Answer:
$78.60
Step-by-step explanation:
0.14x + 31 = 0.14*340 + 31 = 78.6
Consider the spiral curves given parametrically by: (see picture and answer question)
a. The arc length is given by the integral
[tex]L(r) = \displaystyle \int_3^\infty \sqrt{x'(t)^2 + y'(t)^2} \, dt \\\\ ~~~~~~~~ = \int_3^\infty \sqrt{\left(\frac{t\cos(t) - r\sin(t)}{t^{r+1}}\right)^2 + \left(-\frac{t\sin(t) + r\cos(t)}{t^{r+1}}\right)^2} \, dt \\\\ ~~~~~~~~ = \int_3^\infty \sqrt{\frac{(t^2+r^2)\cos^2(t) + (t^2+r^2)\sin^2(t)}{\left(t^{r+1}\right)^2}} \, dt \\\\ ~~~~~~~~ = \boxed{\int_3^\infty \frac{\sqrt{t^2+r^2}}{t^{r+1}} \, dt}[/tex]
b. The integrand roughly behaves like
[tex]\dfrac t{t^{r+1}} = \dfrac1{t^r}[/tex]
so the arc length integral will converge for [tex]\boxed{r>1}[/tex].
c. When [tex]r=3[/tex], the integral becomes
[tex]L(3) = \displaystyle \int_3^\infty \frac{\sqrt{t^2+9}}{t^4} \, dt[/tex]
Pull out a factor of [tex]t^2[/tex] from under the square root, bearing in mind that [tex]\sqrt{x^2} = |x|[/tex] for all real [tex]x[/tex].
[tex]L(3) = \displaystyle \int_3^\infty \frac{\sqrt{t^2} \sqrt{1+\frac9{t^2}}}{t^4} \, dt \\\\ ~~~~~~~~ = \int_3^\infty \frac{|t| \sqrt{1+\frac9{t^2}}}{t^4} \, dt \\\\ ~~~~~~~~ = \int_3^\infty \frac{t \sqrt{1+\frac9{t^2}}}{t^4} \, dt \\\\ ~~~~~~~~ = \int_3^\infty \frac{\sqrt{1+\frac9{t^2}}}{t^3} \, dt[/tex]
since for [tex]3\le t<\infty[/tex], we have [tex]|t|=t[/tex].
Now substitute
[tex]s=1+\dfrac9{t^2} \text{ and } ds = -\dfrac{18}{t^3} \, dt[/tex]
Then the integral evaluates to
[tex]L(3) = \displaystyle -\frac1{18} \int_2^1 \sqrt{s} \, ds \\\\ ~~~~~~~~ = \frac1{18} \int_1^2 s^{1/2} \, ds \\\\ ~~~~~~~~ = \frac1{27} s^{3/2} \bigg|_1^2 \\\\ ~~~~~~~~ = \frac{2^{3/2} - 1^{3/2}}{27} = \boxed{\frac{2\sqrt2-1}{27}}[/tex]
a) The improper integral in simplified form is equal to [tex]L = \int\limits^{\infty}_{3} {\frac{\sqrt{t^{2}+r^{2}}}{t^{r + 1}} } \, dt[/tex].
b) r > 1 for a spiral with finite length.
c) The length of the spiral when r = 3 is (1 - 2√2) / 9 units.
How to characterize and analyze a group of parametric functions
a) The arc length formula for 2-dimension parametric functions is defined below:
L = ∫ √[(dx / dt)² + (dy / dt)²] dt, for [α, β] (1)
If we know that [tex]\dot x (t) = \frac{t \cdot \cos t - r \cdot \sin t}{t^{r+1}}[/tex], [tex]\dot y(t) = \frac{t\cdot \sin t + r\cdot \cos t}{t^{r + 1}}[/tex], α = 0 and β → + ∞ then their arc length formula is:
[tex]L = \int\limits^{\infty}_{3} {\sqrt{\left(\frac{t\cdot \cos t - r\cdot \sin t}{t^{r + 1}}\right)^{2}+\left(\frac{t\cdot \sin t + r\cdot \cos t}{t^{r+1}}\right)^{2}} } \, dt[/tex]
By algebraic handling and trigonometric formulae (cos ² t + sin² t = 1):
[tex]L = \int\limits^{\infty}_{3} {\frac{\sqrt{t^{2}+r^{2}}}{t^{r + 1}} } \, dt[/tex] (2)
The improper integral in simplified form is equal to [tex]L = \int\limits^{\infty}_{3} {\frac{\sqrt{t^{2}+r^{2}}}{t^{r + 1}} } \, dt[/tex].
b) By ratio comparison criterion, we notice that √(t² + r²) is similar to √t² = t and [tex]\frac{\sqrt{t^{2}+r^{2}}}{t^{r + 1}}[/tex] is similar to [tex]\frac{t}{t^{r +1}} = \frac{1}{t^{r}}[/tex].
The integral found in part a) has a finite length if and only the governing grade of the denominator is greater that the governing grade of the numerator. and according to the ratio comparson criterion, the absolute value of the ratio is greater than 0 and less than 1. Therefore, r > 1 for a spiral with finite length.
c) Now we proceed to integrate the function:
L = ∫ [√(t² + 9) / t⁴] dt, for [3, + ∞].
L = ∫ [t · √(1 + 9 / t²) / t⁴] dt, for [3, + ∞].
By using the algebraic substitutions: u = 1 + 9 / t², du = - (18 / t³) dt → - (1 / 18) du.
L = ∫ √u du, for [3, + ∞].
L = - (1 / 9) · √(u³), for [3, + ∞].
L = - (1 / 9) · [√(1 + 9 / t²)³], for [3, + ∞].
L = - (1 / 9) · [√(2³) - √(1³)]
L = - (1 / 9) · (2√2 - 1)
L = (1 - 2√2) / 9
The length of the spiral when r = 3 is (1 - 2√2) / 9 units.
To learn more on arc lengths: https://brainly.com/question/16403495
#SPJ1
PLEASE HELP ME QUICK
In the diagram, points D and E are marked by drawing arcs of equal size centered at B such that the arcs intersect BA and BC
Then, intersecting arcs of equal size are drawn centered at points D and E. Point P is located at the intersection of these arcs.
Based on this construction, m∠ABP is ANSWER ° and m∠ABC is ANSWER°
Answer:
m∠ABP is 32°,m∠ABC is 64°.Step-by-step explanation:
According to the construction we have:
BD = BEPD = PEBP - is common side of triangles BPD and BPEIt gives us:
ΔPBD ≅ ΔPBEThen, corresponding angles of congruent triangles are congruent:
∠DBP ≅ ∠EBPSo,
∠ABP ≅ ∠CBP ⇒ m∠ABP = 32°Then,
m∠ABC = m∠ABP + m∠CBP = 32° + 32° = 64°In politics, marketing, etc. we often want to estimate a percentage or proportion p. One calculation in statistical polling is the margin of error - the largest (reasonble) error that the poll could have. For example, a poll result of 72% with a margin of error of 4% indicates that p is most likely to be between 68% and 76% (72% minus 4% to 72% plus 4%).
In a (made-up) poll, the proportion of people who like dark chocolate more than milk chocolate was 43% with a margin of error of 1.9%. Describe the conclusion about p using an absolute value inequality.
The answer field below uses the symbolic entry option in Mobius. That lets you type in a vertical bar | to represent absolute values. Also, when you type in << and then, the symbolic entry option will automatically convert that to <.I the same way, if you type in> and then, the symbolic entry option will automatically convert that to >
Be sure to use decimal numbers in your answer (such as using 0.40 for 40%).
The absolute value inequality is given as |(p - 0.43)I ≤ 0.019
How to describe the proportion using the absolute value inequalityThe proportion p = 43% = 0.43
Margin of error = 1.9% = 0.019
The value of the proportion can then be said to lie between
(0.43 - 0.019) ≤ p ≤ (0.43 + 0.019)
In order to convert to the absolute inequality we would be having
-0.019 ≤ (p - 0.43) ≤ 0.019
I (p - 0.43)I ≤ 0.019
Read more on margin of error here
https://brainly.com/question/24289590
#SPJ1
In parallelogram DEFG, DH equals X +3, HF equals 3Y, GH equals 2X -5 and HE equals 5Y plus to find the values of X and Y
The values of X and Y are 30 and 11 respectively
How to determine the values of X and Y?The figure that represents the complete question is added as an attachment
The given parameters are:
DH = X +3
HF = 3Y
GH = 2X -5
HE = 5Y
From the attached parallelogram, we have:
DH = HF
GH = HE
Substitute the known values in the above equation
X + 3 = 3Y
2X - 5 = 5Y
Make X the subject in X + 3 = 3Y
X = 3Y - 3
Substitute X = 3Y - 3 in 2X - 5 = 5Y
2(3Y - 3) - 5 = 5Y
Expand
6Y - 6 - 5 = 5Y
Evaluate the like terms
Y = 11
Substitute Y = 11 in X = 3Y - 3
X = 3*11 - 3
Evaluate
X = 30
Hence, the values of X and Y are 30 and 11 respectively
Read more about parallelograms at:
https://brainly.com/question/3050890
#SPJ1
he polynomial of degree 5, P ( x ) has leading coefficient 1, has roots of multiplicity 2 at x = 3 and x = 0 , and a root of multiplicity 1 at x = − 1 Find a possible formula for P ( x ) .
f]
The possible formula for the polynomial in discuss whose roots are described as; having roots of multiplicity 2 at x = 3 and x = 0 , and a root of multiplicity 1 at x = − 1 is; P(x) = x^5 -5x⁴-6x³+18x².
What is the polynomial in discuss whose roots and leading coefficient are as discussed?The polynomial which is as described in the task content whose roots are as given can be written in its factorised form as follows;
P(x) = (x-3) (x-3) (x) (x) (x+1)
The expanded form is therefore;
P(x) = x^5 - 5x⁴- 6x³+ 18x².
Therefore, the polynomial having roots of multiplicity 2 at x = 3 and x = 0 , and a root of multiplicity 1 at x = − 1 is P(x) = x^5 - 5x⁴- 6x³+ 18x².
Read more on polynomials;
https://brainly.com/question/13793580
#SPJ1
Find the area of the trapezoid 19 12.6 29.2 14.5
Answer:
303.66 in²
Option 4 is the correct answer
Earlier in this course, you explored Euclidean geometry, which is the study of flat space. This approach follows the teachings of Euclid, in which he describes the relationships between points, lines, and planes without any numerical measurement. You saw evidence of Euclidean geometry inside several proofs and geometric constructions.
In contrast, the focus of this unit is understanding geometry using positions of points in a Cartesian coordinate system. The study of the relationship between algebra and geometry was pioneered by the French mathematician and philosopher René Descartes. In fact, the Cartesian coordinate system is named after him. The study of geometry that uses coordinates in this manner is called analytical geometry.
It’s clear that this course teaches a combination of analytical and Euclidean geometry. Based on your experiences so far, which approach to geometry do you prefer? Why? Which approach is easier to extend beyond two dimensions? What are some situations in which one approach to geometry would prove more beneficial than the other? Describe the situation and why you think analytical or Euclidean geometry is more applicable.
The Elements can be defined as a mathematical treatise which comprises 13 books that are attributed to the ancient Greek mathematician who lived in Alexandria, Ptolemaic Egypt c. 300 BC and called Euclid.
Basically, the Elements is a collection of the following geometric knowledge and observations:
DefinitionsPostulatesPropositionsMathematical proofs of the propositions.Based on my experiences so far, an approach to geometry which I prefer is Euclidean geometry because it's much easier than analytical geometry. Also, an approach that is easier to extend beyond two-dimensions is Euclidean geometry because it can be extended to three-dimension.
A situation in which one approach to geometry would prove to be more beneficial than the other is when dealing with flat surfaces. In Euclidean geometry, a correspondence can be established between geometric curves and algebraic equations.
Read more on Euclidean here: brainly.com/question/1680028
#SPJ5
I need help with question
Answer
square root of 128 Lies between two square numbe
121 = 11 ^ 2
(11.1) ^ 2 = 133.1
So, √128 lies between 11.0 and 11.1.
Option A: 11.0 and 11.1Decreasing the number of years of a loan decreases the amount of interest repaid over the term of the loan. Suppose a dental hygienist has the option of a 30-year loan or a 25-year loan of $345,000 at an annual interest rate of 3.75%.
(a)
a) Calculate the monthly payment (in dollars) for each loan. (Round your answers to the nearest cent.)
30-year loan
25-year loan
b) Calculate the savings in interest (in dollars) by using the 25-year loan. (Round your answer to the nearest cent.)
Answer:
a) 30 yr: $1597.75; 25 yr: $1773.75
b) $43065.00
Step-by-step explanation:
The monthly payment for each loan can be found using the amortization formula, or a spreadsheet or calculator. The shorter 25-year loan has fewer and larger payments, but the net result is less interest paid.
a)The attached calculator shows the monthly payments to be ...
30 year loan: $1597.75 monthly
25 year loan: $1773.75 monthly
b)The number of payments is the product of 12 payments per year and the number of years. The total repaid is the monthly payment times the number of payments.
The difference in amounts repaid is the difference in interest charged.
360×1597.75 -300×1773.75 = $43065 . . . . savings using 25-year loan
__
Additional comment
The monthly payment on a loan of principal P at annual rate r for t years is ...
A = P(r/12)/(1 -(1 +r/12)^(-12t))
Some calculators and all spreadsheets have built-in functions for calculating this amount.
Which are valid pairs of opposite angle measures for a quadrilateral inscribed
in a circle? Select all that apply.
A. 72°, 108°
B. 66°, 114°
C. 80°, 90°
D. 64°, 106°
Answer:
A., B.
Step-by-step explanation:
Opposite angles of a quadrilateral inscribed in a circle are supplementary, so their sum must equal 180°.
A. 72° + 108° = 180° Answer: yes
B. 66° + 114° = 180° Answer: yes
C. 80° + 90° = 170° Answer: no
D. 64° + 106° = 170° Answer: no
Answer: A., B.
Select all the correct graphs.
Choose the graphs that indicate equations with no solution.
The graph first, and the graph fifth have no solution because there are no intersection options (A) and (E) are correct.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
It is given that:
The graph of equations is shown in the graph.
As we know, if two equations of a function intersect on the coordinate plane that means they have a solution.
If there will be no intersection then the equations have no solution.
Thus, the graph first, and the graph fifth have no solution because there are no intersection options (A) and (E) are correct.
Learn more about the function here:
brainly.com/question/5245372
#SPJ1
a. Based on the picture, what properties can you be sure this figure has? Think about angles, lines, and points.
b. Does ray l bisect ∠ABC? Explain your thinking.
c. What would you need to do to prove that ray l bisects ∠ABC?
The angle measures ABD = 45, DBC = 45 and ABC = 90 imply that ray l bisect ∠ABC?
The properties of the figureFrom the figure, we have the following highlights:
The lines AB and BC are perpendicular lines i.e. the angle at B =90Ray I bisects the angle ABC (because 45 + 45 = 90)Angles ABD and DBC are adjacent anglesThis means that the points ABC can be joined to form a right triangle
Does ray l bisect ∠ABC?Yes, it does.
This is so because it divides the angle ABC into equal segments.
i.e.
ABC = 90
DBC = 45
So, we have
ABD = 90 - 45
ABD = 45
The angle measures ABD = 45, DBC = 45 and ABC = 90 imply that ray l bisect ∠ABC?
What would you need to do to prove that ray l bisects ∠ABC?You would need the measures of ABC and ABD
Read more about rays, angles, lines, and points at
https://brainly.com/question/14366932
#SPJ1
If you are taking a 3 credit college class and fail, and you have a 3.3 GPA. How mush will it affect it?
Answer:
it depend on your total credit load u register, if it's d only credit load it affect your gpa alot
Find the area for the shaded polygon
Taking the distance between dots as 1 unit, we have;
Area of the blue shaded region = square 10 unitsArea of the yellow polygon = 6 square units Which method can be used to find the area of the shaded figures?Taking the figures as comprising of triangles and trapezoids, we have;
In the blue polygon, we have;
Trapezoid area = ((4 + 3)/2) × 2 = 7
Area of the unshaded triangles = 0.5 × 2 × 1 + 0.5 × 2 × 2 + 0.5 × 2 × 1 = 4
Square area = 3 × 2 = 6
Shaded triangle area = 0.5 × 2 × 1 = 1
Sum of the areas is therefore;
A = 7 - 4 + 6 + 1 = 10
Which gives;
Area of the blue shaded region = 10Area of the lower yellow trapezoid is found as follows;
Trapezoid area = ((2 + 3)/2) × 4 = 10
Unshaded triangle area = 0.5 × 2 × 1 + 0.5 × 3 × 3 = 5.5
Area of the top triangle = 0.5 × 3 × 1 = 1.5
Area of the shaded yellow polygon is therefore;
A = 10 - 5.5 + 1.5 = 6
Area of the yellow polygon = 6 square unitsLearn more about basic geometric shapes here:
https://brainly.com/question/9793507
#SPJ1
a) Find the perimeter of a rectangle whose length is 10 10²/3 cm and breadth is 6 cm.
please need fast I will make brilliant
Answer:
40
Step-by-step explanation:
P=2(l+w)
2·(10+10)
=40
The figure below is a scale drawing of an office courtyard using the scale 1 centimeter = 4 feet.
Which figure is a scale drawing of the same courtyard using the scale 1 centimeter = 3 feet?
Using proportions, it is found that option A gives a figure that is a scale drawing of the same courtyard using the scale 1 centimeter = 3 feet.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
Researching this problem on the internet, the figure with a scale of 1 cm = 4 feet has the dimensions of:
51 cm, 75 cm, 30 cm and 72cm.
For a scale of 1 centimeter = 3 feet, these measures will be multiplied by 4/3, hence the figure is given in option A, as:
51 x 4/3 = 68 cm.75 x 4/3 = 100 cm.30 x 4/3 = 40 cm.72 x 4/3 = 96 cm.More can be learned about proportions at https://brainly.com/question/24372153
#SPJ1
Point A and B are respectively 20m north and 48m east of point c.find the distance AB
Answer:
[tex]\boxed {AB = 52 m}[/tex]
Step-by-step explanation:
This forms a right triangle.
Therefore, by using the Pythagorean Theorem, we can find AB.
AB = √AC² + BC²
AB = √(20)² + (48)²AB = √400 + 2304AB = √2704AB = 52mI hope it helped you solve the problem.
Good luck on your studies!
Answer: Distance AB = 52 m
Step-by-step explanation:
Given information
Point A = 20 m north of point C
Point B = 48 m east of point C
Please refer to the attachment below for a graphical understanding
Concept
According to the graph drawn, Point A, Point B, and Point C form a right angle, and the distance between Point A and B would form a right triangle.
Therefore, we can use the Pythagorean theorem to find the distance between points A and B.
Given formula
a² + b² = c²
a = distance between point A and point Cb = distance between point B and point Cc = distance between point A and point BSubstitute values into the formula
a² + b² = c²
(20)² + (48)² = c²
Simplify exponents
400 + 2304 = c²
Simplify by addition
2704 = c²
c = √2704
c = 52 or c = -52 (reject, since no distance can be negative)
Therefore, the distance AB is [tex]\Large\boxed{52~m}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Define the linear programming problems. State the key terms in L.P.P.
Answer:
Step-by-step explanation:
Linear Programming Problems (LPP): Linear programming or linear optimization is a process which takes into consideration certain linear relationships to obtain the best possible solution to a mathematical model. It is also denoted as LPP. It includes problems dealing with maximizing profits, minimizing costs, minimal usage of resources, etc. These problems can be solved through the simplex method or graphical method.
Linear Programming For Class 12
Linear Programming
Linear Programming Worksheet
The Linear programming applications are present in broad disciplines such as commerce, industry, etc. In this section, we will discuss, how to do the mathematical formulation of the LPP.
Mathematical Formulation of Problem
Let x and y be the number of cabinets of types 1 and 2 respectively that he must manufacture. They are non-negative and known as non-negative constraints.
The company can invest a total of 540 hours of the labour force and is required to create up to 50 cabinets. Hence,
15x + 9y <= 540
x + y <= 50
The above two equations are known as linear constraints.
Let Z be the profit he earns from manufacturing x and y pieces of the cabinets of types 1 and 2. Thus,
Z = 5000x + 3000y
Our objective here is to maximize Z. Hence Z is known as the objective function. To find the answer to this question, we use graphs, which is known as the graphical method of solving LPP. We will cover this in the subsequent sections.
Graphical Method
The solution for problems based on linear programming is determined with the help of the feasible region, in case of graphical method. The feasible region is basically the common region determined by all constraints including non-negative constraints, say, x,y≥0, of an LPP. Each point in this feasible region represents the feasible solution of the constraints and therefore, is called the solution/feasible region for the problem. The region apart from (outside) the feasible region is called as the infeasible region.
The optimal value (maximum and minimum) obtained of an objective function in the feasible region at any point is called an optimal solution. To learn the graphical method to solve linear programming completely reach us.
Linear Programming Applications
Let us take a real-life problem to understand linear programming. A home décor company received an order to manufacture cabinets. The first consignment requires up to 50 cabinets. There are two types of cabinets. The first type requires 15 hours of the labour force (per piece) to be constructed and gives a profit of Rs 5000 per piece to the company. Whereas, the second type requires 9 hours of the labour force and makes a profit of Rs 3000 per piece. However, the company has only 540 hours of workforce available for the manufacture of the cabinets. With this information given, you are required to find a deal which gives the maximum profit to the décor company.
Linear Programming problem LPP
Given the situation, let us take up different scenarios to analyse how the profit can be maximized.
He decides to construct all the cabinets of the first type. In this case, he can create 540/15 = 36 cabinets. This would give him a profit of Rs 5000 × 36 = Rs 180,000.
He decides to construct all the cabinets of the second type. In this case, he can create 540/9 = 60 cabinets. But the first consignment requires only up to 50 cabinets. Hence, he can make profit of Rs 3000 × 50 = Rs 150,000.
He decides to make 15 cabinets of type 1 and 35 of type 2. In this case, his profit is (5000 × 15 + 3000 × 35) Rs 180,000.
Similarly, there can be many strategies which he can devise to maximize his profit by allocating the different amount of labour force to the two types of cabinets. We do a mathematical formulation of the discussed LPP to find out the strategy which would lead to maximum profit.
Find the slope and reduce.
P=(-8, 3) Q=(-6, 2)
Slope
Answer:
[tex]-\frac{1}{2}[/tex]
Step-by-step explanation:
Slope/Gradient = [tex]\frac{y1-y2}{x1-x2}[/tex]
P = (-8 , 3) (x1, y1)
Q = (-6 , 2) (x2, y2)
Slope = [tex]\frac{3-2}{-8-(-6)}[/tex] =[tex]\frac{1}{-8+6}[/tex] = [tex]\frac{1}{-2}[/tex] = [tex]-\frac{1}{2}[/tex]
Answer:
-1/2
Step-by-step explanation:
The formula for the slope is (change in y)/(change in x) or Rise/Run.
The change in y for the two points is: 3 --> 2 which is -1
The change in x for the two points is: -8 --> -6 which is +2
If we input these numbers in the slope equation, we end up with -1/2.
Since we cannot simplify -1/2 further, that is our final answer.
Which set of ordered pairs represents a function?
{(-6,-4), (1, -7), (-4, 3), (-4, 8)}
{(-8, -3), (-8, 9), (9, 6), (1, -4)}
{(4,1), (-6, 6), (5,-2), (-4,1)}
{(-3, 6), (-1,0), (-8, 1), (-8, -3)}
Answer:
{(4,1), (-6, 6), (5,-2), (-4,1)} set of ordered pairs represents a function.
Step-by-step explanation:
Because every element or component of domain has unique image in co-domain.
Hope its helpful :-)
If so, please mark me as brainlist :-)
3. In AABC, a = 35, c = 25, and m can be drawn given these measurements?
Only one triangle possible with angle 38.2° at C.
According to the given statement
we have to seek out that the measurement of m with the help of the a and c.
Then for this purpose, we all know that the
The ambiguous case occurs when one uses the law of sines to see missing measures of a triangle when given two sides and an angle opposite one in every of those angles (SSA).
According to the this law
The equation become
35/sin(60) = 25/sinC
sinC = 0.6185895741
C = 38.2, 141.8
Since 141.8+60 = 201.8 > 180
It will not form a triangle.
So, only 1 triangle possible with angle 38.2° at C
Learn more about ambiguous case here
https://brainly.com/question/4372174
#SPJ1
Disclaimer: This question was incomplete. Please find the full content below.
Question:
Law of Sines and the Ambiguous Case.
In ∆ ABC, a =35, c = 25, and m < A = 60*
How many distinct triangles can be drawn given these measurements?
Does the following series converge or diverge?
Σ
n=1
4
8√n +7³√n
O The series diverges.
O The series converges.
Answer:
converges
Step-by-step explanation:
the individual fraction terms go against 0 with larger and larger n.
and therefore the sum converges.
the numerator of the fractions stays constant (4) but the denominator (bottom) of the fraction increases more and more with investing n (it does not matter that it uses roots, compared to the constant 4 they too grow immensely large with large n).
the limit of a/infinity is defined as 0.
!!!!!!!!! Helppppppp plsssss
Answer:
(6 / 4) * (7 + 9)
Step-by-step explanation:
sry that took me so long lol
A recipe calls for 3/4 cups of water, 2/3 cups of flour, and 1/6 cups of sugar. What is the ratio of water: flour: sugar? Express your answer reduced to the lowest terms
Answer:
9:8:2
Step-by-step explanation:
3/4 : 2/3 : 1/6 Multiply by 12.
9 : 8 : 2
If a certain number, , is multiplied by 6, it will be equal to 4 less than thrice the same number. The correct equation for the above statement is?
The correct equation is [tex]x\cdot6=3x-4[/tex].
Let the number be [tex]x[/tex].
According to the question,
Number multiplied by [tex]6[/tex] [tex]=6x[/tex].
[tex]4[/tex] less than thrice the number [tex]=3x-4[/tex].
Hence, the correct equation will be [tex]x\cdot6=3x-4[/tex].
To learn more about equations, refer: https://brainly.in/question/19089782.
#SPJ2
y=3x-2
y=-2x+8 solve this equation
Answer:
x = 2
Step-by-step explanation:
3x - 2 = - 2x + 8
→ Add 2x on both sides
5x - 2 = 8
→ Add 2 on both sides
5x = 10
→ Divide both sides by
x = 2
Answer:
x = 2, y = 4 (2,4)
Step-by-step explanation:
Put both the equation in ax + by = c
-3x + y = -2
2x + y = 8
Find x:
Multiply 8 times 1, -2 by 1, 2 times 1, and -3 by 1
8 - (-) 2/2 - (-) 3 = x
10/5
x = 2
Plug x back into equation:
-3(2)+y = -2
y = 4
What value of b will cause the system to have an infinite number of solutions y=6x+b
-3x+1/2y=-3
A-(-6)
B(-3)
C(3)
D(6)
Answer: -6
Step-by-step explanation:
[tex]-3x+\frac{1}{2}y=-3\\\\\frac{1}{2}y=3x-3\\\\y=6x-6[/tex]
For there to be infinite solutions, b = -6.
There are 96 football players at all levels at Davenport High School. If two-thirds of the players make the honor roll for their grades how many olayers are on the list?
64 players
48 players
72 players
54 players
Name a pair of opposite rays on plane L.
Answer:
GD and GC
Step-by-step explanation:
Opposite rays lie on the same line and extend in opposite directions from the same end point. Rays are named by naming the end point first, then another point on the ray.
Opposite raysPoints D, G, C lie on the same line with point G between the other two. That means rays GD and GC are opposite rays.
Graph the line with a slope of −1 that contains the point (3,6).
Answer:
The equation of the line is y = -1.x + 9
Graph is provided in the attached figure
Step-by-step explanation:
The slope intercept equation of a line in 2D(x,y) coordinates is given by the equation
[tex]y = mx + c[/tex]
where m is the slope of the line and c the y-intercept i.e. where the line crosses the y axis at x = 0
Given slope = -1, we can find c and the equation of the line
Since (3,6) is a point on the graph, these coordinates must satisfy the above equation
Substitute for y = 6 and x = 3
[tex]6 = (-1)3 + c\\\\c = 9\\\\\textrm{Equation of line is }\\y = -1.x + 9 \\y = 9-x[/tex]
In the attached figure you can see that (3,6) is on the line