangent angle UVW is half the difference of the intercepted arcs, that is
∠ UVW = [tex]\frac{1}{2}[/tex] (UW - WU ) , then
5x + 17 = [tex]\frac{1}{2}[/tex] (37x + 5 - (23x - 5) ) ← multiply both sides by 2
10x + 34 = 37x + 5 - 23x + 5
10x + 34 = 14x + 10 ( subtract 14x from both sides )
- 4x + 34 = 10 ( subtract 34 from both sides )
- 4x = - 24 ( divide both sides by - 4 )
x = 6
if cos 0= -3/5 in quadrant ii, what is sin 0
Answers
The value of sin 0 in quadrant 2 is 4/5
How to determine the identityGiven that cos 0 = -3/5
We have;
adjacent = -3hypotenuse = 5Let's find the opposite side, using Pythagorean theorem
5^2 = x^2 + (-3)^2
25 = x^2 + 9
collect like terms
x^2 = 25 - 9
x^2 = 16
x = √ 16
x = 4
We have that
sin 0 = opposite/hypotenuse
sin 0 = 4/5
It is important to note that the trigonometric identity 'sine' is positive in quadrant 2
sin 0 = 4/5
Hence, the value of sin 0 in quadrant 2 is 4/5
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A cone is 10cm high and has a base radius of 8cm.
Find the radius and height of a cylinder that is inscribed in the cone such that the volume of the cylinder is a maximum. Find the maximum volume of the cylinder and leave the answer in exact form.
Answers
The maximum volume of the cylinder in exact form is; V_max = 2560π/27
How to maximize the volume of a cylinder?Let us define the variables as:
Radius of cone = r
Radius of cylinder = x
Height of Cone = h
Height of Cylinder = y
The general equation for volume of the cylinder is;
V = πx²y
Taking a strip of both figures and relating x, y, r & h as well as using ratios of similar triangles, we have:
Height of triangle above cylinder/Base of Triangle above cylinder = Height of full triangle/Base of full triangle
This gives;
(h - y)/2x = h/2r
Making y the subject gives us;
h – y = hx/r
y = h – hx/r
y = h(1 – x/r)
Plug in y into our Volume equation:
V(x) = πx²h(1 – x/r)
V(x) = πh(x² - x³/r)
To get maximum volume, find the derivative of the volume and solve for when the derivative equals zero:
V'(x) = πh(2x - 3x²/r)
V'(x) = 0
Thus;
(2x - 3x²/r) = 0
x( 2r – 3x) = 0
Thus;
x = 0 or x = 2r/3
Put x = 2r/3 in our volume equation to find V_max
V_max = πh((2r/3)² – (2r/3)³/r)
V_max = πh(4r²/9 - 8r²/27)
V_max = πh(12r²/27 - 8r²/27)
V_max = 4πhr²/27
Thus, at r = 8 and h = 10, we have;
V_max = 4π(10)8²/27
V_max = 2560π/27
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Scenario 2
You are at a restaurant with three friends (party of 4) and need to estimate the amount of tip for your portion of the bill without using a calculator. Assume a 20% tip rate. For full credit, you will need the cost of your meal, an explanation of how you would calculate your 20% tip, and the total amount.
Answers
The best approach to calculating the stipulated 20% tip by means of fractions is to note that the tip is one-fifth of the total amount charged on the bill.
What is the equivalent of the 20% tip as indicated in the task content?The percentage represented as; 20% can be expressed as a fraction.
This follows from the fact that the percentage, % symbol translates to divided by 100.
Consequently, we must note that the 20% translates to; 20/100 = 1/5.
Hence, the 20% tip is one-fifth of the total amount.
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PLEASE I NEED THIS FAST a three dight number has one more ten than it has hundreds, and it also has one more than twice as many units as tens the sum of the number and that number reversed is 31 less than 10 cubed find the reverse number
Answers
The reverse number of the three-digit number is 732
How to determine the reverse of the number?Let the three-digit number be xyz.
So, the reverse is zyx
This means that
Number = 100x + 10y + z
Reverse = 100z + 10y + x
From the question, we have the following parameters:
y = x + 1
z = 1 + 2y
The sum is represented as:
100x + 10y + z + 100z + 10y + x = 10^3 - 31
100x + 10y + z + 100z + 10y + x = 969
Evaluate the like terms
101x + 101z + 20y = 969
Substitute y = x + 1
101x + 101z + 20(x + 1) = 969
101x + 101z + 20x + 20 = 969
Evaluate the like terms
101x + 101z + 20x = 949
121x + 101z = 949
Substitute y = x + 1 in z = 1 + 2y
z = 1 + 2(x + 1)
This gives
z = 2x + 3
So, we have:
121x + 101z = 949
121x + 101* (2x + 3) = 949
This gives
121x + 202x + 303 = 949
Evaluate the sum
323x = 646
Divide by 323
x = 2
Substitute x = 2 in z = 2x + 3 and y = x + 1
z = 2*2 + 3 = 7
y = 2 + 1 = 3
So, we have
x = 2
y = 3
z = 7
Recall that
Reverse = 100z + 10y + x
This gives
Reverse = 100*7 + 10*3 + 2
Evaluate
Reverse = 732
Hence, the reverse number of the three-digit number is 732
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Answers for number 32 and 31
Answers
Answer:
32: X=54
31: Xx54+74
Justin recently drove to visit his parents who live 270
miles away. On his way there his average speed was 11 miles per hour faster than on his way home (he ran into some bad weather). If Justin spent a total of 9 hours driving, find the two rates.
Answers
Answer:
66 mph to visit55 mph to homeStep-by-step explanation:
An equation can be set up and solved based on the relation between the two speeds and the relation between time, speed, and distance.
Setuptime = distance/speed
Let x represent the (slower) speed on the way home. Then the total time for the round trip was ...
time going + time coming home = total time
270/(x +11) +270/x = 9
Solution30x +30(x +11) = x(x +11) . . . . . . multiply by x(x+11)/9
x^2 -49x -330 = 0 . . . . . . . . rewrite in standard form
(x -55)(x +6) = 0 . . . . . . . . factor
x = 55 or x = -6 . . . . . . . solutions to this equation; x < 0 is extraneous
Justin's rate on the way there was 66 mph; on the way home, it was 55 mph.
PLEASE HELP ASAP!
A rancher’s herd of 250 sheep grazes over a 40-acre pasture. He would like to find out how many sheep are grazing on each acre of the pasture at any given time, so he has some images of the pasture taken by the state department of agriculture’s aerial photography division. Here are three samples of the images.
Sample 1 4
Sample 2 1
Sample 3 9
How do the sample statistics compare to the population mean and standard deviation?
Answers
The Average number of sheep grazed in per acre is 6 approx. in rancher’s herd.
According to the statement
We have given that the A rancher’s herd of 250 sheep grazes over a 40-acre pasture.
And we have to find the how many sheep are grazing on each acre.
So, For this purpose If we assume that the sheep are equally distributed, to see how many sheep there are in each acre we just divide the number of sheep by the number of acres. So,
we have to find the average of number of sheep in per acre.
We know that
The total area of the rancher’s herd = 40 acre
The number of sheep grazes in the land = 250 sheep
Now, we have to find the Average number
Average number of sheep grazed in per acre = 250/40
Average number of sheep grazed in per acre = 6 approx.
So, The Average number of sheep grazed in per acre is 6 approx. in rancher’s herd.
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find the critical value for the given confidence level c and sample size n c=.90 n=21
Answers
The critical value for the given confidence level, c = 0.90 and n = 21 is [tex]t_c=1.725[/tex].
How to calculate the critical value for t-distribution?The critical value is calculated as follows:
For the given sample size n, find the degree of freedom (d.f)Where d.f = n - 1Using the t-distribution table, the critical value is obtained for the obtained d.f and the confidence level.Calculation:It is given that,
confidence level c = 0.90
sample size n = 21
Then,
degree of freedom,
(d.f) = n - 1 = 21 - 1 = 20
So, from the t-distribution table,
at d.f = 20 and the confidence level 0.90, the critical value is 1.725.
I.e., [tex]t_c[/tex] = 1.725
For this, α = (1 - 0.90)/2 = 0.05
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jelissa determined she needs to have 800000 for retirement in 30 years. her account earns 6% interest
a. how much would she need to deposit in the account each month
b. how much total money will she put into the account.
c. how much total interest will she earn
Answers
The monthly payment is $796.40.
The total amount she would deposit is $286,705.51
The total interest earned is $513,294.49
What is the monthly payment, total amount deposited and interest?The payments made by Jessica are known as deferred annuities. Deferred annuities are when a series of payments are made in exchange for an amount of money in the future.
The formula that can be used to determine the amount of monthly deposit is: future value / annuity factor
Annuity factor = {[(1+r)^n] - 1} / r
Where:
r = interest rate = 6%/12 = 0.5%
n = number of years = 30 x 12 = 360
Annuity factor = ](1.005^360) - 1] / 0.005 = 1004.515
Monthly payments = 800,000 / 1004.515 = $796.40
Total amount she would deposit = monthly payment x number of years x number of months in a year
$796.40 x 30 x 12 = 286,705.51
Total interest earned = value of the retirement account - total amount deposited
800,000 - 286,705.51 = 513,294.49
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HOW MANY DIFFERENT ARRANGEMENTS CAN BE MADE WITH THE NUMBERS
28535852
Answers
Answer:
1,680
Step-by-step explanation:
8 positions with basically 8 choices.
that is 8! arrangements.
but 2 is there 2 times.
8 is there 2 times.
5 is there 3 times.
only 3 is a single digit.
so, we need to eliminate every arrangement, where the 2s trade places, where the 5s trade places, and where the 8s trade places, because they are the same numbers.
that means we have to divide the 8! by 2!, then again by 2!, and again by 3!.
8! / (2! × 2! × 3!) = 8! / 24 = 1,680
find the square (4x-6y^3)^2
Answers
The table below shows the growth of algae cells within the Chesapeake Bay. Which of the following functions models the concentration, C(d), of algae cells per milliliter in d days?
Answers
The exponential function that represent the concentration of algae cells per milliliter in d days is [tex]C(d) = 10(2)^d[/tex]
What is an equation?An equation is an expression that shows the relationship between two numbers and variables.
The standard form of an exponential funtion is in the form:
y = abˣ
Where a is the initial value and b is the multiplication factor.
Let C(d) represent the concentration of algae cells per milliliter in d days
At point (1, 20)
20 = ab (1)
At point (2, 40)
40 = ab² (2)
From equations 1 and 2:
b = 2, a = 10
The exponential function that represent the concentration of algae cells per milliliter in d days is [tex]C(d) = 10(2)^d[/tex]
Find out more on equation at: https://brainly.com/question/2972832
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HELP!!!! Which of the following statements must be true to prove lines m and n are parallel? Question 19 options: A) ∠1 ≅ ∠6 B) m∠3 + m∠5 = 180° C) m∠2 + m∠6 = 180° D) ∠4 ≅ ∠8
Answers
Answer: B) m∠3 + m∠5 = 180°
Step-by-step explanation:
Concept:
For this question, we will be looking at each answer choice and eliminating the incorrect ones
A) ∠1 ≅ ∠6
∠1 is an exterior angle
∠6 is an interior angle
They are in an alternative position
Since they are neither both exterior nor interior, they are not congruent
[tex]\large\boxed{FALSE}[/tex]
B) m∠3 + m∠5 = 180°
∠3 is an interior angle
∠5 is an interior angle
They are in a same-side position
Since they are both interiors, they fulfill the same-side interior angle theorem, which states: that if a transversal cuts two parallel lines, then the interior angles on the same side of the transversal are supplementary, which means their sum adds up to 180°.
[tex]\Huge\boxed{TRUE}[/tex]
C) m∠2 + m∠6 = 180°
∠2 is an exterior angle
∠6 is an interior angle
They are in a same-side position
Since they are on the same side, they fulfill the corresponding angle theorem which states: the angles that occupy the same relative position at each intersection are congruent to each other.
However, they are only congruent, they don't add up to 180°
[tex]\large\boxed{FALSE}[/tex]
D) ∠4 ≅ ∠8
∠4 is an interior angle
∠8 is an exterior angle
They are in an alternative position
Since they are neither both exterior nor interior, they are not congruent
[tex]\large\boxed{FALSE}[/tex]
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