A. 1
B. 9
C. 10
D.1/9

I think you are asked to find the value of the first derivative of f(x) at π/4. Given

[tex]f(x) = \dfrac{\sin(4x)-\cos(x)}{\tan(x)}[/tex]

use the quotient to differentiate and you get

[tex]f'(x) = \dfrac{\tan(x)(4\cos(4x)+\sin(x))-(\sin(4x)-\cos(x))\sec^2(x)}{\tan^2(x)}[/tex]

Then at x = π/4, you have

tan(π/4) = 1

cos(4•π/4) = cos(π) = -1

sin(π/4) = 1/√2

sin(4•π/4) = sin(π) = 0

cos(π/4) = 1/√2

sec(π/4) = √2

==>   f ' (π/4) = (1•(-4 + 1/√2) - (0 - 1/√2)•(√2)²) / 1² = -4 + 1/√2 + √2

Answer:

946 people

Step-by-step explanation:

Find how many you would predict to be satisfied by multiplying 1,100 by 0.86:

1,100(0.86)

= 946

So, you could expect 946 people to be satisfied

Answer:

yes

Step-by-step explanation:

if you change it to standard form, it would be

y=1/2x

because it's in the format of y=ax then it is direct variation

Answer:

SAA

Step-by-step explanation:

HOPE IT HELPS YOU IN YOUR LEARNING PROCESS.

Answer:

13th term

Step-by-step explanation:

41 = 7n - 50

41 + 50 = 7n

91 = 7n

7n = 91

n = 91/7

n = 13

13th term has value 41

Answer:

n = 13

Step-by-step explanation:

7n - 50 = 41

Add 50 to both sides

7n = 41 + 50

7n = 91

Divide both sides by 7

n = 91/7

n = 13

urdxvjok NCAA earth bno

Answer:

1/108

Step-by-step explanation:

each denominator triples, so just triple 36.

Answer:

1/108

Step-by-step explanation:

This is a geometric sequence, where each number is 3 times the previous. Normally you would use the actual formula, however you're just asked to pick up on a pattern so just multiplying the second number by 3 works.

(1) Recall that

sin(x - y) = sin(x) cos(y) - cos(x) sin(y)

sin²(x) + cos²(x) = 1

Given that α lies in the third quadrant, and β lies in the fourth quadrant, we expect to have

• sin(α) < 0 and cos(α) < 0

• sin(β) < 0 and cos(β) > 0

Solve for cos(α) and sin(β) :

cos(α) = -√(1 - sin²(α)) = -3/5

sin(β) = -√(1 - cos²(β)) = -5/13

Then

sin(α - β) = sin(α) cos(β) - cos(α) sin(β) =  (-4/5) (12/13) - (-3/5) (-5/13)

==>   sin(α - β) = -63/65

(2) In the second identity listed above, multiplying through both sides by 1/cos²(x) gives another identity,

sin²(x)/cos²(x) + cos²(x)/cos²(x) = 1/cos²(x)

==>   tan²(x) + 1 = sec²(x)

Rewrite the equation as

3 sec²(x) tan(x) = 4 tan(x)

3 (tan²(x) + 1) tan(x) = 4 tan(x)

3 tan³(x) + 3 tan(x) = 4 tan(x)

3 tan³(x) - tan(x) = 0

tan(x) (3 tan²(x) - 1) = 0

Solve for x :

tan(x) = 0   or   3 tan²(x) - 1 = 0

tan(x) = 0   or   tan²(x) = 1/3

tan(x) = 0   or   tan(x) = ±√(1/3)

x = arctan(0) + nπ   or   x = arctan(1/√3) + nπ   or   x = arctan(-1/√3) + nπ

x = nπ   or   x = π/6 + nπ   or   x = -π/6 + nπ

where n is any integer. In the interval [0, 2π), we get the solutions

x = 0, π/6, 5π/6, π, 7π/6, 11π/6

(3) You only need to rewrite the first term:

[tex]\dfrac{\sin(x)}{1-\cos(x)} \times \dfrac{1+\cos(x)}{1+\cos(x)} = \dfrac{\sin(x)(1+\cos(x))}{1-\cos^2(x)} = \dfrac{\sin(x)(1+\cos(x)}{\sin^2(x)} = \dfrac{1+\cos(x)}{\sin(x)}[/tex]

Then

[tex]\dfrac{\sin(x)}{1-\cos(x)}+\dfrac{1-\cos(x)}{\sin(x)} = \dfrac{1+\cos(x)+1-\cos(x)}{\sin(x)}=\dfrac2{\sin(x)}[/tex]

Answer:

[tex]\frac{y^{6} }{ x^{2} }[/tex]

Step-by-step explanation:

[tex]y^{6} x^{-2}[/tex]

Answer and Step-by-step explanation:

When there is a set of values within parenthesis, and an exponents on the values and on the parenthesis, you multiply the outer exponent with the inner exponent.

When a value has a negative exponent, the value that has the negative exponent will become a fraction and go to the denominator of the fraction (or go immediately to the denominator), or if it is already a fraction, goes to the denominator. If the value that has the negative exponent is in the denominator, the value will go to the numerator. In both instances, the negative exponent will then change to positive.

First, we need to simplify the expression inside the parenthesis.

[tex]y^{\frac{3}{2} } x^{-\frac{1}{2} } --> \frac{y^{\frac{3}{2} } }{x^{\frac{1}{2}} }[/tex]

Now we multiply the 4 to the exponents.

[tex]\frac{y^{\frac{3}{2} *\frac{x4}{1} } }{x^{\frac{1}{2}}*\frac{4}{1} } = \frac{y^{\frac{12}{2}} }{x^{\frac{4}{2}}} = \frac{y^6}{x^2}[/tex]

[tex]\frac{y^6}{x^2}[/tex] is the answer.

#teamtrees #PAW (Plant And Water)

Answer:

In any quantitative science, the terms relative change and relative difference are used to compare two quantities while taking into account the "sizes" of the things being compared. The comparison is expressed as a ratio and is a unitless number.

Step-by-step explanation:

I hope it helps

Answer:

please write in english i cannot understand

Step-by-step explanation:

step by step explanation:

[tex]\mathfrak{x}^{2}+{y}^{2}+16=0[/tex]

=[x2+16=0x26]

=[2x{y}^2{16}~0]

=[4×{y}^0{16}]

=[32x{y}^x]

Answer:

(a): The conditional pmf of Y when X = 1

[tex]p_{Y|X}(0|1) = 0.2353[/tex]

[tex]p_{Y|X}(1|1) = 0.5882[/tex]

[tex]p_{Y|X}(2|1) = 0.1765[/tex]

(b): The conditional pmf of Y when X = 2

[tex]p_{Y|X}(0|2) = 0.0962[/tex]

[tex]p_{Y|X}(1|2) = 0.2692[/tex]

[tex]p_{Y|X}(2|2) = 0.6346[/tex]

(c): From (b) calculate P(Y<=1 | X =2)

[tex]P(Y\le1 | X =2) = 0.3654[/tex]

(d): The conditional pmf of X when Y = 2

[tex]p_{X|Y}(0|2) = 0.025[/tex]

[tex]p_{X|Y}(1|2) = 0.150[/tex]

[tex]p_{X|Y}(2|2) = 0.825[/tex]

Step-by-step explanation:

Given

The above table

Solving (a): The conditional pmf of Y when X = 1

This implies that we calculate

[tex]p_{Y|X}(0|1), p_{Y|X}(1|1), p_{Y|X}(2|1)[/tex]

So, we have:

[tex]p_{Y|X}(0|1) = \frac{p(y = 0\ n\ x = 1)}{p(x = 1)}[/tex]

Reading the data from the given table, the equation becomes

[tex]p_{Y|X}(0|1) = \frac{0.08}{0.08+0.20+0.06}[/tex]

[tex]p_{Y|X}(0|1) = \frac{0.08}{0.34}[/tex]

[tex]p_{Y|X}(0|1) = 0.2353[/tex]

Using the format of the above formula for the rest, we have:

[tex]p_{Y|X}(1|1) = \frac{0.20}{0.34}[/tex]

[tex]p_{Y|X}(1|1) = 0.5882[/tex]

[tex]p_{Y|X}(2|1) = \frac{0.06}{0.34}[/tex]

[tex]p_{Y|X}(2|1) = 0.1765[/tex]

Solving (b): The conditional pmf of Y when X = 2

This implies that we calculate

[tex]p_{Y|X}(0|2), p_{Y|X}(1|2), p_{Y|X}(2|2)[/tex]

So, we have:

[tex]p_{Y|X}(0|2) = \frac{p(y = 0\ n\ x = 2)}{p(x = 2)}[/tex]

Reading the data from the given table, the equation becomes

[tex]p_{Y|X}(0|2) = \frac{0.05}{0.05+0.14+0.33}[/tex]

[tex]p_{Y|X}(0|2) = \frac{0.05}{0.52}[/tex]

[tex]p_{Y|X}(0|2) = 0.0962[/tex]

Using the format of the above formula for the rest, we have:

[tex]p_{Y|X}(1|2) = \frac{0.14}{0.52}[/tex]

[tex]p_{Y|X}(1|2) = 0.2692[/tex]

[tex]p_{Y|X}(2|2) = \frac{0.33}{0.52}[/tex]

[tex]p_{Y|X}(2|2) = 0.6346[/tex]

Solving (c): From (b) calculate P(Y<=1 | X =2)

To do this, where Y = 0 or 1

So, we have:

[tex]P(Y\le1 | X =2) = P_{Y|X}(0|2) + P_{Y|X}(1|2)[/tex]

[tex]P(Y\le1 | X =2) = 0.0962 + 0.2692[/tex]

[tex]P(Y\le1 | X =2) = 0.3654[/tex]

Solving (d): The conditional pmf of X when Y = 2

This implies that we calculate

[tex]p_{X|Y}(0|2), p_{X|Y}(1|2), p_{X|Y}(2|2)[/tex]

So, we have:

[tex]p_{X|Y}(0|2) = \frac{p(x = 0\ n\ y = 2)}{p(y = 2)}[/tex]

Reading the data from the given table, the equation becomes

[tex]p_{X|Y}(0|2) = \frac{0.01}{0.01+0.06+0.33}[/tex]

[tex]p_{X|Y}(0|2) = \frac{0.01}{0.40}[/tex]

[tex]p_{X|Y}(0|2) = 0.025[/tex]

Using the format of the above formula for the rest, we have:

[tex]p_{X|Y}(1|2) = \frac{0.06}{0.40}[/tex]

[tex]p_{X|Y}(1|2) = 0.150[/tex]

[tex]p_{X|Y}(2|2) = \frac{0.33}{0.40}[/tex]

[tex]p_{X|Y}(2|2) = 0.825[/tex]

Answer: [tex]30e^{0.00813x}[/tex]

Step-by-step explanation:

Given

Median age in 1980 is [tex]30[/tex]

It is [tex]35.3[/tex] in year 2000

Suppose the median age follows the function [tex]ae^{bx}[/tex]. Consider 1980 as starting year. Write the equation for year 1980

[tex]\Rightarrow 30=ae^{b(0)}\\\Rightarrow 30=a[/tex]

For year 2000

[tex]\Rightarrow 35.3=30e^{20b}\\\\\Rightarrow \dfrac{30e^{20b}}{30}=\dfrac{35.3}{30}\\\\\Rightarrow e^{20b}=1.17666\\\\\Rightarrow b=0.00813[/tex]

After t years of 1980

[tex]\Rightarrow 30e^{0.00813x}[/tex]

Answer:

[tex]{ \tt{rate \: of \: change \: in \: A = 9}}[/tex]

Rate of change in function A is two times than that in function B

Answer:

108 square metres

Step-by-step explanation:

A=√d square - l square

here

A = area

d= diagonal

l= length

Answer:

129469.3194

342000

212530.6806

Step-by-step explanation:

Going to assume that the 8% is a nominal, montly rate

which means the effective monthly rate is .08/12= .006667

using the annuity immediate formula...

a.)

[tex]950(\frac{1-(1+.006667)^{-30*12}}{.006667})=129469.3194[/tex]

b.) we would pay 950*30*12= 342000

c.) the amount in interest would be 342000-129469.3194=212530.6806

a) The loan one can afford is $1,29,460.2

b) The total amount of money paid to the loan company over the life of the loan is $342,000.

c)  $212539.8 of the total amount paid is interest.

To determine the answers to these questions, we'll need to use the formula for calculating a fixed monthly mortgage payment:

[tex]M = \frac{P \times r \times (1 + r)^n}{((1 + r)^n - 1)}[/tex]

where:

M is the monthly payment,

P is the principal loan amount,

r is the monthly interest rate (annual interest rate divided by 12),

and n is the total number of payments (number of years multiplied by 12).

Given:

Monthly payment (M) = $950

Loan term = 30 years

Interest rate = 8% per year

a) How big of a loan can you afford?

Let's calculate the principal loan amount (P):

First, we need to convert the annual interest rate to a monthly interest rate:

r = 0.08 / 12

= 0.00667

n = 30 years × 12 months

n= 360

Using the formula and plugging in the values we have:

[tex]950 = \frac{P \times 0.00667 \times (1 + 0.00667)^{360}}{((1 + 0.00667)^{360} - 1)}[/tex]

[tex]950 = \frac{P \times 0.00667 \times 10.948}{10.948 - 1}[/tex]

[tex]950=\frac{P \times 0.07302316}{9.948}[/tex]

[tex]950\times9.948 = 0.0730P[/tex]

Divide by 0.073:

Now we can solve for P:

[tex]P=\frac{9450.6}{0.0730}[/tex]

[tex]P = 1,29,460.2[/tex]

Therefore, you can afford a loan amount of $1,29,460.2

b) The total amount paid to the loan company can be calculated by multiplying the monthly payment by the total number of payments:

Total amount = Monthly payment × Total number of payments

Total amount =[tex]$950 \times 360[/tex]

Total amount = [tex]342,000[/tex]

Therefore, the total amount of money paid to the loan company over the life of the loan is $342,000.

c) To find out how much of the total amount paid is interest, we can subtract the principal loan amount from the total amount:

Interest = Total amount - Principal loan amount

Interest = [tex]342,000 - 129460.2[/tex]

=$212539.8

Therefore, $212539.8 of the total amount paid is interest.

To learn more on Simple Interest click:

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Answer:

f(6)=-42

f(0)=0

f(-1)=7

Step-by-step explanation:

since f(x) =-7x

it implies that f(6),f(0) and f(-1) are all equal to f(x)

which is equal to -7x .

so wherever you find x you out it in the

function

===============================================

Work Shown:

A = P*e^(r*t)

A = 47000*e^(0.0526*17)

A = 114,932.799077198

A = 114,932.80

Notes:

Mark's account balance after 17 years would be $114,932.8

[tex]A=Pe^{rt}[/tex]

where,

A = Accrued amount

P = Principal amount

r = interest rate as a decimal

R = interest rate as a percent

r = R/100

t = time in years

For given question,

P = $47000, t = 17 years

R = 5.26%

[tex]\Rightarrow r =\frac{5.26}{100}\\\\\Rightarrow r = 0.0526[/tex]

Using the Continuous Compounding Formula,

[tex]\Rightarrow A=Pe^{rt}\\\\\Rightarrow A=47000\times e^{0.0526\times 17}\\\\\Rightarrow A=114932.8[/tex]

Therefore, Mark's account balance after 17 years would be $114,932.8

Learn more about the Continuous Compounding here:

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Answer:

[tex]m = \frac{1}{12}[/tex]

Step-by-step explanation:

Given

[tex](x,y) = (36,6)[/tex]

[tex]f(x) = \sqrt x[/tex] ----- the equation of the curve

Required

The slope of f(x)

The slope (m) is calculated using:

[tex]m = \lim_{h \to 0} \frac{f(a + h) - f(a)}{h}[/tex]

[tex](x,y) = (36,6)[/tex] implies that:

[tex]a = 36; f(a) = 6[/tex]

So, we have:

[tex]m = \lim_{h \to 0} \frac{f(a + h) - f(a)}{h}[/tex]

[tex]m = \lim_{h \to 0} \frac{f(36 + h) - 6}{h}[/tex]

If [tex]f(x) = \sqrt x[/tex]; then:

[tex]f(36 + h) = \sqrt{36 + h}[/tex]

So, we have:

[tex]m = \lim_{h \to 0} \frac{\sqrt{36 + h} - 6}{h}[/tex]

Multiply by: [tex]\sqrt{36 + h} + 6[/tex]

[tex]m = \lim_{h \to 0} \frac{(\sqrt{36 + h} - 6)(\sqrt{36 + h} + 6)}{h(\sqrt{36 + h} + 6)}[/tex]

Expand the numerator

[tex]m = \lim_{h \to 0} \frac{36 + h - 36}{h(\sqrt{36 + h} + 6)}[/tex]

Collect like terms

[tex]m = \lim_{h \to 0} \frac{36 - 36+ h }{h(\sqrt{36 + h} + 6)}[/tex]

[tex]m = \lim_{h \to 0} \frac{h }{h(\sqrt{36 + h} + 6)}[/tex]

Cancel out h

[tex]m = \lim_{h \to 0} \frac{1}{\sqrt{36 + h} + 6}[/tex]

[tex]h \to 0[/tex] implies that we substitute 0 for h;

So, we have:

[tex]m = \frac{1}{\sqrt{36 + 0} + 6}[/tex]

[tex]m = \frac{1}{\sqrt{36} + 6}[/tex]

[tex]m = \frac{1}{6 + 6}[/tex]

[tex]m = \frac{1}{12}[/tex]

Hence, the slope is 1/12

Answer:

2 feet

Step-by-step explanation:

Displacement at 0 seconds is 0 feet.

Displacement at 2 seconds is 2 feet because it took them 2 seconds to walk 2 feet.

9514 1404 393

Answer:

  p(x) = x³ -3x²+4x -2

Step-by-step explanation:

When the polynomial has real coefficients, the complex roots come in conjugate pairs. You are given one root as 1+i, so there is another that is 1-i.

Each root r gives rise to a factor (x -r). Then the three roots tell you the factorization is ...

  p(x) = (x -1)(x -(1+i))(x -(1-i))

The last two factors can be recognized as the factors of the difference of squares:

  ((x -1) +i)((x -1) -i) = (x -1)² -i²

  = (x² -2x +1) -(-1) = x² -2x +2

Now the whole polynomial can be seen to be ...

  p(x) = (x -1)(x² -2x +2) = x(x² -2x +2) -1(x² -2x +2)

  p(x) = x³ -2x² +2x -x² +2x -2 . . . . eliminate parentheses

  p(x) = x³ -3x²+4x -2

Answer:

A and b Are in quadrant 2. F and D are in quadrant 1. F is in quadrant 3 and C is in quadrant 4

Step-by-step explanation:

each quadrant is in the boxes and the question is asking what is each  coordinate is in what quadrant

Step-by-step explanation:

here is the answer. Feel free to ask for more.

Answer:

x= - 1

Step-by-step explanation:

Answer:

283 flowers

Step-by-step explanation:

c=2pi*r

c = 1130.973 =1131

1131/4

282.75 = 283

Answer:

5.385 < 5.395

Step-by-step explanation:

Compare digits one by one starting form the left.

5.395 and 5.385

The 5s in the ones place are equal.

5.395 and 5.385

The 3s in the tenths place are equal.

5.395 and 5.385

The 9 in the hundredths place is greater than the 8 in the hundredths place, so the number with the 9 is grater than the number with the 8.

That makes the number with the 8 less than the number with the 9.

Answer: 5.385 < 5.395

Answer:

Addition equation = -4-0) + [(-13)-(-4)]

Answer =  -13

Step-by-step explanation:

For the small arrow in the diagram, the expression is (-4 - 0)

For the bog arrow, the expression will be -13 - (-4)

Adding both expressions

Addition = (-4-0) + [(-13)-(-4)]

Addition = (-4) + (-13+4)

Addition = -4 + (-9)

Addition = -4-9

Addition = -13