find the directional derivative of f(x, y) = xy at p(7, 7) in the direction from p to q(10, 3).

Answer:

6

Step-by-step explanation:

Let x by the unknown number.

Given:

Therefore, the equation representing the given information is:

\(\boxed{x^2+85=(x-17)^2}\)

To solve for x, expand the right side:

\(\implies x^2+85=(x-17)^2\)

\(\implies x^2+85=(x-17)(x-17)\)

\(\implies x^2+85=x^2-34x+289\)

Subtract x² from both sides of the equation:

\(\implies 85=-34x+289\)

Add 34x to both sides:

\(\implies 34x+85=289\)

Subtract 85 from both sides:

\(\implies 34x=204\)

Divide both sides by 34:

\(\implies x=6\)

Therefore the unknown number is 6.

\(\sqrt[5]{2}-1 = 1 +x - 1\)Answer:

14.87% per hour

Step-by-step explanation:

Let's pretend we're starting with one bacteria.

Double of one is two

We're gonna have to use this formula: A = P(1 + x)ⁿ

A = Amount (which is 2)

P = Initial amount (which is 1)

x = percentage per time (hour)

n = amount of time (hours)

So our equation will look like this:

2 = 1(1 + x)⁵

First, we need to root both sides to isolate (1 + x)

\(\sqrt[5]{2} = \sqrt[5]{(1+x)}\)

\(\sqrt[5]{2} = 1 +x\)

Then subtract both sides by 1

\(\sqrt[5]{2}-1 = 1 +x - 1\)

\(x=\sqrt[5]{2}-1\)

\(\sqrt[5]{2} = 1.148698355\)

1.148698355 - 1 = 0.148698355

x = 0.148698355

Answer: y values in order: 2, 1, 0.5

Step-by-step explanation:

Just take the x values and put them in place of the x in the above equation.

As for -1, you're flipping 0.5 over to a fraction of 1/0.5, which equals 2, so that's the first y value.

*This is because any negative exponent gets the number in the denominator with 1 in the numerator, then the denominator can change depending on the value of the exponent

For 0, anything to the power of 0 is 1, so that's the second y value.

And then for 1, the number doesn't change, so just put 0.5 in the third y-value.

Also I see it says for you to sketch a graph, in this case the picture I have showing is what the graph would look like

Hope this helps at least :)

By using the vertex of the quadratic equation, we will get the equation:

y = -2*(x + 6)^2

For a quadratic equation with a leading coefficient "A" and a vertex (h, k), the equation can be written as:

y = A*(x - h)^2 + k

Here we can see that the vertex is (-6, 0), so we have:

y = A*(x + 6)^2

We also can see that the parabola passes through the point (-4, -8), replacing these values above we will get:

-8 = A*(-4 + 6)^2

-8 = A*(2)^2

-8 = 4A

-8/4 = A

-2 = A

Then the quadratic equation is:

y = -2*(x + 6)^2

Laern more about quadratic equations:

https://brainly.com/question/1214333

#SPJ1

The introduction of B should not have impacted the preference between A and C.

Preference relations that violate Independence of the expected utility theorem:

Independence of irrelevant alternatives (IIA) refers to a preference relation principle that states that the decision maker's preference between two choices should be the same, regardless of the presence or absence of a third, unrelated option.

Suppose the following preferences:

Lottery A: 0.1 chance to win $2,000,000, 0.8 chance to win $1,000,000, 0.1 chance to win nothing

Lottery B: 0.12 chance to win $2,000,000, 0.03 chance to win $1,000,000, 0.85 chance to win nothing, and

Lottery C: 0.4 chance to win $2,000,000, 0.1 chance to win $1,000,000, 0.4 chance to win nothing.

Lottery A over B: A is chosen over B with probability 1

Lottery C over A: C is chosen over A with probability 0.5

Lottery C over B: C is chosen over B with probability 0

Suppose you're trying to decide between A and B, and you choose A. This implies that you have a specific preference between the two options. Similarly, if you choose C over A, it implies that you have a specific preference between those two options as well.

However, if you now compare C to B, you'll see that C is selected over B with probability 0, indicating that there is no preference between the two alternatives. This is in violation of the Independence of irrelevant alternatives theorem because the introduction of B should not have impacted the preference between A and C. Thus, this violates the Independence of the expected utility theorem.

Learn more about probability at

https://brainly.com/question/29176120

#SPJ11

Answer:

quotient

Step-by-step explanation:

Answer:

quotient

Step-by-step explanation:

Cancelling identical factors in the numerator and the denominator will give the quotient. For example,x2+5x+6x+3=(x+2)(x+3)x+3 = x + 3

Answer:

0.0065509804

Step-by-step explanation:

Answer:

If you follow the order of operations it would be 0.12103072956 or approximately

0.12

0.121

0.1210

0.12103

0.121031

Taylor polynomials p1, ..., p5 centered at a=0 for f(x)=7e^(-x) are:

p1(x) = 7 - 7x

p2(x) = 7 - 7x + 3.5x^2

p3(x) = 7 - 7x + 3.5x^2 - 1.17x^3

p4(x) = 7 - 7x + 3.5x^2 - 1.17x^3 + 0.205x^4

p5(x) = 7 - 7x + 3.5x^2 - 1.17x^3 + 0.205x^4 - 0.025x^5

To find the Taylor polynomials p1, ..., p5 centered at a=0 for f(x)=7e^(-x), we need to calculate the derivatives of f(x) and evaluate them at x=0:

f(x) = 7e^(-x)

f(0) = 7

f'(x) = -7e^(-x)

f'(0) = -7

f''(x) = 7e^(-x)

f''(0) = 7

f'''(x) = -7e^(-x)

f'''(0) = -7

f''''(x) = 7e^(-x)

f''''(0) = 7

Using these derivatives, we can write the Taylor polynomials p1, ..., p5 centered at a=0 as:

p1(x) = f(0) + f'(0)x = 7 - 7x

p2(x) = p1(x) + (1/2!) f''(0)x^2 = 7 - 7x + (1/2)(7)x^2 = 7 - 7x + 3.5x^2

p3(x) = p2(x) + (1/3!) f'''(0)x^3 = 7 - 7x + (1/2)(7)x^2 - (1/6)(7)x^3 = 7 - 7x + 3.5x^2 - 1.17x^3

p4(x) = p3(x) + (1/4!) f''''(0)x^4 = 7 - 7x + (1/2)(7)x^2 - (1/6)(7)x^3 + (1/24)(7)x^4 = 7 - 7x + 3.5x^2 - 1.17x^3 + 0.205x^4

p5(x) = p4(x) + (1/5!) f^(5)(0)x^5 = 7 - 7x + (1/2)(7)x^2 - (1/6)(7)x^3 + (1/24)(7)x^4 - (1/120)(7)x^5 = 7 - 7x + 3.5x^2 - 1.17x^3 + 0.205x^4 - 0.025x^5

Therefore, the Taylor polynomials p1, ..., p5 centered at a=0 for f(x)=7e^(-x) are:

p1(x) = 7 - 7x

p2(x) = 7 - 7x + 3.5x^2

p3(x) = 7 - 7x + 3.5x^2 - 1.17x^3

p4(x) = 7 - 7x + 3.5x^2 - 1.17x^3 + 0.205x^4

p5(x) = 7 - 7x + 3.5x^2 - 1.17x^3 + 0.205x^4 - 0.025x^5

Know more about  Taylor polynomials click here:

https://brainly.com/question/30551664

#SPJ11

we find that the numerical approximation using Euler's method gives y(2) ≈ 1.865, while the analytical solution gives y(2) = 2.5.

Using the formula y(n+1) = y(n) + Δx * f(x(n), y(n)), where f(x, y) = x² √y, we can calculate the values of y at each step. Here's the step-by-step calculation:

Step 1: For x = 0, y = 1 (initial condition).

Step 2: For x = 0.2, y = 1 + 0.2 * (0.2)² * √1 = 1.008.

Step 3: For x = 0.4, y = 1.008 + 0.2 * (0.4)² * √1.008 = 1.024.

Step 4: For x = 0.6, y = 1.024 + 0.2 * (0.6)² * √1.024 = 1.052.

Step 5: For x = 0.8, y = 1.052 + 0.2 * (0.8)² * √1.052 = 1.094.

Step 6: For x = 1.0, y = 1.094 + 0.2 * (1.0)² * √1.094 = 1.155.

Step 7: For x = 1.2, y = 1.155 + 0.2 * (1.2)² * √1.155 = 1.238.

Step 8: For x = 1.4, y = 1.238 + 0.2 * (1.4)² * √1.238 = 1.346.

Step 9: For x = 1.6, y = 1.346 + 0.2 * (1.6)² * √1.346 = 1.483.

Step 10: For x = 1.8, y = 1.483 + 0.2 * (1.8)² * √1.483 = 1.654.

Step 11: For x = 2.0, y = 1.654 + 0.2 * (2.0)² * √1.654 = 1.865.

Therefore, using Euler's method with a step size of Δx = 0.2, we approximate y(2) to be 1.865.

To obtain the analytical solution to the ODE, we can separate variables and integrate both sides:

∫(1/√y) dy = ∫x² dx

Integrating both sides gives:

2√y = (1/3)x³ + C

Solving for y:

y = (1/4)(x³ + C)²

Using the initial condition y(0) = 1, we can substitute x = 0 and y = 1 to find the value of C:

1 = (1/4)(0³ + C)²

1 = (1/4)C²

4 = C²

C = ±2

Since C can be either 2 or -2, the general solution to the ODE is:

y = (1/4)(x³ + 2)² or y = (1/4)(x³ - 2)²

Now, let's evaluate y(2) using the analytical solution:

y(2) = (1/4)(2³ + 2)² = (1/4)(8 + 2)² = (1/4)(10)² = 2.5

Learn more about Integrate here : brainly.com/question/31744185

#SPJ11

Answer:38

Step-by-step explanation:

they were born in 1933 and 1971 minus 1933 is 38.

Answer:

2 3/5

Step-by-step explanation:

1/5÷1/3

and solve

1×3

5/1

=3/5

Therefore:

1/5÷1/3=3/5

Answer:

A'=(-1, 5)  B'=(-2, 3)  C'=(-5, 4)

Step-by-step explanation:

Reflecting over the y-axis changes the only the first point changes into a negative, while the second stays the same.

The voltage of the speaker when the power is 400 watts will be given by ± 80 volt.

Given the equation is,

V = 4 √P

here V is the voltage of an audio system's speaker and P is the power of the audio system's speaker.

Here it is given that we have to design a speaker with 400 watts of power. So the equation becomes when P = 400

V = 4 √400

We know that, √400 = ± 20

So, V = 4 * (± 20) = ± 80

Hence the voltage of the speaker will be given by ± 80 volt.

To know more about equation here

https://brainly.com/question/14603452

#SPJ4

Answer:

61.2

Step-by-step explanation:

base=6

height=10

Area of parellelogram=base x height

=6x 10.2

=61.2 sq.ft

MARK ME BRAINLIEST THANKS MY ANSWER PLEASE

Answer:

15 cake pops

Step-by-step explanation:

60 cake pops = 4 hours

x cake pops = 1 hour

60/4 = 15

hence Julia can make 15 cake pops per hour

The simplified value of the given expression is 49/288.

To simplify the given expression (2/9 * 3/6) + (3/4 % 12/5) - [1/4 - (1/4 * 2/3)], first, we need to simplify the brackets. Let's start by simplifying the expression inside the brackets.[1/4 - (1/4 * 2/3)]

Step 1: Multiply 1/4 and 2/3= 1/4 × 2/3= 2/12= 1/6Step 2: Subtract 1/6 from 1/4= 1/4 - 1/6= (3/12) - (2/12)= 1/12Therefore, [1/4 - (1/4 * 2/3)] = 1/12

Now, let's substitute this value in the original expression and simplify it.(2/9 * 3/6) + (3/4 % 12/5) - 1/12Step 1: Simplify the multiplication expression2/9 * 3/6= (2*3)/(9*6)= 6/54= 1/9Step 2: Simplify the modulo expression 3/4 % 12/5= (3/4) / (12/5)= (3/4) × (5/12)= 15/48= 5/16

Now, substituting these values in the original expression, we get1/9 + 5/16 - 1/12= 16/144 + 45/288 - 12/144= (16+45-12)/288= 49/288Therefore, the simplified value of the given expression is 49/288.

For more such questions on simplified value

https://brainly.com/question/30643403

#SPJ8

Question:

A financial transaction that is added to a ledger balance is called a credit.

Answer:

The answer is True, I just took the test

The value of the numerical expression will be 36. Then the correct option is 36.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The numerical expression is given below.

\(\rightarrow \dfrac{\left ( 27 \right)^{2/3} \times \sqrt{16}}{5^0}\)

Simplify the expression, then we have

⇒ (∛(27)² × √16) / 5⁰

⇒ (3)² × 4

⇒ 9 × 4

⇒ 36

The value of the numerical expression will be 36. Then the correct option is 36.

More about the Algebra link is given below.

https://brainly.com/question/953809

#SPJ1

The complete question is given below.

Compute the expression \(\dfrac{\left ( 27 \right)^{2/3} \times \sqrt{16}}{5^0}\)

a) 36

b) 35

c) 34

d) 1

Answer:

745 k/hr

Step-by-step explanation:

mathematically, 1 day = 24 hours

1670 days = 1670 * 24 = 40,080 hours

The speed is thus;

(29,870,000)/40,080 = 745.259

= 745 km/h

Direction Cosine expresses the relationship of a vector or line in three dimensions with each of the three axes. The direction cosine is the cosine of the angle formed by this line with the x, y, and z axes, in that order.

The operation is used to calculate the magnitude of the vector is dividing by cosine.

cosine function

cos θ = ca / ​​H

ca=adjacent leg (x-axis) and

H= hypotenuse (vector module)

H = ca / ​​cos θ

therefore, to find the magnitude of the vector, the method is to divided by the cosine.

Cosine matrix in one direction (DCM) is a  3 x 3 rotation matrix C, the columns of which represent unit vectors in the body axes projected along the reference axes, specifies the direction cosine matrix, which represents the attitude of the body frame relative to the reference frame.

Direction Cosine

Direction cosine is the cosine of the angle formed by a line in three-dimensional space with the x, y, and z axes. In three dimensions, direction cosines can be calculated for a vector or a straight line. It is the cosines of the angle formed by the line intersected by the three axes.

To learn more about cosine angles

https://brainly.com/question/24327456

#SPJ4

Answer:

I'm guessing the y axis would be velocity and the x axis would be time, seconds then the top box could be time v velocity

This question is incomplete

Complete Question

A baker uses 5.5 Ibs of flour daily

The baker's recipe for a loaf of bread calls for 12 oz of flour. If he uses all of his flour to make loaves of bread, how many loaves can he bake in seven days?

Answer:

51.3 loaves of bread

Step-by-step explanation:

Converting 5.5 Ibs to oz (ounces)

1 Ibs =>12 oz

5.5 Ibs => x

Cross Multiply

12 × 5.5 => 88 oz

1 loaf of bread =>12 oz

Hence, in 1 day

12 oz =>1 loaf of bread

88 oz => x

x =>88 oz/ 12 oz

x => 7.3333333333 loaves of bread

Hence, he can make 7.3333333333 loaves of bread in 1 day

Hence, in 7 days

1 day => 7.3333333333 loaves

7 days => x

x => 7 × 7.3333333333 loaves

x => 51.333333333 loaves of bread

Approximately => 51.3 loaves of bread

To answer this question, we need to use the formula for finding the sum of the interior angles of a convex polygon, n = 30

Sum of interior angles = (n-2) x 180 degrees
Here, n represents the number of sides of the polygon. We are given that the sum of the interior angles is 5040 degrees. So we can set up an equation as follows:
5040 = (n-2) x 180
Simplifying this equation, we get:
n - 2 = 28
Therefore, the polygon has 30 sides, which means the answer is option C. It is important to note that this formula only applies to convex polygons, which are polygons with all interior angles less than 180 degrees and no sides that "cave in". If the polygon is not convex, this formula will not work.

To know more about convex polygon visit:

https://brainly.com/question/29210694

#SPJ11

Sequence diagrams are used in conjunction with detailed use case descriptions or with activity diagrams.

Sequence diagrams are a type of interaction diagram that display the sequential flow of actions and interactions between objects and components in a system.

These diagrams help to visualize the timing and order of events, making it easier to understand and design complex processes.

By incorporating sequence diagrams with use case descriptions and activity diagrams, a clearer and more comprehensive understanding of a system's functionality can be achieved.

Learn more about diagram at https://brainly.com/question/15153299

#SPJ11

(a) The series Σ(1/(2n²+1) + 1/(3n²-4n+1)) converges, (b)  The series Σ(ln(5n)) from n=0 diverges and  (c) the series Σ(ln(n)/ln(2)) from n=2 to m² diverges. to check convergence we can do :

a. Σ(1/(2n²+1) + 1/(3n²-4n+1))
b. Σ(ln(5n)) from n=0
c. Σ(ln(n)/ln(2)) from n=2 to m²
a. To check convergence for the series Σ(1/(2n²+1) + 1/(3n²-4n+1)), we'll use the Comparison Test. Since both terms in the sum are positive and the denominators are greater than n²we can compare it with the series Σ(1/n²) which converges according to the p-series test (p=2 > 1). Therefore, the series Σ(1/(2n²+1) + 1/(3n²-4n+1)) converges.

b. For the series Σ(ln(5n)) from n=0, we'll use the Divergence Test. As n approaches infinity, ln(5n) doesn't approach 0 but increases indefinitely. Hence, the series Σ(ln(5n)) from n=0 diverges.
c. To check the convergence for the series Σ(ln(n)/ln(2)) from n=2 to m², we'll use the Integral Test. Let's first note that ln(n)/ln(2) is positive, continuous, and decreasing for n ≥ 2. The integral from 2 to infinity of ln(x)/ln(2) dx doesn't converge, as it's an improper integral of a function that decreases too slowly (ln(x) decreases much slower than any power function). Therefore, the series Σ(ln(n)/ln(2)) from n=2 to m² diverges.

To know more about convergence click here

brainly.com/question/28157994

#SPJ11

A. we can conclude that Σ(2n^2+1)/(3n^2-4n+21) is also convergent.

B.  we can conclude that Σln(n) is divergent. Therefore, Σln(5n) is also divergent.

C. Σ2^mm is a known divergent series, we can conclude that ΣIn(n)Ln(2m^2) is also divergent.

a. To check the convergence of this series, we can use the comparison test. We know that 2n^2+1 < 3n^2 for all n > 1. Therefore, we can write:

Σ(2n^2+1)/(3n^2-4n+21) < Σ(3n^2)/(3n^2-4n+21)

Now, we can use the limit comparison test with the series Σ(3n^2)/(3n^2-4n+21) and Σ(1/n^2), which is a known convergent series. Taking the limit of the ratio of these two series as n approaches infinity, we get:

lim n→∞ (3n^2)/(3n^2-4n+21) / (1/n^2) = lim n→∞ (3n^4)/(3n^2-4n+21) = 3

Since this limit is finite and nonzero, and since Σ(1/n^2) is convergent, we can conclude that Σ(2n^2+1)/(3n^2-4n+21) is also convergent.

b. To check the convergence of this series, we can use the integral test. We know that ln(x) is a monotonically increasing function for x > 1, and that ln(5) > 1. Therefore, we can write:

Σln(5n) > Σln(n)

Now, we can use the integral test with the series Σln(n) and the integral ∫ln(x)dx from 1 to infinity. Evaluating this integral, we get:

∫ln(x)dx = xln(x) - x + C

Taking the limit of this expression as x approaches infinity, we get:

lim x→∞ (xln(x) - x + C) = infinity

Since this limit is infinite, we can conclude that Σln(n) is divergent. Therefore, Σln(5n) is also divergent.

c. To check the convergence of this series, we can use the Cauchy condensation test. We know that In(n) is a monotonically increasing function for n > 1. Therefore, we can write:

ΣIn(n)Ln(2m^2) < ΣIn(2m)Ln(2m^2)

Now, we can use the Cauchy condensation test with the series ΣIn(2m)Ln(2m^2) and Σ2^m In(2^m)Ln(2(2^m)^2), which simplifies to:

Σ2^m In(2^m)Ln(2^(2m+2)) = Σ2^m(m ln(2) + ln(2))Ln(2^2) = 4ln(2)Σ2^mm

Since Σ2^mm is a known divergent series, we can conclude that ΣIn(n)Ln(2m^2) is also divergent.

To learn more about comparison test, refer below:

https://brainly.com/question/31362838

#SPJ11

from the question;

we to find |x| when x = 15 and when x = -15

by definition of absolute value we have

Thats for every value of x, the absolute value is always positive

Hence,

Also

Therefore the correct answer is

Both values are 15

option B

To show that the vectors ⟨1,2,1⟩, ⟨1,3,1⟩, ⟨1,4,1⟩ do not span ℝ³, we can find a vector that cannot be written as a linear combination of these vectors.

To determine if the vectors ⟨1,2,1⟩, ⟨1,3,1⟩, ⟨1,4,1⟩ span ℝ³, we need to check if any vector in ℝ³ can be expressed as a linear combination of these vectors.

Let's consider a vector ⟨a, b, c⟩ that we want to test if it belongs to the span of the given vectors. In order for ⟨a, b, c⟩ to be in their span, there must exist scalars x, y, and z such that:

x⟨1, 2, 1⟩ + y⟨1, 3, 1⟩ + z⟨1, 4, 1⟩ = ⟨a, b, c⟩

Expanding the equation, we have:

⟨x + y + z, 2x + 3y + 4z, x + y + z⟩ = ⟨a, b, c⟩

From this, we can equate the corresponding components:

x + y + z = a

2x + 3y + 4z = b

x + y + z = c

Now, we need to find a vector ⟨a, b, c⟩ that does not satisfy these equations. One such example is when a = 1, b = 2, and c = 3. Solving the equations, we get:

x + y + z = 1

2x + 3y + 4z = 2

x + y + z = 3

Solving these equations simultaneously, we find that there is no solution. Therefore, the vector ⟨1, 2, 3⟩ cannot be expressed as a linear combination of the given vectors ⟨1, 2, 1⟩, ⟨1, 3, 1⟩, and ⟨1, 4, 1⟩.

Since we have found a vector that does not belong to their span, we can conclude that the vectors ⟨1, 2, 1⟩, ⟨1, 3, 1⟩, ⟨1, 4, 1⟩ do not span ℝ³.

To learn more about

Vector

brainly.com/question/30958460

#SPJ11

The next term in the sequence is 36.

Yes, the given sequence could be arithmetic. To determine the first difference, we subtract consecutive terms:

4 - (-4) = 8

12 - 4 = 8

20 - 12 = 8

28 - 20 = 8

The first difference between consecutive terms is 8. To find the next term, we add the first difference to the last term:

28 + 8 = 36

Therefore, the next term in the sequence is 36.

Learn more about sequence:

https://brainly.com/question/7882626

#SPJ11

The area of the composite figure is

321 square m

The area is calculated by dividing the figure into simpler shapes.

The simple shapes used here include

Area of triangle = 1/2 x base x height

height = √(22² + 15²) = 16

= 1/2 x 15 x 16

= 120 square m

Area of quarter of circle = 1/4 x π x r²

= 1/4 x π x 16²

= 201 square m

Total area

= 201 square m + 120 square m

=  321 square m

Learn more about composite shapes at

https://brainly.com/question/8370446

#SPJ1