When 12 is divided by 2/3 which statement about the quotient is true?

The value of df, when x = π/4 and dx = 1/24, is (-5π - 5√2)/(96√2).

To find the derivative of the function f(x) = -5cos(x) + xtan(x), we'll use the sum and product rules of differentiation. Let's start by finding df/dx.

Apply the product rule:

Let u(x) = -5cos(x) and v(x) = xtan(x).

Then, the product rule states that (uv)' = u'v + uv'.

Derivative of u(x):

u'(x) = d/dx[-5cos(x)] = -5 * d/dx[cos(x)] = 5sin(x) [Using the chain rule]

Derivative of v(x):

v'(x) = d/dx[xtan(x)] = x * d/dx[tan(x)] + tan(x) * d/dx[x] [Using the product rule]

= x * sec^2(x) + tan(x) [Using the derivative of tan(x) = sec^2(x)]

Applying the product rule:

(uv)' = (5sin(x))(xtan(x)) + (-5cos(x))(x * sec^2(x) + tan(x))

= 5xsin(x)tan(x) - 5xcos(x)sec^2(x) - 5cos(x)tan(x)

Simplify the expression:

df/dx = 5xsin(x)tan(x) - 5xcos(x)sec^2(x) - 5cos(x)tan(x)

Now, we need to evaluate df/dx at x = π/4 and dx = 1/24.

Substitute x = π/4 into the derivative expression:

df/dx = 5(π/4)sin(π/4)tan(π/4) - 5(π/4)cos(π/4)sec^2(π/4) - 5cos(π/4)tan(π/4)

Simplify the trigonometric values:

sin(π/4) = cos(π/4) = 1/√2

tan(π/4) = 1

sec(π/4) = √2

Substituting these values:

df/dx = 5(π/4)(1/√2)(1)(1) - 5(π/4)(1/√2)(√2)^2 - 5(1/√2)(1)

Simplifying further:

df/dx = 5(π/4)(1/√2) - 5(π/4)(1/√2)(2) - 5(1/√2)

= (5π/4√2) - (10π/4√2) - (5/√2)

= (5π - 10π - 5√2)/(4√2)

= (-5π - 5√2)/(4√2)

= (-5π - 5√2)/(4√2)

Now, to evaluate df/dx when dx = 1/24, we'll multiply the derivative by the given value:

df = (-5π - 5√2)/(4√2) * (1/24)

= (-5π - 5√2)/(96√2)

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Answer:

It is just 65.

Step-by-step explanation:

Answer:

7 shirts 8 pairs of pants

Step-by-step explanation:

:(

:)

Answer:

8 pants, and 7 shirts

Step-by-step explanation:

because there are only two factors in here, you can just subtract:

15-7=8

can i get brainliest please?

A correlation coefficient between number of miles driven and number of gallons of gas remaining is most likely to be 0 to -1. Then the correct option is A.

A mathematical indicator of the degree of the association seen between fluctuation of 2 factors is the correlation coefficient.

A correlation coefficient between number of miles driven and number of gallons of gas remaining is most likely to be 0 to -1.

Then the correct option is A.

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The two cars must be approximately 177.34 feet apart from each other for Spiderman to have different depression angles to each car.

To find the distance between the two cars, we can use trigonometry and the concept of similar triangles. Let's denote the distance between Spiderman and the nearest car as d1 and the distance between Spiderman and the farther car as d2.

In a right triangle formed by Spiderman, the height of the hotel, and the line of sight to the nearest car, the tangent of the depression angle (52 degrees) can be used:

tan(52) = 600 / d1

Rearranging the equation to solve for d1:

d1 = 600 / tan(52)

Similarly, in the right triangle formed by Spiderman, the height of the hotel, and the line of sight to the farther car, the tangent of the depression angle (46 degrees) can be used:

tan(46) = 600 / d2

Rearranging the equation to solve for d2:

d2 = 600 / tan(46)

Using a calculator, we can compute:

d1 ≈ 504.61 feet

d2 ≈ 681.95 feet

The distance between the two cars is the difference between d2 and d1:

Distance = d2 - d1

Plugging in the values, we have:

Distance ≈ 681.95 - 504.61

Distance ≈ 177.34 feet

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Answer:

1058 times 0.13= 137.54 then the Answer= 1237.86

Step-by-step explanation: :0

Answer: 375 bolts

Step-by-step explanation:

Just do 225*(40/24)

Answer:

1 2 5 . 6 9

1 2 5 . 6 7 0

125.69 Would be Greater.

Step-by-step explanation:

First number to the right of the decimal is the tenths place 2nd number would be hundredths and you'd increase etc.

Answer:

5

Step-by-step explanation:

The area of the square with a side length of 3.1 meters is 9.61 square meters.

To find the area of a square, we need to multiply the length of one side by itself. In this case, the square has a side length of 3.1 m.

Area of a square = side length × side length

Substituting the given side length into the formula:

Area = 3.1 m × 3.1 m

To perform the calculation:

Area = 9.61 m²

It's worth noting that when calculating the area, we are working with squared units. In this case, the side length is in meters, so the area is expressed in square meters (m²). The area represents the amount of space enclosed within the square.

Remember, to find the area of any square, you simply need to multiply the length of one side by itself.

The area of the square with a side length of 3.1 meters is 9.61 square meters.

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Answer:

k ( k + 5 )( k - 2 )

Step-by-step explanation:

\(\frac{2}{k^2 +5k}\) = \(\frac{2}{k(k+5)}\)

\(\frac{8}{k^2 +3k-10}\) = \(\frac{8}{(k-2)(k+5)}\)

The least common denominator of rational expressions is

k ( k + 5 )( k - 2 )

Answer:

160

Step-by-step explanation:

Answer:

160

Step-by-step explanation:

Answer:

179.5 - 180.5

Step-by-step explanation:

Time is a continuous variable. The minimum sleep time per night per subject here, is given as 1 minute.

Larger sleep times could be 1.08 minutes, 2.99 minutes, and other continuous/infinite values. Remember there are 60seconds in a minute and in-between seconds, there are milliseconds. So time is a continuous variable.

In this case though, our measurement of time is given in whole number units (integers). Our precision of measurement is 1 unit. We have an observed value of 180 minutes (the first subject's sleep time). The real limits of this value are 179.5 to 180.5

Answer:

d . candle burns down 1 cm per hour .

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Got it correct

The value of x in the triangles are 9.

For variable x : ax² + bx + c = 0, where a≠0 is a standard quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution since it is a second-order polynomial equation, which is guaranteed by the algebraic basic theorem.

Given:

The triangles are congruent.

That means, their corresponding angles are also congruent.

In ΔJKL,

the sum of all the angles of the triangle is 180°.

So,

x²-2x + x + 29 + 3x + 52 = 180

x² + 2x - 99 = 0

Solving the quadratic equation,

x² +11x - 9x - 99 = 0.

x (x + 11) -9 (x + 11) = 0

x = 9 and x = -11

Here, we take x = 9.

Therefore, the value of x is 9.

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Answer:

70 percent

Step-by-step explanation:

Answer:

70%

Step-by-step explanation:

you take the number of students who drive Divide by the number of high school students.

To find arcsin, we need to use the identity:

sin(arcsin(x)) = x

Since arcsin is negative, sin(arcsin) is also negative. Therefore, we can say:

sin(arcsin) = -sqrt(1 - (cos)^2)

where (cos)^2 = 8/17

Substituting, we get:

sin(arcsin) = -sqrt(1 - (8/17))

Simplifying, we get:

sin(arcsin) = -sqrt(17/17 - 8/17)

Simplifying further, we get:

sin(arcsin) = -sqrt(9/17)

Therefore, arcsin = -sqrt(9/17)

To find arctan, we need to use the identity:

tan(arctan(x)) = x

Substituting, we get:

tan(arctan) = -8/17

Therefore, arctan = -8/17

So, arcsin is -sqrt(9/17) and arctan is -8/17.

Answers :-

a. No. of regions that do not have it = 50 - 24 = 26 regions

b. Fraction = 26/50

= 13/25

Answer:

sin(-x)=-0.42

Step-by-step explanation:

Because we know sin is an odd function, sin(-x)=-sin(x). Then enter your given values and you get -0.42

Answer:

Michael is 17 years old.

Step-by-step explanation:

If Adam is 14 years old and he is three years younger than Michael, then Michael is:

Answer:

The polynomial is  2 x² - 2x + 7

Step-by-step explanation:

Given polynomial

                   (8 x² + 9 ) - (6x² +2x +2)

           =   8 x² +9 - 6x² - 2x -2

          =    8x² - 6x² - 2x + 9-2

         =    2 x² - 2x + 7

The polynomial is   2 x² - 2x + 7

Answer:

  about 1.1%

Step-by-step explanation:

Given a moon has a diameter of 22% of the diameter its planet, you want the volume of the moon as a percent of the planet's volume.

The ratio of moon diameter to planet diameter is given as 22%. The ratio of moon volume to planet volume will be the cube of this scale factor:

  moon volume / planet volume = (0.22)³ ≈ 0.0106 = 1.06%

The volume of the moon is about 1.1% of the volume of the planet.

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Explanation

We are asked to find the remainder when

To do so, we can use the remainder theorem

The remainder theorem states that the remainder when p(x) is divided by (x - a) is p(a).

So in our case

So we will substitute -2 into p(x) to get the remainder

Therefore, the remainder is -49

Answer:

\( P(0.55 <X<1.1)= F(1.1) -F(0.55) \)

And replacing we got:

\( P(0.55 <X<1.1)= (1-e^{-\frac{1}{0.66} *1.1}) -(1-e^{-\frac{1}{0.66} *0.55})\)

\( P(0.55 <X<1.1)=e^{-\frac{1}{0.66} *0.55}- e^{-\frac{1}{0.66} *1.1}=0.2457\)

And rounded the answer would be 0.246

Step-by-step explanation:

For this case we can define the random variable X as "The commute time for people in a city" and for this case the distribution of X is given by:

\( X \sim exp (\lambda = \frac{1}{0.66}= 1.515)\)

And for this case we want to find the following probability:

\( P(0.55 <X<1.1)\)

And we can use the cumulative distribution function given by:

\( F(x) =1- e^{-\lambda x}\)

And using this formula we got:

\( P(0.55 <X<1.1)= F(1.1) -F(0.55) \)

And replacing we got:

\( P(0.55 <X<1.1)= (1-e^{-\frac{1}{0.66} *1.1}) -(1-e^{-\frac{1}{0.66} *0.55})\)

\( P(0.55 <X<1.1)=e^{-\frac{1}{0.66} *0.55}- e^{-\frac{1}{0.66} *1.1}=0.2457\)

And rounded the answer would be 0.246

The equation of logarithm are solved and

a) A = 2 + 3 log x + 4 log b

b) B = ( 36 + x + y ) ( log 6 )

c) C = ( 1/2 )x log 5

d) D = ln ( x⁴ / y² )

Given data ,

Let the logarithmic equation be represented as A

Now , the value of A is

a)

A = 2 log 10 + 3 log x + 4 log b

The base of the logarithm is 10 , so

A = 2 + 3 log x + 4 log b

b)

B = log 6³⁶ + log 6ˣ - log 6^ ( y )

From the properties of logarithm , we get

log A + log B = log AB

log A − log B = log A/B

log Aⁿ = n log A

B = 36 log 6 + x log 6 + y log 6

On taking the common term , we get

B = ( 36 + x + y ) ( log 6 )

c)

C = ( 1/2 )log 5ˣ

From the properties of logarithm , we get

C = ( 1/2 )x log 5

d)

D = 4 ln x - 2 ln y

From the properties of logarithm , we get

D = ln x⁴ - ln y²

On further simplification , we get

D = ln ( x⁴ / y² )

Hence , the logarithmic equations are solved

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The sine and cosine of the angle of point P are sin θ = 143/145 and cos θ = -24/145 respectively. Option b. is the answer

Given the coordinate of the point as P (-24/145, 143/145)

This implies x = -24/145 and y =  143/145

To determine the sine and cosine of the angle of point P, we can make a sketch using this information (see attached image).

opposite = 143/145, adjacent = -24/145

hypotenuse = √[(-24/145)² + (143/145)²] = √1 = 1

Using trigometric ratios:

sin θ =   (143/145) / 1 = 143/145    [sin θ = opposite/ hypotenuse]

cos θ =  (-24/145) / 1 = -24/145    [cos θ = adjacent/ hypotenuse]

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Answer:

go by basics u will get it easier

Step-by-step explanation:

assume X2 + e3x as some function t

now find derivative you get (1/t )dt/dx

now find dt /dx. simply derivative with respect to x

for second question use formula

dy/dx = - partial derivative of function with x / partial derivative of function with respect to y

Answer:

See below ↓

Step-by-step explanation:

ii.

Solving

Answer:

Brainliest please

Step-by-step explanation: