If x^2=y^2+2y+6 and dx/dt=8. Find dy/dt at the point (3,1). I don't know how to find it at the point or how to start finding the derivatives.

Answer: 1/4

Step-by-step explanation:

Answer:

-9

Step-by-step explanation: Definitely correct

The expression to represent the weekly revenue function for Windies Cricket is R = -0.006\(p^2\) + 15p.

The weekly revenue function for Windies Cricket can be determined by multiplying the quantity of jerseys demanded q by the wholesale price per jersey p. The given equation for the quantity demanded is q = -0.006p + 15. We can substitute this equation for q in the revenue equation to get an expression for the revenue as a function of the price.

R = q * p

R = (-0.006p + 15) * p

R = -0.006\(p^2\) + 15p

Therefore, the expression for the weekly revenue function is R = -0.006\(p^2\) + 15p. This function is a quadratic function, which means that it has a maximum or minimum point. Windies Cricket can use this function to determine the price that will maximize their revenue. They can do this by finding the vertex of the quadratic function, which will give them the price that will maximize their revenue.

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Answer:

264

Step-by-step explanation:

(251 + 277) / 2 = 264

Answer:

30x-18

Step-by-step explanation:

(6)(5x+−3)

=(6)(5x)+(6)(−3)

=30x-18

Answer:

Step-by-step explanation:

Bob made a little mistake there. 5 multiplied by 800 is actually equal to 4,000.

Answer:

X=11 trust me on my mom

Answer:

d

Step-by-step explanation:

Answer:

W=8

Step-by-step explanation:

First you divide both sides by 3 then you square root both sides getting 8

192/3=3w^2/3

64=w^2

w=8

Answer:  h^-1(-4)= -2

Step-by-step explanation:

To determine the function that models the data, we need to analyze the relationship between the cost per photo and the number of photos a customer buys. From the given information, we can observe that the cost per photo varies inversely with the number of photos. This implies that as the number of photos increases, the cost per photo decreases, and vice versa.

To model this relationship, we can use the inverse variation equation, which can be expressed as:

y = k/x

Here, y represents the cost per photo, x represents the number of photos, and k is the constant of variation.

Let's examine the data given in the table to find the value of k:

Number of Photos (x) Cost per Photo (y)

10 10

25 4

50 2

100 1

We can see that as the number of photos increases, the cost per photo decreases. We can use any pair of values from the table to solve for k. Let's choose the pair (50, 2):

2 = k/50

Solving for k:

k = 2 * 50 = 100

Now that we have the value of k, we can write the function that models the data:

y = 100/x

Therefore, the function that models the data is y = 100/x, where y represents the cost per photo and x represents the number of photos a customer buys.

The value of x in the pentagon JKLMN is 7.2.

A polygon is a plane figure that is described by a finite number of straight line segments connected to form a closed polygonal chain.

The pentagons ABCDE and JKLMN are similar.

when two figures have the same shape but their sizes are different, then such figures are called similar figures.

We need to find the value of x.

1/1.8=4/x

Apply cross multiplication

x=4×1.8

x=7.2

Hence, the value of x in the pentagon JKLMN is 7.2.

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Answer:

Step-by-step explanation:

a and d

The length of AC is 12.5 and the length of AD is 3.

A triangle is a three-sided polygon because it has three edges and three vertices. The most important attribute of a triangle is the sum of its internal angles to 180 degrees

Given triangle ABC,

and D is a point on AB and E is a point on AC,

and forms a triangle ADE,

and  DE is parallel to AC,

taking ΔABC and ΔBDE

∠B = ∠B  (common angle)

because DE is parallel to AC, so corresponding angles are equal,

so ∠A = ∠D

and ∠C = ∠E

ΔABC ≈ ΔBDE (triangles are similar)

since both triangles are similar the ratio of their corresponding sides is equal,

AB/BD = AC/DE = BC/BE

given BD = 2, BE = 4, DE = 5 and EC = 6

BC = EC + BE = 4 + 6

BC = 10

AC/DE = BC/BE

AC = 5(10/4)

AC = 12.5

and AB/BD = BC/BE

AB = 2(10/4)

AB = 5

AD = AB - BD

AD = 5 - 2

AD = 3

Hence AC = 12.5 and AD = 3.

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The figure is in image.

According to the FIFO method, the ending inventory balance for Commodity Z is $1,405

FIFO means that earlier inventory is sold first and later inventory would be the last goods left.

Since there were 23 units left, all 16 units from the last purchase and 7 units from the second purchase would be available:

= (16 x 62) + (7 x 59)

= 992 + 413

= $1,405

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1. Initial prediction for the data set with smaller Mean Absolute Deviation was Period A. Prediction was wrong.

2. The Mean Absolute Deviation for Period A is 1.8 and Period B, 1.1

This means that period B has a smaller Mean absolute deviation.

We start by finding the mean for each set;

Period A: Mean = (1×92 + 1×94 + 3×95 + 1×96 + 2×97 + 1×99 + 1×100)/10

= 960/10

= 96

Period B: Mean = (1×94 + 3×95 + 1×96 + 4×97 + 1×98)/10

= 961/10

= 96.1

Period A:

Mean Absolute Deviation = ((92-96) + (94-96) + 3(95-96) + (96-96) + 2(97-96) + (99-96) + (100-96))/10

Mean Absolute Deviation = (4 + 2 + 3 + 0 + 2 + 3 + 4)/10

Mean Absolute Deviation = 1.8

Period B:

Mean Absolute Deviation = ((94-96.1) + 3(95-96.1) + (96-96.1) + 4(97-96.1) + (98-96.1))/10

Mean Absolute Deviation = (2.1 + 3.3 + 0.1 + 3.6 + 1.9)/10

Mean Absolute Deviation = 1.1

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Answer:

58.45

Step-by-step explanation:

Use BIDMAS

14.5 X 3.1 = 44.95

44.95 + 13.5 = 58.45

Answer:

58.45

Step-by-step explanation:

Step-by-step explanation:

\(15^{10}+15^{11}+15^{12}+15^{13}\)

You can look at it like this:

\(15^{10}+15^{11}+15^{12}+15^{13}=15^{10}+15^{10}\cdot15+15^{10}\cdot15^2+15^{10}\cdot15^3\\\\=15^{10}\cdot(1+15+15^2+15^3)=15^{10}\cdot(1+15+225+3375)\\\\=15^{10}\cdot3616=15^{10}\cdot32\cdot113=15^{10}\cdot2^5\cdot113=2.085.167.812.500.000\)

Answer:

Below.

Step-by-step explanation:

15^10 + 15^11 + 15^12+ 15^13

= 15^10(1 + 15 + 15^2 + 15^3)

= 15^10 * 3616

= 2,085,167,812,500,000

Answer:

Step-by-step explanation: a= E

b=D

c=A

Answer:

A. E

B. D

C. A

Step-by-step explanation:

you can start by dividing the total length of the road by the distance that can be repaired per week:

13 km ÷ 3 1/2 km/week = 3.71 weeks

Rounding up, it will take 4 weeks to repair the entire 13 km stretch of road.

Answer:

1/2  of all the days in the city are sunny , also the city does not have sunny days most of the time

Step-by-step explanation:

Given data :

90% chance of sunny day when it rains the previous day

30% chance of rain when it is sunny the previous day

Determine :

If the city has sunny days most of the time and the fraction of the days that is sunny

First step : construct a transition matrix

\(P = \left[\begin{array}{ccc}0.70&0.3&\\0.10&0.90&\\\end{array}\right]\)

lets assume the frequency of the long = β = [ β1, β2 ]

from our matrix equation we can say ; β = βP

β1 = 0.70β1 + 0.30β2 ---- ( 1 )

β2 = 0.10β1 + 0.90β2 ----- ( 2 )

Given that : β1 + β2 = 1 , hence β2 = 1 - β1

plug this value into equation 1

β1 = 0.70β1 + 0.30( 1 - β1 )

∴ β1 = 0.5

also β2 = 1 - 0.5 = 0.5

( This means that half of all the days in the city are sunny ) also the city does not have sunny days most of the time

Answer:

(0.5X) - 3 = Distance from the finish line

Step-by-step explanation:

Given that a student is running a 3-kilometer race, and runs 1 kilometer every 2 minutes, to determine the function that describes the distance from the finish line after X minutes, the following calculation must be performed:

1 = kilometers for every 2 minutes

X = every number of minutes

1/2 = 0.5 = kilometers per minute

(0.5X) - 3 = Distance from the finish line

Thus, if the student runs for 4 minutes, the equation would operate as follows:

0.5 x 4 - 3 = X

2 - 3 = X

-1 = X

Answer:

The slope of the tangent line at x = 1 is -25.

Step-by-step explanation:

We are given the function:

\(f(x)=-7x^3-8x+2x^2\)

And we want to find the slope of the tangent line at x = 1.

The slope of the tangent line at a point for a function is given by its derivative. Find the derivative of the function:

\(f'(x)=-21x^2+4x-8\)

Then the slope of the tangent line at x = 1 is:

\(f'(1)=-21(1)^2+4(1)-8=-25\)

Answer:

10

Step-by-step explanation:

The vertices of ABCD after 90 degrees clockwise rotation about point C are: A' (0,6), B' (3,7), C' (4,6) and D' (4,3)

The image of the polygon ABCD is not given; however, the question can still be answered because the coordinates are known.

The vertices of polygon ABCD are given as:

A = (4, 6)

B = (5, 3)

C = (4, 2)

D = (1, 2)

The rule of rotation about point C is:

(x,y) = (a + b - y, x + b - a)

Where:

(a, b) = (4, 2) --- the point of rotation.

So, we have:

(x,y) = (4 + 2 - y, x + 4 - 2)

(x,y) = (6 - y, x + 2)

The above means that:

A' = (6 - 6, 4 + 2) = (0,6)

B' = (6 - 3, 5 + 2) = (3,7)

C' = (6 - 2, 4 + 2) = (4,6)

D' = (6 - 2, 1 + 2) = (4,3)

Hence, the image of the rotation and their vertices (i.e. coordinates) are:

A' = (0,6)

B' =  (3,7)

C' = (4,6)

D' =  (4,3)

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Answer:

triangle and rectangle??

Step-by-step explanation:

Answer:

\(\Large \boxed{\sf 384 \ m^2}\)

Step-by-step explanation:

Surface area ⇒ area of 2 triangles + area of 3 rectangles

\((8 \times 3 \times 0.5 \times 2)+(20 \times 5 \times 2+20 \times 8)=384\)

Answer:

Surface Area = 384 m²

Step-by-step explanation:

The given figure is a triangular prism.

The surface area of a triangular prism is made up of:

From inspection of the diagram, the dimensions of the triangular bases are:

\(\boxed{\begin{aligned}\textsf{Area of a triangle}&=\dfrac{1}{2} \times \sf base \times height\\\\\implies \textsf{Area of triangular base}&=\dfrac{1}{2} \times 8 \times 3\\&=4 \times 3\\&=12\; \sf m^2 \end{aligned}}\)

From inspection of the diagram, there are two congruent rectangles with dimensions:

and one rectangle with dimensions:

\(\boxed{\begin{aligned}\textsf{Area of a rectangle}&=\sf width \times length\\\\\implies \textsf{Area of rectangle 1}&=5 \times 20\\&=100\; \sf m^2 \\\\\implies \textsf{Area of rectangle 2}&=8 \times 20\\&=160\; \sf m^2\end{aligned}}\)

Therefore, the total surface area of the given triangular prism is:

\(\begin{aligned}\textsf{Total Surface Area}&=\sf 2\;Triangles + 2\;Rectangle\;1+Rectangle\;2\\& = 2 \times 12+ 2 \times100+160\\& = 24+200+160\\& = 224+160\\& = 384\; \sf m^2\\\end{aligned}\)

An equation which is true include the following: A. 4 × n × n × n × n = 4n⁴.

In Mathematics, an exponent is a mathematical operation that is typically used in conjunction with an algebraic expression in order to raise a quantity to the power of another.

This ultimately implies that, an exponent is represented by the following mathematical expression;

bⁿ

Where:

By applying the multiplication law of exponents for powers to each of the expressions, we have the following:

4 × n × n × n × n = 4n⁴

4 × n⁴ = 4n⁴

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For the fractions, the calculation of 3/5 of 2/3 of 3/4 of 560 is equal to 168.

To calculate 3/5 of 2/3 of 3/4 of 560, break it down step by step:

Step 1: Calculate 3/4 of 560:

3/4 × 560 = (3 × 560) / 4 = 1680 / 4 = 420

Step 2: Calculate 2/3 of the result from Step 1:

2/3 × 420 = (2 × 420) / 3 = 840 / 3 = 280

Step 3: Calculate 3/5 of the result from Step 2:

3/5 × 280 = (3 × 280) / 5 = 840 / 5 = 168

Therefore, 3/5 of 2/3 of 3/4 of 560 is equal to 168.

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