find the directional derivative of the function at point p (5, 5) in the direction of v = 3i 4j.

Answer:

C.

Step-by-step explanation:

Thus, this option represents a linear function.

A unit for each quantity in the worksheet for the mat width are 5.357 inches.

The size of a rectangle. A = l × b. Once the length and width are known for any rectangle, the area may be determined. The area of the rectangle is calculated as a square-unit dimension by multiplying length and width.

Add the height and the width together to get the area of a rectangle. Given that each side of a square is the same length, all you need to do to determine its area is multiply the length of one of its sides by itself.

Length = 7 inches  

Width = 6 inches

Area of photograph = length  width = 7  6 = 42

Total area of photograph and frame = 84

frame length ( 7 + 2x)

frame width ( 6 + 2x)

Total area = Total area of photograph and frame

( 7 + 2x)  ( 6 + 2x) = 84

2 + 13x - 21 = 0

x = 5. 357

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a) The instantaneous rate of change on day 6 is 84.

b) The inflection point is at t = 4.

a) To find the instantaneous rate of change of the function f(t) at day 6, we need to take the derivative of f(t) with respect to t and evaluate it at t = 6. Differentiating f(t) = 12t^2 - t^3, we get f'(t) = 24t - 3t^2. Plugging in t = 6, we have f'(6) = 24(6) - 3(6)^2 = 144 - 108 = 36. This means that on day 6, the number of newly infected people is increasing at a rate of 36 per day.

b) To find the inflection point of f(t), we need to find the values of t where the second derivative of f(t) changes sign. Taking the second derivative of f(t), we get f''(t) = 24 - 6t. Setting f''(t) = 0, we find t = 4. This is the inflection point of f(t). At t = 4, the rate of change of the number of newly infected people transitions from increasing to decreasing or vice versa.

In the context of the flu epidemic, the inflection point at t = 4 suggests a change in the trend of the spread of the flu. Prior to t = 4, the rate of new infections was increasing, indicating the exponential growth of the epidemic. After t = 4, the rate of new infections starts to decrease, potentially indicating a peak in the number of new infections and a transition towards a decline in the epidemic.

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Answer: To find the equation of the tangent line y(x) of the curve r(t) = (t^9, t^5), we need to find the derivative of the curve and then evaluate it at the point where we want to find the tangent line.

The derivative of r(t) is:

r'(t) = (9t^8, 5t^4)

To find the equation of the tangent line at a specific point (x0, y0), we need to evaluate r'(t) at the value of t that corresponds to that point. Since r(t) = (t^9, t^5), we can solve for t in terms of x0 and y0:

t^9 = x0

t^5 = y0

Solving for t, we get:

t = (x0)^(1/9)

t = (y0)^(1/5)

Since these two expressions must be equal, we have:

(x0)^(1/9) = (y0)^(1/5)

Raising both sides to the 45th power, we get:

(x0)^(5/9) = (y0)^(9/45)

(x0)^(5/9) = (y0)^(1/5)

(x0)^(9/5) = y0

So the point where we want to find the tangent line is (x0, y0) = (t0^9, t0^5) = (x0, x0^(5/9 * 9/5)) = (x0, x0).

Now we can evaluate r'(t) at t0:

r'(t0) = (9t0^8, 5t0^4) = (9x0^(8/9), 5x0^(4/9))

The slope of the tangent line at (x0, y0) is given by the derivative of y(x) with respect to x:

y'(x) = (dy/dt)/(dx/dt) = (5t^4)/(9t^8) = (5/x0^4)/(9/x0^8) = 5x0^4/9

So the equation of the tangent line is:

y - y0 = y'(x0) * (x - x0)

y - x0 = (5x0^4/9) * (x - x0)

y = (5/9)x + (4/9)x0

Therefore, the equation of the tangent line y(x) of the curve r(t) = (t^9, t^5) at the point (x0, y0) = (x0, x0) is y = (5/9)x + (4/9)x0.

To find the equation of the tangent line at a point on the curve, we need to find the derivative of the curve at that point. So, we start by finding the derivative of r(t):

r'(t) = (9t^8, 5t^4)

Now, let's find the tangent line at the point (1, 1):

r'(1) = (9, 5)

So, the slope of the tangent line at (1, 1) is 5/9. To find the y-intercept, we can use the point-slope form:

y - y1 = m(x - x1)

where (x1, y1) is the point on the curve. Plugging in (1, 1) and the slope we just found, we get:

y - 1 = (5/9)(x - 1)

Simplifying, we get:

y = (5/9)x + 4/9

So, the equation of the tangent line at the point (1, 1) is y = (5/9)x + 4/9.

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To find the value of x such that the probability of the sum of independent normal random variables X and Y being greater than x is equal to the probability of X being greater than 15, we can utilize the properties of normal distributions. By considering the mean and variance of X and Y, we can determine that x is approximately 25.177.

Let's denote the sum of X and Y as Z = X + Y. Since X and Y are independent normal random variables, the sum Z follows a normal distribution with a mean equal to the sum of the individual means (10 + 10 = 20) and a variance equal to the sum of the individual variances (4 + 4 = 8). Therefore, Z ~ N(20, 8).

To find x, we need to calculate the probability P(Z > x) and set it equal to P(X > 15). Since X ~ N(10, 4), we can standardize the variables using the formula z = (x - μ) / σ, where μ is the mean and σ is the standard deviation.

Using standardization, we have P(Z > x) = P((Z - 20) / √8 > (x - 20) / √8) = P(z > (x - 20) / √8). Similarly, P(X > 15) = P((X - 10) / 2 > (15 - 10) / 2) = P(z > 2.5).

Now, we equate the two probabilities: P(z > (x - 20) / √8) = P(z > 2.5). Since the standard normal distribution is symmetric, we can use the z-table or a statistical calculator to find that P(z > 2.5) ≈ 0.0062.

Thus, we have (x - 20) / √8 ≈ 2.5. Solving for x, we get x ≈ 25.177. Therefore, the value of x for which P(X + Y > x) = P(X > 15) is approximately 25.177.

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The correct description regarding each table is given as follows:

1. Rate of change of 4, linear.

2. Rate of change of -2/3, linear.

3. Rate of change of 1/4, linear.

4. Rate of change of -1, linear.

5. Not linear.

6. Rate of change of 3, linear.

A linear function has the definition presented as follows:

y = mx + b.

In which:

A data-set will only be classified as linear if the rate of change is constant.

Hence the tables in this problem are classified as follows:

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Answer:

Step-by-step explanation:

BA has initial point B. So, you want a ray with initial point B pointing the other way. That would, of course, be BD.

Lean systems coupled with statistical process control require a high degree of regimentation which in turn can lead to Worker stress.

Statistical process control is a system of quality control where statistical model, algorithm and and methods are used to monitor a process.

SPC is mainly practiced or implemented in two steps

While other processes uses correction from results, SPC helps in early detection and solving of the problem.

Now using SPC requires a high degree of regimentation from Man, Machine, Material, Method,  Environment. Now such high level of regimentation is not always effective on workers of a factory or system which in turn increase the worker stress.

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The  expression that makes the equation true is A)40 ÷ (5 x 2) x 17.55.

What is expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. Unknown variables, integers, and arithmetic operators are the components of an algebraic expression. There are no symbols for equality or inequality in it.

Here first solve given expression then,

=> 13.5 x (1.2 + 4) = 13.5×1.2+13.5×4 = 70.2

Now solving option expressions then,

A) 40 ÷ (5 x 2) x 17.55 = 40÷10×17.55 = 4×17.55 = 70.2

B) 36 ÷ (4.8 − 2.6) x 3 = 36÷2.4×3 = 45

C) 22 x (3.6 − 1.2) + 4 = 22×(2.4)+4 = 56.8

D) 18 ÷ (3 x 3) x 35.2 = 18÷ 9×35.2 = 2×35.2 = 70.4

Hence the  expression that makes the equation true is A)40 ÷ (5 x 2) x 17.55.

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the image (new coordinate) after the translation is (-2.5, 9.8)

Here we have a rule (also called a transformation or an operator) that works as:

T(x, y) = (x - 7.5, y + 6.8)

So we decrease the x-value by 7.5 and increase the y-value by 6.8. This is a translation of 7.5 units to the left and 6.8 units upwards.

Now, our point is (5, 3), if we apply that transformation we will get:

T(5, 3) = (5 - 7.5, 3 + 6.8) = (-2.5, 9.8)

That is the image after the translation.

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Write your answer below:

The algebraic representation that shows a dilation that is an enlargement is (5/2 x,5/2 y). (Option D)

A dilation is a type of transformation that changes the size of the shape or object.  It refers to a process of changing an object’s size by decreasing or increasing its dimensions by a scaling factor. A dilation produces an image that has the same shape as the original image but is a different size.

A dilation that results in a larger image is called an enlargement while a dilation that generates a smaller image is called a reduction. A dilation is described using the scale factor and the center of the dilation (which is a fixed point in the plane).

For a scale factor > 1, the image is an enlargement; for a scale factor < 1 and  > 0, the image is a reduction; and for a scale factor = 1, the figure and the image are congruent. Hence, for a point (x,y), algebraic representation that shows a dilation that is an enlargement is (5/2 x,5/2 y) as the scale factor is greater than 1. For the remaining options, the scale factor is between 0 and 1, hence they are reduction.

Note: The question is incomplete. The complete question probably is: Which of the following algebraic representation shows a dilation that is an enlargement? A) (1/3 x,1/3 y) B) (0.1x, 0.1y) C) (5/6 x,5/6 y) D) (5/2 x,5/2 y)

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Answer:

C

Step-by-step explanation:

We have the equation:

\(\displaystyle y=\frac{4}{5}x-3\)

This is in slope-intercept form:

\(y=mx+b\)

Where m is the slope and b is our y-intercept.

Therefore, whatever number in front of our x, the coefficient, is our slope.

The coefficient of x is 4/5.

Therefore, the slope of the line is 4/5.

Hence, our answer is C.

Consider the attached diagram. Segment KO is an altitude of the triangle, so KO ⊥ LM. ∠L has measure 180° -105° -30° = 45°, so ΔKOL is an isosceles right triangle.

If we let segment LO have measure 1, then KO also has measure 1 and KL has measure √(1²+1²) = √2 by the Pythagorean theorem.

ΔKMO is half of an equilateral triangle, so KM has measure 2, and MO has measure √(2²-1²) = √3 by the Pythagorean theorem.

Then the ratio of KM to LM is 2:(1+√3) and the ratio of KL to LM is √2:(1+√3). That is, ...

... KL = LM×(√2)/(1+√3) = (20√3)(√2)/(1 +√3)

... KL = (20√6)/(√3 +1) = (20√6)(√3 -1)/(3 -1) . . . . . with denominator rationalized

... KL = 30√2 -10√6 ≈ 17.9315

and

... KM = LM×2/(1+√3) = KL×√2

... KM = (30√2 -10√6)√2

... KM = 60 -20√3 ≈ 25.3590

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

The Law of Sines tells you ...

... KL/sin(M) = KM/sin(L) = LM/sin(K)

Then ...

... KL = sin(M)·LM/sin(K) = sin(30°)·20√3/sin(105°) ≈ 17.9315

... KM = sin(L)·LM/sin(K) = sin(45°)·20√3/sin(105°) ≈ 25.3590

Answer:

Step-by-step explanation:

Since m∠1 = m∠2, KF is angle bisector of ∠K

In the ΔKFM we have:

Using low of sines:

Answer:

I agree with you its b

Step-by-step explanation:

Answer:

the number of seconds to reach the height is 3 seconds

Step-by-step explanation:

The computation of the seconds that reach the height is as follows;

Given that

h = -16t^2 + 96t + 48

here

H = 192 feet

So,

192 = -16t^2 + 96t + 48

-16t^2 + 96t - 144 = 0

Divide by -16

t^2 - 6t + 9 = 0

t^2 - 3t - 3t + 9

t(t - 3) - 3(t - 3)

t = 3 seconds

Hence, the number of seconds to reach the height is 3 seconds

Answer:

I think the moon is seven and the star is 4.

Step-by-step explanation:

Answer:

6h+14k

Step-by-step explanation:

Multiply 2by 3h which gives 6h then multiply 7k by 2 which gives 14k.

Since 6h and 14k are not like terms u cannot add so your answer will be 6h + 14k.

Answer:

9h² + 42hk + 49k²

Step-by-step explanation:

Given

(3h + 7k)²

= (3h + 7k)(3h + 7k)

Each term in the second factor is multiplied by each term in the first factor, that is

3h(3h + 7k) + 7k(3h + 7k) ← distribute both parenthesis

= 9h² + 21hk + 21hk + 49k² ← collect like terms

= 9h² + 42hk + 49k²

Every integer n ≥ 1 can be written in the form

\(n = cr · 3^r + cr-1 · 3^(r-1) + ... + c2 · 3^2 + c1 · 3 + c0\), where

cr = 1 or 2 and

ci = 0, 1, or 2 for all integers i = 0, 1, 2, ..., r - 1.

To prove that every integer n ≥ 1 can be written in the form:

\(n = cr · 3^r + cr-1 · 3^(r-1) + ... + c2 · 3^2 + c1 · 3 + c0,\)

where cr = 1 or 2 and ci = 0, 1, or 2 for all integers i = 0, 1, 2, ..., r - 1, we can use a constructive proof.

Start with the base case: For n = 1, we have n = 1 = 1 · 3^0, which satisfies the given form.

Assume the statement holds for all positive integers up to k.

Consider the integer k + 1.

Divide k + 1 by 3: If k + 1 is divisible by 3, then set cr = 1 and use the remaining quotient (k + 1) / 3 as the next value for k in the assumption. Repeat this process until the quotient becomes 1.

If k + 1 is not divisible by 3, set cr = 2 and use the remaining quotient (k + 1 - 1) / 3 as the next value for k in the assumption. Repeat this process until the quotient becomes 1.

At each step, we update the values of cr, and the resulting expression follows the given form.

By repeatedly applying this process, we eventually reach 1, and the final expression satisfies the specified form.

Therefore, by induction, every integer n ≥ 1 can be written in the specified form.

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Answer:

the answer is 45%.

Step-by-step explanation:

if you add 5% divided by 3 = 15%.

So if you add all of those plus the 30% you will be getting 45%.

The temperature of the liquid at noon would be of:

-2.25ºC.

The linear function in this problem is defined in the slope-intercept format, as follows

y = mx + b.

In which the coefficients of the function are given as follows:

The values of these coefficients are given as follows:

m = -3/4, b = 0.

Then the function that gives the temperature in x hours after 9 A.M. is of:

y = -3/4x.

Noon is three hours after 9 A.M., hence the estimate is given as follows:

y = -3/4(3) = -9/4 = -2.25ºC.

The problem states that the initial temperature is of 0ºC at 9 A.M.

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Answer:

13,505,599 good luck

Answer:

3675

3680-

0015

3670

15

18350

3670+

1202

Measure of arc MLK is 270°

Angle MKL = 135 degrees

We are looking for the measure of the arc MLK

The diagram shows an angle formed by a chord (MK) and tangent

The relationship between angle formed by a chord and tangent:

Measure of arc MLK:

Answer: 2/5

Step-by-step explanation:

16/40 = 2/5

Answer:

\(\frac{2 hr}{5 hr}\)

Step-by-step explanation:

=> 16 hr:40 hr

Writing it in fraction form

=> \(\frac{16hr}{40 hr}\)

=> \(\frac{4 hr}{10 hr}\)

=> \(\frac{2 hr}{5 hr}\)

Using the first four terms of the Taylor series with a step size of h=0.1, the value of y(1.2) is approximately 0.346.


To approximate the value of y(1.2), we can use the Taylor series expansion. The general form of the Taylor series for a function y(x) is:
Y(x + h) = y(x) + h * y’(x) + (h^2 / 2!) * y’’(x) + (h^3 / 3!) * y’’’(x) + …
In this case, we are given the differential equation dy/dx = -y + x*dx and the initial condition y(1) = 0.
Using the first four terms of the Taylor series, the approximation for y(1.2) can be calculated as follows:
Calculate y(1.1) using the initial condition and the first term of the Taylor series.
Calculate y’(1.1) using the given differential equation and the first term of the Taylor series.
Calculate y’’(1.1) using the given differential equation and the second term of the Taylor series.
Calculate y’’’(1.1) using the given differential equation and the third term of the Taylor series.
Finally, substitute the calculated values into the Taylor series formula to approximate y(1.2). Using the provided information and the first four terms of the Taylor series, the approximation for y(1.2) is approximately 0.346.

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Answer:

BCA

Step-by-step explanation:

\(\pi ^2\), 9.88888888888, \(\sqrt{99}\)

Answer:

-8

Step-by-step explanation:

16(m) = -128

The opposite of multiplication is division, so 16(m) = =128 is equal to -128 divided by 16 = m

-128 divided by 16 = -8

16(-8) = -128

The statement that is true about rhombus is d. some rhombuses have four right angles.

A rhombus is a parallelogram with equal-length sides, though the angles at the opposing ends need not be equal, nor must the sides be parallel. If a rhombus is also a cube, it can have four right angles. It can be viewed as an equal-sided trapezoid as well.

A parallelogram has two sets of parallel sides, whereas a trapezoid only has one pair of parallel sides. Therefore, it is untrue that a trapezoid has two sets of parallel edges. Not all rectangles are squares, but they are all quadrilaterals with four right angles. A unique variety of parallelogram called a square has equal-length edges. Therefore, it is untrue to say that all circles are squares.

Complete Question:

which statement about a quadrilateral is true?

a. a rhombus has exactly one pair of parallel sides.

b. a trapezoid has two pairs of parallel sides.

c. all rectangles are squares.

d. some rhombuses have four right angles.

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In triangle DEF, with sides d=20 ft, e=25 ft, and angle F measuring 98°, the measure of angle D cannot be determined without additional information.

To find the measure of angle D in triangle DEF, given that d = 20 ft, e = 25 ft, and m∠F = 98°, we can use the fact that the sum of the angles in a triangle is 180°.

Let's label angle D as m∠D. We know that m∠F = 98°. Let's denote the measure of angle E as m∠E.

Using the fact that the sum of the angles in a triangle is 180°, we have:

m∠D + m∠E + m∠F = 180°

Substituting the given values, we have:

m∠D + m∠E + 98° = 180°

Now, let's solve for m∠D. First, subtract 98° from both sides:

m∠D + m∠E = 82°

Since the sum of the measures of angles D and E is 82°, we don't have enough information to determine the exact measure of angle D.

Additional information about the relationship between the sides or angles of the triangle would be needed to find the measure of angle D. Without such information, we cannot determine the specific measure of angle D in triangle DEF.

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hi, I'm no bot just in case...

the grapgh of the line shows y intercept of -9 and rate of change by 4

SoThe equation of the lline will be: \(y=4x-9\)