Please help me solve and explain these two questions:

1. Find f'(x) for f(x) = ln(x^2 + e^(3x))

2. Find dy/dx by implicit differentiation for ysin(x) = xsin(y)

Yes,  negative 6 a rational number because it can be represented as a fraction of two integers.

A rational number is a number that can be expressed as a fraction of two integers, where the denominator is not zero.

It is any number that can be written in the form "a/b," where "a" and "b" are integers and "b" is not equal to zero.

The number -6 can be expressed as -6/1.

Here, -6 is the numerator and 1 is the denominator.

Both the numerator and denominator are integers, and the denominator is not zero.

Therefore, -6 can be represented as a fraction of two integers and meets the definition of a rational number.

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Answer:

Step-by-step explanation:

y = (1.066)x

The equation to represent the relationship between the original cost of the meal and the cost after the sales tax is y = 1.066x

The sales tax is the amount charged on the price of goods and services.

Let x be the original cost for the meal

Let y be the cost after the sales

If the sales tax rate in Tyler's county is 6.6%, the tax charged is expressed as:

0.066 of theoriginal cost
0.066x

Cost after tax = original cost + tax
Cost after tax = x + 0.066x
y = 1.066x

Hence the equation to represent the relationship between the original cost of the meal and the cost after the sales tax is y = 1.066x

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Answer:

143

Step-by-step explanation:

6(3³)-2(3²)+3-4=

6(27)-2(9)-1=

162-18-1=

143

Answer:

4y = -3x - 48

Step-by-step explanation:

y - y1 = m(x - x1)

y1 = -9 x1= -4 m = -3/4

y -(-9) = -3/4(x -(-4)

y + 9 = -3/4(x + 4)

y + 9 = -3/4x -12/4

multiply through by 4

4y + 36 = -3x -12

4y = -3x -12-36

4y = -3x -48 in the form y = mx + c

Answer:

compress vertically with factor of 0.5

Step-by-step explanation:

f (x) = 0.5 (2) ˣ : compress vertically from f(x) = 2ˣ by a factor of 0.5

Explanation:

You want to first to substitute to form 3 equations.

5=4a+2b+c

12=9a+3b+c

-4=a-b+c

Now solve with whatever way you fell comfortable, I'm going to use elimination.

First eliminate c

7=5a+b

16=8a+4b --> 4=2a+b

Then I'll eliminate b,

3=3a

a=1

Now solve for b and c

7=5+b

b=2

1-2+c=-4

c=-3

Now for the equation:

y=x^2+2b-3

Hope this helps!

Answer:

[tex] y = 4 [/tex]

Step-by-step explanation:

Given:

[tex] y = \frac{7x + 1}{3x - 6} [/tex],

To find the value of y, let's find x by solving 3x = 15.

3x = 15

Divide both sides by 3

x = 15/3

x = 5

Plug in the value of x into [tex] y = \frac{7x + 1}{3x - 6} [/tex]

[tex] y = \frac{7(5) + 1}{3(5) - 6} [/tex]

[tex] y = \frac{35 + 1}{15 - 6} [/tex]

[tex] y = \frac{36}{9} [/tex]

[tex] y = 4 [/tex]

Answer:

[tex]1\frac{1}{2}[/tex]

Answer:

when u divide u get 1.5

Step-by-step explanation:

1.5 is the same thing as "one and five-tenths," or "one and five over ten, or one and half," which is written as 112 as a fraction.

Answer:

67

6+7=13

76-67=9

Done!

Answer:

A, B

Step-by-step explanation:

Answer:

your answers would be 19/20 as a fraction and 9/10 as a fraction

Step-by-step explanation:

:P

Answer:

15/20(3/4), 9/10

Step-by-step explanation:

well in order to add or subtract fractions for that matter, you must have the a common denominator meaning the bottom number on both of the fractions must be the same. and in order to do that you must take the smaller denominator and find what can multiply that into the bigger denominator so in your case 5 is the smaller denominator so in order to get 20 we multiply by 4 and so what you do to the bottom you must also do to the top so we have 3 and now we must also multiply that by 4 leaving us with 12/20 as our new fraction. so now the adding is easy, 7+12=15 and you keep the same denominator 20

so your first answer would be 15/20 and if you need that simplified then you do the same thing once again and you find a common factor between your denominator (the bottom number) and the numerator (the top number) and in this case they do have a common factor which is 5 therefore if you divide both parts ofthe fraction by 5 it will leave you with 3/4 which is your simplified answer to this first question

now for the second equation i'm not going to go through the steps one by one again, as we already have but you may feel free to practice these on your own, but if we skip the step of creating the denominators to be the same with a common factor, then we will should have 6/10+3/10 leaving us with 9/10 as our simplified answer because 9 and 10 do not have any number in common to divide by.

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Answer 1 maybe

Step-by-step explanati

Answer:

I believe it would be 90

Step-by-step explanation:

The required age of Mollie's is 32years and age of Heather's is 72years.

Given that,

The ratio of Mollie’s age to Heather’s age is 4:9,

Heather is 40 years older than Mollie.

We have to determine,

How old is Mollie.

According to the question,

The ratio of Mollie’s age to Heather’s age is 4:9,

The age of Mollie's = 4x

And age of Heather's = 9x

Then ,

The age of Mollie is calculated in the following steps.

The difference between the age of both is 40 years

Age of Heather's - Age of Mollie = Difference of their ages

Then,

[tex]= 9x-4x = 40\\\\= 5x = 40\\\\= x = \frac{40}{5} \\\\= x = 8[/tex]

The value of x is 8.

Therefore,

Age of Mollie's = 4x = (4).(8) = 32years

And Age of Heather's = 9x = (9).(8) = 72years

Hence, The required age of Mollie's is 32years and age of Heather's is 72years.

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Answer:

Your answer is.....

In every big pieces there will be 3 * 1/3 pieces.

So total 12 of 1/3 pieces

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Step-by-step explanation:

Answer:

[tex]R_t=300\ \Omega[/tex]

Step-by-step explanation:

Given that,

R₁ = 100 ohms

R₂ = 200 ohms

We need to find the equivalent resistance of the circuit. So,

[tex]R_t=R_1+R_2\\\\R_t=100+200\\\\R_t=300\ \Omega[/tex]

So, the equivalent resistance is [tex]300\ \Omega[/tex].

Answer:

Answer and explanation below:

Step-by-step explanation:

The formula to convert radians to degrees is 180/pi

For A:π/8=180/π

Cross multiply

The pi's cross each other out and you're left with

1440 degrees as your answer

Hope this helps! :)

Answer:

41

Step-by-step explanation:

Answer:

AA similarity postulate

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Answer:

0.9009

Step-by-step explanation:

Let X be the event that Current will flow

Let Y be the event that the first relay which is 1 is closed

Thus, we can say that every element of Y is in X, but X possesses more elements. Thus, Y ⊂ X.

Thus, we can say that;

P(X ∩ Y) = P(Y)

Thus, given that current flowed, the probability that relay 1 functioned will be expressed as;

P(Y | X) = (P(Y ∩ X))/P(X)

From earlier, we saw that P(X ∩ Y) = P(Y). Thus;

P(Y | X) = P(Y)/P(X)

From the question, P(Y) = 0.9

Since there are 3 relays, then we have;

P(X) = 1 - 0.1³ = 0.999

Thus;

P(Y | X) = 0.9/0.999

P(Y | X) = 0.9009

The  probability that relay 1 functioned is 0.9009

Let us assume X be the event that Current will flow

And,

Let us assume Y be the event that the first relay

So,  Thus, Y ⊂ X.

Now

P(X ∩ Y) = P(Y)

The probability that relay 1 functioned should be

P(Y | X) = (P(Y ∩ X)) ÷ P(X)

From earlier, we saw that P(X ∩ Y) = P(Y).

So,

P(Y | X) = P(Y) ÷ P(X)

Now

P(X) =[tex]1 - 0.1^3[/tex] = 0.999

So,

P(Y | X) = 0.9  ÷0.999

P(Y | X) = 0.9009

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Answer:

popvana used struggle

Step-by-step explanation:

Answer:

P =  24

After 24h will be 108p

Each c is 6m

12 laps

Step-by-step explanation:

36 - 33 = 3

33 - 30 = 3

30 - 27 = 3

27 - 3 = 24

12h = 36p

12h × 3 = 36h

So 36p need to × 3 too

36p × 3 108p

Because 3c to 5c, 18m to 30m need 12m. There was no 4c so the 12m need to  divide two. 12m ÷ 2 = 6m.

So each c is 6.

72 ÷ 6 = 12

The six is from the last question.

Answer:

The midpoint of FH is (3;1)

Step-by-step explanation:

Answer/Step-by-step explanation:

Recall the acronym SOHCAHTOA. This is what we would apply as appropriate in each case.

8. θ = 40°

Opp = m

Adj = 20

Thus, apply TOA

Tan (θ) = opp/adj

Plug in the values

Tan (40) = m/20 (equation)

20×Tan(40) = m

m = 16.7820

9. θ = 22°

Hyp = w

Adj = 18

Thus, apply CAH

Cos (θ) = adj/hyp

Plug in the values

Cos 22 = 18/w (equation)

w×cos 22 = 18

w = 18/(cos 22)

w = 19.4136

10. θ = 35°

Hyp = 55

Opp = x

Thus, apply SOH

Sin θ = opp/hyp

Plug in the values

Sin 35 = x/55 (equation)

55×sin 35 = x

x = 31.5467

11. θ = 33°

Hyp = 19

Adj = x

Thus, apply CAH

Cos θ = adj/hyp

Plug in the values

Cos 33 = x/19 (equation)

19×cos 33 = x

x = 15.9347

12. θ = 17°

Opp = 7

Hyp = x

Thus, apply SOH

Sin θ = opp/hyp

Plug in the values

Sin 17 = 7/x (equation)

x×sin 17 = 7

x = 7/(sin 17)

x = 23.9421

13. θ = 40°

Opp = 15

Adj = x

Thus, apply TOA

Tan θ = opp/adj

Plug in the values

Tan 40 = 15/x (equation)

x×Tan 40 = 15

x = 15/(Tan 40)

x = 17.8763

Answer:

31333.75cm³

Step-by-step explanation:

Volume = πr²h

= 3.14 × (46.45/2)² × 18.5 = 31333.75cm³

a^2 + b^2 = c^2

A-15.1

B-13

Answer:

Diagonal = 10.44 m

Step-by-step explanation:

(3×3)+(10×10) = 109

Sq rt 109 = 10.44 m

Answer:

Step-by-step explanation:

the factors of 9 are 1,3,9

Answer:

1, 3, 9

[tex] \\ \\ \\ \\ [/tex]

Answer:

Step-by-step explanation:

Given the sequence -1,-7,-49,-343,....

We are to find the nth term of the sequence

dn = ar^n-1

a is the first term = -1

r is the common ration = -7/-1 = -49/-7 = 7

n is the number of terms

Substitute

dn = -1(7)^n-1

dn = -7^n-1

hence the nth term of the sequence is dn = -7^n-1

Answer:

a=3

Step-by-step explanation:

Answer:

a = 3

Step-by-step explanation: