Need help with this :(

The vector equation with parameter t for the line of intersection of the planes x + y + z = 2 and x + z = 0 is r(t) = <0, 2, 0> - t<1, -1, 0>.

To find a vector equation with parameter t for the line of intersection of the planes x + y + z = 2 and x + z = 0, we can solve the system of equations formed by the planes.
First, let's solve for y in terms of x and z from the equation x + y + z = 2. Rearranging the equation, we have y = 2 - x - z.
Now, substitute this expression for y in the equation x + z = 0. We have x + (2 - x - z) + z = 2, which simplifies to 2 - z = 2.
Solving for z, we find z = 0.
Substituting z = 0 into the equation x + z = 0, we have x = 0.
Now that we have the values of x, y, and z, we can form a vector equation for the line of intersection as follows:
r(t) =  = <0, 2 - x - z, 0> = <0, 2, 0> - t<1, -1, 0>.

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The given problem involves calculating the work involved in each process and determining the indicated thermal efficiency of a four-cylinder compression-ignition engine operating on the air-standard dual cycle. The engine parameters such as capacity, compression ratio, air-fuel ratio, and initial conditions are provided. Additionally, the effect of reduced fuel injection pressure on smoke emission in a diesel engine is discussed.

(a) To calculate the work involved in each process and the indicated thermal efficiency, we need to apply the air-standard dual cycle analysis. The dual cycle consists of two processes: the constant volume heat addition process and the constant pressure heat addition process. Using the given engine parameters, we can determine the specific heat capacities, the initial conditions, and the heat addition during each process. By calculating the work done during each process and using the definition of thermal efficiency, we can find the indicated thermal efficiency of the engine.

(b) In a diesel engine, the fuel injectors play a crucial role in delivering fuel into the combustion chamber. When the fuel injection pressure is reduced, it can negatively impact the combustion process and result in increased smoke emission.

Lower fuel injection pressure may cause poor atomization of fuel, leading to incomplete combustion. Incomplete combustion produces more unburned fuel particles, which contribute to smoke formation. These particles are typically composed of partially oxidized hydrocarbons and carbon particles.

Therefore, a reduction in fuel injection pressure can lead to increased smoke emission in a diesel engine.

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Answer:

\(\huge\boxed{\sf 7 \frac{13}{20} \ in. ^2}\)

Step-by-step explanation:

Length of the rectangle = \(\displaystyle 2 \frac{1}{4} = \frac{9}{4} \ in.\)

Width of the rectangle =  \(\displaystyle 3 \frac{2}{5} = \frac{17}{5} \ in.\)

Area of the rectangle:

= Length × Width

\(\displaystyle = \frac{9}{4} \times \frac{17}{5} \\\\= \frac{9 \times 17}{4 \times 5} \\\\= \frac{153}{20} \\\\= 7 \frac{13}{20} \ in.^2\\\\\rule[225]{225}{2}\)

Answer:

Above is the solution to the question

Answer:

1/5 or 20%

All sectors have an equal area, so that means that all have an equal chance of being landed on. There is only 1 sector containing a ladybug out of all 5 sectors. That means you have a 1 out of 5 chances of landing on the ladybug if you spin once.

The major clinical factor that determine whether or not the woman should take the rh immune globulin is whether or not the baby is rh positive.

The term post partum refers to the period that extends between the last month of pregnancy as far as the first five months after child birth. Now if a woman has a rh negative blood, there are certain factors that would determine whether the woman should take the rh immune globulin.

The major clinical factor that determine whether or not the woman should take the rh immune globulin is whether or not the baby is rh positive.

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Answer:

Step-by-step explanation: 13 is a prime number because Its only divisors are 1 and 13.

13 is a prime number because It can only be divided by 1 and 13.

What are prime numbers?

Prime numbers are natural numbers that are divisible by only 1 and the number itself. In other words, prime numbers are positive integers greater than 1 with exactly two factors, 1 and the number itself. Some of the prime numbers include 2, 3, 5, 7, 11, 13, etc. Always remember that 1 is neither prime nor composite. Also, we can say that except for 1, the remaining numbers are classified as prime and composite numbers. All prime numbers are odd numbers except 2, 2 is the smallest prime number and is the only even prime number.

First Ten Prime Numbers

The first ten prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29.

Now,

As 13 has only two factors, 1 and 13.

Hence,

          It is a prime number.

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Answer:

$1,260

Step-by-step explanation:

You first need to find 30% of 1,800, which is 540. And then, because it's 30$ less than retail price, you would need to subtract that from the initial price:

1,800-540 = 1,260

A polynomial function of degree n has at most n real zeros and at most n - 1 turning points.

Function is a type of relation, or rule, that maps one input to specific single output.

In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable (the dependent variable) (the dependent variable). In mathematics and the physical sciences, functions are indispensable for formulating physical relationships.

Linear function is a function whose graph is a straight line

We are given that;

A polynomial function

Now,

Because of the Fundamental Theorem of Algebra states that a polynomial function of degree n has exactly n complex roots (or zeros), some of which may be repeated or non-real. The number of real roots is equal to or less than the number of complex roots.

A turning point is a point where the graph of the polynomial function changes direction from increasing to decreasing or vice versa. The number of turning points is equal to or less than one less than the degree of the polynomial function. This is because each turning point corresponds to a change in the sign of the first derivative of the function, and the first derivative is a polynomial function of degree n - 1.

Therefore, by the function the answer will be n - 1.

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Answer:

x=1

Step-by-step explanation:

Answer:

The speed of one car is 45 miles per hour

The speed of other car is 55 miles per hour

Step-by-step explanation:

Given as :

The distance between the two cities = 500 miles

The Time at which the two cars meets = 5 hours

The speed of one car was 10 mph greater than the speed of other

Now, let the speed of one car = s mph

So, The speed of the other car = ( 10 + s ) mph

According to question both car moving towards each other

So, The relative speed = s +  ( 10 + s )

Since distance = speed × time

Or, 500 miles = [ s +  ( 10 + s ) ] × 5

Or, 500 = ( 10 + 2 s )  × 5

Or, 10 + 2 s =

Or,  10 + 2 s = 100

or, 2 s = 100 - 10

Or, 2 s = 90

∴ s =  

I.e s = 45 mph

So, the speed of one car = s = 45 mph

The speed of other car = 10 + s = 10 + 45 = 55 mph

Hence The speed of one car is 45 miles per hour

And The speed of other car is 55 miles per hour  Answer

Answer:

i weally need points - lil sister of jevahnie

Step-by-step explanation:

To find the volume we use an equation:

volume = length x width x height

Since this shape is a cube, you only need to know one side to find the volume since all of the sides are equal.

So all you need to find the volume is to multiply 4(1/2) which I am going to simplify to 4.5, is plug it into the equation.

volume = 4.5 x 4.5 x 4.5

Which will get you an answer of 91.125 inches cubed

\(91.125in^{3}\)

Hope this helps :)

Answer:

answer is 792

Step-by-step explanation:

........................ .

Answer: 2 quarts 1 pint

Step-by-step explanation: Kim needs 10 cups of apple juice 2 cups are 1 pint so that makes it already 5 pints so now we need to turn the 5 pints into quarts so 2 quarts is what we have but we have some left over we have 1 pint left so we have 2 quarts and 1 pint, we could always convert the pint into a fraction depends on how or what way your teacher wants it wrote

Answer:

(x, y) =(-1, - 1)

Step-by-step explanation:

-Substitute the value of x

-solve the equation

-Substitute the value of y

-check the possible solution

-check solution

-simplify

Answer:

\(2.\bar{81}mm\)

Step-by-step explanation:

First the formula for find the are of a trapezoid is:

\(A = \frac{h(a+b)}{2}\)

Where \(a\) is the top, \(h\) the height and \(b\) the base measures.

Then we need to know what is the base (\(b\)), for that isolate \(b\) from the equation

\(2A = h(a+b)\\\frac{2A}{h} = a+b\\\frac{2A}{h} - a = b\)

Then in the new equation replace the given values:

\(A = 65mm^2\\a = 9mm\\h = 11mm\)

\(\frac{2 \cdot 65mm^2}{11mm} -9mm = b\\\frac{130mm^2}{11mm} -9mm = b\\11.\bar{81}mm -9mm = b\\2.\bar{81}mm = b\)

So the final answer is \(2.\bar{81}mm\)

equation of circle : (x - h)² + (y - k)² = r²

h = x coordinate of center

k = y coordinate of center

hence h = 10, k = 8

center - (10 , 8)

The correct statements are "There is a vertical stretch by 4" and "There is a horizontal shift left 7."Hence, option A is correct.

Given logarithmic function is \(y=4\log3(x+7)-2\).

We need to select the correct statements from the given options. Let's discuss each statement one by one:

There is a vertical stretch by 4In general, the logarithmic function of the form y = logb(x) has the domain (0, ∞) and range (-∞, ∞). Here, we have \(y = 4\log3(x + 7) - 2\).

Inside the log function, we have x + 7. This means that there is a horizontal shift to the left by 7 units.

Also, the coefficient 4 outside the log function will cause the vertical stretch.

Therefore, the statement "There is a vertical stretch by 4" is true.  There is horizontal shift right 2

Similarly, we can say that the logarithmic function y = logb(x) has the vertical asymptote x = 0 and the horizontal asymptote y = 0.

But in the given logarithmic function \(y=4\log3(x+7)-2\), we have the inside function as x + 7, which means that there is a horizontal shift left by 7 units

.Therefore, the statement "There is horizontal shift right 2" is false.  There is a vertical shift up 7

The general form of the logarithmic function \(y = \log b(x)\) has a y-intercept of (1, 0).

In the given logarithmic function \(y=4\log3(x+7)-2\), we have y-intercept as (1, -2). This implies that there is a vertical shift down by 2 units.

Therefore, the statement "There is a vertical shift up 7" is false.  

There is a vertical stretch by 3

Here, we have \(y = 4\log3(x + 7) - 2\).

Inside the log function, we have x + 7. This means that there is a horizontal shift to the left by 7 units. Also, the coefficient 4 outside the log function will cause the vertical stretch by a factor of 4.

Hence, the statement "There is a vertical stretch by 3" is false.

Therefore, the statement "There is a vertical stretch by 3" is false.  

There is a horizontal shift left 7

As we have already discussed that inside the log function, we have x + 7. This means that there is a horizontal shift to the left by 7 units.

Therefore, the statement "There is a horizontal shift left 7" is true.  Therefore, the correct statements are "There is a vertical stretch by 4" and "There is a horizontal shift left 7."Hence, option A is correct.

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There is a vertical stretch by 4 and a horizontal shift left 7 in the logarithmic function y = 4log3(x + 7)-2.

Consider the logarithmic function y = 4log3(x + 7)-2.

Explanation: In the logarithmic function, the equation is y = loga(x-h) + k where the logarithmic base is a, horizontal shift is h, and vertical shift is k. Logarithmic functions are the inverse of exponential functions so they have similarities in their transformations.

We can identify the true statements by comparing the given function with the standard form of the logarithmic function which is y = loga(x).

Given: y = 4log3(x + 7)-2

Comparing it to the standard form, there is a horizontal shift of 7 units to the left and a vertical shift of -2 units down. This makes the false statements:

There is a horizontal shift right 2.

There is a vertical shift up 7.

The vertical stretch or shrink is given by the coefficient of x. In this case, it is 4. So, there is a vertical stretch by 4. The coefficient of x can be either positive or negative so there is no horizontal stretch. Thus, the correct statements are:

There is a vertical stretch by 4.

There is a horizontal shift left 7.

Conclusion: There is a vertical stretch by 4 and a horizontal shift left 7 in the logarithmic function y = 4log3(x + 7)-2.

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(a). The above context-free grammar (CFG) generates the language that has at least five "a's" and any combination of "b's".

(b). The above CFG generates the language {a¹b³c¹|i, j, k ≥ 0 and i =jor i = k}.

(c).  it is ambiguous.

(a). Context-free grammar for L₁ = {w = {a, b}*w contains at least five as}:

S → aaaaaA | aaaaS | bS | aA | bA | ε

A → aA | bAb → bB | ε

B → bB | aB | ε

The above CFG generates the language that has at least five "a's" and any combination of "b's".

(b). Context-free grammar for L₂ = {a¹b³c¹|i, j, k ≥ 0 and i =jor i = k}:

S → AbC | AcB | BCa | CBa

A → aA | ε

B → bBb

B → bBbBbBb

C → cC | ε

C → cC | ε

The above CFG generates the language {a¹b³c¹|i, j, k ≥ 0 and i =jor i = k}.

(c). Yes, the language for b) is inherently ambiguous. It is because there are two variables A and B in the grammar, so the string can be generated in two ways. Thus, it is ambiguous.

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Answer:

Option (D).

Step-by-step explanation:

In the figure attached,

ΔACB is a right triangle with AC = 24 units, BC = 10 units and AB = 26 units

For angle A,

Adjacent side = AC

Opposite side = BC

Hypotenuse = AB

SinA = \(\frac{\text{Opposite side}}{\text{Hypotenuse}}\)

        = \(\frac{BC}{AB}\)

        = \(\frac{10}{26}\)

SinA = 0.3846

        ≈ 0.385

Therefore, Option (D) will be the answer.

Answer:

The equation of hyperbola :  \(\frac{y^{2} }{49 } - \frac{x^{2} }{32 }\)

Step-by-step explanation:

Given - This hyperbola is centered at the origin.

Foci: (0,-9) and (0,9) Vertices: (0,-7) and (0,7)​

To find - Find its equation.

Solution -

We know  that,

Equation of Hyperbola is represented by

\(\frac{y^{2} }{a^{2} } - \frac{x^{2} }{b^{2} }\)

Now,

Given that,

Foci : F(0, -9) and F'(0, 9)

So,

c = 9

And

Vertices : A(0,-7) and A'(0,7)​

So,

a = 7

Also, we know that,

c² = a² + b²

⇒b² = c² - a²

⇒b² = 9² - 7²

⇒b² = 81 - 49

⇒b² = 32

So,

The equation of hyperbola becomes

\(\frac{y^{2} }{49 } - \frac{x^{2} }{32 }\)

Answer:

The measure of angle WVX is 140°.

Step-by-step explanation:

Let x be the measure of angle WVX.

\( \frac{14}{9} \pi = 2x\)

\( x = \frac{7}{9} \pi( \frac{180}{\pi}) = 140 \: degrees\)

Answer:

angle = arc length/radius
in this case, the arc length is 14/9*\(\pi\) and the radius is 2. Upon multiplying these, you get 140.

so, the answer is 140 degrees.

Answer:

X intercepts: (21,0)

Y intercepts: (0, -15)

Step-by-step explanation:

To find the x-intercept, substitute 0 for y and solve for x. To find the y-intercept, substitute in 0 for x and solve for y.

The answer is random sampling in my thinking.

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The solution to the systems of equations graphically is (2, 4)

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

y = 2x

y = -x + 6

Next, we plot the graph of the system of the equations

See attachment for the graph

From the graph, we have solution to the system to be the point of intersection of the lines

This points are located at (2, 4)

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