Determine the domain of the following graph:

To find a vector v orthogonal to the plane through the points p(4, 0, 0), q(0, 3, 0), and r(0, 0, 5), we can use the cross product of two vectors that lie in the plane.

Let's first find two vectors that lie in the plane. We can take the vectors p to q and p to r.

Vector p to q can be calculated as q - p, which is (0 - 4, 3 - 0, 0 - 0) = (-4, 3, 0).

Vector p to r can be calculated as r - p, which is (0 - 4, 0 - 0, 5 - 0) = (-4, 0, 5).

Now, we can find the cross product of these two vectors.

To calculate the cross product, we take the determinant of a 3x3 matrix.

The cross product is given by:

(i  j  k)
(-4  3  0)
(-4  0  5)

Using the determinant formula, we get:

(3 * 5 - 0 * 0)i - (-4 * 5 - 0 * -4)j + (-4 * 0 - 3 * -4)k

Simplifying, we have:

15i - (-20)j - (-12)k

Which gives us:

15i + 20j - 12k

Therefore, a vector v orthogonal to the plane through the points p, q, and r is given by 15i + 20j - 12k.

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Answer:

He runs 28 Miles every week!

Step-by-step explanation:

(The week is 7 days long)

1st DAY = 4M

2nd DAY = 4M

3rd DAY = 4M

4th DAY = 4M

5th DAY = 4M

6th DAY = 4M

7th DAY = 4M

(The M next to the 4 means miles you don't have to include it in your answer on your homework!)

4 + 4 + 4 + 4 + 4 + 4 + 4 = 28

OR

4 x 7 = 28

~ LadyBrain

Andrea earns a total of $48 for washing 6 cars at the rate.

By using the cross multiplication approach, the denominator of the first term is multiplied by the numerator of the second term, and vice versa.

Using the cross multiplication method, we may determine the answer to a pair of linear equations. Using the mathematical rule of three, we may determine the answer based on proportions. The best illustration is cross multiplication, where we can write in a proportion to determine the values of unknown variables.

Given that,

$32 = 4 cars

$x = 6 cars

Using the method of cross multiplication:

x = 32(6) / 4

x = $48

Hence, Andrea earns a total of $48 for washing 6 cars at the rate.

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The interest rate is (1/3)(y*)² - 0.01 and the capital-output ratio is 50.

In the steady state, the output per worker, denoted as y*, is constant.

To find the steady state level of capital, denoted as K*, we can use the following equation:

sY* = (d + n + g)K*

where s is the saving rate, n is the population growth rate (assumed to be zero in this model), and g is the technological progress rate (also assumed to be zero).

Plugging in the values we have, we get:

0.5Y* = 0.01K*

Solving for K*, we get:

K* = 50Y*

Next, we can find the steady state output per worker, y*, by substituting K* into the production function:

y* = (K*/L)^(1/3) = \((50Y^*/L)^{1/3}\)

The interest rate is given by:

r = MPK - d

where MPK is the marginal product of capital, which represents the additional output that can be produced by adding one unit of capital. In this case, MPK is given by:

MPK = \((1/3)(Y^*/K^*)^{2/3}\) = (1/3)(y*)²

Plugging in the values we have, we get:

r = (1/3)(y*)² - 0.01

Finally, we can find the capital-output ratio, K/Y, by substituting K* and Y* into the equation:

K/Y = K*/Y* = 50

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Answer:

B

Step-by-step explanation:

Answer:

37

Step-by-step explanation:

147= 15x +5+ 22x +4. 120 = 37

Answer:

If angle 5=147 then angle 2 would be 33 since it needs to equal 180

then angle one would also equal angle 2, or =33

Step-by-step explanation:

Answer:

4 ft shadow=3 ft tall

?(x)=6 ft

4×6=3x

24=3x

24/3=x

8=x

that's my answer I think

The substance that is element in the list is O₂

A substance that cannot be broken down chemically is referred to as an  element. Although chemical processes cannot modify an element, nuclear reactions can create new elements.

The quantity of protons an element has defines it. An element's atoms all contain the same amount of protons, but its electron and neutron counts can vary. Ions are produced by altering the electron to proton ratio, and isotopes are produced by altering the neutron content.

Other substances can be broken down further chemically except O₂ and hence it is the only element in the list

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Answer:

No solution!

Just turned it in <3

Answer:

21sq

Step-by-step explanation:

multiply the l times the w which would be 3x7 and get 21.

Answer:

21 cm

Step-by-step explanation:

Answer:

\( y = 5 - x \)

Step-by-step explanation:

The graph of the equation that will contain the points (2, 3) and (3, 2) is the graph that has a slope value that is equivalent to the slope value of the line running through the two points.

Slope of the line running through (2, 3) and (3, 2):

\( slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2 - 3}{3 - 2} = \frac{-1}{1} = -1 \).

Slope (m) = -1.

The equation, \( y = 5 - x \) , is given in the slope-intercept form, which means it has a slope value of -1. I.e. the term "-x" is equivalent to -1x. So therefore, the graph of the equation that contains the points (2, 3) and (3, 2) is \( y = 5 - x \).

Answer:

A

Step-by-step explanation:

a) ✔️

This is the principle of mathematical induction. If P holds for the base case k=1 and we can show that if it holds for any arbitrary k (e.g. k=n) then it must also hold for the next value (e.g. k=n+1), then we have shown it holds for all natural numbers.

b) ❌

There is no guarantee that P holds for all natural numbers from the statement alone. It only guarantees that for any k where P does not hold, there exists a smaller number i where P does not hold.

c) ❌

This is the principle of weak mathematical induction. It only shows that if P holds for a given k and for all smaller values i then it must hold for k+1. It does not guarantee that P holds for all natural numbers.

d) ❌

This statement is the negation of the principle of mathematical induction. It is known as the "strong induction" principle, which assumes that if P does not hold for k, then there exists a smaller i where P does not hold. However, this principle is not sufficient to prove that P holds for all natural numbers k.

The amount of money the student owe for the lost uniform is given by the equation A = 0.75S , where S is the cost of the uniform

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Let the cost of the uniform be represented as S

Now , the percentage of fee when the student loses uniform = 75 %

Now , the equation will be

The amount of money the student owe for the lost uniform A = cost of the uniform x percentage of fee when the student loses uniform

Substituting the values in the equation , we get

The amount of money the student owe for the lost uniform A = ( 75/100 )S

The amount of money the student owe for the lost uniform A = 0.75S

Now , when S = $ 100

The amount of money the student owe for the lost uniform A = $ 75

Now , when S = $ 105

The amount of money the student owe for the lost uniform A = $ 78.75

Hence , the equation is A = 0.75S

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The number that makes the mixed fraction equation true is -1.

The number that makes the equation true is calculated by applying the following formula as follows;

The given equation;

-7 ¹/₂ + ? = - 8 ¹/₂

The solution of the equation is calculated as follows;

Convert each mixed fraction into improper fraction;

-7 ¹/₂ = -15/2

-8 ¹/₂ = -17/2

-15/2 + ? = -17/2

Collect the similar terms together as follows;

? = -17/2 + 15/2

? = (-17 + 15) / 2

? = -2/2

? = - 1

Thus, the number that makes the equation true is -1.

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The slope field shown in the question is that of a differential equation of the form y'= f(x,y).

The solutions of this equation are the curves in the slope field that emanate from each point and that have the same slope as the line at that point. Thus, for each point (x,y) in the slope field, it is possible to calculate the particular solution that passes through that point.

The first statement is false because it involves the second derivative of the particular solution, which cannot be determined from the slope field. The second statement is false because a concave up graph requires that the derivative of the solution be increasing at x=0, but the slope field does not indicate the sign of the derivative of the particular solution. The third statement is false because a concave up graph requires that the derivative of the solution be decreasing at x=-1, which cannot be determined from the slope field. The fourth statement is false because a concave down graph requires that the derivative of the solution be increasing at x=0, which cannot be determined from the slope field.

In summary, none of the statements can be determined to be true or false from the slope field shown.

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Answer:

Corresponding angles

Step-by-step explanation:

Answer:

y=-2x+1

Step-by-step explanation:

Answer:

x³+1

Step-by-step explanation:

4x-8 | 4x⁴ - 8x³ + 4x - 8

       _4x⁴ - 8x³______ <-- x³

                           4x - 8

                          4x - 8 <-- 1

                                  0 | x³+1

Therefore, (4x⁴-8x³+4x-8)/(4x-8) = x³+1

\(\textit{area of a trapezoid}\\\\ A=\cfrac{h(a+b)}{2}~~ \begin{cases} h~~=height\\ a,b=\stackrel{parallel~sides}{bases~\hfill }\\[-0.5em] \hrulefill\\ a=5\\ b=7\\ A=24 \end{cases}\implies 24=\cfrac{h(5+7)}{2} \\\\\\ 24=\cfrac{h(12)}{2}\implies 24=6h\implies \cfrac{24}{6}=h\implies 4=h\)

Answer:

See below

Step-by-step explanation:

g (h(6))   :

   h (6) =  3 ( 6^2) + 2 = 110

   then g (110) =   sqrt (110)

h (g(5))

    g(5) = sqrt 5

        then h( sqrt5) = 3 ( sqrt5)^2 + 2 = 17

Answer:

y = - \(\frac{1}{2}\) x + \(\frac{3}{2}\)

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (- 7, 5 ) and (x₂, y₂ ) = (3, 0 )

m = \(\frac{0-5}{3-(-7)}\) = \(\frac{-5}{3+7}\) = \(\frac{-5}{10}\) = - \(\frac{1}{2}\) , then

y = - \(\frac{1}{2}\) x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

using (3, 0 ) , then

0 = - \(\frac{2}{2}\) + c ⇒ c = \(\frac{3}{2}\)

y = - \(\frac{1}{2}\) x + \(\frac{3}{2}\) ← equation of line

The value of y is 2/3

An algebraic expression is an expression made up of variables and constants, along with algebraic operations such as addition, subtraction, multiplication, division, etc

Given;

8y+4(5y-3)

With the knowledge of BODMAS,

Expand the bracket

8y + 20y - 12

Now, let's add like terms

18y - 12

Make into an equation

18y - 12 = 0

18y = 12

Make 'y' the subject of formula

y = 12/ 18

Find a common divisor

y = 2/ 3

Thus, the value of y is 2/3

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9514 1404 393

Answer:

  m∠W = m∠S = 126°

  m∠E = m∠T = 54°

  x = 24

  y = 8

Step-by-step explanation:

Opposite angles of a parallelogram are congruent, so we have ...

  ∠E = ∠T

  3x -18 = 2x +6

  x = 24 . . . . . . . . . add 18-2x

Then the measure of these angles (in degrees) is ...

 ∠E = ∠T = 2x+6 = 2(24) +6 = 54

__

The adjacent angle W is supplementary to either of these:

  ∠W = 180° -∠E

  15y +6 = 180 -54

  15y = 120

  y = 8

  ∠W = ∠S = 126°

Answer:

y = 8

Angle S= 126°

Step-by-step explanation:

Answer:

dont answer it

Answer:

= a(7b + 1)

Step-by-step explanation:

7ab + a

a(7b + 1).

Answer:

3

Step-by-step explanation:

Therefore, the Taylor polynomial T₃(x) for the function f(x) = e^(-3x) * sin(2x) centered at a = 0 is given by T₃(x) = -3x - 6x² - 6x³.

To find the Taylor polynomial T₃(x) for the function f(x) = e^(-3x) * sin(2x) centered at a = 0, we need to calculate the derivatives of f(x) at x = 0 and use them to construct the polynomial.

First, let's find the derivatives of f(x):

f(x) = e^(-3x) * sin(2x)

f'(x) = (-3e^(-3x) * sin(2x)) + (2e^(-3x) * cos(2x))

= e^(-3x) * (-3sin(2x) + 2cos(2x))

f''(x) = e^(-3x) * (9sin(2x) - 12cos(2x))

f'''(x) = e^(-3x) * (-27sin(2x) - 36cos(2x))

Next, let's evaluate these derivatives at x = 0:

f(0) = e^0 * sin(0) = 0

f'(0) = e^0 * (-3sin(0) + 2cos(0)) = -3

f''(0) = e^0 * (9sin(0) - 12cos(0)) = -12

f'''(0) = e^0 * (-27sin(0) - 36cos(0)) = -36

Now, we can construct the Taylor polynomial T₃(x) using the derivatives:

T₃(x) = f(0) + f'(0)(x - a) + f''(0)(x - a)²/2! + f'''(0)(x - a)³/3!

= 0 - 3x + (-12)(x - 0)²/2! + (-36)(x - 0)³/3!

Simplifying further:

T₃(x) = -3x - 6x² - 6x³

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The cooling rate of the turkey is 0.45°F per minute. This means that every minute, the temperature of the turkey decreases by 0.45°F.

The cooling rate of a roasted turkey can be determined by the rate at which it loses heat to its surroundings. In this case, the temperature of the turkey was 191°F when it was taken out of the oven and placed on a table in a room with a temperature of 75°F. After half an hour, the temperature of the turkey had decreased to 155°F.

To calculate the cooling rate, we can use Newton's law of cooling, which states that the rate of heat loss of an object is proportional to the difference in temperature between the object and its surroundings. The equation for Newton's law of cooling is:

dT/dt = -k (T - Ts)

where dT/dt is the rate of change of temperature with respect to time, T is the temperature of the turkey at time t, Ts is the temperature of the surroundings (75°F), and k is a constant that depends on the specific heat of the turkey, its surface area, and other factors.

To solve for k, we can use the data given:

dT/dt = -k (T - Ts)

-36 = -k (155 - 75)

-36 = -k (80)

k = 0.45

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*see attachement for the diagram that is being referred to

Answer:

m<ACB = 50°

Step-by-step explanation:

From the diagram, <DCB is a right angle = 90°

Therefore:

m<DCA + m<ACB = 90° (complementary angles)

m<DCA = 40° (given)

Thus:

40° + m<ACB = 90° (Substitution)

m<ACB = 90° - 40° (Subtraction property of equality)

m<ACB = 50°