Paul rides his bike for 2 hours at a constant rate of 20 mph. He then bikes for 3 hours at a constant rate of 25 mph. How far did Paul travel in the 5 hours?
A. 15 mi.
B. 52 mi.
C. 115 mi.
D. 165 mi.

Your first differential equation is incomplete, so I'll just look at the second one.

y' + 2xy = 4x

Multiply both sides by exp(x ²):

exp(x ²) y' + 2x exp(x ²) y = 4x exp(x ²)

The left side is the derivative of a product:

(exp(x ²) y )' = 4x exp(x ²)

Integrate both sides:

exp(x ²) y = ∫ 4x exp(x ²) dx

For the integral, substitute u = x ² and du = 2x dx :

exp(x ²) y = 2 ∫ exp(u) du

Solve for y :

exp(x ²) y = 2 exp(u) + C

exp(x ²) y = 2 exp(x ²) + C

y = 2 + C exp(-x ²)

Answer:

x ≈ 24.4

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Trigonometry

Step-by-step explanation:

Step 1: Define

Identify variables

Angle θ = 38°

Adjacent Leg = x

Hypotenuse = 31 cm

Step 2: Solve for x

Try this solution, note the answer is marked with green colour.

Answer:

585.57

Step-by-step explanation:

Maya got 286.00

if lian got 192.84 less than we do 286-192.84 which is 93.16

if lian got 93.16, we add 113.25 to 93.16 to get rei's amount.

113.25 + 93.16 = 206.41

Now we add all their amounts, 286+93.16+206.41

585.57

Answer:

-3/7

Step-by-step explanation:

To find the slope use the slope formula

m = ( y2-y1)/(x2-x1)

    = ( 1-4)/(4 - -3)

   = (1-4)/(4+3)

   = -3/7

Answer:

slope = - 3/7

step-by-step explanation:

we have two points which are (-3,4) and (4,1).

To find the slope of line , use the slope formula which is

m = ( y² - y¹ ) / ( x² - x¹)

Where,

substitute the values

m = ( 1 - 4 ) / ( 4 - ( - 3 ))

m = -3 / 7

Hence, slope is -3/7.

Point of intersection is the solution of the system of equations.

Both of them intersect at point (-3,5)

So, (-3,5) is the solution of the system of equations.

OPTION B

Answer:

(-3,5)

Step-by-step explanation:

The solution to the system is where the two graphs intersect.  They intersect at two points

(-3,5) and (1,-3)

The only solution listed as a choice is (-3,5)

Answer:

5/8

Step-by-step explanation:

First, find how many slices are yellow or blue.

There are 2 yellow slices and 3 blue slices, so 5 of them are either yellow or blue.

There is a total of 8 slices.

So, the probability that it will stop on a yellow or blue slice is 5/8.

Answer:

Family size

Step-by-step explanation:

40 oz of the regualr size would cost $8.40, therefor making the family size a better deal.

Hope this helps, correct me if i am wrong :)

Answer:

is that a question?????????????

Answer:

slope = 6

y-intercept is (0,-1)

Step-by-step explanation:

the equation y = 6x-1 is written in slope-intercept form so it's easy to find the slope and the y-intercept

Answer:

The amount of money one may spend in a month may be greater than that of ones monthly payment especially when the payment is at a lower rate.

Answer:

ans: additive inverse is -5

multiplicative inverse is 1/5

Step-by-step explanation:

adding what value to 5 makes it 0 i.e

5 + (- 5)= 0 ( so additive inverse is -5)

multiplying what value to 5 makes it 1 i.e

5×( 1/5)=1 ( so multiplicative inverse is 1/5)

Answer:

22/ b hope this helps

Step-by-step explanation:

Answer:

40 square units

Step-by-step explanation:

First of all, lets say that square has side [tex]l[/tex], so, the area unit is [tex]l^2[/tex]

the diagonal's square is [tex]l\sqrt{2}[/tex]

CALCULATION OF TRIANGLES'S AREA (there are 4 triangles)

[tex]A_{triangles}=4*base*heigh*0.5=2*(l\sqrt{2} )(2l\sqrt{2} )=8l^2[/tex]

CALCULATION OF MAIN SQUARE AREA

[tex]A_{square}=side*side=(4\sqrt{2} l)(4\sqrt{2} l)=32l^2[/tex]

TOTAL AREA

[tex]A_{total}=A_{triangles}+A_{square}=8l^2+32l^2=40l^2[/tex]

Answer:

7, 11, 13, 17, 19 and 23

Step-by-step explanation:

Answer:

7,11,13,17,23

hope it helps

thank you

Answer:

[tex]6x^2-x+15[/tex]

Step-by-step explanation:

(3x + 5)(2x - 3) = [tex]6x^2-9x+10x-15=6x^2+x-15[/tex]

Answer:

is equidistant from a focus point and a line

Answer:

what

Step-by-step explanation:

pa brainliest tol please

Answer:

1628.89

2593.74

2653.30

Because the interest forms an exponential function. This means that the amount of interest earned in each period is increasing and should therefore be more than double.

Step-by-step explanation:

A: 1000*(1.05)¹⁰= 1628.89

B: 1000(1.1)¹⁰= 2593.74

C: 1000(1.05)²⁰= 2653.30

D: Because the interest forms an exponential function. This means that the amount of interest earned in each period is increasing and should therefore be more than double.

Answer:

-3/2

Step-by-step explanation:

The slope of the perpendicular line is the negative reciprocal. This means you change the sign of the slope to its opposite.

Answer:

a

Step-by-step explanation:

I believe it is answer a. the helicopter is the distance in the air that it is cruising and the angle is how it has to begin its decent down to the fireman

Answer:

[tex]{ \tt{(2 \sin x. \cos x) - \cos x = 0}} \\ \\{ \tt{ \cos x(2 \sin x - 1) = 0 }} \\ either : { \tt{ \cos x = 0 \: \: or \: \: (2 \sin x - 1) = 0}} \\ \\ { \boxed{ \bf{x = 30 \degree, \: 90 \degree, \: 150 \degree,\:270\degree}}}[/tex]

Answer:

A Rational numbers

B Integers

Answer:

B. 30 units³

Step-by-step explanation:

the volume= 5×2×3 = 30

Answer:

cos theta = 4/5

Step-by-step explanation:

Since this is a right triangle

Cos theta = opp side/ hypotenuse

Cos theta = 8/10

cos theta = 4/5

Answer:

B)785.0 cubic inches

Step-by-step explanation:

amount of soup the pot can hold is equal to its volume

Volume of a cylinder is πr²h

π(5inches)²x 10inches

785.39816339744830

~785.0 cubic inches

Answer:

Letter A

Step-by-step explanation:

Hope this helps

Answer:

its A

Step-by-step explanation: