What is the equation of a vertical line passing through (−5, −2)? a: x = −5 b: x = −7 c: y = −3 d: y = −2

DaniilM [7]

$\bf (2x^2)^4(5x^6)\impliedby \textit{distributing the exponent}
\\\\\\
2^4x^{2\cdot 4}5x^6\implies 2^4\cdot 5x^{2\cdot 4}x^6\implies 16\cdot 5x^8x^6\implies 80x^{8+6}
\\\\\\
80x^{14}$

8 0

3 years ago

Use Euler's method with step size 0.2 to estimate y(1), where y(x) is the solution of the initial-value problem y' = x2y − 1 2 y

irina [24]

Answer:

Therefore the value of y(1)= 0.9152.

Step-by-step explanation:

According to the Euler's method

y(x+h)≈ y(x) + hy'(x) ....(1)

Given that y(0) =3 and step size (h) = 0.2.

$y'(x)= x^2y(x)-\frac12y^2(x)$

Putting the value of y'(x) in equation (1)

$y(x+h)\approx y(x) +h(x^2y(x)-\frac12y^2(x))$

Substituting x =0 and h= 0.2

$y(0+0.2)\approx y(0)+0.2[0\times y(0)-\frac12 (y(0))^2]$

$\Rightarrow y(0.2)\approx 3+0.2[-\frac12 \times3]$ [∵ y(0) =3 ]

$\Rightarrow y(0.2)\approx 2.7$

Substituting x =0.2 and h= 0.2

$y(0.2+0.2)\approx y(0.2)+0.2[(0.2)^2\times y(0.2)-\frac12 (y(0.2))^2]$

$\Rightarrow y(0.4)\approx 2.7+0.2[(0.2)^2\times 2.7- \frac12(2.7)^2]$

$\Rightarrow y(0.4)\approx 1.9926$

Substituting x =0.4 and h= 0.2

$y(0.4+0.2)\approx y(0.4)+0.2[(0.4)^2\times y(0.4)-\frac12 (y(0.4))^2]$

$\Rightarrow y(0.6)\approx 1.9926+0.2[(0.4)^2\times 1.9926- \frac12(1.9926)^2]$

$\Rightarrow y(0.6)\approx 1.6593$

Substituting x =0.6 and h= 0.2

$y(0.6+0.2)\approx y(0.6)+0.2[(0.6)^2\times y(0.6)-\frac12 (y(0.6))^2]$

$\Rightarrow y(0.8)\approx 1.6593+0.2[(0.6)^2\times 1.6593- \frac12(1.6593)^2]$

$\Rightarrow y(0.6)\approx 0.8800$

Substituting x =0.8 and h= 0.2

$y(0.8+0.2)\approx y(0.8)+0.2[(0.8)^2\times y(0.8)-\frac12 (y(0.8))^2]$

$\Rightarrow y(1.0)\approx 0.8800+0.2[(0.8)^2\times 0.8800- \frac12(0.8800)^2]$

$\Rightarrow y(1.0)\approx 0.9152$

Therefore the value of y(1)= 0.9152.

4 0

3 years ago

Can someone please help me? If it is correct ai will give Brainliest<br> Thank you

Rasek [7]

9514 1404 393

Answer:

A

Step-by-step explanation:

Collecting terms of the expression, we have ...

x + 0.1x = x(1 +0.1) = 1.1x

In words, adding 10% is the same as multiplying the value by 1.1. Choice A is appropriate.

7 0

2 years ago

One number is 6 times a first number. A third number is 100 more than the first number. If the sum of the three numbers is580 ,

jenyasd209 [6]

Answer:

x = 60

1) 60

2) 360

3) 160

60 + 360 + 160 = 580

Step-by-step explanation:

1) x

2) 6x

3) x + 100

x + 6x + x + 100 = 580

8x = 580 - 100

x = 480/8

x = 60

7 0

2 years ago

Given that 110ₓ = 40₅ , find the value of x.

MrRa [10]

Answer:

x = 4

Step-by-step explanation:

110ₓ = 40₅ --------- change all to base ten.

<u>the system called binary</u>

1x²+1x ¹+0x⁰ = 45¹+0*5⁰

x² + x + 0 = 20

x² + x – 20 = 0

solve x using Quadratic equation

-1 ± $\sqrt{1^2 - 4* 1 (-20)}$

x = ------------------------------------

2 * 1

x = -5; x = 4

therefore, x = 4

3 0

2 years ago