If f(x) = -1x + 1and g(x) = x4, what is (f º g)(x)?

Answer:

Step-by-step explanation:

According to the construction we have:

It gives us:

Then, corresponding angles of congruent triangles are congruent:

So,

Then,

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.

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.

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].

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[tex]\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & 80\\ P=\textit{initial amount}\dotfill &40\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ t=years \end{cases} \\\\\\ 80=40(1 + 0.05)^{t}\implies \cfrac{80}{40}=1.05^t\implies 2=1.05^t\implies \log(2)=\log(1.05^t) \\\\\\ \log(2)=t\log(1.05)\implies \cfrac{\log(2)}{\log(1.05)}=t\implies 14.2\approx t[/tex]

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.

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:

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Answer:

40

Step-by-step explanation:

P=2(l+w)

2·(10+10)

          =40

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.

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.

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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.

The answer is -7.

The coefficient is the part of the variable that does not change with respect to the variable.

Hence, in the monomial -7x²y⁴, the coefficient is -7.

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.

The attached calculator shows the monthly payments to be ...

  30 year loan: $1597.75 monthly

  25 year loan: $1773.75 monthly

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.

Answer:

a)

Step-by-step explanation:

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.

Points D, G, C lie on the same line with point G between the other two. That means rays GD and GC are opposite rays.

Answer:

it's simple, put the values in the equation.

5 + d( 3b-2d) = 5 + 4( 3×-3 - 2× 4)

= 5 + 4( -9-8)

= 5+ 4 × -17

= 5-68 = -63 ans.

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

I 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

Substitute 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

Answer:

9:8:2

Step-by-step explanation:

3/4 : 2/3 : 1/6 Multiply by 12.
9 : 8 : 2

The graph first, and the graph fifth have no solution because there are no intersection options (A) and (E) are correct.

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.

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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

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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?

Answer:

x = 5

Step-by-step explanation:

There's a Secant Theorem that someone else figured out (waaaay back in history) we just need to memorize it. So a secant is a line that touches the circle in two places. Your picture has two secants that both go thru the same point that's outside the circle. The secants each have a bit that's inside the circle and a bit that's outside the circle. And we could add together the inside and outside bits and get a total for the whole thing.

The secant theorem says that the outside piece × the whole thing on one secant = the outside piece × the whole thing on the other secant.

For the secant on top the "outside" bit is 9 and the whole thing is (2x+1+9). We'll times these together.

For the bottom secant the outside piece is 10 and the whole thing is (x+3+10). We'll multiply these together.

9(2x+1+9)=10(x+3+10)

simplify.

9(2x+10) = 10(x+13)

distribute.

18x + 90 = 101x + 130

combine like terms.

8x + 90 = 130

subtract 90

8x = 40

divide by 8

x = 5

see image.

Let [tex]n[/tex] be the total number of stickers. If she puts 21 stickers on a page, she will fill up [tex]p[/tex] pages such that

[tex]n = 21p + 14[/tex]

Suzanna has between 90 and 100 stickers, so

[tex]90 \le n \le 100 \implies 76 \le n - 14 \le 86[/tex]

[tex]n-14[/tex] is a multiple of 21, and 4•21 = 84 is the only multiple of 21 in this range. So she uses up [tex]p=4[/tex] pages and

[tex]n-14 = 4\cdot21 \implies n = 4\cdot21 + 14 = \boxed{98}[/tex]

stickers.

The angle measures ABD = 45, DBC = 45 and ABC = 90 imply that ray l bisect ∠ABC?

From the figure, we have the following highlights:

This means that the points ABC can be joined to form a right triangle

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?

You would need the measures of ABC and ABD

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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.

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.

Answer:

it depend on your total credit load u register, if it's d only credit load it affect your gpa alot

Answer:

The statement "q + 5 is odd" is FALSE.

Step-by-step explanation:

Let p = 2 and q = 3.

A. p + q is odd ... 2 + 3 = 5   TRUE

B. pq is even ... 2*3 = 6   TRUE

C. q + 1 is even ... 3 + 1 = 4   TRUE

D. q + 5 is odd ... 3 + 5 = 8   FALSE

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

Taking the distance between dots as 1 unit, we have;

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 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

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The absolute value inequality is given as |(p - 0.43)I ≤ 0.019

The 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

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