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3 years ago

Hello can anyone please help me find the answer to this.

Mathematics

1 answer:

Law Incorporation [45]3 years ago

8 0

Answer:

Step-by-step explanation:

No. Starting out, Maria walks away from home at a constant speed (which we recognize because the graph is at first a straight line). Then she stops for a little while, turns around and heads for home at the same speed as before (positively sloped graph), level graph, negatively sloped graph).

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A researcher studied the relationship between the number of times a certain speciesof cricket will chirp in one minute and the t

cricket20 [7]

Answer:

C. Actual temperature of 57.1°F when the cricket has chirped 116 times

Explanation:

The x-axis represents the number of chirps per minute.

The values on the y-axis represent the temperature (in °F).

Given the point (116, 57.1)

• The number of chirps per minute = 116

• Temperature = 57.1°F

Thus, the point (116, 57.1) represent an actual temperature of 57.1°F when the cricket has chirped 116 times.

4 0

1 year ago

Solve the differential equation dy/dx=x/49y. Find an implicit solution and put your answer in the following form: = constant. he

anygoal [31]

Answer:

The general solution of the differential equation is $\frac{49y^{2} }{2}-\frac{x^{2} }{2} = c_{3}$

The equation of the solution through the point (x,y)=(7,1) is $y=\frac{x}{7}$

The equation of the solution through the point (x,y)=(0,-3) is $\:y=-\frac{\sqrt{441+x^2}}{7}$

Step-by-step explanation:

This differential equation $\frac{dy}{dx}=\frac{x}{49y}$ is a separable first-order differential equation.

We know this because a first order differential equation (ODE) $y' =f(x,y)$ is called a separable equation if the function $f(x,y)$ can be factored into the product of two functions of x and y

$f(x,y)=p(x)\cdot h(y)$ where p(x) and h(y) are continuous functions. And this ODE is equal to $\frac{dy}{dx}=x\cdot \frac{1}{49y}$

To solve this differential equation we rewrite in this form:

$49y\cdot dy=x \cdot dx$

And next we integrate both sides

$\int\limits {49y} \, dy=\int\limits {x} \, dx$

$\mathrm{Apply\:the\:Power\:Rule}:\quad \int x^adx=\frac{x^{a+1}}{a+1}\\\int\limits {49y} \, dy=\frac{49y^{2} }{2} + c_{1}$

$\int\limits {x} \, dx=\frac{x^{2} }{2} +c_{2}$

$\int\limits {49y} \, dy=\int\limits {x} \, dx\\\frac{49y^{2} }{2} + c_{1} =\frac{x^{2} }{2} +c_{2}$

We can subtract constants $c_{3}=c_{2}-c_{1}$

$\frac{49y^{2} }{2} =\frac{x^{2} }{2} +c_{3}$

An explicit solution is any solution that is given in the form $y=y(t)$ . That means that the only place that y actually shows up is once on the left side and only raised to the first power.

An implicit solution is any solution of the form $f(x,y)=g(x,y)$ which means that y and x are mixed (y is not expressed in terms of x only).

The general solution of this differential equation is:

$\frac{49y^{2} }{2}-\frac{x^{2} }{2} = c_{3}$

To find the equation of the solution through the point (x,y)=(7,1)

We find the value of the $c_{3}$ with the help of the point (x,y)=(7,1)

$\frac{49*1^2\:}{2}-\frac{7^2\:}{2}\:=\:c_3\\c_3 = 0$

Plug this into the general solution and then solve to get an explicit solution.

$\frac{49y^2\:}{2}-\frac{x^2\:}{2}\:=\:0$

$\mathrm{Add\:}\frac{x^2}{2}\mathrm{\:to\:both\:sides}\\\frac{49y^2}{2}-\frac{x^2}{2}+\frac{x^2}{2}=0+\frac{x^2}{2}\\Simplify\\\frac{49y^2}{2}=\frac{x^2}{2}\\\mathrm{Multiply\:both\:sides\:by\:}2\\\frac{2\cdot \:49y^2}{2}=\frac{2x^2}{2}\\Simplify\\9y^2=x^2\\\mathrm{Divide\:both\:sides\:by\:}49\\\frac{49y^2}{49}=\frac{x^2}{49}\\Simplify\\y^2=\frac{x^2}{49}\\\mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}$

$y=\frac{x}{7},\:y=-\frac{x}{7}$

We need to check the solutions by applying the initial conditions

With the first solution we get:

$y=\frac{x}{7}=\\1=\frac{7}{7}\\1=1\\$

With the second solution we get:

$\:y=-\frac{x}{7}\\1=-\frac{7}{7}\\1\neq -1$

Therefore the equation of the solution through the point (x,y)=(7,1) is $y=\frac{x}{7}$

To find the equation of the solution through the point (x,y)=(0,-3)

We find the value of the $c_{3}$ with the help of the point (x,y)=(0,-3)

$\frac{49*-3^2\:}{2}-\frac{0^2\:}{2}\:=\:c_3\\c_3 = \frac{441}{2}$

Plug this into the general solution and then solve to get an explicit solution.

$\frac{49y^2\:}{2}-\frac{x^2\:}{2}\:=\:\frac{441}{2}$

$y^2=\frac{441+x^2}{49}\\\mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}\\y=\frac{\sqrt{441+x^2}}{7},\:y=-\frac{\sqrt{441+x^2}}{7}$

We need to check the solutions by applying the initial conditions

With the first solution we get:

$y=\frac{\sqrt{441+x^2}}{7}\\-3=\frac{\sqrt{441+0^2}}{7}\\-3\neq 3$

With the second solution we get:

$y=-\frac{\sqrt{441+x^2}}{7}\\-3=-\frac{\sqrt{441+0^2}}{7}\\-3=-3$

Therefore the equation of the solution through the point (x,y)=(0,-3) is $\:y=-\frac{\sqrt{441+x^2}}{7}$

4 0

3 years ago

What is 5/7*w=40 1/2

sukhopar [10]

Answer:

56 7/10

Step-by-step explanation:

convert 40 1/2 to a fraction 40 1/2 = 81/2

multiply both sides by 7/5

this gets w by itself on the left

81/2 x 7/5 = 567/10 = 56 7/10

7 0

3 years ago

Is (-3, -2) a solution to the equation y = -2x + -8?

denis23 [38]

Answer:

(-3, -2) is a solution of y = -2x + -8

Step-by-step explanation:

y = -2x + -8

(-3, -2) are the coordinates of P(x,y)

-2= -2(-3) - 8

-2 = +6 - 8

-2 = -2

Since LHS = RHS, (-3, -2) is a solution of y = -2x + -8

4 0

3 years ago

Question number 29 you work in the shipping department of an organic food company and need to calculate the net weight of a jar

umka2103 [35]

The net weight of a jar of raspberry preserves will be 4.45 ounces.

The volume of the cylinder can be calculated as the product of the base of the cylinder and the height of cylinder.

The volume of cylinder= base of cylinder * height of the cylinder

⇒ volume of cylinder = πd²*h/4

Here, given that

the inside diameter of the cylinder is 1.5 inches.

d= 1.5 inches

the inside height of the cylinder is 4.75 inches.

h= 4.75 inches

putting these above values for calculating the volume of the cylinder

Volume =V = πd²*h/4

⇒ V= π*(1.5)²*4.75/4

⇒V = 8.40 cube inches

Given that the raspberry preserve weighs 0.53 ounces per one cubic.

for one cubic the weight is 0.53 ounces

for 8.40 cubic the weight will be 8.40*0.53= 4.45 ounces

Therefore The net weight of a jar of raspberry preserves will be 4.45 ounces.

Learn more about volume of the cylinder

here: brainly.com/question/9554871

#SPJ10

5 0

2 years ago