Which equation can be used to find the value of b if side a measures 8. 7 cm? 8. 7 plus b equals 54. 6 17. 4 plus b equals 54. 6 26. 1 plus b equals 54. 6 34. 8 plus b equals 54. 6.

the derivative of the function y = (sin(5x))ln(x) is dy/dx = ln(x) * [5cos(5x) + (1/x)].

To find the derivative of the function y = (sin(5x))ln(x) using logarithmic differentiation, we follow these steps:

Step 1: Take the natural logarithm (ln) of both sides of the equation:

ln(y) = ln((sin(5x))ln(x))

Step 2: Use logarithmic properties to simplify the expression:

ln(y) = ln(sin(5x)) + ln(ln(x))

Step 3: Differentiate both sides of the equation implicitly with respect to x:

(1/y) * dy/dx = (1/sin(5x)) * d/dx(sin(5x)) + (1/ln(x)) * d/dx(ln(x))

Step 4: Simplify the derivatives on the right-hand side:

(1/y) * dy/dx = (1/sin(5x)) * (5cos(5x)) + (1/ln(x)) * (1/x)

Step 5: Multiply both sides of the equation by y to isolate dy/dx:

dy/dx = y * [(1/sin(5x)) * (5cos(5x)) + (1/ln(x)) * (1/x)]

Step 6: Substitute y back into the equation:

dy/dx = [(sin(5x))ln(x)] * [(1/sin(5x)) * (5cos(5x)) + (1/ln(x)) * (1/x)]

Step 7: Simplify the expression further:

dy/dx = ln(x) * [5cos(5x) + (1/x)]

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Answer:

4

Step-by-step explanation:

Answer:

m = 5

Step-by-step explanation:

to one side length of 4 to 2, we divided by 2 so why not divide 10 by 2

10 ÷ 2 = 5

Please give me brainliest!

The top of the ladder touches a height of 8 feet on the wall. To determine how high on the wall the top of the ladder touches, we can use the Pythagorean theorem.

In this case, the ladder forms the hypotenuse of a right triangle, and the base of the wall and the height on the wall form the other two sides.

Let's denote the height on the wall as 'h'. According to the problem, one end of the ladder is 6 feet from the base of the wall, so the base of the triangle is 6 feet.

We can set up the equation using the Pythagorean theorem:

\((6)^2 + (h)^2 = (10)^2\)

Simplifying the equation:

36 + \(h^2\) = 100

\(h^2\) = 100 - 36

\(h^2\)= 64

Taking the square root of both sides:

h = √64

h = 8

Therefore, the top of the ladder touches a height of 8 feet on the wall.

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Answer: rearrange the formula A=lw and make the width the subject of the formula

therefore to find width, the formula is w=A/l

Step-by-step explanation:

Answer: -1/2

Step-by-step explanation:

y/-7=1/14 (cross multiply)

14y=7 (divide both sides)

y=-1/2

Answer:

Yes, it is possible

Step-by-step explanation:

Take a function y= f(x). When it is reflected across the x-axis the x-coordinates do not change but the y coordinates become the negative of the pre-image

In other words reflection f'(x) of f(x) over the x-axis is y = -f(x)

If we reflect f'(x) over the x-axis then the resultant reflection is

f''(x) = -f'(x) = -(-f(x)) = f(x)

So we get the original image after two consecutive reflections along the x-axis

The original length is 250 meters and the scale drawing width is 0.67 cm

From the question (see attachment), we have the following parameters that can be used in our computation:

Scale length = 0.5 meters

So, we have

Original length = 0.5/(1/500)

Evaluate

Original length = 250

This means that the original length is 250 meters

Here, we have

Scale drawing width = 335 cm * 1/500

Scale drawing width = 0.67 cm

Hence, the scale drawing width is 0.67 cm

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Our strategy to win $200 is to use $100 in just one chance. It is the best bet for winning $200.

Given that we start with $100 at a casino and can bet any amount of that particular money to play a game to any amount of times where we have a 40% chance of winning in each game. If we win, we will gain the amount we bet and return the amount that we bet. If we lose, we will lose our bet.

It has been asked that what should be our strategy to win get $200.

We can write from the given information that:

Probability of wining = 40 % = 0.4

Probability of losing = 1 - 0.4 = 0.6

The best bet to win $200 is to bet $100 in one go itself.

For the above bet chance of winning $100 is 0.4

But let us assume that we are betting $50 two times,

Then L-Lose and W-Win

There will be 4 rational possible cases (WW,WL,LW,LL)

Probability of all the 4 above given cases will be as follows:

Probability of (WW) = 0.4 X 0.4 = 0.16

Probaility of (WL) = 0.4 X 0.6 = 0.24

Probability of (LW) = 0.6 X 0.4 = 0.24

Probability of (LL) = 0.6 X 0.6 = 0.36

Now for winning $100 we need to win both the bets of $50.

But the probability of winning both the bets = 0.16 ( very less than 0.4)

Hence the best bet would be to use $100 in one chance itself.

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Our strategy to win $200 is to use $100 in just one chance. It is the best bet for winning $200.

It has been asked that what should be our strategy to win get $200.

We can write from the given information that:

Probability of wining = 40 % = 0.4

Probability of losing = 1 - 0.4 = 0.6

The best bet to win $200 is to bet $100 in one go itself.

For the above bet chance of winning $100 is 0.4

But let us assume that we are betting $50 two times,

Then L-Lose and W-Win

There will be 4 rational possible cases (WW,WL,LW,LL)

Probability of all the 4 above given cases will be as follows:

Probability of (WW) = 0.4 X 0.4 = 0.16

Probability of (WL) = 0.4 X 0.6 = 0.24

Probability of (LW) = 0.6 X 0.4 = 0.24

Probability of (LL) = 0.6 X 0.6 = 0.36

Now for winning $100 we need to win both the bets of $50.

But the probability of winning both the bets = 0.16 ( very less than 0.4)

Hence the best bet would be to use $100 in one chance itself.

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The graph is  a coordinate grid with one line that passes through the points 0 comma 1 and 3 comma negative 1 and another line that passes through the points 0 comma negative 1 and 2 comma negative 5.

The system of linear equations is:

y = -2/3x + 1

y = -2x - 1

To determine which graph shows the solution to the system, we need to graph the two equations on the same coordinate grid and find their intersection point, which represents the solution to the system.

For the first equation, y = -2/3x + 1, the y-intercept is 1 and the slope is -2/3. We can use this to find one more point, say by setting x = 3:

y = -2/3(3) + 1 = -1

So one point on the line is (3, -1), and we can plot it on the coordinate grid.

For the second equation, y = -2x - 1, the y-intercept is -1 and the slope is -2. We can use this to find another point, say by setting x = 0:

y = -2(0) - 1 = -1

So another point on the line is (0, -1).

Thus, the answer is a coordinate grid with one line connecting points 0 comma 1 and 3 comma negative 1 and another line connecting points 0 comma negative 1 and 2 comma negative 5.

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Answer:

answer is B..as x approaches negative infinity,f(x) approaches positive infinity.

The Derivative Of A Position Function Is A Velocity Function. The Derivative Of A Velocity Function Is An acceleration function.

The derivative of a position function with respect to time gives the velocity function, which represents the rate of change of position over time. The derivative of a velocity function with respect to time gives the acceleration function, which represents the rate of change of velocity over time.

Acceleration is the second derivative of the position function, indicating how the velocity is changing with respect to time. It measures the rate at which the velocity is changing, whether it is speeding up, slowing down, or changing direction. Therefore, the derivative of a velocity function is an acceleration function.

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Answer:

no bc if you simplify it's 17=18 which is not right

Answer:

true

Step-by-step explanation:

because that has a solution

The correct answer is (c) x's tens digit. , if x = 693, that  yield  9 is (x / 10) % 10

Here's how we have to evaluate the expression:

Substitute x = 693 into the expression to get:

(693 / 10) % 10

Perform the division first:

693 / 10 = 69 with a remainder of 3.

Substitute the result of the division into the expression:

(69 % 10)

To Evaluate the remainder use the modulo operator (%):

69 % 10 = 9

The result, 9, is the tens digit of 693.

=(x / 10) % 10.

The tens digit of a number refers to the digit in the second place from the right, or the digit that represents the multiple of 10. For example, in the number 365, the tens digit is 6 because it represents 6 tens or 60.

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The equation of the line that passes through the point (2, 1) and has a slope of -5/2 is y=(-5/2)*x+6.

An equation can be represented by a linear function. The standard form for the linear equation is: y= mx+b , for example, y=3x+4. Where:

m= the slope.

b= the constant term that represents the y-intercept.

For the given example: m=3 and b=4.

The question gives:

Point : (2,1) , where x=2 and y=1

Slope= -5/2

From the  standard form of the linear equation ( y= mx+b) and the given point and the slope, you can write:

y=mx+b

1=-5/2*(2)+b , thus you can find b.

1=-5+b

-b=-5-1

-b=-6

b=6

If b=6 and m=-5/2, you can write the linear equation:

y=mx+b

y=(-5/2)*x+6

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The equation of line that models this is y = -5/2x + 6

The equation of a line is typically written in slope-intercept form, which is y = mx + b, where m is the slope of the line, and b is the y-intercept.

The slope (m) is a measure of how steep the line is, and it can be calculated using the formula:

y = mx + c

In the given question, the slope is -5/2 and the points are (2, 1)

Substituting the values into the formula of equation of line;

y = mx + c

1 = -5/2(2) + c

1 = -5 + c

c = 1 + 5

c = 6

The equation is y = -5/2 + 6

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The rental company charges $10 for insurance and an additional $3 for every 5 kilometers traveled.

The rule of correspondence for the cost of renting a motorcycle from this company can be described as follows: The base cost is $10 for insurance. In addition to that, there is an additional charge of $3 for every 5 kilometers traveled. This means that for every 5 kilometers, an extra $3 is added to the total cost.

To calculate the total cost of renting the motorcycle, you would need to determine the number of kilometers you plan to travel. Then, divide that number by 5 to determine how many increments of $3 will be added. Finally, add the $10 insurance fee to the calculated amount to get the total cost.

For example, if you plan to travel 15 kilometers, you would have three increments of $3 since 15 divided by 5 is 3. So, the additional charge for distance would be $9. Adding the base insurance cost of $10, the total cost would be $19.

In summary, the cost of renting a motorcycle from this company includes a base insurance fee of $10, and an additional charge of $3 for every 5 kilometers traveled. By calculating the number of increments of $3 based on the distance, you can determine the total cost of the rental.

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The area of the region bounded by the curves y=x^2 +4, y=x, x=0 and x=3 is 16.5 square units.

Integrate the function using partial fractions:

∫ [(x+1)(x−2)(x+3)] / [2x² + 9x - 35] dx

The area A between the curves y=f(x) and y=g(x) from x=a to x=b is given by:

A = ∫ |f(x) - g(x)| dx, from x=a to x=b

The absolute difference between these two functions on this interval is:

|x² + 4 - x|

x² + 4 - x = x² - x + 4

Therefore, the area A is:

A = ∫ (x² - x + 4) dx, from x=0 to x=3

A = [1/3x³ - 1/2x² + 4x] (from 0 to 3)

= (1/33³ - 1/23² + 43) - (1/30³ - 1/20² + 40)

= 9 - 4.5 + 12

= 16.5 square units

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3. Integrate - \int \frac{(x+1)(x-2)(x+3)}{2x^{2}+9x-35} dx = \frac{54}{7} \ln|x-5| + \frac{5}{12} \ln|2x+7| + C

4. The required area of the region is 27/2.

3. Integrating using partial fractions:

To solve the following integral, we will begin by performing the partial fraction decomposition of the given function. Here, we have a quadratic factor, so we will begin by setting the function equal to the sum of two fractions that have first-degree polynomial denominators like this :

\frac{(x+1)(x-2)(x+3)}{2x^{2}+9x-35} = \frac{A}{x-5}+\frac{B}{2x+7}

Since the denominators are of different degrees, we must find the least common denominator of both sides.

That is (x-5)(2x+7)

Multiplying by this common denominator, we have (x+1)(x-2)(x+3) = A(2x+7) + B(x-5)

Let us now solve for A and B by substituting the values of x:

\begin{aligned}\text{Let }x&=5:\ \ 6 \cdot 8 \cdot 8 = 7A\\A&=\frac{384}{7}\\\\\text{Let }x&=-\frac{7}{2}:\ \ \frac{5}{2} \cdot -\frac{9}{2} \cdot -\frac{1}{2} = -\frac{9}{2}B\\B&=\frac{5}{6}\end{aligned}

Therefore,\begin{aligned}\frac{(x+1)(x-2)(x+3)}{2x^{2}+9x-35} &= \frac{\frac{384}{7}}{x-5}+\frac{\frac{5}{6}}{2x+7}\\\\&=\frac{54}{7} \int \frac{1}{x-5}dx + \frac{5}{6} \int \frac{1}{2x+7}dx\\\\&=\frac{54}{7} \ln|x-5| + \frac{5}{12} \ln|2x+7| + C\end{aligned}

Thus,\int \frac{(x+1)(x-2)(x+3)}{2x^{2}+9x-35} dx = \frac{54}{7} \ln|x-5| + \frac{5}{12} \ln|2x+7| + C

4. Area of the region bounded by the curves:

The area of the region bounded by the curves y=x^2, y=x, x=0, and x=3 is given by\int_0^3 (x^2-x) dx = \frac{1}{3}x^3-\frac{1}{2}x^2 \Bigg|_0^3 = \boxed{\frac{27}{2}}

Hence, the required area of the region is 27/2.

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es la respuesta del de abajo pero es 62 no 61 ya que marca 61,5 y se aproxima 62 sí o sí xf

The value of c that makes the equation true is c = 64, when x = 6 and y = 3.

To find the value of c that makes the equation true, we can start by simplifying both sides of the equation using exponent rules and canceling out common factors.

First, we can simplify 3√(x^3) to x√x, and 3√y to y√y, giving us:

x√x/cy^4 = x/4y(y√y)

Next, we can simplify x/4y to 1/(4√y), giving us:

x√x/cy^4 = 1/(4√y)(y√y)

We can cancel out the common factor of √y on both sides:

x√x/cy^4 = 1/(4)

Multiplying both sides by 4cy^4 gives us:

4x√x = cy^4

Now we can solve for c by isolating it on one side of the equation:

c = 4x√x/y^4

We can substitute in the values of x and y given in the problem statement (x>0 and y>0) and simplify:

c = 4x√x/y^4 = 4(x^(3/2))/y^4

c = 4(27)/81 = 4/3 = 1.33 for x = 3 and y = 3

c = 4(64)/81 = 256/81 = 3.16 for x = 4 and y = 3

c = 4(125)/81 = 500/81 = 6.17 for x = 5 and y = 3

c = 4(216)/81 = 64 for x = 6 and y = 3

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Given,

F= Fixed Cost = $18,000

V= Variable Cost per unit = $0.90

P= Price per unit = $3.20

a) Q= Quantity = 12,000 cupcakes annually

Total Cost (TC) formula is:TC = F + V x Q = 18,000 + 0.90 × 12,000 = $29,400

Total Revenue (TR) formula is:TR = P × Q = 3.20 × 12,000 = $38,400

Profit formula is:Profit = TR − TC = 38,400 − 29,400 = $9,000.

b) The bakery will need to sell 6,924 cupcakes in order to break even.

The formula for the Break-even point (BEP) is BEP = F / (P - V) = 18,000 / (3.20 - 0.90) = 6,923.08 ≈ 6,924 cupcakes

5. The graphical representation of the Break-even volume for the Gobblecakes bakery is shown below:

8. Break-even volume as a percentage of maximum operating capacity will be = 58%

Break-even volume as a percentage = (Break-even volume / Maximum operating capacity) x 100%

                                                             = (6,923.08 / 12,000) x 100% = 57.69% ≈ 58%

11. The new Break-even point (BEP) will increase from 6,924 cupcakes to 8,750 cupcakes.

When the selling price for a cupcake changes from $3.20 to $2.75, the new Break-even point (BEP) will be:

BEP = F / (P - V) = 18,000 / (2.75 - 0.90) = 8,750 cupcakes

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Answer:

each rope should be 1 1/7 yard long

Step-by-step explanation:

9 1/7 ÷8

1 1/7

Answer:

8/7 yd per piece

Step-by-step explanation:

To answer this, divide the total rope length 9 1/7 yd by 8 pieces:

 64 yd

------------------ = 8/7 yd per piece

7(8 pieces)

Check:  does 8 times (8/7 yd/piece) come out to 64/7 yd, or 9 1/7 yd?  YES

1st 2nd and last

Step-by-step explanation:

simplify your inequality

6x >= 3 + 4(2x -1)

6x >= 3 + 8x - 4

2x >= 1

x >= 1/2

so indeed the

1st one , the 2nd and the last one

first, second, last

Hope it helps

The quadrilateral ABCD is a square.

To show  that a quadrilateral is a square, we need to show that all four sides are equal in length and that the angles are all right angles.

So let's calculate the distances between the given points like this

AB  = √((3-0) ² + (0 -4)²)

= √(9  + 16) =   √(25)

= 5

BC = √((7-3)² + (3-0)²)

= √(16 + 9)

= √(25) = 5

CD = √((4-7) ² + (7-3) ²)

= √(9 + 16)

= √(25)

= 5

DA = √ ((0-4) ² + ( 4- 7) ²)

= √(16 + 9)

= √(25)

= 5

This shows that all the sides are equal in lenght. Now, lets solve for the slopes.

mAB = (0-4)/(3-0)

= -4/3

m BC

= (3- 7)/(0-3)

= 4/3

mCD  = ( 7-4)/(3- 0)

= 3/3 = 1

mDA = (0-4)/(4-0)

= -4/4 = -1

Since the slopes of opposites sides are reciprocals thus, the quadrilateral ABCD is a Square.

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Complete question is below

What type of quadrilateral is A B C D ? Explain your reasoning.

9514 1404 393

Answer:

  Y = (-1, 5)

Step-by-step explanation:

The diagonals of a parallelogram bisect each other, so have the same midpoint. That is ...

  (M +R)/2 = (A +Y)/2

  Y = M + R - A . . . . . . multiply by 2 and subtract A

  Y = (-3, 1) +(5, 7) -(3, 3) = (-3 +5 -3, 1 +7, -3) . . . . . substitute point coordinates

  Y = (-1, 5)

Coordinate geometry was used to find Y that makes MARY a parallelogram. The fact that there is a solution is proof enough that MARY is a parallelogram.

_____

Your teacher may expect the "proof" to be either or both of ...

Given the method used above, both of these are unnecessary. However, in the interest of completeness, we will demonstrate.

Slope and Length of MA

  slope = (3 -1)/(3 -(-3)) = 2/6 = 1/3

  length = √(2²+6²) = √40

Slope and Length of AR

  slope = (7 -3)/(5 -3) = 4/2 = 2

  length = √(4² +2²) = √20

Slope and Length of RY

  slope = (5 -7)/(-1 -5) = -2/-6 = 1/3 . . . . same as opposite side MA

  length = √((-2)²+(-6)²) = √40 . . . . . . . same as opposite side MA

Slope and Length of YM

  slope = (1 -5)/(-3 -(-1)) = -4/-2 = 2 . . . . same as opposite side AR

  length = √((-4)² +(-2)²) = √20 . . . . . .  same as opposite side AR

Opposite sides have the same slopes, so the figure is a parallelogram.

Opposite sides have the same lengths, so the figure is a parallelogram.

There for the diameter is 2(4.8 )= 9.6 ft

Given: Volume of the cone is 83.7 m³

We know that:

\(\bigstar \ \ \boxed{\sf{\textsf{Volume of cone is given by} : \dfrac{\pi r^2h}{3}}}\)

where r is the radius of the cone and h is the height of the cone

Given: Height of the cone = 5m

Substituting the values in the formula, we get:

\(\sf{\implies \dfrac{\pi r^2(5)}{3} = 83.7}\)

\(\sf{\implies \pi r^2 = 83.7 \times \dfrac{3}{5}}\)

\(\sf{\implies \pi r^2 = 83.7 \times 0.6}\)

\(\sf{\implies \pi r^2 = 50.22}\)

\(\sf{\implies r^2 = \dfrac{50.22}{\pi}}\)

\(\sf{\implies r^2 = 16}\)

\(\sf{\implies r = 4}\)

We know that : Diameter is two times the radius

⇒  Diameter of the Cone is 8 meters

blue with green is 5/10 green and red 3/10 both red 2/10 both blue 4/10

The simple interest is $14.53

We are given:

Principal amount p = $725,

Rate of interest r = 7.5%,

Time t = 90 days = 90/360 years (assuming 360 days in a year)

To calculate: Simple interest

Formula for calculating Simple Interest:

Simple interest = (P × R × T)/100

where, P is the principal amount, R is the rate of interest and T is the time period involved.

Now, substituting the given values in the formula above,

Simple interest = (725 × 7.5 × 90) / (100 × 360)

Simple interest = 14.53

Therefore, the simple interest is $14.53 (rounding up to two decimal places).

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Answer:

The correct answer is "66"

Step-by-step explanation:

P(-2) = 3*16 + 4*4 + 2

P(-2) = 48 + 16 + 2

P(-2) = 66