What is the slope of the line that passes through (2,3) and (6,

Please please please help and solve this with steps, much help needed thank you :) 20 points for this!

leonid [27]

Answer:

$y=\sqrt{\frac{x^4-6x^2+12x+c_1}{2}},\:y=-\sqrt{\frac{x^4-6x^2+12x+c_1}{2}}$

(Please vote me Brainliest if this helped!)

Step-by-step explanation:

$\frac{dy}{dx}y=x^3+2x-5x+3$

$\mathrm{First\:order\:separable\:Ordinary\:Differential\:Equation}$

$\mathrm{A\:first\:order\:separable\:ODE\:has\:the\:form\:of}\:N\left(y\right)\cdot y'=M\left(x\right)$

1. $\mathrm{Substitute\quad }\frac{dy}{dx}\mathrm{\:with\:}y'\:$

$y'\:y=x^3+2x-5x+3$

2. $\mathrm{Rewrite\:in\:the\:form\:of\:a\:first\:order\:separable\:ODE}$

$yy'\:=x^3-3x+3$

$N\left(y\right)\cdot y'\:=M\left(x\right)$

$N\left(y\right)=y,\:\quad M\left(x\right)=x^3-3x+3$

3. $\mathrm{Solve\:}\:yy'\:=x^3-3x+3:\quad \frac{y^2}{2}=\frac{x^4}{4}-\frac{3x^2}{2}+3x+c_1$

4. $\mathrm{Isolate}\:y:\quad y=\sqrt{\frac{x^4-6x^2+12x+4c_1}{2}},\:y=-\sqrt{\frac{x^4-6x^2+12x+4c_1}{2}}$

5. $\mathrm{Simplify}$

$y=\sqrt{\frac{x^4-6x^2+12x+c_1}{2}},\:y=-\sqrt{\frac{x^4-6x^2+12x+c_1}{2}}$

7 0

3 years ago

Read 2 more answers

on a scale drawing, 5 metres is represented by 4 centimetres. write the scale as a ratio in it's simplest form.

ryzh [129]

Answer:

<em>The scale factor is 1:125</em>

Step-by-step explanation:

<u>Scaling</u>

Objects can be represented in a reduced or augmented size by using scaling which consists of multiplying or dividing by a constant factor. We use scaling when representing geographic locations on a map.

On a scale drawing, a distance of 5 meters = 500 cm is represented by 4 centimeters. The scale factor is usually represented as a ratio of the smallest to the biggest magnitude:

$\frac{4}{500}=\frac{1}{125}$

The scale factor is 1:125

8 0

3 years ago

A Family travels at a constant rate and drove 420 miles in 7 hours.If they drive at the same speed ,How many miles will they dri

Mazyrski [523]

Answer:

240 miles

Step-by-step explanation:

Step 1

We find the constant rate at which the family travels

Speed(Rate) = Distance/Time

A Family travels at a constant rate and drove 420 miles in 7 hours.

Speed(Rate) = 420 miles/7 hours

= 60 miles per hour

Step 2

If they drive at the same speed ,How many miles will they drive in the next four hours.?

We are to finally calculate the distance for the next 4 hours

Distance = Speed × Time

Speed = 60 miles per hour

Time = 4 hours

Distance = 60 miles per hour × 4 hours

Distance = 240 miles

Therefore, for the next 4 hours the number of miles they would drive is 240 miles

5 0

3 years ago

The loudness of a jackhammer is a 96 dB. It sounds intense is about _____ . The Loudness of a compactor is 94 dB. It's sound int

aleksandr82 [10.1K]

Answer:

loudness of a jack hammer .004 loudness of a compactor .0025

Step-by-step explanation:

Because edge

8 0

3 years ago

This is the graph of y=x^2+2x-2 what is the range of this function

Sedaia [141]

The range is [-3, ∞)

3 0

3 years ago

What is the slope of the line that passes through (2,3) and (6, - 4)?