Simplify, assume the variable represents a positive real number

Answer:

C π/2

Step-by-step explanation:

Amplitude: 1

Period: π2

Phase Shift: None

Vertical Shift: None

We will solve as follows:

So, we are trying to find:

Now, we proceed as follows:

*We take the constant term of the divisror with the opposite sign and write it to the left.

*We write the coefficients of the dividenf to the right:

Then, we proceed to operate:

From this, we will have that the quotient is:

And the remainder is 0.

So, (x + 1) is in fact a factor of (5x^3 -12x^2 -11x + 6).

Answer: 7

Step-by-step explanation:

Since there are 42 tubes and each tray can hold 6 tubes, it will be 42/6 which is 7.

Answer:

Step-by-step explanation:

By the Pythagorean Theorem we know

(r+7)^2=r^2+14^2

r^2+14r+49=r^2+196

14r+49=196

14r=147

r=10.5

The general solution of the partial differential equation is:

U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)

The partial differential equation (PDE) is given as:

Uxx = (1/2)Ut with the boundary and initial conditions as 0< X <3 with U(0,t) = U(3, t)=0, U(0, t) = 5sin(4πx)

Assume that the solution can be written as a product of two functions:

U(x, t) = X(x)T(t)

Substituting this into the PDE, we have:

X''(x)T(t) = (1/2)X(x)T'(t)

Dividing both sides by X(x)T(t), we get:

(X''(x))/X(x) = (1/2)(T'(t))/T(t)

Since the left side only depends on x and the right side only depends on t, both sides must be equal to a constant, denoted as -λ²:

(X''(x))/X(x) = -λ²

(1/2)(T'(t))/T(t) = -λ²

Simplifying the second equation, we have:

T'(t)/T(t) = -2λ²

Solving the second equation, we find:

T(t) = Ce^(-2λ²t)

Applying the boundary condition U(0, t) = 0, we have:

U(0, t) = X(0)T(t) = 0

Since T(t) ≠ 0, we must have X(0) = 0.

Applying the boundary condition U(3, t) = 0, we have:

U(3, t) = X(3)T(t) = 0

Again, since T(t) ≠ 0, we must have X(3) = 0.

Therefore, we can conclude that X(x) must satisfy the following boundary value problem:

X''(x)/X(x) = -λ²

X(0) = 0

X(3) = 0

The general solution to this ordinary differential equation is given by:

X(x) = Asin(λx) + Bcos(λx)

Applying the initial condition U(x, 0) = 5*sin(4πx), we have:

U(x, 0) = X(x)T(0) = X(x)C

Comparing this with the given initial condition, we can conclude that T(0) = C = 5.

Therefore, the complete solution for U(x, t) is given by:

U(x, t) = Σ [Aₙsin(λₙx) + Bₙcos(λₙx)]*e^(-2(λₙ)²t)

where:

Σ represents the summation over all values of n

λₙ are the eigenvalues obtained from solving the boundary value problem for X(x).

To find the eigenvalues λₙ, we substitute the boundary conditions into the general solution for X(x):

X(0) = 0: Aₙsin(0) + Bₙcos(0) = 0

X(3) = 0: Aₙsin(3λₙ) + Bₙcos(3λₙ) = 0

From the first equation, we have Bₙ = 0.

From the second equation, we have Aₙ*sin(3λₙ) = 0. Since Aₙ ≠ 0, we must have sin(3λₙ) = 0.

This implies that 3λₙ = nπ, where n is an integer.

Therefore, λₙ = (nπ)/3.

Substituting the eigenvalues into the general solution, we have:

U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)

where Aₙ are the coefficients that can be determined from the initial condition.

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Carl has a to arrange 3 1/2 feet long cabinets on a wall that is 21 feet long. This means Carl has to divide the entire wall into 3 1/2 feet and see how many of those can fit into it. The solution is shown below;

Answer:

  y -1 = 2(x -3)

Step-by-step explanation:

The given equation is in slope-intercept form:

  y = mx +b . . . . line with slope m and y-intercept b

  y = 2x +3 . . . . . line with slope 2 and y-intercept 3

__

A parallel line will have the same slope. Since you are given a point, it is convenient to use the point-slope form for the equation you want:

  y -k = m(x -h) . . . . . line with slope m through point (h, k)

  y -1 = 2(x -3) . . . . . . line with slope 2 through point (3, 1)

__

Additional comment

If you want the slope-intercept form you can solve for y:

  y = 2(x -3) +1 = 2x -6 +1

  y = 2x -5 . . . . . slope-intercept form of the parallel line

Answer:

Step-by-step explanation:

B because after having the star and the circle comes the square.

The equation that represents the relationship is y = 1/3x

The missing graph in the complete question is added as an attachment

From the question, we have the following points that can be used in our computation:

(x, y) = (0, 0) and (3, 1)

A linear equation is represented as

y = mx + c

Where

c = y when x = 0

So, we have

y = mx

Using the points, we have

1 = 3m

Divide

m = 1/3

Substitute 1/3 for m in y = mx

y = 1/3x

Hence, the function of the relation is y = 1/3x

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Answer:

5/3

Step-by-step explanation:

Multiply the denominator by the whole number

3 x 1= 3

Add the answer from above to the numerator

3 + 2= 5

Write the answer from the step above over to the denominator

5/3

Answer:

-4\(\frac{1}{2}\)

Step-by-step explanation:

I hope this helps!

We have

x is the number of hour working as a lifeguard

y is the number of hour washing cars

The first inequality is

we isolate the y

the second inequality is

then we isolate the y

then we will plot the inequalities

We have as a solution the area where the two areas intercept each other

One solution to these systems of inequalities could be

x=12

y=2

Julian could work 12 hours lifeguarding and 2 hours washing cars

Answer:

23

if you have 15 gallons of gas and it makes it 345 miles that is 345 divided by 15 which is 23 or 023

15x2 equals 30 34 - 30 equals 4 bring the 5 down you have 45 15x3 equals 45, 45 - 45 equals 0

Answer:

B 1/2

Step-by-step explanation:

This is right

The probability that the sum of the two numbers is odd, given that the product is 6 will be 2/3. Option C is correct.

Probability is synonymous with possibility. It is concerned with the occurrence of a random event. Probability can only have a value between 0 and 1.

Ethan cranks the arrow on the spinner after rolling the number cube. There is a list of all conceivable outcomes.

{(1, 1), (1, 2), (1,3), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3), (4,1),(4,2), (4,3), (5, 1), (5,2), (5,3), (6, 1), (6,2), (6,3)}

The no of sets having the sum of the number is odd=9

The no of sets having the product of the number is 6=3

The total number including the two conditions=3+9=12

Probability is found as;

P=12/18

P=2/3

The probability that the sum of the two numbers is odd, given that the product is 6 will be 2/3.

Hence, option C is correct.

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Answer: E

Step-by-step explanation:

8V+3=105

clt

8v=105-3

=102

divide both sides by 8v

8v=102/8v

V=12.75

Answer:

A

Step-by-step explanation:

36*12*6+12*24*3=3456

Answer:

3456

Step-by-step explanation:

36*12*6 + 24*12*3

just add up the two volumes

The distance from the island to Gatsby's dock is 1.3 miles.

A Pythagoras theorem is a principle that can be used to determine the unknown side of a right angled triangle when the other two sides are known.

Applying the Pythagoras theorem to the given question, let the distance from island to Gatsby's dock be represented by s. Then;

/Hyp/^2 = /Opp/^2 + /Adj/^2

s^2 = 1.2^2 + 0.5^2

      = 1.44 + 0.25

      = 1.69

s = 1.69^1/2

  = 1.3

Thus, the straight-line distance from the island to Gatsby's dock is 1.3 miles.

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The function f(x) = 2x² - 7x + 10 is an odd function.

f(-x) = 2(-x)² - 7(-x) + 10

      = 2x² + 7x + 10

-f(x) = -[2x²- 7x + 10]

      = -2x² + 7x - 10

To determine whether the function f(x) = 2x² - 7x + 10 is even, odd, or neither, we compare f(-x) and -f(x).

1. f(-x) = 2x² + 7x + 10

2. -f(x) = -2x² + 7x - 10

To determine if f(-x) = -f(x) (even function), we substitute -x for x in f(x) and check if the equation holds.

1. f(-x) = 2x² + 7x + 10

         = f(x) (not equal to -f(x))

Since f(-x) is not equal to -f(x), the function is not even.

Next, to determine if f(-x) = -f(x) (odd function), we substitute -x for x in f(x) and check if the equation holds.

2. -f(x) = -2x² + 7x - 10

        = -(2x² - 7x + 10)

        = -(f(x))

Since -f(x) is equal to -(f(x)), the function is odd.

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Answer: Rx + 20r

Step-by-step explanation:

The probability that the next respondent questioned will indicate that they are planning to vote is 0.59.

Given that, 315 respondents indicated that they were planning to vote and 217 said that they were not.

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

We know that, probability of an event = Number of favourable outcomes/Total number of outcomes

Now, probability of voting is

P(voting)=315(315+217)

= 315/532

= 0.59

Therefore, the probability that the next respondent questioned will indicate that they are planning to vote is 0.59.

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Answer:

-4^2= 16

Step-by-step explanation:

a^2 when A=-4 means -4^2 which, when expanded means, -4*-4 that equals a positive 16 because the negatives cancel out.

Answer:

-4^2= 16

Step-by-step explanation:

Answer:

18

Step-by-step explanation:

25 + 11 = 36

36/2 = 18

hope this helps

Answer:

Step-by-step explanation:

Answer:

5.573.75

Step-by-step explanation:

because math

1. 3/7 = 72/x

By cross multiplication we get :

➟ 3x = 72 × 7

➟ x = 72 × 7/3

➟ x = 24 × 7

➟ x = 168

2. m/8 = 8/20

By cross multiplication we get :

➟ 20m = 8 × 8

➟ 20m = 64

➟ m = 64/20

➟ m = 16/5

The area of a shape is the amount of space it can occupy.

Laura's design will be light enough

The shape is given as a trapezium (see attachment).

First, calculate the height (h) of the trapezium using the following Pythagoras theorem

\(5^2 = h^2 + x^2\)

Where:

\(x = \frac{11 - 9}{2} = 1\)

So, we have:

\(5^2 = h^2 + x^2\)

\(5^2 = h^2 + 1^2\)

\(25 = h^2 + 1\)

Collect like terms

\(h^2 = 25 -1\)

\(h^2 = 24\)

Take square roots

\(h = 4.90\)

The area of the shape is then calculated as follows:

\(Area = \frac{1}{2}(11 + 9) \times h\)

\(Area = \frac{1}{2}(11 + 9) \times 4.90\)

\(Area = \frac{1}{2} \times 20 \times 4.90\)

\(Area = 10 \times 4.90\)

\(Area = 49\)

The area of the shape is 49 square inches.

Hence, the shape will be light enough (because 49 is less than 80)

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Answer: The required number of heads = 30

Step-by-step explanation:

Given, Total tosses = 50

The theoretical probability of getting head = \(\dfrac{1}{2}\)

As per given,

Experimental probability = Theoretical probability + 20% of Theoretical probability

= \(\dfrac{1}{2}+\dfrac{20}{100}\times\dfrac{1}{2}\)

= \(\dfrac{1}{2}+\dfrac{1}{10}=0.5+0.1=0.6\)

Required number of heads = (Experimental probability) x (Total tosses )

= 0.6 x 50

= 30

Hence, the required number of heads = 30

For example: {(1,2), (3,4), (2,3), (4,1))}

Answer:

35 is the Answer

Answer:

Step-by-step explanation:

\( \space\)

A = b × h

=> 154.5 = b × 15

=> b = \( \sf{\frac{154.5}{15} }\)

=> 10.3 cm

\( \space\)

Hope it helps!

Have a great day! :)

Answer:

x=10,y=120

Step-by-step explanation:

3x-30=60 CDA

3x=30

x=10

again,

y+60=180 straight line

y = 120