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3 years ago

13

Help plz correct answer get brainliest

1 answer:

Elina [12.6K]3 years ago

6 0

No it is a straight line they are not collinear

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Two numbers are in the ratio 7:9 if the sum of the number is 112 then the lrger number is?

nordsb [41]

Answer:

63

Step-by-step explanation:

the numbers are in ratio 7 : 9 = 7x : 9x ( x is a multiplier )

given the sum of the numbers = 112 , then

7x + 9x = 112 , that is

16x = 112 ( divide both sides by 16 )

x = 7 , then

9x = 9 × 7 = 63 ← value of larger number

7 0

2 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

3 years ago

Kari, katelynn, and Morgan went out for dinner and split the bill evenly. The total bill was $46.68. How much did each pay?

Murrr4er [49]

46.68 ÷3=15.56 each because it's being split by 3

5 0

3 years ago

Read 2 more answers

A line passes through the points (-15, 4) and (5,8). What is its equation in slope-intercept

vovangra [49]

Answer:

y=1/5x+7

Step-by-step explanation:

just checked it on paper

7 0

2 years ago

jake made some tarts. He sold 3/5 of them and gave 1/4 of the remainder to his friends. If he had 150 tarts left, how many did h

Sergeu [11.5K]

Answer: 90 tarts

Step by Step: 150/5 = 30

30 multiplied times 3 = 90

6 0

2 years ago