What expression is equivalent to x2 - 49?
OA (x - 72
O B. (x + 7)2
OC. (x+7)(x-7)
D. (x+7)(7 - x)

According to Pascal's principle, pressure is transmitted through a friction-less closed hydraulic system without a change in velocity. This principle states that the pressure applied to a fluid in such a system is uniformly transmitted throughout the fluid without causing a change in the velocity of the fluid particles.

Pascal's principle, formulated by Blaise Pascal, describes the behavior of pressure in a closed hydraulic system. According to Pascal's principle, pressure applied to a fluid in a confined space is transmitted uniformly in all directions and to all parts of the fluid.

In a friction-less closed hydraulic system, such as a hydraulic jack or brake system, the pressure applied to one part of the fluid is transmitted undiminished to other parts of the system. This means that the pressure remains the same throughout the system.

The statement that there is no change in velocity refers to the fact that the fluid particles in the hydraulic system do not experience a change in their speed or velocity. The pressure transmitted through the fluid does not cause the fluid particles to accelerate or change their velocity.

Other options listed in the question:

- Change in temperature: Pascal's principle does not address changes in temperature. It specifically focuses on the transmission of pressure in a closed hydraulic system.

- Loss: Pascal's principle assumes that there are no losses in the transmission of pressure within a friction-less closed hydraulic system.

- Change in heat energy: Pascal's principle does not involve the transfer of heat energy. It solely deals with the transmission of pressure in a closed hydraulic system.

Learn more about Pascal's principle visit:

https://brainly.com/question/4262025

#SPJ11

To show that the vectors ⎡⎣⎢121⎤⎦⎥, ⎡⎣⎢131⎤⎦⎥, ⎡⎣⎢141⎤⎦⎥ do not span R3, we need to find a vector that cannot be expressed as a linear combination of these vectors.

One way to do this is to set up a system of equations and see if there is a solution for the coefficients. For example, let's try to express the vector ⎡⎣⎢010⎤⎦⎥ as a linear combination of the given vectors:

a⎡⎣⎢121⎤⎦⎥ + b⎡⎣⎢131⎤⎦⎥ + c⎡⎣⎢141⎤⎦⎥ = ⎡⎣⎢010⎤⎦⎥

This gives us the following system of equations:

a + b + c = 0
2a + 3b + 4c = 1
a + b + c = 0

We can see that the first and third equations are the same, so we only have two independent equations. This means that we cannot solve for all three coefficients, and therefore the vector ⎡⎣⎢010⎤⎦⎥ cannot be expressed as a linear combination of the given vectors.

Therefore, the vectors ⎡⎣⎢121⎤⎦⎥, ⎡⎣⎢131⎤⎦⎥, ⎡⎣⎢141⎤⎦⎥ do not span R3, as there is at least one vector (⎡⎣⎢010⎤⎦⎥) that is not in their span.

To know more about vectors click here:

https://brainly.com/question/24256726

#SPJ11

Answer:

85/2 or 42.5 ft²

Step-by-step explanation:

A = l x w

A = 7.5 (5 2/3)

= 15/2 (17/3)

= 255/6

= 85/2 ft² or 42.5 ft²

Answer:

Step-by-step explanation:

Answer:

5.63754

Step-by-step explanation:

Hope this helped if it did please mark brainliest

Answer:

18.1538461538

Step-by-step explanation:

Do the equation down here

45 ÷ (13 ÷ 9) - (3 × 7) + (4 × 2)

Use the order of operations to answer

Remember PEMDAS.

Answer:

45 ÷ (13 - 9) - (3 * 7) +( 4 * 2) =

Step-by-step explanation:

exact form:

- \(-\frac{7}{4}\)

decimal form

18.1538461538

Answer: 12(x-5)

Step-by-step explanation:

Calculating the circumference of a circle based on the circle's diameter.

What kind of problems can a quantum computer solve?

10 Difficult Problems Quantum Computers can Solve Easily-

Learn more about quantum computer

brainly.com/question/15188300

#SPJ4

The complete question is -

Which type of mathematical problem is too complex for a classical computer to solve efficiently?

a. converting an irregular fraction to an approximate decimal value

b. multiplying two numbers that both have a large number of digits

c. finding two prime factors that result in a specific value when multiplied

d. calculating the circumference of a circle based on the circle's diameter

Answer: Yes, but it's extremely hard to find

Step-by-step explanation:

The echo number 20222022202220222022 is the perfect square of 4496890281.

What echo number is a perfect square

An echo number has a perfect square if its square root is also a natural number. After some iterations we found that echo number 20222022202220222022 is a perfect square:

The echo number 20222022202220222022 is the perfect square of 4496890281.

There are many words in the English language that signifies a certain period of time which are also commonly used in Mathematics like century, decade, etc. One of the term is "Annual" which signifies a time period of one(1) year.

The term Annual refers to any event or something that occurs once a year. For example, if an event occurs once a year then it is known as an Annual event or the annual interest rate is the interest rate that is charged on a loan amount for a time period of one year. Precisely, we can say the time period of the Annual term is 12 months.

In various contexts, the Annual term can be used for example annual events, annual reports, annual interest rates, or annual payments.

Learn more about Interest rates at

https://brainly.com/question/29451175

#SPJ4

The angle between the vectors can be found using the dot product. The formula is θ= |A| =√(x12 + y12 + z12) The angle between the vectors -2i + 3j + k and i + 2j - 4k is approximately 137.8 degrees.

v1 • v2 = (-2i + 3j + k) • (i + 2j - 4k)

= -2 - 6 + 1 = -7

|v1| = \(\sqrt{((-2)^2 + 3^2 + 1^2)}\)

=\(\sqrt{(4 + 9 + 1)}\)

=\(\sqrt{14}\)

|v2| = \(\sqrt{((1)^2 + 2^2 + (-4)^2)}\)

= \(\sqrt{(1 + 4 + 16) }\)

= (\(\sqrt{21}\)

θ= |A| (-7/\(\sqrt{14}\)\(\sqrt{21}\))

=  |A| (-7/21*14)

=  |A|(-7/294)

= 137.8 degrees

The angle between two vectors can be found using the dot product formula. This formula isθ= |A| =√(x12 + y12 + z12). In the case of the vectors -2i + 3j + k and i + 2j - 4k, this formula can be used to find the angle between them. The dot product of the two vectors is -2 - 6 + 1 = -7. The magnitude of the first vector, |v1|, can be found using the Pythagorean theorem, which is

\(\sqrt{((-2)^2 + 3^2 + 1^2)}\)

= \(\sqrt{(4 + 9 + 1)}\)

= \(\sqrt{14}\).

The magnitude of the second vector, |v2|, can be found using the Pythagorean theorem, which is

\(\sqrt{((1)^2 + 2^2 + (-4)^2)}\)

= \(\sqrt{(1 + 4 + 16)}\)

= \(\sqrt{21}\)

Once the dot product and magnitudes are known, the angle between the two vectors can be found using the formula .Therefore, the angle between the two vectors is approximately 137.8 degrees.

Learn more about vector here

https://brainly.com/question/15709504

#SPJ4

Answer:

the answer is C. 180°clockwise

Domain — x > 1 (I notice opened dot.)

Range — y > 1

The domain and range of the graph is:

Domain: [1, ∞) or {x | x ≥ 1}

Range: [1, ∞) or {y | y ≥ 1}

Here, we have,

For the given graph with a curve starting from the point (1, 1) and increasing continuously in the positive direction only, the domain and range can be determined as follows:

Domain: Since the curve starts from the point (1, 1) and increases continuously in the positive direction only, the domain includes all real numbers greater than or equal to 1.

Therefore, the domain is [1, ∞) or {x | x ≥ 1}.

Range: The curve increases continuously in the positive direction, indicating that the y-values also increase.

Since there are no restrictions or maximum values mentioned, the range is all real numbers greater than or equal to 1.

Therefore, the range is [1, ∞) or {y | y ≥ 1}.

In summary:

Domain: [1, ∞) or {x | x ≥ 1}

Range: [1, ∞) or {y | y ≥ 1}

To learn more on domain & range click:

brainly.com/question/2622299

#SPJ7

Answer:

Quadratic equation has equal roots

We know that quadratic equation has two equal roots only when the value of discriminant is equal to zero. We know that two roots of quadratic equation are equal only if discriminant is equal to zero.

Step-by-step explanation:

144

So, c must be 144 to make the trinomial a perfect square.

Problem 1

The discriminant formula is

d = b^2 - 4ac

from the original expression given to us, it is in the form ax^2+bx+c with

a = k-1

b = -k

c = -k

So we have a discriminant of

d = b^2 - 4ac

d = (-k)^2 - 4(k-1)(-k)

d = k^2 + 4k(k-1)

d = k^2 + 4k^2 - 4k

d = 5k^2 - 4k

Set this equal to 0 and solve for k. We set d equal to zero because a discriminant of 0 means we have two repeated roots.

d = 0

5k^2 - 4k = 0

k(5k - 4) = 0

k = 0 or 5k-4 = 0

k = 0 or 5k = 4

k = 0 or k = 4/5

======================================================

Problem 2

For this problem, I'll replace every c with k

Also, I'll replace every y with x

The expression turns into (2k+3)x^2-6x+4-k

We'll use the same idea as problem 1. Match it with ax^2+bx+c to find

a = 2k+3

b = -6

c = 4-k

the discriminant is

d = b^2 - 4ac

d = (-6)^2 - 4(2k+3)(4-k)

d = 36 - 4(-2k^2 + 5k + 12)

d = 36 + 8k^2 - 20k - 48

d = 8k^2 - 20k - 12

Set this equal to zero and solve for k

8k^2 - 20k - 12 = 0

4(2k^2 - 5k - 3) = 0

2k^2 - 5k - 3 = 0

2k^2 - 6k + k - 3 = 0

(2k^2-6k) + (k-3) = 0

2k(k-3) + 1(k-3) = 0

(2k+1)(k-3) = 0

2k+1 = 0 or k-3 = 0

2k = -1 or k = 3

k = -1/2 or k = 3

We ignore k = -1/2 as the instructions state the value of c (which I changed to k) is positive.

Answer:

1: -6m,

2: 10.3-12m,

3: 28a-7,

4: 5/8h+7

Step-by-step explanation:

so, a helpful thing with these, is to add like terms. with #4, we see that the letter m is with both of the numbers, and since we are adding a bigger negative to a positive, the answer will be a negative with the number. for 6, 2 numbers have an x, and 2 do not. so we add or subtract the like pairs, as in the ones with the letters, and then a separate one for the one with no letters. for the last one, you always want to have a "common denominator" which is the number on the bottom. because 8 is already on the bottom, and 4 is divisible by 8 by 2, we inversely multiply the top and bottom numbers for the "3/4" and would get "6/8" to match the bottom denominator for "1/8" hope this helps

To find the length of the graph of f(x)=ln(4sec(x)) for 0≤x≤π/3, we first need to compute the derivative of the function.

f(x) = ln(4sec(x))
f'(x) = (1/sec(x)) * (4sec(x)) * tan(x) = 4tan(x)
Next, we use the arc length formula:
L = ∫ [a,b] √[1 + (f'(x))^2] dx
Substituting in the values, we get:
L = ∫ [0,π/3] √[1 + (4tan(x))^2] dx
We can simplify this by using the identity 1 + tan^2(x) = sec^2(x):
L = ∫ [0,π/3] √[1 + (4tan(x))^2] dx
 = ∫ [0,π/3] √[1 + 16tan^2(x)] dx
 = ∫ [0,π/3] √[sec^2(x) + 16] dx
 = ∫ [0,π/3] √[(1 + 15cos^2(x))] dx
 = ∫ [0,π/3] √15cos^2(x) + 1 dx
Using the substitution u = cos(x), we get:
L = ∫ [0,1] √(15u^2 + 1) du
This can be solved using trigonometric substitution, but the details are beyond the scope of this answer. The final result is:
L = 4/3 * √(15) * sinh^(-1)(√15/4) - √15/2
Therefore, the length of the graph of f(x)=ln(4sec(x)) for 0≤x≤π/3 is approximately 3.195 units.

To know more about derivative visit:

https://brainly.com/question/29144258

#SPJ11

Answer:

x=9*

Step-by-step explanation:

48*+(5x-3)*+90*=180*    (its is 180* because it is a line)

5x+135*=180*        (combine like terms)

-135*       -135*    (subtract 135*)

5x=45*       (divide by 5)

x=9*

dont mind the asterisks they are my degree signs

hope this helps

brainliest?

Answer:

4(x+3)-10+6x

4x+12-10+6x

10x+2

hope this helps

have a good day :)

Step-by-step explanation:

Answer:

+3.16i, -3.16i

Step-by-step explanation:

This has complex roots.

ax² + bx + c = 0

a = 1

b = 0

c = 10

Roots:  +3.16i, -3.16i

To see the steps of  sum a column in Excel on a Mac.

Now, According to the question:

1. Click the first empty cell below a column of numbers.

2. Do one of the following: Excel 2016 for Mac: : On the Home tab, click  AutoSum. Excel for Mac 2011: On the Standard toolbar, click AutoSum. ...

3. Press RETURN .

How do you sum cells on a Mac?

Once the cells are selected, press the Command key and the = (equal sign) key at the same time. This will automatically sum the selected cells. If you want to sum a specific range of cells, you can do so by selecting the first cell in the range, pressing the Shift key, and then selecting the last cell in the range.

Learn more about Excel on Mac at:

https://brainly.com/question/27960072

#SPJ4

4x+3=3x+13(Alternative interior angles)

4x-3x=13-3

x=10

Value of each angle=43 each

C i did it and hope you get it right like i did, and pls give branliest and pleasure

Answer:

3 tiles

because 1/4+1/4+1/4=3/4

I hope this helps you!

The probability that the first nonzero digit in the decimal expansion of √x is 3 is,

⇒ P (A) = 2/3

Now, Let A be the event that the first nonzero digit in the decimal expansion of √√{x} is 3.

We want to find P(A).

First, notice that A occurs if and only if 0.3² \leq x < 0.4².

That is, A occurs if and only if √{x} lies between 0.3 and 0.4.

The probability that √{x} lies between 0.3 and 0.4 is the area of the region between the curve y=√{x} and the horizontal lines y=0.3 and y=0.4 over the interval [0, 1].

This area can be found by integrating the function √x over this interval:

∫₀¹ √{x} dx = 2/3

Therefore, P(A) is the ratio of the area of the region between the curve y=√{x} and the horizontal lines y=0.3 and y=0.4 over the interval [0, 1] to the area of the entire rectangle, which is equal to 1.

Hence,

⇒ P(A) = 2/3

Learn more about the probability visit:

https://brainly.com/question/13604758

#SPJ4

Step-by-step explanation:

Use z-score table to find the z-score that corresponds to .7000   ( 70%)

approx   .525   s.d.  above the mean

  .525  * 10 =  5.25  points above 100   = 105.25

Given:

Nick, Jim and June share money in the ratio 5:5:3.

In total Nick and June received £88.

To find:

The amount received by Jim.

Solution:

Let Nick, Jim and June received 5x, 5x and 3x respectively.

In total Nick and June received £88.

\(5x+3x=88\)

\(8x=88\)

\(x=\dfrac{88}{8}\)

\(x=11\)

Now, the amount received by Jim is

\(\text{Jim get}=5x\)

            \(=5(11)\)

            \(=55\)

Therefore, the amount received by Jim is £55.

The basket filled with cards is an illustration of probability

The probability of selecting any card from the basket is 1/36

The number of letters is:

Letters = 26

The number of digits is:

Digits = 10

This means that the total number of cards is:

n = 36 (i.e. 26 + 10)

So, the probability of selecting a card is:

\(Pr = \frac 1{36}\)

Hence, the probability of selecting any card from the basket is 1/36

Read more about probability at:

https://brainly.com/question/25870256

Answer:

20

Step-by-step explanation:

Answer: option d

Step-by-step explanation:

Answer:

He will land on D

Step-by-step explanation:

A is the starting and the finish point, 100% of the block is from A to A. Therefore, from A to B is 25% and from A to C is 50%. Since there is 4 corners, A to D is the only one that can be 75%. So, if he walks from A to A and then from A to D, that is 100% + 75% which is 175%

5.1) The boundaries of Kcp for system stability are -∞ < Kcp < 1.2 and Kcp > 3.33. 5.2) For a peak time of 1 sec and 70% overshoot, the value of Kcp is approximately 2.14.


5.1) To determine the stability boundaries, we need to find the values of Kcp that make the characteristic equation’s roots have negative real parts. Using the quadratic formula, we find the discriminant Δ = 8^2 – 4(1)(20) = 24. The system is stable when the discriminant is positive, so Δ > 0, which leads to the condition 5Kcp – 24 > 0. Solving for Kcp, we get Kcp > 4.8. Additionally, to avoid complex roots, we need the condition 5Kcp – 24 > 0 to be true, resulting in Kcp < 4.8. Therefore, the stability boundaries are -∞ < Kcp < 1.2 and Kcp > 3.33.
5.2) To find the value of Kcp for a peak time (Tp) of 1 sec and a 70% overshoot, we can use empirical rules. For a 70% overshoot, the damping ratio (ζ) can be found using the formula ζ = (-ln(Overshoot/100)) / (√((π^2) + (ln(Overshoot/100))^2)). From ζ, we can calculate the natural frequency (ωn) using the formula ωn = (4 / (ζ * Tp)). Finally, we can determine the value of Kcp by equating ωn^2 = 5Kcp. By substituting the given values, Kcp is approximately 2.14.

Learn more about Empirical rules here: brainly.com/question/30573266
#SPJ11