if z^2=x^3 + y^2, dx/dt=−2, dy/dt=−3, and z>0, find dz/dt at (x,y)=(4,0).dz/dt =

The explicit formula for f^−1(x) is f^−1(x) = ((x^2 - 9) / 8)^0.5. The graph of f^−1, f, and the line y = x will show that f and f^−1 are reflections about the line y = x.

To find the explicit formula for f^−1, we need to swap the roles of x and y in the equation f(x) = √(8x + 9) and solve for y.

1. Start with the equation f(x) = √(8x + 9).

2. Swap x and y to get x = √(8y + 9).

3. Solve for y by isolating it on one side of the equation.

Now, let's graph f^−1, f, and the line y = x to check if f and f^−1 are reflections about the line.

1. Plot the points on the graph of f by choosing values of x and calculating the corresponding values of f(x) using the equation f(x) = √(8x + 9).

2. Plot the points on the graph of f^−1 by choosing values of x and calculating the corresponding values of f^−1(x) using the equation f^−1(x) = ((x^2 - 9) / 8)^0.5.

3. Plot the line y = x.

4. Observe the graphs and check if the graph of f is a reflection of the graph of f^−1 about the line y = x. If they are reflections, they will be symmetric with respect to the line y = x.

By comparing the graphs of f and f^−1, we can confirm whether they are reflections about the line y = x. If the graphs are symmetric, it indicates that f and f^−1 are indeed reflections of each other.

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Answer: 34.5

Step-by-step explanation:

50 + 10 = 60 (birthday and dog walking)

60 - 7.50 = 53.5 (paid what she owed)

52.5 - 18 = 34.5 (bought a shirt)

The calculated value of the area of the circle with radius 7 feet is 153.93 square feet.

To find the area of a circle with radius 7 feet, we can use the formula A = πr^2, where A is the area and r is the radius.

Substituting the given value of radius, we get:

A = π(7)^2

Simplifying this expression, we get:

A = 49π square feet

Evauate the expression

So, we have

A = 153.93 square feet

Therefore, the area of the circle with radius 7 feet is 153.93 square feet.

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The probability of selecting a defective DVR randomly from the inventory is 0.08.

The probability that a randomly selected item from an inventory of 100 digital video recorders (DVRs) is defective is 0.08. Therefore, the answer to this question is 0.08.

The formula for calculating the probability of a defective digital video recorder is:P(defective) = number of defective DVRs / total number of DVRs in inventory According to the problem, there are 8 defective DVRs out of a total of 100 DVRs. This means that:P(defective) = 8 / 100= 0.08

Therefore, the probability of selecting a defective DVR randomly from the inventory is 0.08.

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The power series representation for the function f(x) = x sin(4x) can be found as follows:

Firstly, we can find the power series representation of sin(4x) using the formula for the sine function:$

$\sin x = \sum_{n=0}^{\infty} \frac{(-1)^n}{(2n+1)!}x^{2n+1}$$

Substitute 4x for x to obtain:$$\sin 4x

= \sum_{n=0}^{\infty} \frac{(-1)^n}{(2n+1)!}(4x)^{2n+1}

= \sum_{n=0}^{\infty} \frac{(-1)^n}{(2n+1)!}4^{2n+1}x^{2n+1}$$

Multiplying this power series by x gives:

$$x\sin 4x

= \sum_{n=0}^{\infty} \frac{(-1)^n}{(2n+1)!}4^{2n+1}x^{2n+2}$$

Therefore, the power series representation for the function

f(x) = x sin(4x) is:$$f(x)

= x\sin 4x

= \sum_{n=0}^{\infty} \frac{(-1)^n}{(2n+1)!}4^{2n+1}x^{2n+2}$$

Therefore, the power series representation for the function f(x) = x sin(4x) is:$$f(x) = x\sin 4x = \sum_{n=0}^{\infty} \frac{(-1)^n}{(2n+1)!}4^{2n+1}x^{2n+2}$$

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By solving an exponential equation, we can see that the investment will be doubled after 10.6 years.

The investment can be modeled by the exponential equation:

P(x) = A*(1 + 6.75%/100%)^x

Where A is the initial value of the investment (the amount invested).

We can simplify this to get:

P(x) = A*(1 + 0.0675)^x

The investment will be doubled when:

2*A = A*(1 + 0.0675)^x

We want to solve this for x.

2 = (1 + 0.0675)^x

2 = (1.0675)^x

If we apply the natural logarithm in both sides:

ln(2) = ln((1.0675)^x)

ln(2) = x*ln(1.0675)

ln(2)/ln(1.0675) = x

10.6 = x

The investment will be doubled after 10.6 years.

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Answer:

Step-by-step explanation:

2(x+y)=32  means :

x+y =16

(a) Is this an observational study or an experiment?

ans=Observational study – no treatment was imposed

(b) What are the explanatory and response variables?

ans=explanatory – time spent in child care from birth to age 4 response – adult rating of children’s behavior

d) Does this study show that child care causes children to be more aggressive? Explain.

No. Observational studies cannot show cause-and-effect

Researchers=someone whose job is to study a subject carefully, especially in order to discover new information or understand the subject better: She is a leading researcher in the field.

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Answer:

                 calories

Breakfast: 670  

Lunch:      555

Dinner:     910

Total = 2135 calories

Step-by-step explanation:

Let B, L and D, stand for the calories from Breakfast, Lunch, and Dinner

One day his calories from breakfast were 115 more, than his calories from​ lunch:  

B = L + 115

his calories from dinner were 200 less than twice his calories from lunch.:

D = 2L - 200

total caloric intake from meals was 2135:

B + L + D = 2135

------

We have B and D defined in terms of L from the first two equations, so use them in the third:

B + L + D = 2135

[L+115] + L + [2L-200] = 2135

4L - 85 = 2135

4L = 2220

L = 555 calories

B = L + 115

B = 555 + 115

B = 670 calories

D = 2L - 200

D = 2(555) - 200

D = 910 calories

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

CHECK

Does B + L + D = 2135 calories?

  670 + 555 + 910 = 2135?

 2135 = 2135?   YES

Answer:

Tony poured is 9% of the total

Step-by-step explanation:

Given data

The capacity of the container= 60000 liters

Amount of water that tony pours=  5400 liters

Let us compute the percentage to know if it is up to 10%

= 5400/60000*100

=0.09*100

=9%

Hence the amount of water Tony poured is 9% of the total

Answer:

He is wrong

Step-by-step explanation:

60 000 LB=55000

60 000 UB=65000

5400 LB= 5350

5400 UB=5450

65000x0.10=6500

55000x0.10=5500

he is wrong

Answer:

well, one john isnt that smart . he scored a 57% (0.5666....repeating)

Step-by-step explanation:

17 divided by

30

The number that corresponds to the null hypothesis and the alternative hypothesis will be 3 and 6 respectively.

Specify the correct number from the list below that corresponds to the appropriate null and alternative hypotheses for this problem.

It should be noted that the null hypothesis suggests that there's no statistical relationship between the variables.

The alternative hypothesis is different from the null hypothesis as it's the statement that the researcher is testing.

In this case, the number that corresponds to the null hypothesis and the alternative hypothesis will be 3 and 6 respectively.

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Answer:

John is 20 years old.

Step-by-step explanation:

Given the second mean is 18, it is equal to the first mean age plus John's unknown age. The sum is also divided by 2 because there are 2 values in the sum (1. John's age and 2. the mean, 16 yrs old).

Set up an equation: \(\frac{x+16}{2}=18\)

multiply both sides by 2: \(x+16=36\)

simplify: \(x=20\)

Answer:

D. 10

Step-by-step explanation:

9+4=13

x+3=13

x=10

The value of x is 10 which is correct option (D).

Angles of Intersecting Secants Theorem states that, If two lines intersect outside a circle, then the measure of an angle formed by the two lines is one half the positive difference of the measures of the intercepted arcs.

Given that,

Length of CW = 9 units,

Length of WV = 4 units,

Length of WU = 3 units,

Length of TW = x units,

⇒ Length of CW + Length of WV = Length of CV

⇒ 9 + 4

⇒  13

⇒ Length of TW + Length of WU = Length of CV

⇒ x + 3 = 13

⇒ x = 10 - 3

⇒ x = 10

Hence, the value of x is 10 which is correct option (D).

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Answer:

x=2

Step-by-step explanation

The value of x for this problem is given as follows:

x = 5.

Hence the angle measures are given as follows:

We have that angles A and D are congruent for this problem, meaning that they have the same measure.

Hence the value of x is obtained as follows:

7x - 3 = 5x + 7

2x = 10

x = 5.

Hence the angle measures are given as follows:

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Hi there!

»»————-　★　————-««

I believe your answer is:  

X - Intercept: (-9, 0)

Y - Intercept: (0, -6)

»»————-　★　————-««

Here’s why:

The x and y-intercepts of a line is where a given function intercepts the x or y axes.

I have graphed the equation given on a program. The graph shows that the line passes through the points (0, -6) and (-9, 0).

Therefore:

\(\rightarrow\text{The x-intercept of the given equation is }\boxed{\text{(-9,0)}}.\\\\\rightarrow\text{The y-intercept of the given equation is }\boxed{\text{(0,-6)}}.\)

See the graph attached below!

»»————-　★　————-««

Another way to solve this problem is to do this algebraically.

\(\text{X-Intercept: Substitute the 'y' variable for zero and solve for 'x'.}\\\\2x + 3y = -18\\-------\\\rightarrow2x+3(0)=-18\\\\\rightarrow2x=-18\\\\\rightarrow\frac{2x=-18}{2}\\\\\rightarrow\boxed{x=-9}\\-------\\\boxed{\text{X-Intercept: (-9,0)}}\)

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

\(\text{Y-Intercept: Substitute the 'x' variable for zero and solve for 'y'.}\\\\2x+3y=-18\\\-------\\\rightarrow2(0)+3y=-18\\\\\rightarrow3y=-18\\\\\rightarrow\frac{3y=-18}{3} \\\\\rightarrow\boxed{y=-6}\\\-----\\\\\boxed{\text{Y-Intercept: (0,-6)}}\)

»»————-　★　————-««

Hope this helps you. I apologize if it’s incorrect.  

Answer:

D

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

12x+16x= 4(3x+4x) because of the distributive property

Answer:

the answer would be a % because of the divisibility rule

The critical numbers of g(θ) on the interval 0 ≤ θ < 2π are:  θ = π/3, 2π/3, 4π/3, 5π/3, 7π/3, 8π/3, 10π/3, and 11π/3.

To find the critical numbers of g(θ) = 4θ - tan(θ) on the interval 0 ≤ θ < 2π, we need to find the values of θ where the derivative of g(θ) is equal to 0 or undefined.

First, we find the derivative of g(θ) using the chain rule and quotient rule:

g'(θ) = 4 - sec²(θ)

To find where g'(θ) is equal to 0, we set the derivative equal to 0 and solve for θ:

4 - sec²(θ) = 0

sec²(θ) = 4

Taking the square root of both sides, we get:

sec(θ) = ±2

Since sec(θ) = 1/cos(θ), we can rewrite this as:

cos(θ) = ±1/2

We know that on the interval 0 ≤ θ < 2π, the cosine function is positive in the first and fourth quadrants and negative in the second and third quadrants.

Therefore, we need to find the values of θ in the first and fourth quadrants where cos(θ) = 1/2, and the values of θ in the second and third quadrants where cos(θ) = -1/2.

For cos(θ) = 1/2, we have:

θ = π/3 or 5π/3 in the first quadrant
θ = 7π/3 or 11π/3 in the fourth quadrant

For cos(θ) = -1/2, we have:

θ = 2π/3 or 4π/3 in the second quadrant
θ = 8π/3 or 10π/3 in the third quadrant

Therefore, the critical numbers of g(θ) on the interval 0 ≤ θ < 2π are:

θ = π/3, 2π/3, 4π/3, 5π/3, 7π/3, 8π/3, 10π/3, and 11π/3.

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0.66 litres will be used if she wants to use equal amounts of the solution in 3 experiments.

In mathematics, division is the process of breaking a number into equal parts and determining how many equal parts can be made. For example, dividing 15 by 3 divides 15 into three equal groups of five.

The symbol '÷' or '/' is used to represent division.

Any positive number with no decimal or fractional part is referred to as a whole number. Because these criteria are met, the numbers 1,2,15,500, and 1546 are all whole numbers.

Children will practise dividing whole numbers as they begin to learn their multiplication tables. This is due to the fact that all of the numbers in the times tables are whole numbers!

They will also learn that division is the inverse operation to multiplication, which simply means that division and multiplication perform opposite functions in mathematics.

We have 2 litres of saline water

and want to divide them in 3 experiment equally, i.e.

2 ÷ 3 = 0.6667

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Answer:

Step-by-step explanation:

11

Answer:

3.76

Step-by-step explanation:

2.82×12÷9

33.84

3.76

Answer:

6.4 × 10^8

Step-by-step explanation:

Answer:

He will be able to carry the 6 boxes one go

Step-by-step explanation:

\(1000g = 1kg \\720g = \frac{720 \times 1}{1000} \\ = 0.72kg\)

So each box is 0.72kg

then 6 boxes =

\(0.72 \times 6 \\ = 4.32\)

and that's approximately 4 so in total the the 720g is actually 4kg and can be carried at once

Answer:

-2.25x = 30

Step-by-step explanation:

I hope this helps!

1.75, 1.5, 1.25, 1, 0.75, 0.5, 0.25, 0

(Idk if 0 would be considered to be positive but the rest are for sure.)

To find these just subtract 0.25 each time until you hit a negative number.