Mathematics puzzle from my calculus text book.

Mathematics Puzzle From My Calculus Text Book.

Answers

Answer 1

Answer:

[tex]{ \tt{g(x) = a {x}^{2} + bx + c = 0 }} \\ { \tt{f(x) = {a'x}^{2} + b 'x + c' = 0}} \\ { \boxed{ \bf{f(g(x)) = g(f(x))}}} : \\ { \tt{ =( \frac{a}{a'})x {}^{2} + ( \frac{b}{b'}) x} + \frac{c}{c'} } = 0[/tex]


Related Questions

prove this qns plzz ​

Answers

Answer:

L.H.S.

= (cos5a.sin2a-cos4a.sin3a)/ (sin5a.sin2a-cos4a.cos3a)

Multiply numerator and denominator by 2.

= 2(cos5a.sin2a - cos4a.sin3a) / 2(sin5a.sin2a - cos4a.cos3a)

= (2cos5a.sin2a - 2cos4a.sin3a)/

(2sin5a.sin2a - 2cos4a.cos3a) = [sin(5a+2a)-sin(5a-2a)-sin(4a+3a)

+sin(4a-3a)]/[cos(5a-2a)-cos(5a+2a)-sin(4a-3a) +cos(4a+3a)]

= (sina - sin3a)/(cso3a-cosa)

= (-2cos2a.sina)/(-2sin2a.sina)

= cos2a/sin2a

= cot2a

= R.H.S.

answer is in a picture have a look

Find the equivalent expression using the
same bases.
(98.41)

Answers

9684.5281 I think that’s the answer

[tex]3x+7=12-2x;1[/tex]

Answers

Step-by-step explanation:

[tex]3x + 7 = 12- 2x \\ 3x + 2x = 12 - 7 \\ 5x = 5 \\ x = \frac{5}{5} \\ x =1[/tex]

a. The first five terms of n^2 + 5 are


Answers

Given:

The nth term of a sequence is:

[tex]n^2+5[/tex]

To find:

The first five terms of the given sequence.

Solution:

The given sequence is:

[tex]a_n=n^2+5[/tex]

For n=1,

[tex]a_1=1^2+5[/tex]

[tex]a_1=1+5[/tex]

[tex]a_1=6[/tex]

For n=2,

[tex]a_2=2^2+5[/tex]

[tex]a_2=4+5[/tex]

[tex]a_2=9[/tex]

For n=3,

[tex]a_3=3^2+5[/tex]

[tex]a_3=9+5[/tex]

[tex]a_3=14[/tex]

For n=4,

[tex]a_4=4^2+5[/tex]

[tex]a_4=16+5[/tex]

[tex]a_4=21[/tex]

For n=5,

[tex]a_5=5^2+5[/tex]

[tex]a_5=25+5[/tex]

[tex]a_5=30[/tex]

Therefore, the first five terms of the given sequence are 6, 9, 14, 21, 30.

Assume that $4,000 I deposited into an investment account doubled in value over a six year period. What annual interest rate must I have earned over this period? Is the initial amount of the deposit relevant to the calculation of the annual interest rate? Why or why not?

Answers

Answer:

Interest rate is about 12.246%

The initial deposit doesn't matter because when you divide both sides by the initial deposit you're always left with (1+i)ⁿ=2

Step-by-step explanation:

[tex]4000(1+i)^6=8000\\(1+i)^6=2\\1+i=\sqrt[6]{2} \\1+i=1.122462048\\i=.12246[/tex]

Suppose f(x) = x2. What is the graph of g(x)= 1/4 f(x)?

NEWD HELP ASAP!

Answers

Answer:

g(x) =1/4 x²

The choose (1)

first drawing

What is the value of x in the triangle?​

Answers

Answer:b

Step-by-step explanation:

Ive done this

Any good tv shows on Netflix

Has to be atleast 3 season long

Answers

Well I like criminal minds (15 seasons)
I like ncis (also 15 seasons I think)
I like cobra Kai ( 3 season 4 one coming out )
:)

Answer:

Grey's Anatomy

Step-by-step explanation:

Plz help ASAP problem down below

Answers

Answer: Choice B) 60

Explanation:

This is known as a cyclic quadrilateral since all four points are on the circle's edge, and the quadrilateral is entirely inside the circle (no parts of the quadrilateral spill outside the circle). Another term is "inscribed quadrilateral"

Since we have an inscribed quadrilateral, this means the opposite angles of the quadrilateral are supplementary.

B+D = 180

120+x = 180

x = 180-120

x = 60

A three-year interest rate swap has a level notional amount of 300,000. Each settlement period is one year and the variable rate is the one-year spot interest rate at the beginning of the settlement period. One year has elapsed and the one-year spot interest rate at the start of year 2 is 4.45%.
Time to Maturity 1 2 3 4 5
Price of zero coupon bond with Maturity value 1 0.97 0.93 0.88 0.82 0.75
Calculate the net swap payment by the payer at the end of the second year.
A. −400
B. −300
C. −200
D. −100
E. 0
Hint : Find the swap rate R using the table and then use R and the one-year spot rate at the start of year 2 to find the net swap payment at the end of year 2.

Answers

Answer:

A. -400

Step-by-step explanation:

We solve for the swap rate

R = (1-p3)/(p1+p2+p3)

R = 1-0.88/0.97+0.93+0.88

= 0.12/2.78

= 0.04317

Remember 4.45% is the one year spot rate for the second option

Net swap

= 300000*0.04317-300000*0.0445

= 12951-13350

= -399

This is approximately -400

So the net swap payment at the end of the second year is option a, -400

Unit: Decimals
Progress
The movement of the progress bar may be uneven becouse questions can be worth more or less (including zero) depending on your answer.
Which digit is in the thousandths place in the number 48.5302?
O 3
O 5
O 2
O 0
Submit
Pass
Don't know answer

Answers

Answer:

0

Step-by-step explanation:

48.5302

The number just to the left of the decimal point is the ones place. The 8 is in the ones place. Every place to the left is 10 times greater than the previous one, and every place to the right is 10 times smaller than the previous one.

48.5302

4 - tens place - 4 tens means 40

48.5302

8 - ones place - 8 ones means 8

48.5302

5 - tenths place - 5 tenths means 0.5

48.5302

3 - hundredths place - 3 hundredths means 0.03

48.5302

0 - thousandths place - 0 thousandths means 0.000

48.5302

2 - ten-thousandths place - 2 ten-thousandths means 0.0002

Answer: 0

Please help!!! Picture included

Answers

Step-by-step explanation:

A is your answer.

You just have to solve for each function individually and see what the roots are.

9514 1404 393Answer:

  (a)  f(x) = 2x² -2

Step-by-step explanation:

The function has two zeros, at -1 and 1, so is not a linear or square root function. The only viable choice is the correct one:

  f(x) = 2x² -2


find the value of Y in the figure above .

Answers

9514 1404 393

Answer:

x = 37y = 22

Step-by-step explanation:

Consecutive interior angles are supplementary.

  (x -20)° +(4x +15)° = 180°

  5x = 185 . . . . . . . . . . . . . . divide by °, add 5

  x = 37 . . . . . . . . . . . . divide by 5

__

  74° +(5y -4)° = 180°

  5y = 110 . . . . . . . . . . . divide by °, subtract 70

  y = 22 . . . . . . . . . . divide by 5

If the measure of angle 2 is 920 and the measure of angle 4 is 2
what is the value of x?
14.
23

Answers

Step-by-step explanation:

the value of x will be 920

If f(x) = 3x^2 - x, find f(-2)

Answers

Answer:

14

Step-by-step explanation:

Substitute x for -2

3(-2)^2 - (-2)

3(4) +2

12+2=14

Craig made a mobile using geometric shapes including triangles shaped as shown. For what value of X and Y can you use a triangle congruence theorem to show that the triangles are congruent? Which triangle congruence theorem can you use? Explain.
.
.
.
May you also show the work? Please help. Thank you.

Answers

Answer:

x = 3

y = 8

Step-by-step explanation:

In the given triangle FGH,

m∠F + m∠G + m∠H = 180° [Triangle sum theorem]

60° + 90° + m∠H = 180°

m∠H = 30°

If the given triangles FGH and TUV are congruent, their corresponding sides will be equal in measure.

m∠F = m∠T

7y + 4 = 60°

7y = 56

y = 8

GH ≅ UV

8x - 12 = 12

8x = 24

x = 3

Using the AAS congruence theorem, the values of x and y that show that both triangles are congruent are: x = 3 and y = 8.

What is the AAS Congruence Theorem?

According to the angle-angle-side congruence theorem (AAS), two triangles are congruent if they have two corresponding congruent angles and one pair of corresponding non-included sides that are congruent.

Thus, by the AAS theorem, we have:

8x - 12 = 12

8x = 12 + 12

8x = 24

x = 3

Also,

7y + 4 = 60

7y = 60 - 4

7y = 56

y = 8

Therefore, using the AAS congruence theorem, the values of x and y that show that both triangles are congruent are: x = 3 and y = 8.

Learn more about AAS congruence theorem on:

https://brainly.com/question/3168048

answer it correctly:)
can anyone help me?:) ​

Answers

Answer:

JAR WITH MARBLES.

There's

5 Blue Marbles

3 Red Marbles

2 Yellow Marbles

Pr = No of desired outcome/No of Possible Outcomes

No of Possible Outcomes = 10.

1. Pr(yellow) = 2/10 = 1/5.

2. Pr(Red) = 3/10

3. Pr(Blue) = 5/10 = 1/2

4. Pr(Yellow and Red) = 2/10 x 3/10 = 6/100 = 3/50.

5.Pr(Blue and Red)= 5/10 x 3/10 = 15/100 = 3/20.

6.Pr( Yellow and Blue) = 2/10 x 5/10 = 10/100 = 1/10.

THE CHIPS ARE PLACED IN A JAR AND MIXED.

No of Possible Outcomes = 8.

The Numbers are 1,2,3,4,5,6,7,8.

There's

4 Even Numbers

4 Odd Numbers

1. Pr(Even) = 4/8 = 1/2

2. Pr(Odd) = 4/8 = 1/2

3. Pr(Chip with Biggest No) = 1/8.

Reason. There can only be one Number which Is the biggest amongst all. So the Probability of picking it is 1.

4.Pr(Smallest Number) = 1/8 (Same concept).

5.Pr(Prime Number)

The prime Numbers above are 2,3,5,7

Pr(Prime) = 4/8 = 1/2.

Hope this helps!.

The dimensions of a closed rectangular box are measured as 60 centimeters, 50 centimeters, and 70 centimeters, with an error in each measurement of at most 0.2 centimeters. Use differentials to estimate the maximum error in calculating the surface area of the box.

Answers

Answer:

The maximum error in calculating the surface area of the box is 72 square centimeters.

Step-by-step explanation:

From Geometry, the surface area of the closed rectangular box ([tex]A_{s}[/tex]), in square centimeters, is represented by the following formula:

[tex]A_{s} = w\cdot l + (w + l)\cdot h[/tex] (1)

Where:

[tex]w[/tex] - Width, in centimeters.

[tex]l[/tex] - Length, in centimeters.

[tex]h[/tex] - Height, in centimeters.

And the maximum error in calculating the surface area ([tex]\Delta A_{s}[/tex]), in square centimeters, is determined by the concept of total differentials, used in Multivariate Calculus:

[tex]\Delta A_{s} = \left(l+h\right)\cdot \Delta w + \left(w+h\right)\cdot \Delta l + (w+l)\cdot \Delta h[/tex] (2)

Where:

[tex]\Delta w[/tex] - Measurement error in width, in centimeters.

[tex]\Delta l[/tex] - Measurement error in length, in centimeters.

[tex]\Delta h[/tex] - Measurement error in height, in centimeters.

If we know that [tex]\Delta w = \Delta h = \Delta l = 0.2\,cm[/tex], [tex]w = 60\,cm[/tex], [tex]l = 50\,cm[/tex] and [tex]h = 70\,cm[/tex], then the maximum error in calculating the surface area is:

[tex]\Delta A_{s} = (120\,cm + 130\,cm + 110\,cm)\cdot (0.2\,cm)[/tex]

[tex]\Delta A_{s} = 72\,cm^{2}[/tex]

The maximum error in calculating the surface area of the box is 72 square centimeters.

2. Find the area of a trapezium shaped field with a base of 45m, top is 35m and with a height of 55m applying the formula for trapezium = 0.5x b+axh

Given:

Base=

Top (a) =

Height =

3. Find the area of a Parallelogram shaped field where the base measures 19m and with a h of 37m.

Applying the formula for parallelogram=bxh

Given:

Base=

Height=

pahelp po thanks​

Answers

Answer:

2. 2200 m²

3. 703 m²

Step-by-step explanation:

2. Given,

Base (b) = 45m

Top (a) = 35m

Height (h) = 55m

Area = (a+b)*h/2

= (45+35)*55/2

= 85*55/2 = 2200 m²

3. Given,

Base (b) = 19m

Height (h) = 37m

Area = b*h

= 19*37

= 703 m²

(The * sign represents the multiplication sign)

Answered by GAUTHMATH

Answer:

2. area = 2200 m²

3. area = 703 m²

Step-by-step explanation:

2. Find the area of a trapezium shaped field with a base of 45m, top is 35m and with a height of 55m applying the

formula for trapezium = 0.5 * (b+a) * h

Given:

Base= 45 m

Top (a) = 35 m

Height = 55 m

area = 0.5 * (b+a) * h

area = 0.5 * (45 m + 35 m) * 55 m

area = 2200 m²

3. Find the area of a Parallelogram shaped field where the base measures 19m and with a h of 37m.

Applying the formula for parallelogram = b * h

Given:

Base= 19 m

Height= 37 m

area = b * h

area = 19 m * 37 m

area = 703 m²

Find the width of a photograph whose length is 24 inches and whose proportions
are the same as a photograph that is 3 inches wide by 4 inches long.

Answers

A photograph having length of 24 inches which is proportionate to another photograph having dimensions 3 × 4 inches, has width of 18 inches.

What is proportion?

In general, the term "proportion" refers to a part, share, or amount that is compared to a whole. According to the definition of proportion, two ratios are in proportion when they are equal.

Let the width of the photograph be x inches.

The length of the photograph is 24 inches.

A similar proportion photograph has width as 3 inches.

A similar proportion photograph has length as 4 inches.

The equation to find the width of photograph is -

x / 24 = 3 / 4

Simplify the equation -

x = (24 × 3) / 4

x = 72 / 4

x = 18

Therefore, the width value is 18 inches.

To learn more about proportion from the given link

https://brainly.com/question/19994681

#SPJ1

PLEASE EMERGENCY!!!!
Which of the following statements is FALSE?

Answers

Answer:

Third one.

BO is not 7.8 cm

Step-by-step explanation:

find the slope and y-intercept of line 3x +y -9=0

Answers

Answer:

x-intercept(s):(3,0)

y-intercept(s):(0,9)

Step-by-step explanation:

if an orange weighs 570 grams what is the weight of an apple​

Answers

Answer:

THE SAME

Step-by-step explanation:

HELP
-5(2m-3)-4<81
I need the steps also well

Answers

Answer:

m>-7

Step-by-step explanation:

expand

-10m+15-4<81

-10m+11<81

collect like terms

-10m<81-11

-10m<70

m>-7

A system of equations is said to beinconsistentif the system has no solution. Show by usingthe pivot operation that the following system is inconsistent. Is the system equivalent to asystem in canonical form?

x1 + x2 - 3x3= 7
-2x1 + x2 +5x3 = 2
3x2 - x3 = 15

Answers

Answer:

The system is inconsistent

Step-by-step explanation:

Given the matrix system solutions in the attachment, we can see that the coefficient of the matrix rank has become zero. This shows that it has no solution.

plz g0ive me solution

Answers

Answer:

separate the x from the numbers it will make the equation easier

Here is the general information about the Learn by Doing discussion board exercises (directions, grading, feedback). Prompt
1) Give an example of a research question that involves estimating a characteristic about the population of part-time students at your college.
2) Improve this poorly stated research question: Do students work a lot of hours

Answers

Answer:

Step-by-step explanation:

Answer to question 1:

On average do part-time students spend less than 20 hours per work on academic work and assignments ?

Answer to question 2:

On average do students work greater than 50 hours a week ?

An assignment is worth 300 points for each day the assignment is late the professor deduct 10 points from the assignment and grade

Answers

Answer:

Eh whats the question? it takes 30 days for the assignemnt to be zero if that is the question.

Step-by-step explanation:

Answer:

points = 300 - 10 L

x = 300 - 10Y

x = points, Y = days late

Step-by-step explanation:

Which angle is an adjacent interior angle?

Triangle L M N. Angle L is 1, angle M is 2, angle N is 3. Side M N extends to form angle 4.
1
2
3
4

Answers

Step-by-step explanation:

Triangle LNM is an adjecent interior angle

Answer:

I think it's C

Step-by-step explanation:

Let me know if it's incorrect.

Using the digits 2 through 8, find the number of different 5-digit numbers such that, digits can be used more than once.

Answers

Answer:

7 digits can be used for each position

There are a total of 5 positions

N = 7^5 = 16,807 numbers

You have 7 choices for the first position, second position, etc.

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