The numbers In the boxes are arranged in a pattern. Find the pattern. Then find the missing numbers.

Solve using the quadratic formula x^2-4x+1=0

sergiy2304 [10]

Answer:

x=2+ or - the square root of 3

Step-by-step explanation:

solve the equation for x by finding a, b, and c of the quadratic then applying the quadratic formula.

4 0

3 years ago

Read 2 more answers

In the function f(t) = sin(t), what is the effect of multiplying t by a coefficient of 2?

liubo4ka [24]

Answer:

"changes the period to pi"

Step-by-step explanation:

f(t) = Sin(t),

Here, t is the period, by definition.

Multiply t by a number that is GREATER THAN 1, makes the period shorter and compressed.

Multiplying t by a number that is between 0 and 1 makes the period expanded.

For the first, if we multiply the period by a, the period becomes $\frac{2\pi}{a}$

Since the problem tells us to multiply by 2, we know the period becomes compressed and becomes :

$\frac{2\pi}{2}=\pi$

Third answer choice is right.

5 0

3 years ago

(10 points) Consider the initial value problem y′+3y=9t,y(0)=7. Take the Laplace transform of both sides of the given differenti

Rashid [163]

Answer:

The solution

$Y (s) = 9( -1 +3 t + e^{-3 t} ) + 7 e ^{-3 t}$

Step-by-step explanation:

Explanation:-

Consider the initial value problem y′+3 y=9 t,y(0)=7

Step(i):-

Given differential problem

y′+3 y=9 t

Take the Laplace transform of both sides of the differential equation

L( y′+3 y) = L(9 t)

Using Formula Transform of derivatives

L(y¹(t)) = s y⁻(s)-y(0)

By using Laplace transform formula

$L(t) = \frac{1}{S^{2} }$

Step(ii):-

Given

L( y′(t)) + 3 L (y(t)) = 9 L( t)

$s y^{-} (s) - y(0) + 3y^{-}(s) = \frac{9}{s^{2} }$

$s y^{-} (s) - 7 + 3y^{-}(s) = \frac{9}{s^{2} }$

Taking common y⁻(s) and simplification, we get

$( s + 3)y^{-}(s) = \frac{9}{s^{2} }+7$

$y^{-}(s) = \frac{9}{s^{2} (s+3}+\frac{7}{s+3}$

Step(iii):-

By using partial fractions , we get

$\frac{9}{s^{2} (s+3} = \frac{A}{s} + \frac{B}{s^{2} } + \frac{C}{s+3}$

$\frac{9}{s^{2} (s+3} = \frac{As(s+3)+B(s+3)+Cs^{2} }{s^{2} (s+3)}$

On simplification we get

9 = A s(s+3) +B(s+3) +C(s²) ...(i)

Put s =0 in equation(i)

9 = B(0+3)

B = 9/3 = 3

Put s = -3 in equation(i)

9 = C(-3)²

C = 1

Given Equation 9 = A s(s+3) +B(s+3) +C(s²) ...(i)

Comparing 'S²' coefficient on both sides, we get

9 = A s²+3 A s +B(s)+3 B +C(s²)

0 = A + C

put C=1 , becomes A = -1

$\frac{9}{s^{2} (s+3} = \frac{-1}{s} + \frac{3}{s^{2} } + \frac{1}{s+3}$

Step(iv):-

$y^{-}(s) = \frac{9}{s^{2} (s+3}+\frac{7}{s+3}$

$y^{-}(s) =9( \frac{-1}{s} + \frac{3}{s^{2} } + \frac{1}{s+3}) + \frac{7}{s+3}$

Applying inverse Laplace transform on both sides

$L^{-1} (y^{-}(s) ) =L^{-1} (9( \frac{-1}{s}) + L^{-1} (\frac{3}{s^{2} }) + L^{-1} (\frac{1}{s+3}) )+ L^{-1} (\frac{7}{s+3})$

By using inverse Laplace transform

$L^{-1} (\frac{1}{s} ) =1$

$L^{-1} (\frac{1}{s^{2} } ) = \frac{t}{1!}$

$L^{-1} (\frac{1}{s+a} ) =e^{-at}$

Final answer:-

Now the solution , we get

$Y (s) = 9( -1 +3 t + e^{-3 t} ) + 7 e ^{-3t}$

5 0

3 years ago

What is the least number of cuts you would need to make to cut a 3 by 3 by 3 inch block of cheese into 1 by 1 by 1 inch blocks o

Semenov [28]

Answer:

6 Cut Minimum

Step-by-step explanation:

According to the Question,

You have a 3x3x3 cube.

First make two cuts parallel to base of the cube each at a distance of 1 unit . This leaves you with three cuboids of dimensions 3x3x1.
Now make two parallel cuts parallel to the height of the cube. This leaves you with nine cuboids of dimensions 3x1x1.
Now make the final two cuts each 1 unit apart parallel to width and you are left with 27 cubes of 1x1x1.

So , the final answer is 6 cuts.

5 0

3 years ago

Help me I really need this done

e-lub [12.9K]

Answer: I think it's 24

Step-by-step explanation:

3 0

3 years ago