The maker of an automobile advertises that it takes 15 seconds to accelerate from 20 kilometers per hour to 70 kilometers per hour. Assuming constant acceleration, compute the following. (a) The acceleration in meters per second per second (Round your answer to three decimal places.) m/sec2 (b) The distance the car travels during the 15 seconds (Round your answer to two decimal places.)

Answer:

9

Step-by-step explanation:

We have been given a graph of a function and we are asked to find the value of our function at x equals 2.

To find the value of f(2), we will see what is the value of y when x is 2.

We can see from our given graph that at x equals 2 our function is at 9.

Answer:

Step-by-step explanation:

2u - 1 = 3

In this equation, you would first take 3 + 1 to get 4. You know that 2 x 2 = 4 so u = 2.

Answer:

356 boxes

Step-by-step explanation:

Just divide 4272 by 12

you do this because that is how many apples are needed in each box

Answer:

356

Step-by-step explanation:

Since this is a division problem we need to set it up. Since 4272 is the total number it will be on the top of the fraction.

4272/12

Then you solve just like any other division problem to get 356

The solution to the given differential equation 2xy(dy/dx) = y², with the initial condition y(2) = 3, is y = (27 * e⁽ˣ⁻²⁾\()^{1/4}\).

To solve the given differential equation

2xy(dy/dx) = y²

We will use separation of variables and integrate to find the solution.

Start with the given equation

2xy(dy/dx) = y²

Divide both sides by y²:

(2x/y) dy = dx

Integrate both sides:

∫(2x/y) dy = ∫dx

Integrating the left side requires a substitution. Let u = y², then du = 2y dy:

∫(2x/u) du = ∫dx

2∫(x/u) du = ∫dx

2 ln|u| = x + C

Replacing u with y²:

2 ln|y²| = x + C

Using the properties of logarithms:

ln|y⁴| = x + C

Exponentiating both sides:

|y⁴| = \(e^{x + C}\)

Since the absolute value is taken, we can remove it and incorporate the constant of integration

y⁴ = \(e^{x + C}\)

Simplifying, let A = \(e^C:\)

y^4 = A * eˣ

Taking the fourth root of both sides:

y = (A * eˣ\()^{1/4}\)

Now we can incorporate the initial condition y(2) = 3

3 = (A * e²\()^{1/4}\)

Cubing both sides:

27 = A * e²

Solving for A:

A = 27 / e²

Finally, substituting A back into the solution

y = ((27 / e²) * eˣ\()^{1/4}\)

Simplifying further

y = (27 *  e⁽ˣ⁻²⁾\()^{1/4}\)

Therefore, the solution to the given differential equation with the initial condition y(2) = 3 is

y = (27 * e⁽ˣ⁻²⁾\()^{1/4}\)

To know more about differential equation:

https://brainly.com/question/2273154

#SPJ4

Answer: 218.5

Step-by-step explanation:

Detailed steps are shown in the attached document below.

The semi-annual payment is $1662.47

Given : A 3 year loan of $8,561 at 9.1% compounded semi-annually.

We have to determine the semi annual payment.

We know,

\(P=\dfrac{PV.r}{1-(1+r)^{-n}}\)

Where PV is present value of loan.

r is rate of interest

n is time period.

Given loan is calculated semi annually,

So PV = $ 8561

r=9.1 % =9.1/200

and time period is 3 years = 6 number of period as semi annually.

Thus, Substitute,

We get,

\(P=\dfrac{8561(\dfrac{9.1}{200})}{1-(1+\dfrac{9.1}{200})^{-6}}\)

\(P=1662.47\)

Hence the semi-annual payment is $1662.47

To know more about Amount follow

https://brainly.com/question/25109150

Answer:28

Step-by-step explanation:

Break it up! 6x3 is 18. Then 18 + 10 is 28 :P

Hope this helps :D

Chloe put approximately 52.467 pounds of potting soil in each of the 77 flowerpots. we need to divide the total weight of the soil by the number of pots.

1. We know that Chloe has a 4040-pound bag of potting soil.
2. She wants to divide the soil equally among 77 flowerpots.
3. To find the amount of soil per pot, we need to divide the total weight by the number of pots: 4040 pounds ÷ 77 pots.

4040 ÷ 77 = 52.467 (rounded to three decimal places)

So, Chloe put approximately 52.467 pounds of potting soil in each of the 77 flowerpots.

To learn more about weight click here:  brainly.com/question/31527377

#SPJ11

Step-by-step explanation:

4x-2^{x}=6

this is the answer

Answer:

  x = log₂(3) ≈ 1.5849625

Step-by-step explanation:

We want to find the solution to an exponential equation that is in the form of a quadratic.

Let z = 2^x. Then the equation becomes ...

  z^2 -z -6 = 0 . . . . . a quadratic relation in z

This quadratic can be factored to find the solutions for z:

  (z -3)(z +2) = 0

Values of z that make this true are ...

  z = 3  and  z = -2

We know that 2^x = -2 is impossible for real values of x, so the solution z=-2 is extraneous. The useful solution is ...

  z = 3 = 2^x

Taking the logarithm, base 2, we have ...

  x = log₂(3) ≈ 1.5849625

__

Additional comment

The logarithm gives a complex result for negative arguments. The other solution is ...

  x = log₂(-2) ≈ 1 +4.5323601i

The imaginary part is π/ln(2).

The attachment shows a graphing calculator solution. The same calculator can provide an iterated numerical solution without much additional effort. It gives the same answer as above.

Answer:

Step-by-step explanation:

I can help you with this finance question.

According to The Calculator Site,  the formula for compound interest is:

A = P (1 + r/n)^nt

where

A = future value of the investment

P = principal amount

r = annual interest rate (decimal)

n = number of times interest is compounded per year

t = time in years

To find the total interest earned, we need to subtract the principal amount from the future value. The formula for total interest is:

I = A - P

where

I = total interest

Now, we can plug in the given values into the formulas. We have:

P = $1,450

r = 0.05

n = 2 (semiannually means twice a year)

t = 15 (from January 2003 to December 2017)

First, we calculate the future value using the compound interest formula:

A = P (1 + r/n)^nt

A = 1450 (1 + 0.05/2)^(2 x 15)

A = 1450 (1.025)^30

A = 1450 x 2.098

A = $3042.10

Then, we calculate the total interest by subtracting the principal amount from the future value:

I = A - P

I = 3042.10 - 1450

I = $1592.10

Therefore, the total interest earned by the end of December in 2017 is $1592.10.

a)

Values of the given angles  ∠A = 123°  , ∠B = 123° ,∠C = 57.

Given ,

One angle of the figure as 123°.

Now,

∠C and 123° form linear pair.

So,

∠C + 123° = 180°

∠C = 57°

Now,

∠C and ∠B are pairs of interior angles on same side of transversal, thus they are supplementary.

∠C + ∠B = 180°

Substitute the value of ∠C

53° + ∠B = 180°

∠B = 127°

Now,

∠B and ∠A are vertically opposite angles.

Thus,

∠B = ∠A

So,

∠A = 127° .

Hence,

∠A= 127°

∠B = 127°

∠C = 57°

b)

Values of ∠D = 98°, ∠E = 98°, ∠F = 98° .

Given one angle as 82°

Now,

∠F and 82° form linear pair.

So,

∠F + 82° = 180°

∠F = 98°

Now,

∠D and ∠F are corresponding angles. Thus,

∠D = ∠F

∠D = 98° .

Now,

∠D and ∠E are vertically opposite angles.

Thus,

∠D = ∠E

∠E = 98°.

Hence,

∠D = 98°

∠E = 98°

∠F = 98°

c)

Values of ∠G = 75° and ∠H = 75°

Given one angle as 75° .

∠H and 75° are corresponding angles. Thus,

∠H = 75°

Now,

∠H and ∠G are vertically opposite angles.

So,

∠G = 75° .

Hence,

∠G = 75°

∠H = 75°

To learn more about angles by transversal line,

https://brainly.com/question/11293539

#SPJ1

a. The ratio of A: B: C is  6:10:21. b. The two numbers are 5(5/3) and 7(5/3) i.e., 25/3 and 35/3.

1. Let’s assume that the monthly income of the family is x.

Therefore, the savings of the family = 9000.

We know that the ratio of monthly income to savings in a family is 5/4.

So, we can write this as:

x/9000 = 5/4

=> 4x

= 45000

=> x

= 11250

Therefore, the monthly income is $11,250.

The expenses of the family can be calculated as follows:

Savings of the family = Income of the family - Expenses of the family

=> 9000

= 11250 - Expenses of the family

=> Expenses of the family

= $2,250

Therefore, the expenses of the family are $2,250.2.

Given, Ratio is 5:11.

Let’s assume that x should be added to the ratio 5:11 so that the ratio becomes 3:4.

So, we can write this as:

5x/11x + x = 3/4

=> 20x

= 33x + 3x

=> 14x

= 3x

=> x

= 3/11

Therefore, 3/11 should be added to the ratio 5:11, so that the ratio becomes 3:4.3.

Given, the two numbers are in the ratio Z 5.

Let’s assume that the numbers are 5x and x.

If 2 is subtracted from each of them, the ratio becomes 3:2.

So, (5x-2)/(x-2) = 3/2

=> 10x - 4

= 3x - 6

=> 7x

= -2

=> x

= -2/7

Therefore, the two numbers are (5*(-2/7)) and (-2/7) i.e., -10/7 and -2/7.4.

Let's assume that the two numbers are 3x and 7x.

We know that the sum of the two numbers is 710.

Therefore,3x + 7x = 710

=> 10x

= 710

=> x

= 71

Therefore, the two numbers are 3x71 = 213

7x71 = 497.5.

(a) Let's assume that A is 3x and B is 5x.

Then, A:C = 6:7

=> A/C

= 6/7

=> (3x)/(7y)

= 6/7

=> 21x

= 6y

=> y

= 3.5x

Therefore, A:B:C = 3x:5x:7(3.5x)

=> 6:10:21

(b) Let's assume that B is 2y and C is 6y.

Also, A:B = 1/3:1/5

=> A:B

= 5:3

=> A/B

= 5/3

=> (5x)/(2y)

= 5/3

=> 15x

= 2y

=> y

= 7.5x

Therefore, A:B:C = 5(7.5x):2y:6y

=> 37.5:15:45.6.

Let's assume that the total money is x.

If the ratio of money is divided among Ron and Andy in the ratio 4:7.

Then, the share of Ron is (4/11)*x. We know that Andy’s share is $616.

Therefore, we can write this as:

(7/11)*x = 616

=> x

= (616*11)/7

=> x

= $968

Therefore, the total money is $968.7.

Let's assume that the two numbers are 5x and 7x.

We know that on adding 1 to the first and 3 to the second, the ratio becomes 7:11.

So, (5x+1)/(7x+3)

= 7/11

=> 55x + 11

= 49x + 21

=> 6x

= 10

=> x

= 5/3

Therefore, the two numbers are 5(5/3) and 7(5/3) i.e., 25/3 and 35/3.

Learn more about monthly income from the given link

https://brainly.com/question/1286047

#SPJ11

An approximate solution to the equation f(x) = g(x) to the nearest quarter of a unit is; A: 2.5

We are given;

f(x) = ¹/₄x³ + 2x - 1

g(x) = [5^(x - 1)] - 3

Thus;

f(x) = g(x) gives;

¹/₄x³ + 2x - 1 = [5^(x - 1)] - 3

At x = 2, we have;

LHS = 5

RHS = 2

At x = 2.5, we have;

LHS = 7.90625

RHS = 8.180

The answer to the two sides are close and so we can adopt that.

Read more about Simultaneous equations at; https://brainly.com/question/16863577

The height and width of the box shipped is 15 and 8 inches respectively.

A cuboid is a three-dimensional closed figure which has volume along with surface area.

The volume of a cuboid is the product of its length, width, and height.

The total surface area of a cuboid is 2( lw + wh + wl) and the lateral surface area is 2(l + w)×h.

Given, The width of the box is seven inches less than the height.

Assuming the width to be 'w' hence the height(h) = w + 7 and has a length of 24 inches with a volume of 2880 cubic inches.

We know the volume(V) of a cuboid is l×w×h.

Therefore,

24×w×(w + 7) = 2880.

24w(w + 7) = 2880.

24w² + 168w = 2880.

6w² + 42w = 720.

w² + 7w = 120.

w² + 7w - 120 = 0.

w² + 15w - 8w - 120 = 0.

w(w + 15) - 8(w + 15) = 0.

(w + 15)(w - 8) = 0.

w = 8 and hence h = 8 = 7 = 15.

So, the width and height of the box is 8 and 15 inches respectively.

learn more about cuboids here :

https://brainly.com/question/29568631

#SPJ5

Answer:     the answer is X^2 • Y^2 • Z^2.

Step-by-step explanation:

Expanding the expression (xyz)^2, we get:

(xyz)^2 = (xyz) x (xyz)

(xyz)^2 = x^2 y^2 z^2

Step-by-step explanation:

I attached The photo of answer

-TheUnknownScientist

Answer:for the vertex I believe it is y-9 and x-2 for axis of symmetry

Step-by-step explanation:

Answer:

a. Downwards

b1. x intercept = (-4,0) (8,0)

b2. Y intercept (0,8)

c. Vertex (2,9)

d. Axis of symmetry 2

Step-by-step explanation:

The approximation for the value of cos(12) using the fourth-degree Taylor polynomial is approximately 505.

We have,

To approximate the value of cos(12) using the fourth-degree Taylor polynomial for cos(x) about x = 0, we can use the formula:

cos(x) ≈ \(1 - (x^2 / 2) + (x^4 / 24)\)

Substituting x = 12 into the formula, we have:

cos(12) ≈ \(1 - (12^2 / 2) + (12^4 / 24)\)

≈ 1 - 72 + 576

≈ 505

Therefore,

The approximation for the value of cos(12) using the fourth-degree Taylor polynomial is approximately 505.

Learn more about polynomials here:

https://brainly.com/question/2284746

#SPJ12

Answer:

The remaining 15 athletes did not participate in any type of flexibility program

The two independent events from the given options are;

An independent event is an event that changes as a change occurs in a variable.

Learn more about independent event:

https://brainly.com/question/82796

#SPJ4

Answer:

A: A and C

I just got it wrong since the top answer didnt say the answer

Step-by-step explanation:

The value of k will be equal to 3.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

The given expression will be solved as follows:-

3 log 3x- log 9x⁴ + log x = log( 3x)³ -log9x⁴ + logx

                                        = log( 27x³) - log(9x⁴) + logx

                                        = log\(\dfrac{27x^3}{9x^4}\) + logx

                                        = log \(\dfrac{3}{x}\) + logx

                                        = log\(\dfrac{3}{x}\times x\)

                                        = log3

Therefore the value of k will be equal to 3.

To know more about Expression follow

https://brainly.com/question/723406

#SPJ1

The equation of the plane passing P(1,2,1) and is orthogonal to the two planes: x-y-z-10 = 0, x-2y + z-2=0 is 3x + 2y + z = 8.

We need a point b and a vector v along the line in order to characterize it. We might alternatively begin with the two points a and b and use the formula v = ab.
A point Q and a vector n perpendicular to the plane are required in order to describe a plane. Later on, we'll look at how to get n from various types of information, such as the positions of three points on a plane.

A plane is a flat, endlessly long, two-dimensional surface. A plane is a point with zero dimensions, a line with one dimension, and space with three dimensions in two dimensions. The picture below that is attached shows the answer.

Here is another question with an answer similar to this about equation of the plane: https://brainly.com/question/27190150

#SPJ4

Question correction:

Find the equation of the plane passing P(1,2,1) and is orthogonal to the two planes: x-y-z-10 = 0, x-2y + z-2=0

The maximum deflection of the beam with the given data is the result obtained using the formula:

δ max = (S × L³ / (384 × E × (1/12) × b × h³))

Given, the concentrated load "S" at midspan of the simply supported beam of length "L". We have to determine the maximum deflection in the beam.

To find the maximum deflection, we need to use the formula for deflection at midspan:

δ max = (5/384) × (S × L³ / EI)

where,

E = Modulus of Elasticity

I = Moment of Inertia of the beam.

To obtain I, we need to use the formula:

I = (1/12) × b × h³

where, b = breadth

h = depth

Substitute the value of I in the first equation to get the maximum deflection in the simply supported beam.

δ max = (S × L³ / (384 × E × (1/12) × b × h³))

The conclusion is that the maximum deflection of the beam with the given data is the result obtained using the formula above.

To know more about maximum visit

https://brainly.com/question/1944901

#SPJ11

Answer:

Step 2: it should be P - 2x, not P + 2x.

Step-by-step explanation:

The runner's average speed in kilometers per hour is 24.257 km.

The total distance covered by the runner is 1 mile. The relation between kilometers and miles is given as 1 km = 0.62 mi. Converting 1 mile to km by using the given relation, we get-

Distance = 1 mile

 = 1 mile × [1 km/0.62 mile]

= 1.6129 km

The time taken to complete a 1-mile run is 3 minutes and 59.37 seconds. The relation between hours and minutes is given below.

1 hour = 60 minutes ……(1)

Converting 3 minutes to hours using equation (1), we get-

3 minutes = 3 minutes × [1 hour/60 minutes]

= 0.05 hours

The relation between hours and seconds is given below.

1 hour = 3600 second …….(2)

Converting 59.37 seconds to hours using equation (2), we get-

59.37 seconds = 59.37 seconds × [1 hour/3600 seconds]

= 0.016492 hours

Total time to cover 1 mile = (0.05 + 0.016491) hours = 0.066492 hours

The average speed of the runner is calculated by the following relation-

Average Speed = Distance (km)/time (hours)

= 1.6129 km/0.066492 hours

= 24.257 km/hour

Therefore, the average speed in kilometers per hour is 24.257km.

For more such questions on average speed

https://brainly.com/question/12322912

#SPJ4

Answer:

Given value = 2384.653

We are required to round off to the nearest whole number.

Step-by-step explanation:

To round the digit or number nearest whole number first see the digit or number at the first decimal place and tenth place value. If the value at the tenth place is 5 or more than 5 then the one place number will be increased by one. For example. 9.63 will be written as the 10  because after decimal the value is more than 5.

Similarly, the 2384.653 is written as 2385.

the solid is really just a right-cylinder missing a chunk.

so a full circle is 360°, now from the one in the picture above we're missing 90°, that means the cylinder is only using 270°, 360-90=270.

Well, 270° is just 3/4 of a full circle, and since the circle extends all the way down the solid cylinder, we can also say that's 3/4 of the volume of the cylinder, so hmmm let's just get the full volume of the cylinder with a radius of 6 and a height of 12 and then only grab 3/4 of it.

\(\textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=6\\ h=12 \end{cases}\implies V=\pi (6)^2(12)\implies V=432\pi \\\\\\ \stackrel{\textit{now let's just grab }\frac{3}{4}}{432\pi \cdot \cfrac{3}{4}}\implies 324\pi ~~ \approx ~~ \text{\LARGE 1017.88}\)

Answer:

Your answer is <, Hope it helps.