A bead slides along the curve x^3+xy^2 = 2x+3. As it reaches the point (1,2), its x-coordinate is increasing at the rate of 3 cm/s. How fast is the y-coordinate of the bead changing at that instant?

Step-by-step explanation:

the correct answer is exponent because 6 is its power.

hope this answer will help u.

have a great time.

Answer:

0.81

Step-by-step explanation:

\(\frac{100-19}{100} =0.81\)

Step-by-step explanation:

To make your answer concrete, suppose there will be 30 guests and the genie will tell you either x-bar= 5 cans or M=3 cans. Which of these two measures would best help you determine how many can you should have on hand?

Answer:

this just helped me so much

Step-by-step explanation:

Omg ilysm and thank you for spreading such positivity Muaahhh<3

The solution to the equation 3.3 + 4x = -6.9x + 6.6, rounded to the nearest tenth, is x ≈ 0.3.

To solve the equation 3.3 + 4x = -6.9x + 6.6, we need to isolate the variable x on one side of the equation.

First, let's simplify the equation by combining like terms:

3.3 + 4x = -6.9x + 6.6

Next, let's move the variable terms (4x and -6.9x) to one side and the constant terms (3.3 and 6.6) to the other side:

4x + 6.9x = 6.6 - 3.3

Combine the x terms on the left side:

10.9x = 3.3

Now, divide both sides of the equation by 10.9 to solve for x:

x = 3.3 / 10.9

Using a calculator, we can find the decimal approximation of x:

x ≈ 0.3028

Rounding to the nearest tenth, the solution to the equation is x ≈ 0.3.

In summary, the solution to the equation 3.3 + 4x = -6.9x + 6.6, rounded to the nearest tenth, is x ≈ 0.3.

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Answer:

a=14.9

Step-by-step explanation:

first tan25=0.4663076582

so 32tan(25)=a

32*0.4663076582=a

a=14.921845061 or

a=14.9√√√√√√√√√√√√√

i hope it will help you

The value of pH for a sample of grape juice would be 4.4.

Given that,

A grape juice sample has a concentration of hydroxide ions of \(1.4 \times10^{-10} m\)

Now, The hydroxyl ion concentration in grape juice is, \(1.4 \times10^{-10} m\).

Hence, the value of pOH will be;

\(pOH = - log[1.4 \times10^{-10} ]\)

\(pOH = 9.6\)

Now the value of pH will be;

\(pH = 14 - pOH\)

\(pH = 14 - 9.6\)

\(pH = 4.4\)

Rounded to the nearest tenth.

Therefore, the value of pH is 4.4

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The grape juice sample has a hydroxide ion concentration of 1.4 x 10−10 m. After calculating for the hydronium ion concentration, we use the formula pH = -log [H3O+] to determine that the pH of the sample is approximately 4.2.

The subject of your question pertains to chemistry, specifically relating to the concept of pH and its calculation from the hydroxide ion concentration. As the sample of grape juice you mentioned has a hydroxide ion concentration of 1.4 x 10−10 m, we first need to find the concentration of hydronium ions. This can be determined using Kw (the ion product of water) which equals [H3O+][OH-] = 1.0 x 10-14 at 25°C. Given your hydroxide ion concentration, we have [H3O+] = Kw / [OH-], so [H3O+] = (1.0 x 10^-14) / (1.4 x 10^-10) = 7.14 x 10^-5 M.

Now, we can calculate the pH using the formula pH = -log [H3O+]. Substituting the value of [H3O+] into the equation gives pH = -log(7.14 x 10^-5) = 4.15. Rounded to the nearest tenth, this results in a pH value of 4.2 for your grape juice sample.

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Answer:

9. (a) 1/4

   (b) remove 3 alphabet cards

   (c)  add 4 number cards

10.  1/8

Step-by-step explanation:

Question 9

Given:

⇒ total number of cards = 8 + 10 + 6 = 24 cards

\(\mathsf{Probability \ of \ an \ event \ occurring = \dfrac{Number \ of \ ways \ it \ can \ occur}{Total \ number \ of \ outcomes}}\)

(a) P(picture card) = 6/24 = 1/4

(b) P(alphabet card) = 10/24 = 5/12

If we remove 3 alphabet cards from the box

⇒ number of alphabet cards = 10 - 3 = 7

⇒ total number of cards = 24 - 3 = 21

Therefore, P(alphabet card) = 7/21 = 1/3

(c)  P(number card) = 8/24 = 1/3

If we add 4 number cards to the box:

⇒ number of number cards = 8 + 4 = 12

⇒ total number of cards = 24 + 4 = 28

Therefore, P(number card) = 12/28 = 3/7

--------------------------------------------------------------------

Question 10

Given:

⇒ area of ΔSDR = area of ΔPRQ = 1/2 × 4 × 4 = 8 cm²

As PR = SD = 4cm

Area of rectangle = (4 + 4) × (12 + 4) = 128 cm²

P(point lies in ΔSDR) = 8/128 = 1/16

P(point lies in ΔPRQ) = 8/128 = 1/16

P(point lies in ΔSDR) OR P(point lies in ΔPRQ) = 1/16 + 1/16 = 2/16 = 1/8

Answer:5

2

Step-by-step explanation:

7

no way i can do math like that

Answer:

x= -7 and x= -3

Step-by-step explanation:

(x+7)(x+3)=0 (Think about the numbers that will add to 10 and multiply to 21)

x= -7 and x= -3

Answer:

x = −3 or x = −7

Step-by-step explanation:

Let's solve your equation step-by-step.

x^2 +  10x + 21 = 0

Step 1: Factor left side of equation.

(x+3) (x+7) = 0

Step 2: Set factors equal to 0.

x + 3 = 0 or x + 7 = 0

x = −3 or x = −7

I hope this helps you with your assignment and have a fantastic day! :D

The maximum angle of the incline for the car to be at rest using only friction is 38.7° if, for the car on the incline, the coefficient of static friction is 0.8 and the coefficient of kinetic friction is 0.6.

If the car is at rest on the incline, the force of gravity acting on the car down the incline is balanced by the force of static friction acting up the incline. The maximum angle \($\theta$\) of the incline is the angle at which the force of static friction is at its maximum, which is given by the product of the coefficient of static friction and the normal force.

Let's assume that the mass of the car is m and the incline makes an angle of \($\theta$\) with the horizontal. Then, the force of gravity acting on the car down the incline is given by \($mg\sin(\theta)$\), where g is the acceleration due to gravity. The normal force acting on the car perpendicular to the incline is given by \($mg\cos(\theta)$\).

For the car to be at rest on the incline, the force of static friction acting up the incline must be equal in magnitude to the force of gravity down the incline. Therefore, we have:

\($$\mu_s mg\cos(\theta) = mg\sin(\theta)$$\)

here \($\mu_s$\) is the coefficient of static friction. Simplifying this equation,

we get:

\($$\tan(\theta) \leq \mu_s$$\)

Therefore, the maximum angle \($\theta$\) of the incline is:

\($$\theta \leq \tan^{-1}(\mu_s)$$\)

Substituting the value of \($\mu_s = 0.8$\), we get:

\($$\theta \leq \tan^{-1}(0.8) \approx 38.7^{\circ}$$\)

Therefore, the maximum angle of the incline for the car to be at rest using only friction is approximately 38.7°.

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The exponential function that models the population of Trenton, NJ since 1980 is: P(t) = 92124 * \((1-0.0272)^t\)

1. The initial population in 1980 is given as 92,124.

2. The rate of decrease is 2.72% or 0.0272 in decimal form.

3. Since the population is decreasing, we subtract the rate from 1 (1 - 0.0272 = 0.9728).

4. The exponential function is written in the form P(t) = P₀ * \((1 +r)^t\) , where P₀ is the initial population, r is the rate of change, and t is the number of years after 1980.

5. In this case, P₀ = 92124, r = -0.0272, and we want to find the population at time t.

6. Therefore, the exponential function that models this situation is P(t) = 92124 * \((0.9728)^t\) .

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Answer:

H. 163.3

Step-by-step explanation:

The formula for the surface area of a cone is πrl(area of the side) + π\(r^{2}\)(area of the base), where l is the slant height and r is the radius. We know that the radius is 4 and the slant height is 9, so we plug it into the equation to get π(4)(9) + \(\pi r^{2}\) = 36π+16π = 52π which rounds to 163.3.

Answer:

Step-by-step explanation:

d=-10--1=-10+1=-9

a(n) = a +(n-1)d

a(n) = -1 +(n-1)-9

a(204) = -1 +(204-1)-9

           =-1828

hope this help

Answer:

12 children

Step-by-step explanation:

1/4 of 16 is 4. 16 subtract the 4 slices she sold is 12 slices of cake for each of her children.

Answer:

12children (wow)

Step-by-step explanation:

1/4 is equal to 4/16 thats how much cake was left so she gave away 12 piecs (3/4 of the cake or 12/16)

16-4 = 12

The probability that the volume of a can chosen at random is ≥382 is 0.47725

Probability is the likelihood or chance that an event will occur. For the given question, we need to calculate the  z value as shown;

\(z=\dfrac{x-\mu}{\sigma}\)

Given the following parameters

\(x=382mL\\\mu (mean)=372mL\\\sigma(S.D)=5mL\)

Substitute

\(z=\dfrac{382-372}{5} \\z=\dfrac{10}{5}\\ z=2\)

In order to calculate the probability that the volume of a can chosen at random is ≥382, we will look for (z≥2)

z≥2 according to probability table is equivalent to 0.47725

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Answer:

isolate the variable by dividing each side by factors that dont contain the variables. so this mean -3(x+n)=x becomes x= -3n over 4, I hope this helps.

Answer:

Explanation:

FIrst we find the angle that is complementary to 55 degrees.

55 + k = 90

k = 90 - 55 = 35

Now we find the blue angle

The blue angle forms the interior angle of the triangle; therefore,

35 + 35 + blue = 180 (the angles in a triangle add up to 180 )

70 + blue = 180

blue = 180 - 70

blue = 110

Finally, we are in a position to find the yellow angle x.

The yellow angle x is supplementar to the blue angle; therefore,

110 + x = 180

subtracting 110 from both sides gives

x = 180 - 110

x = 70

which is our answer!

The derivative dy/dx for the implicit function 3xy² - (5y² + 2x)³ = 8x - 11 is: dy/dx = (6xy - 30y(5y² + 2x)² + 8)/(6x(5y² + 2x)² - 6y²)

To find the derivative dy/dx using implicit differentiation, we differentiate both sides of the equation with respect to x, using the chain rule for terms containing y.

Starting with the left side of the equation, we have:

d/dx [3xy² - (5y² + 2x)³] = d/dx [8x - 11]

Applying the chain rule to the first term, we get:

(6xy + 6y² dy/dx) - 3(5y² + 2x)² (10y dy/dx + 2) = 0

Simplifying and grouping the terms involving dy/dx, we get:

(6xy - 30y(5y² + 2x)² + 8)/(6x(5y² + 2x)² - 6y²) = dy/dx

Therefore, the derivative dy/dx of the given implicit function is: dy/dx = (6xy - 30y(5y² + 2x)² + 8)/(6x(5y² + 2x)² - 6y²)

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An essential concept in mathematics and can be applied to a variety of fields such as physics, economics, and engineering.

The slope of a line in a Cartesian plane is a numerical representation of its steepness and inclination relative to the x-axis.

The slope of a straight line refers to the rise or fall of the y-coordinate as it moves from left to right along the x-axis.

There are a few different ways to interpret the slope of a line, but generally it can be thought of as the rate at which the dependent variable changes with respect to the independent variable.
When the slope is positive, the line rises from left to right, indicating that the dependent variable is increasing as the independent variable increases.

In other words, there is a direct relationship between the two variables.

Conversely, when the slope is negative, the line falls from left to right, indicating that the dependent variable is decreasing as the independent variable increases.

This means that there is an inverse relationship between the two variables.
The magnitude of the slope can also provide information about the relationship between the variables.

If the slope is close to zero, then the relationship between the two variables is weak or nonexistent.

However, if the slope is large in magnitude (i.e. close to 1 or -1), then there is a strong relationship between the variables.

A slope of zero indicates that there is no change in the dependent variable as the independent variable changes, while a slope of undefined means that the line is vertical and has no slope.
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The length of the QR is 16 cm when PQR ~MNO

In the given question, it is given that two similar triangles as PQR ~MNO

Then, the corresponding sides will be in equal proportion to each other as follows

PQ / MN = PR / MO = QR / NO

We need to find the length of the side QR

As above relations are given,

\(\frac{PQ}{MN}\) = \(\frac{PR}{MO}\) = \(\frac{QR}{NO}\)

\(\frac{30}{10}\) = \(\frac{5x + 7}{x+5}\) = \(\frac{4x}{\frac{16}{3} }\)

Equating all the fractions, equal to each we'll find

\(\frac{5x + 7}{x+5}\) = \(\frac{30}{10}\)

5x + 7 = 3(x +5)

5x + 7 = 3x + 15

2x = 8

x = 4

We know that, the length of the QR = 4x cm = 4 x 4 cm = 16 cm

Therefore, the length of the QR is 16 cm when PQR ~MNO

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Answer:

n+8+6

Sum means = and and means + so n+8+6

The interval where the derivative function f'(x) has a relative maximum is -2.478 and 1.732 (B) only.

To find the relative maximum of a function, we need to find the critical points of the derivative function. Critical points are where the derivative function is equal to zero or undefined. In this case, the derivative function is f'(x) = sin(x^2 − 3).

To find the critical points, we need to set the derivative function equal to zero and solve for x:
sin(x² − 3) = 0

x² − 3 = nπ, where n is an integer

x² = nπ + 3

x = ±√(nπ + 3)

We need to find the values of x that are in the interval −3 < x < 3. By plugging in different values of n, we can find the critical points in this interval:

n = 0: x = ±√3 ≈ ±1.732

n = 1: x = ±√(π + 3) ≈ ±2.478

n = 2: x = ±√(2π + 3) ≈ ±2.915 (not in the interval)

So the critical points in the interval are -2.478, -1.732, 1.732, and 2.478.

To determine which of these are relative maximums, we need to look at the sign of the derivative function on either side of the critical points. If the derivative function changes from positive to negative at a critical point, then that point is a relative maximum.

At x = -2.478, the derivative function changes from positive to negative, so this is a relative maximum.

At x = -1.732, the derivative function changes from negative to positive, so this is not a relative maximum.

At x = 1.732, the derivative function changes from positive to negative, so this is a relative maximum.

At x = 2.478, the derivative function changes from negative to positive, so this is not a relative maximum.

Therefore, the values of x in the interval −3 < x < 3 where f has a relative maximum are -2.478 and 1.732.

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Answer:

this is a math problem that involves using the Pythagorean theorem. The ladder, the roof and the ground form a right triangle, where the ladder is the hypotenuse and the roof and ground are the legs. The length of the ladder can be found by using this formula:

ladder^2 = roof^2 + ground^2

Plugging in the given values, we get:

ladder^2 = 3^2 + 2^2

ladder^2 = 9 + 4

ladder^2 = 13

To find the length of the ladder, we need to take the square root of both sides:

ladder = sqrt(13)

Using a calculator, we can approximate this value as:

ladder ≈ 3.6

Rounding to the nearest tenth, we get:

ladder ≈ 3.6 meters

Therefore, the ladder is about 3.6 meters long.

Step-by-step explanation:

For a straight line graph, the point at which the line crosses the y axis is called the y intercept. From the information given, the line crosses the y axis at - 5. This means that the y intercept is - 5

We would write the equation in the slope intercept form whicg is expressed as

y = mx + c

Where m represents the slpoe

We would substitute x = 2, y = 3 and c = - 5 in the equation above to determine the slope, m. It becomes

3 = m * 2 - 5

3 = 2m - 5

3 + 5 = 2m

2m = 8

m = 8/2

m = 4

The equation would be

y = 4x - 5y interceptF

1.-

Circumference = 2 pi r

= 2 * 3.14 * 28.1/2

= 44.1 yd letter B

2.- Circumference = 2*pi* r

= = 2*3.14*11

= 69.08 in letter H

3.- Area = pi*r^2

= 3.14*(9)^2

= 254.34 mm^2 Letter B

Answer:

Step-by-step explanation:

The proper loop condition test to quit iterating if x < 10 and y > 3 would be:

while (!(x < 10 && y > 3))

This condition will be true as long as either x is not less than 10 or y is not greater than 3. Once both conditions are met, the loop will exit.

The output of the code fragment would be:

"That is all. Goodbye"

Since the condition "x > 5" in the if statement is not true (x is equal to 5), the printf statement inside the if block will not be executed. The following printf statements outside the if block will be executed and will print the corresponding text.

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Answer:

number 1 is right but i don't know about the other ones

Step-by-step explanation:

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

Explanation:

Let's calculate the volume of one small spherical bead

V = (4/3)*pi*r^3

V = (4/3)*pi*3^3

V = 36pi

The volume of 27 such identical beads is 27*36pi = 972pi cubic units.

----------

This is the new volume and we'll use this to find the radius r of the larger sphere.

V = (4/3)*pi*r^3

972pi = (4/3)*pi*r^3

3*972pi = 4pi*r^3

2916pi = 4pi*r^3

r^3 = (2916pi)/(4pi)

r^3 = 729

r = (729)^(1/3)

r = 9 units is the radius of the larger gold sphere