All categories

3 years ago

What is the solution to this equation?

Mathematics

1 answer:

padilas [110]3 years ago

6 0

Answer:

x=3

Step-by-step explanation:

10-3x+8x=25

-10 -10

-3x+8x= 15

5x=15

5x/5=15/5

x=3

You might be interested in

Jane and Jill both love to collect books. Jane has twice as many books as Jill. Together, they have a total of 216 books in thei

mezya [45]

Answer:

144

Step-by-step explanation:

Jane has 2 times as many books as Jill, so there are 3 parts. Two parts Jane and one part Jill. So, divide 216 by 3 and it's 72, which equals one part. Jane has two parts, so 72 x 2. Jane has 144 books.

5 0

3 years ago

Consider the differential equation:

Wewaii [24]

(a) Take the Laplace transform of both sides:

$2y''(t)+ty'(t)-2y(t)=14$

$\implies 2(s^2Y(s)-sy(0)-y'(0))-(Y(s)+sY'(s))-2Y(s)=\dfrac{14}s$

where the transform of $ty'(t)$ comes from

$L[ty'(t)]=-(L[y'(t)])'=-(sY(s)-y(0))'=-Y(s)-sY'(s)$

This yields the linear ODE,

$-sY'(s)+(2s^2-3)Y(s)=\dfrac{14}s$

Divides both sides by $-s$ :

$Y'(s)+\dfrac{3-2s^2}sY(s)=-\dfrac{14}{s^2}$

Find the integrating factor:

$\displaystyle\int\frac{3-2s^2}s\,\mathrm ds=3\ln|s|-s^2+C$

Multiply both sides of the ODE by $e^{3\ln|s|-s^2}=s^3e^{-s^2}$ :

$s^3e^{-s^2}Y'(s)+(3s^2-2s^4)e^{-s^2}Y(s)=-14se^{-s^2}$

The left side condenses into the derivative of a product:

$\left(s^3e^{-s^2}Y(s)\right)'=-14se^{-s^2}$

Integrate both sides and solve for $Y(s)$ :

$s^3e^{-s^2}Y(s)=7e^{-s^2}+C$

$Y(s)=\dfrac{7+Ce^{s^2}}{s^3}$

(b) Taking the inverse transform of both sides gives

$y(t)=\dfrac{7t^2}2+C\,L^{-1}\left[\dfrac{e^{s^2}}{s^3}\right]$

I don't know whether the remaining inverse transform can be resolved, but using the principle of superposition, we know that $\frac{7t^2}2$ is one solution to the original ODE.

$y(t)=\dfrac{7t^2}2\implies y'(t)=7t\implies y''(t)=7$

Substitute these into the ODE to see everything checks out:

$2\cdot7+t\cdot7t-2\cdot\dfrac{7t^2}2=14$

5 0

2 years ago

Find the product (x - 10) ( x - 5)

Hatshy [7]

꙰ Hello there mohammedsaquibali45 ! My Name is ⚝Tobie⚝ and I'm glad you asked! Let me walk you step by step in order to comprehend the question better! ꙰

{x}^{2}-5x-10x+50

−5x−10x+50

ii Collect like terms.

{x}^{2}+(-5x-10x)+50

+(−5x−10x)+50

iii Simplify.

{x}^{2}-15x+50

−15x+50

8 0

2 years ago

On average, Tanner has noticed that 22 trains pass by his house daily (24 hours) on the nearby train tracks. What is the probabi

blondinia [14]

Answer:

0.11069

Step-by-step explanation:

We will assume that the trains pass by his house following a uniform distribution with values between 0 and 24. The probability of a train passing on a 9-hour time period is 9/24 = 3/8 = 0.375. Lets call Y the amount of trains passing by his house during that 9-hour period. Y follows a Binomail distribution with parameters 22 and 0.375.

P(Y ≤ 5) = P(Y = 0) + P(Y=1) + P(Y=2) + P(Y=3) + P(Y=4) + P(Y=5) =

${22 \choose 0} * 0.375^0*(1-0.375)^{22} + {22 \choose 1}*0.375^1*(1-0.375)^{21} +\\\\{22 \choose 2} * 0.375^2*(1-0.375)^{20} + {22 \choose 3}*0.375^3*(1-0.375)^{19} + \\{22 \choose 4} * 0.375^4*(1-0.375)^{18} + {22 \choose 5}*0.375^5*(1-0.375)^{17} = 0.11069$

I hope that works for you!

4 0

2 years ago

What are the first 5 terms of 4n+4,8n+3and 18-3n?Please?

dimulka [17.4K]

Assuming the first 5 terms are:

n = 0
n = 1
n = 2
n = 3
n = 4

a) 4n + 4
4(0) + 4 = 4
4(1) + 4 = 8
4(2) + 4 = 12
4(3) + 4 = 16
4(4) + 4 = 20

b) 8n + 3
8(0) + 3 = 3
8(1) + 3 = 11
8(2) + 3 = 19
8(3) + 3 = 27
8(4) + 3 = 35

c) 18 - 3n
18 - 3(0) = 18
18 - 3(1) = 15
18 - 3(2) = 12
18 - 3(3) = 9
18 - 3(4) = 6

7 0

3 years ago