Use the laplace transform to solve the given initial-value problem. y'' − 8y' 16y = t, y(0) = 0, y'(0) = 1

Answer:

1/311875200.

There is exactly 1 way to have all 5 of these cards.  For the first card, there are 52 total cards to be had; for the second, 51; for the third, 50; for the fourth, 49; and for the fifth, 48:

(1/52)(1/51)(1/50)(1/49)(1/48) = 1/311875200.

Step-by-step explanation:

Expand the binomials.

[tex](x+y)^2 - (x-y)^2 = (x^2 + 2xy + y^2) - (x^2 - 2xy + y^2) = 4xy[/tex]

Now let [tex]x=1[/tex] and [tex]y=\sin(A)[/tex].

is there a picture included in this problem? if so please comment it so i can answer this problem.

Angelique takes 8 hours to drive from a to b.

How quickly something or someone is moving is indicated by their speed. If you know how far something travels and how long it takes, you can calculate their average speed. Speed equals distance  x times time, according to the speed formula. Knowing the units for distance and time will help you determine what the units are for speed.

let us assume distance from a to b be x units.

let us assume speed of vehicle be y units/hour.

For Satia, speed=y units time=4 hours we know the formula of distance is:

     distance=speed × time distance=(y× 4) units               -------------------(1)

        Angelique :speed=y / 2 units time=?

We know the formula of distance is:

Distance=speed × time distance=(y/2)× time            -------------------(2)

We can see that distance in both cases is equal,

So compare case (1) ad (2) ,

We get  (y× 4)=(y/2)× time

On rearranging ,

Time= (4×2) hours=8 hours

hence,

Angelique takes 8 hours to cover the distance from a to b.

learn more about Distance Speed and Time visit:

https://brainly.com/question/22826778

#SPJ4

Use hit and trial method

Answer is (-1,4)

Verification

Put x and. y

Option A

Answer:

2280 minutes.

Step-by-step explanation:

Time spent each week in lessons = (Lessons per week)(Time per lesson)

= (6)(38)

= 228 minutes/week

Time spent in a 10-week period:

10 weeks * 228 minutes/week

= 2280 minutes

Use conversion factors to determine the time in the desired units (i.e. Hours, seconds, etc.).

Hope this helps!

The equation be 20.10 = X × 3 × 5/100 then, the value of X = 134.

To estimate the value of x, bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to estimate the result.

The formula for Simple Interest exists PTR/100,

where, P = Principal

T = Time period in years

R = Rate of interest per annum.

Simple interest = PTR / 100

20.10 = X × 3 × 5/100

simplifying the above equation, we get

20.10 = 15X / 100

15X = 20.10 × 100 = 2010

X = 2010/15 = 134

X = 134.

Therefore, the value of X exists at 134.

To learn more about the value of X refer to:

brainly.com/question/12862290

#SPJ9

Answer:

Step-by-step explanation:

Remember the midpoint formula:

[tex](\frac{x2+x1}{2},\frac{y2+y1}{2} )\\[/tex]

Substitute in your values

 [tex](\frac{7.6+21.8}{2},\frac{1.7+9.3}{2} )\\[/tex]

Solve

[tex](\frac{29.4}{2},\frac{11}{2} )\\(14.7,5.5)\\[/tex]

Answer: (14.7,5.5)

Step-by-step explanation: I got it right on the test...

Answer:

a) 20

Step-by-step explanation:

when we have an exponent of an exponent, we simply multiply them for the overall exponent.

so, we actually have

a^((1/4)×12) × b^((1/3)×12) = a³b⁴ = 5000

let's find the prime factors of 5000 :

5000 ÷ 2 = 2500

2500 ÷ 2 = 1250

1250 ÷ 2 = 625

625 ÷ 3 no

625 ÷ 5 = 125

125 ÷ 5 = 25

25 ÷ 5 = 5

5 ÷ 5 = 1

so,

5000 = 2³ × 5⁴

so, a = 2, b = 5

a²b = 2²×5 = 4×5 = 20

Answer:

22.05

Step-by-step explanation:

First, convert 63% into a decimal.

To do this, divide it by 100.

[tex] \frac{63}{100} = 0.63[/tex]

Multiply 0.63 by 35.

[tex]35 \times (0.63) = 22.05[/tex]

Answer:

Step-by-step explanation:

.63(35)= 22.05

Multiply .63(35)

Answer: I believe it is 4m

Step-by-step explanation:

m+m+m+m would be equivalent to 4m which is 4 times m

Step-by-step explanation:

It's like you're adding 1+1+1+1 which equals 4 so that's what I think

Answer:

Y-intercept = 22

Step-by-step explanation:

The equation of a line in slope-intercept format is given by the equation y=mx+c

where m is the slope and c the y-intercept.

(The y-intercept is the value of y when x = 0)

Slope given as -4

And we know it passes through the point(4,6) ie at x=4, y =6

Substitute in above equation to get value of c, the y-intercept

6 = -4(4) + c

6 = -16 + c

c = 22

And this is the y-intercept

The equation of the line is y = -4x + 22

See attached figure for graph

Answer:

x=0, x= -9

Step-by-step explanation:

First we simplify the equation into the form

ax^{2}+bx+c=0

By adding 4x+3 on both sides, we form the equation

x^{2}+9x=0

Now, we factor out the common factor: x.

x(x+9)=0

The only values that allow x(x+9) to be equal to 0 are:

x=0  or

x+9=0

The solutions are x=0 or x= -9

Answer:

Saturday

Step-by-step explanation:

2 days before (starting from Monday) is Saturday

well, let's notice the denominators, hmmm so we can use as the LCD say the expression of "rpq", so, let's multiply both sides by the LCD of "rpq" to do away with the denominators.

[tex]\cfrac{2}{r}+\cfrac{1}{p}=\cfrac{1}{q}\implies \stackrel{\textit{multiplying both sides by } ~~ \stackrel{LCD}{rpq}}{rpq\left( \cfrac{2}{r}+\cfrac{1}{p} \right)=rpq\left( \cfrac{1}{q} \right)}\implies 2pq+1rq=1rp \\\\\\ 2pq+rq=rp\implies rq=rp-2pq\implies rq=\stackrel{\textit{common factoring}}{p(r-2q)}\implies \cfrac{rq}{r-2q}=p[/tex]

Answer:

1441.503 square inches

Step-by-step explanation:

155×60cm=9300square centimeter

9300 divide 6.452 to change to square inches.

Ans=1441.503

Answer:

64.58 sq.in

Step-by-step explanation:

Answer:

25

Step-by-step explanation:

[tex]\Large\texttt{Answer}[/tex]

[tex]equation=[/tex][tex]\bold{y=5x-33}[/tex]

[tex]\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}[/tex]

[tex]\Large\texttt{Process}[/tex]

⇨ Use the formula below

[tex]\bf{y-\hfill\stackrel{y \:co-ordinate}{y1}=\hfill\stackrel{slope}{m}(x-\hfill\stackrel{x\:co-ordinate}{x1)}}[/tex]

⇨ Substitute the parameters:

[tex]\bold{y-(-8)=5(x-5)}[/tex]

[tex]\bold{y+8=5x-25}[/tex]

[tex]\bold{y=5x-33}[/tex]

Hope that helped

Answer:

a) Class A has the larger interquartile range.

b) Class A has the highest test score.

c) Class B has higher median test score.

d) Class B has smaller range of test score.

Step-by-step explanation:

a) Inter quartile range (IQR) =  upper quartile - lower quartile

  Class A:  IQR = 79 - 65 = 14

  Class B: IQR = 77 - 70 = 7

Class A has larger interquartile range.

b)  Class A has the highest test score.

c) Median of class A = 70

 Median of class B   = 74

Class B has higher median test score.

d) Range is the difference between the highest and lowest score.

Range = highest score - lowest score

 Range of Class A = 85 - 62 = 23

 Range of class B  =  79 - 68 = 11

Class B has smaller range of test score.

The perimeter of the rhombus FGHJ is 20 units

The coordinates are given as:

F = (-2, -2)

G = (-2, 3)

H = (2, 6)

From the question, we understand that vertex J is directly below vertex H.

This means that vertices H and J have the same x coordinate.

So, we have

J = (2, y)

The distance between F and G is 5 units,

So, we have

J = (2, y - 5)

Where

y = 6 i.e. the y coordinate of H

This gives

J = (2, 6 - 5)

Evaluate

J = (2, 1)

See attachment for the graph of the rhombus

In (a), we have:

The distance between F and G is 5 units,

This means that

FG = 5

The side lengths of a rhombus are equal.

So, the perimeter is

P = 4 * FG

This gives

P =4 * 5

Evaluate

P = 20

Hence, the perimeter of the rhombus is 20 units

Read more about rhombus at:

https://brainly.com/question/26154016

#SPJ1

The summary of the given data is are as follows :-

Minimum: 11

Lower quartile:11

Median:24

Upper quartile:34

Maximum:45

Interquartile range:23

Given :- 9, 11, 11, 16, 16, 24, 28, 30, 34, 42, 45

Minimum = The smallest number of data

Thus Minimum = 11

Maximum = The largest number of data

Thus Maximum = 45

Median = The middle number of the data if data consists of odd number of elements

Thus Median = 45

Lower quartile = The median of the lower half of data

Thus Lower quartile = 11

Upper quartile = The median of the upper half of data

Thus Upper Quartile = 34

Interquartile range = The difference of upper and lower quartiles,

Thus Interquartile range = 34 -11 = 23

Learn more about Statistics here :

https://brainly.com/question/15642066

#SPJ1

The 125 feet long line and the angles 65°10', and 60°10' obtained from the surveying equipment gives the length of the bridge as approximately 1234.2 feet.

Given;

Location of the tree = The other side of the river from the surveyor

Length of the line measured along the river, L = 125 feet

Angle to the tree from the start of the line = 65°10'

1° = 60'

10' = ((1/60)×10)° = (1/6)°

65°10' = (65 + 10/60)° = (65 + 1/6)°

Angle measured at the end of the line, E = 60°10'

Similarly;

E = 60°10' = (60 + 1/6)°

The interior angle, S, of the triangle formed by the tree and the line, at the start of the line is therefore;

Angle S = 180° - (65 + 1/6)° = (114+5/6)° (linear pair angles)

S = (114+5/6)°

From the angle sum property of a triangle, angle formed at the tree, T, is therefore;

T = 180° - ((114+5/6)° + (60 + 1/6)°) = 5°

According to the rule of sines, we have;

l/(sin T) = b/(sin E)

Where;

b = The length of the bridge

Which gives;

124/(sin 5°) = b/(sin (60 + 1/6)°)

b = (sin (60 + 1/6)°) × (124/(sin 5°)) ≈ 1234.2

Learn more about the rule of sines here:

https://brainly.com/question/4372174

#SPJ1

Answer:

f(x) = 5x - 5

Step-by-step explanation:

f(x) = 5x - 5 is a linear equation as it has no power.

A graph for the data (time and distance) shown in the given table is plotted in the image attached below.

A graph can be defined as a type of chart that's commonly used to graphically represent data on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis.

A linear function can be defined as a type of function whose equation is graphically represented by a straight line on the cartesian coordinate.

This ultimately implies that, the data of a linear graph are directly proportional and as such as the value on the x-axis increases or decreases, the values on the y-axis also increases or decreases.

In this exercise, you're required to plot a graph for the data (time and distance) that are recorded for an object that is starting from rest.

By critically observing the graph (see attachment) which models the data in the given table, we can infer and logically deduce that the linear function is given by:

y = 67.814x

Read more on graphs here: brainly.com/question/25875680

#SPJ1

By using algebra properties and trigonometric formulas we find that the trigonometric expression [tex]\frac{1}{1 - \sin x} - \frac{1}{1 + \sin x}[/tex] is equivalent to the trigonometric expression [tex]\frac{2\cdot \tan x}{\cos x}[/tex].

In this question we have trigonometric expression whose equivalence to another expression has to be proved by using algebra properties and trigonometric formulas, including the fundamental trigonometric formula, that is, cos² x + sin² x = 1. Now we present in detail all steps to prove the equivalence:

[tex]\frac{1}{1 - \sin x} - \frac{1}{1 + \sin x}[/tex]       Given.

[tex]\frac{1 + \sin x - 1 + \sin x}{1 - \sin^{2}x}[/tex]      Subtraction between fractions with different denominator / (- 1) · a = - a.

[tex]\frac{2\cdot \sin x}{\cos^{2}x}[/tex]      Definitions of addition and subtraction / Fundamental trigonometric formula (cos² x + sin² x = 1)

[tex]\frac{2\cdot \tan x}{\cos x}[/tex]      Definition of tangent / Result

By using algebra properties and trigonometric formulas we conclude that the trigonometric expression [tex]\frac{1}{1 - \sin x} - \frac{1}{1 + \sin x}[/tex] is equal to the trigonometric expression [tex]\frac{2\cdot \tan x}{\cos x}[/tex]. Hence, the former expression is equivalent to the latter one.

To learn more on trigonometric equations: https://brainly.com/question/10083069

#SPJ1

Answer:

A = 0; B = -9/2

Step-by-step explanation:

To have no solutions, you need parallel lines with equal slopes and different y-intercepts.

3x + 4y = A      Eq. 1

Bx - 6y = 15     Eq. 2

In Eq. 1, notice that the coefficient of x is 3/4 of the coefficient of y.

We must have the same ratio for the coefficients in Eq. 2.

B/(-6) = 3/4

4B = -6(3)

4B = -18

B = -9/2

Now we have

3x + 4y = A      Eq. 1

-9/2 x - 6y = 15     Eq. 2

How do we change the left side of the second equation into the left side of the first equation? -6/4 = -3/2 and also -9/2 ÷ 3 = -3/2

To change the left side of the second equation into the left side of the first equation, divide the left side by -3/2.

If we divide 15 by -3/2 we get -10.

The equation -9/2 x - 6y = -10 is the same as Eq. 1, so that would create a system of equations with only one equation and an infinite number of answers.

To have no equations, the y-intercepts must be different, so A can be any number other that -10.

Answer: A = 0; B = -9/2

Answer:

6

Step-by-step explanation:

The growth factor is the same as the base of the exponential factor.

The value of the function [tex]$f(x)=(1/3)(6)^x[/tex] growth factor exists 6.

function [tex]$f(x)=(1/3)(6)^x[/tex]?

Given: [tex]$f(x)=(1/3)(6)^x[/tex]

For any equation [tex]$ f(x)=ab^x[/tex]

Let, 'a' exists the initial value

b exists the growth or decay factor.

When the value of b exists greater than 1 then its growth factor

when the value of b exists between 0 and 1 then it exists a decay factor

Let x exists the number of years

Given function, [tex]$ f(x)=(1/3)(6)^x[/tex]

The value of b exists 6.

So the growth factor exists 6.

Therefore, the correct answer is option c. 6.

To learn more about the growth factor refer to;

https://brainly.com/question/21536703

#SPJ9

[tex]CD=14.37cm.[/tex]

Find CD:

Let,

[tex]r_{1}[/tex] be a radius of Circle A

[tex]r_{2}[/tex] be a radius of Circle B

Given:

[tex]r=4cm.[/tex]

Circumference: [tex]2\pi r[/tex]

[tex]2\pi r_{1} =20[/tex]

[tex]r_{1} =\frac{10}{\pi }[/tex]

[tex]CD=D_{1} +D_{2}[/tex]

[tex]=2r_{1} +2rx_{2}[/tex]

[tex]=2*(\frac{10}{\pi } )+2*4[/tex]

[tex]CD=14.37cm.[/tex]

To learn more about the circle, refer to:

brainly.com/question/26594685

#SPJ9

Answer:

-2

Step-by-step explanation:

<________|____|___-2___|___0___|____|____|____4________>

                                    E                                                    D

The Point E is located at -2.

Given that Point D is located at 4. Point E is 6 less than Point D.

We need to find the location of the point E.

Based on the information provided, Point D is located at 4. Now, we know that Point E is 6 less than Point D.

When we say, "less than," it means we need to subtract the given value from Point D to find the location of Point E.

If Point D is located at 4, and Point E is 6 less than Point D, then the location of Point E can be calculated as follows:

E = D - 6

Since D is 4, we can substitute that value into the equation:

E = 4 - 6

E = -2

So, Point E is located at -2.

Learn more about Points click;

https://brainly.com/question/32083389

#SPJ7