20 POINT MATH PROBLEM HELP

Start with the underlying homogeneous equation:

[tex]y''-7y'+6y=0[/tex]

which has characteristic equation

[tex]r^2-7r+6=(r-6)(r-1)=0[/tex]

with roots at r = 6 and r = 1. So the characteristic solution is

[tex]y_c=C_1e^{6x}+C_2e^x[/tex]

Now for the particular solution, we can use the method of undetermined coefficients, with the following ansatz (the "guess" solution) and its derivatives,

[tex]y_p=a\cos x+b\sin x[/tex]

[tex]{y_p}'=-a\sin x+b\cos x[/tex]

[tex]{y_p}''=-a\cos x-b\sin x[/tex]

Substituting these into the original equation gives

[tex](-a\cos x-b\sin x)-7(-a\sin x+b\cos x)+6(a\cos x+b\sin x)=\sin x[/tex]

[tex](5a-7b)\cos x+(7a+5b)\sin x=\sin x[/tex]

[tex]\implies\begin{cases}5a-7b=0\\7a+5b=1\end{cases}\implies a=\dfrac7{74},b=\dfrac5{74}[/tex]

So the particular solution is

[tex]y_p=\dfrac7{74}\cos x+\dfrac5{74}\sin x[/tex]

and hence the general solution is

[tex]y=y_c+y+p=\boxed{C_1e^{6x}+C_2e^x+\dfrac7{74}\cos x+\dfrac5{74}\sin x}[/tex]

Answer:

6 4/5

Step-by-step explanation:

Find the Greatest Common Factor (GCF) of 238 and 35, if it exists, and reduce our fraction by dividing both numerator and denominator by it. GCF = 7,

=238÷7/35÷7=34/5

Converting to a mixed number using long division with remainders for 34 ÷ 5.

34÷5=6R4

Therefore:

34/5=6 4/5

Answer:

Tiene 9 monedas de $50 y 15 monedas de $100.

Step-by-step explanation:

Sergio tiene $1950 en monedas de $100 y $50, entonces la primera ecuación es la siguiente:

[tex] 100x + 50y = 1950 [/tex]   (1)

Ahora, en total tiene 24 monedas:

[tex] x + y = 24 [/tex]   (2)

De la ecuación (2) tenemos:

[tex] x = 24 - y [/tex]   (3)

Ahora introduciendo la ecuación (3) en la ecuación (1) y resolviendo para "y" nos queda:

[tex] 100(24 - y) + 50 y = 1950 [/tex]

[tex] 2400 - 100y + 50y = 1950 [/tex]

[tex] y = \frac{450}{50} = 9 [/tex]

Con la ecuación (3) podemos hallar el valor de "x":

[tex] x = 24 - 9 = 15 [/tex]

Por lo tanto, tiene 9 monedas de $50 y 15 monedas de $100.

Espero que te sea de utilidad!                                        

Answer:

y =x+1

Step-by-step explanation:

The y intercept is 1

The slope is positive

We go up 1 and to the right 1

y = mx+b  where m is the slope and b is the y intercept

y = 1x+1

y =x+1

Answer:

Apr 16, 2018 — p>Which exponential function is represented by the graph?</p><span>f(x) = 2(1/​2)^x </span><span>f(x) = 1/2(2)^x </span><span>f(x) = 1/2

Step-by-step explanation:

Answer:

384950c or $3849.50

Step-by-step explanation:

240x1540=369600

100x125=12500

30x95=2850

369600+12500+2850=384950

Answer:

5

Step-by-step explanation:

The mode of a data set is the number that appears most

9514 1404 393

Answer:

Step-by-step explanation:

The angle is in the 2nd quadrant, where the sine is positive and the cosine is negative.

tan^2(θ) +1 = sec^2(θ) = (-9/4)^2 +1 = 97/16   ⇒   sec = -(1/4)√97

cot(θ) = 1/tan(θ) = -4/9

csc^2(θ) = cot^2(θ) +1 = (-4/9)^2 +1 = 97/81   ⇒   csc = (1/9)√97

sin(θ) = 1/csc(θ) = (9√97)/97

cos(θ) = 1/sec(θ) = (-4√97)/97

Answer:

8

Step-by-step explanation:

Let the unknown number be x.

Therefore, we can write the question as a mathematical statement and this will be:

3x^2 - 137 = 55.  (Note: ^2 = to the power of 2 or "squared"

(In the question, we can break it up as being three times of a square of a natural number = (3x^2) and 137 is subtracted from = (- 137) and the result is 55 = (= 55). Therefore, this gives 3x^2 - 137 = 55

Then, we add 137 first to get rid of the (-137)

Therefore:

3x^2 = 192

Then, we divide 3 from both sides to get rid of the (3) in (3x^2).

Therefore,

x^2 = 64.

So, we square root 64. This gives

x = 8.

Therefore, the answer is 8.

Answer:

y+1=7(x+4) for first one

y-4=5(x-0) for second one

Step-by-step explanation:

point slope form for both of those questions.

the formula for point slope form is

y-y1(y coordinate) = slope(x+x2(x coordinate))

y+1=7(x+4)

Second question:

-1,-1 to 0,4

change in x +1, change in y +5.

5/1 = 5

slope is 5

y-4=5(x-0)

9514 1404 393

Answer:

  $6190.48

Step-by-step explanation:

The price is now 1 -16% = 84% of the original price (p).

 $5200 = 0.84p

  p = $5200/0.84 = $6190.48

The price before the discount was $6190.48.

Answer:

d). 14 and 240

Step-by-step explanation:

According to the Question,

We need to find out the numerator and denominator freedom degrees ,

k = 14 regression variable

= n - k - 1

= 255 - 14 - 1

= 240 residuals

df=14,240

F_{k,n-k-1}=F_{14,240}

So, The df of the numerator is 14 and df of the denominator is 240

Answer:

8/3

Step-by-step explanation:

2/ (3/4) = 2*4/3 =8/3

Answer:

301.6 ft³

Step-by-step explanation:

Volume of the cone = ⅓*πr²h

Where,

radius (r) = 6 ft

height (h) = √(10² - 6²) => Pythagorean theorem

h = √(100 - 36)

h = √64

h = 8 ft

Plug in the values

Volume = ⅓*π*6²*8

Volume = 301.6 ft³ (nearest tenth)

Answer:

Equation: y = 0.25x + 7.50

Cost: $10.50

Step-by-step explanation:

Let x be the number of miles and y be the total cost in $.

y = 0.25x + 7.50

If we want to find the total cost of a 12 mi trip, we plug in x=12.

y = 0.25 * 12 + 7.50

y = 3 + 7.50

y=10.50

Answer:

1. $950

2. 80

Step-by-step explanation:

Answer:

hey. pls post a pic of the pattern or type in the number of sticks in each term so we could help tou determine the nth term

Answer:

1: x intercept:2 y intercept:5

2: x intercept:-7 y intercept:1

3: x intercept:2 y intercept:-2

4: x intercept: 1 y intercept: -2

Step-by-step explanation:

The y intercept is whenever the x unit is at 0, and the x intercept is whenever the y intercept is at 0.  

(-5/2;5)           (1/7;1)            (1;-2)           (2;-2)

Answer:

4/15 gallon per bottle

Step-by-step explanation:

First, we find the remaining fraction of fertilizer after using 1/5. Using our fraction calculator, we see:

1 - 1/5 = 4/5

To find the amount of fertilizer per bottle, we then divide 4/5 by 3 and we get:

4/15 gallon per bottle

Answer:

242

Step-by-step explanation:

14 * 7 = 98

18 * 8 = 144

98 +144 = 242

9514 1404 393

Answer:

  5

Step-by-step explanation:

The number 5 is a counterexample, as is any number ending in 5.

  5 ÷ 2 = 2 remainder 1

The non-zero remainder indicates 5 is not divisible evenly by two.

Answer:

...

Step-by-step explanation:...

Answer:

6.75 * x =y

Step-by-step explanation:

In this question, for is a keyword here we can use to represent division. If he charges $40.50 for 6 hours, this means we can represent this as [tex]\frac{40.50dollars}{6 hours}[/tex] to calculate the amount babysitting costs for an hour. Our answer is then [tex]\frac{6.75 dollars}{1 hour}[/tex]. A similar division of $54.00 for 8 hours results in a calculation of [tex]\frac{54.00 dollars}{8 hours} = \frac{6.75 dollars}{1hour}[/tex]. This means that for each hour, he charges 6.75 dollars, the same amount of money each hour.

Given this information, we can say that an equation to represent this relationship would be that, to calculate the total money Steven earns, we can multiply 6.75 dollars by the amount of hours he works, as he earns 6.75 dollars for each hour, making our equation 6.75 * x =y, with y representing the total amount he charges. If your teacher would

Step-by-step explanation:

2³×2^n+2=32

2^3+n+2=2⁵

n+5=5

n=0

[tex]_____________________________________[/tex]

[tex]\sf\huge\underline\red{ANSWER:}[/tex]

[tex]\tt n = 0[/tex]

[tex]\sf\huge\underline\red{SOLUTION:}[/tex]

[tex]\tt8 \times {2}^{n + 2} = 32 \\ = \tt {2}^{3} \times {2}^{n + 2} = 32 \\ = \tt {2}^{n + 5} = 32 \\ = \tt {2}^{n + 5} = {2}^{5} \\ = \tt n + 5 = 5 \\ = \tt n = 5 - 5 \\ = \large\boxed{\tt{\green{n = 0}}}[/tex]

[tex]_____________________________________[/tex]

[tex]\large\boxed{\sf{\green{CarryOnLearning}}}[/tex]

[tex]\large\boxed{\sf{\red{MathDemonQueenシ︎✌︎}}}[/tex]

[tex]\large\boxed{\sf{\green{ItsMoreFunInThePhilippines✌︎}}}[/tex]

Answer:

a) V(3) = 8.6.

b) The resale value will be 7.3 thousand dollars at the start of 2015.

c) [tex]t(V) = \frac{12.5 - V}{1.3}[/tex]

d) 2017

Step-by-step explanation:

We are given the following function:

[tex]V(t) = 12.5 - 1.3t[/tex]

(a) Calculate V(3).

This is V when t = 3. So

[tex]V(3) = 12.5 - 1.3(3) = 8.6[/tex]

So

V(3) = 8.6.

(b) In what year will the resale value be 7.3 thousand dollars?

t years after the start of 2011, and t is found when [tex]V(t) = 7.3[/tex]. So

[tex]V(t) = 12.5 - 1.3t[/tex]

[tex]7.3 = 12.5 - 1.3t[/tex]

[tex]1.3t = 5.2[/tex]

[tex]t = \frac{5.2}{1.3}[/tex]

[tex]t = 4[/tex]

2011 + 4 = 2015

The resale value will be 7.3 thousand dollars at the start of 2015.

(c) Solve for t in the formula above to obtain a formula expressing t as a function of V.

[tex]V(t) = 12.5 - 1.3t[/tex]

[tex]1.3t(V) = 12.5 - V[/tex]

[tex]t(V) = \frac{12.5 - V}{1.3}[/tex]

(d) In what year will the resale value be 3.4 thousand dollars?

t years after 2011, and t is found t when [tex]V = 3.4[/tex]. So

[tex]V(t) = 12.5 - 1.3t[/tex]

[tex]3.9 = 12.5 - 1.3t[/tex]

[tex]1.3t = 8.6[/tex]

[tex]t = \frac{8.6}{1.3}[/tex]

[tex]t = 6.62[/tex]

2011 + 6.62 = 2017

So the year is 2017.

Answer:

C. 3/8

HOPE THIS HELPS :)

Answer:

c. 3/8

Step-by-step explanation:

first you need the denomerator by adding all marbles together which equals 32. now for the munerator you need the sum of the green and yellow marbles. this equals 12. so your fraction is 12/32. next we simplify. we can divide both numbers by 4. getting us a fraction of 3/8.

Answer:

I would say 4 to 6 since everything else is decreasing

Step-by-step explanation:

Answer: 103.534%

I used a calculator and everything