Assume x and y are functions of t. Evaluate х for the following dt y² = 2x² + 6 3 +; dx = 3, X = 1, y = 2 dt dy dt II (Round to two decimal places as needed.) Assume x and y are functions of t. Evaluate dy for 4xy - 4x + 3y3 = - 129, with the conditions dx = -12, X = 3, y = -3. dt dt dy dt (Type an exact answer in simplified form.) dy dx Assume x and y are functions of t. Evaluate for 3xe Y = 9 - In 729 + 6In x, with the conditions = 6, x= 3, y=0. dt dt dy dt (Type an exact answer in simplified form.)

Answer: 2.5

Step-by-step explanation: subtract 2x from both sides and get 4x-2=8 so then add 2 on both sides to get 4x=10 and last step is to divide both sides by 4 which wild get you x=2.5

No, Green's theorem cannot be applied to the given line integral -5x dx + 3y dy / (x² + y⁴) over the unit circle x² + y² = 1, because C is not positively oriented.

In order to apply Green's theorem, the curve must be a simple, closed, and positively oriented boundary of a region with a piecewise smooth boundary, and the vector field must have continuous partial derivatives in the region enclosed by the curve.

In this case, while the unit circle is a simple and closed curve with a smooth boundary, it is not positively oriented since the orientation is counterclockwise, whereas the standard orientation is clockwise.

Therefore, we cannot apply Green's theorem to this line integral.

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The result of ANDing 11001111 with 10010001 is 10000001. Option C

To find the result from ANDing (bitwise AND operation) the binary numbers 11001111 and 10010001, we compare each corresponding bit of the two numbers and apply the AND operation.

The AND operation returns a 1 if both bits are 1; otherwise, it returns 0. Let's perform the operation:

11001111

AND 10010001

10000001

By comparing each corresponding bit, we can see that:

The leftmost bit of both numbers is 1, so the result is 1.

The second leftmost bit of both numbers is 1, so the result is 1.

The third leftmost bit of the first number is 0, and the third leftmost bit of the second number is 0, so the result is 0.

The fourth leftmost bit of the first number is 0, and the fourth leftmost bit of the second number is 1, so the result is 0.

The fifth leftmost bit of both numbers is 0, so the result is 0.

The sixth leftmost bit of both numbers is 1, so the result is 1.

The seventh leftmost bit of both numbers is 1, so the result is 1.

The rightmost bit of both numbers is 1, so the result is 1.

Option C

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Answer:

Given : PQ = RQ

to find : angle B

Answer:

b=40

Step-by-step explanation:

PQ=RQ

That means both sides are the same length which also means they both have the same angel measure of 140.

A super easy way to solve this would be to realize that where p is, the angel is 140.

A straight line is 180.

b and 140 are supplementary angels. [which means they equal 180]

To find b you can make an equation.

b+140=180

or

180-140=b

I'll show you both.

First one you would subtract 140 on both sides to get the variable alone, leaving you with b=40.

For the second one, you just do 180-140 and it also equals 40.

Either way it leaves you with b=40

If you need any more help with angels and whatnot, don't be afraid to reach out. I hope that helps! <3

Answer:

75%

Step-by-step explanation:

In order to get a percent all you have to do is take the fraction and multiply that decimal by 100! So 33/44=.75 and .75*100= 75%

Answer:

i believe the answer would be 75 but i am not sure.

Step-by-step explanation:

If a stock priced at $40 increases at a rate of 8% per year then it will take 2.91 years for the value of the stock to reach $50.

We will use a logarithmic expression to determine the number of years it will take for a stock priced at $40 to increase at a rate of 8% per year and reach a value of $50.

Firstly, setting up the exponential growth formula:
Final value = Initial value \(\times (1 + Rate)^{Years}\)

Then, plug in the values:
$50 = $40 \(\times (1 + 0.08)^{Years}\)

Solving for Years using a logarithmic expression:
\((1 + 0.08)^{Years}\) = $50 / $40 = 1.25

Applying the logarithm base change formula \((log_a b = ln b / ln a)\):
Years = ln(1.25) / ln(1.08)

Evaluating the logarithmic expression:
Years ≈ 2.9128

So, it will take approximately 2.91 years for the value of the stock to reach $50.

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Z is the value from the standard normal distribution for the chosen degree of confidence; for example, Z=1.96 for a 95% level of confidence. In real life, we frequently don't know what the population standard deviation () is.

The percentage of times you anticipate coming close to the same estimate if you repeat your experiment or resample the population in the same way is known as the confidence level.

A 95% confidence interval is a range of values above and below the point estimate that, with 95% confidence, contains the true value for the population..

A normal distribution is a kind of continuous probability distribution in which the majority of data points cluster near the middle of the range, but the remaining ones taper off symmetrically toward either end. The distribution's mean is another name for the midpoint of the range.

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Answer:

84 ÷ -12 = -7

21 ÷ -3 = -7

Step-by-step explanation:

49 ÷ -7 = -7

Means that __ ÷ __ must equal -7

There are many options, here are a few:

84 ÷ -12 = -7

or -84 ÷ 12 = -7

21 ÷ -3 = -7 etc

Answer:

Tomas

Step-by-step explanation:

Divide Distance by Time

\(\frac{distance}{time}\) = speed

Answer:

Tomas is the fastest

Step-by-step explanation:

To find out who is the fastest, divide the distance by the time to get the unit rate. (The amount they drove each hour.)

Maren: 60 / 1 = 60

Safiya: 120 / 3 = 40

Tomas: 84 / 1.2 = 70

Cam: 75 / 1.5 = 50

Tomas has the largest unit rate therefore he is  the fastest.

Answer:

1000000000000

Step-by-step explanation:

if you =have 10^12 power you multiply 10*10 12 times

so to work it out you would do:

10*10*10*10*10*10*10*10*10*10*10*10=1000000000000

and since your bored to death here's a cool pic

Answer:14x+4

Step-by-step explanation:

edit: the answer is 14x + 4

(the reason i edited was to cause less confusion)

Answer:

a

Step-by-step explanation:

23 tickets are purchased for children and 9 tickets are purchased for adults.

Given,

In the question:

A group entering a zoo purchased 32 admission tickets for a total of $148. Adult tickets cost $7. 50, and tickets for children cost $3. 50.

To find the how many of each type of ticket were purchased?

Now, According to the question:

It is given in the question that 32 tickets are purchased by group which cost total $148.

Let the number of children of the group who are entering the zoo be x. Then the number of adults will be 32- x

Now cost of one ticket for adult = $7.50

Total amount spent on adult tickets = 7.50 × (32-x)

Similarly, cost of one ticket for child= $3.50

Total amount spent on children tickets = 3.50 × x =3.5x

Total amount spent by group on tickets =  $148

⇒ 7.5 × (32-x) + 3.5x = 148

⇒ 240 - 7.5x + 3.5x = 148

⇒ 7.5x - 3.5x = 240 - 148

⇒ 4x = 92

⇒ x = 23

Children = 23

Adults = 32-x = 32-23 = 9

Hence, 23 tickets are purchased for children and 9 tickets are purchased for adults.

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Answer: No, it is not a function

Why not? Because the graph fails the vertical line test. It is possible to draw a single vertical line through more than one point on the graph. For instance, we can draw a vertical line through x = 1 on the x axis, and this vertical line crosses the curve at two different points.

A function is only possible if any input x leads to exactly one y output.

A graph may or may not represent a function depending on the relationship between the x and y values of the graph.

The given graph does not represent a function

From the graph, we observe that;

The same value of x points to the different values of y.

For instance:

\((x,y) \to (-6,3)\)

\((x,y) \to (-6,-3)\)

When x = -6, the values of y are 3 and -3.

This is a many-to-one relation.

And a many-to-one relation does not represent a function.

Also, from the graph; there are several other values of x, that point to multiple values of y

Hence, the graph does not represent a function.

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Answer:

He caught 13 squirtles

Step-by-step explanation:

104/8 = 13 squirtles

Squirtles divided by pidgeys

Answer:

$7 dollar per adult

$4 dollars per child

two adults and two children would cost $22

Step-by-step explanation:

Answer:

width = 7 and length = 9

Step-by-step explanation:

Let's assume width = w, and length = 2 + w

So area of a rectangle = width * length

63 ft² = w (2 + w)

63 = 2w + w²

w² + 2w - 63 = 0

Use the quadratic formula to solve this

here, a = 1, b = 2 and c = -63

w = 7 or -9

The dimensions of a rectangle cannot be negative. So we take the dimension, w = 7.

Width = 7 and Length = 7+2 = 9

Answer:

B is correct

Step-by-step explanation:

adding the amount taken away and then subtracting it is the same as subtracting twice

Answer:

either b or c

Step-by-step explanation:

a) The linearized function is 2x - 1. b) The linearized function is ex. c) The linearized function is 1. d) The linearized function is 5x - 5.

To linearize the given functions around the specified points, we can use the first-order Taylor series expansion. The linearized function will be in the form f(x) ≈ f(a) + f'(a)(x - a), where a is the specified point.

a) f(x) = \(x^1\) + x', around x = 2

To linearize this function, we evaluate the function and its derivative at x = 2:

f(2) = \(2^1\) + 2' = 2 + 1 = 3

f'(x) = 1 + 1 = 2

Therefore, the linearized function is f(x) ≈ 3 + 2(x - 2) = 2x - 1.

b) f(x) = \(e^x\), around x = 1

To linearize this function, we evaluate the function and its derivative at x = 1:

f(1) = \(e^1\) = e

f'(x) = \(e^x\) = e

Therefore, the linearized function is f(x) ≈ e + e(x - 1) = e(1 + x - 1) = ex.

c) f(x) = cos(x), around x = 0

To linearize this function, we evaluate the function and its derivative at x = 0:

f(0) = cos(0) = 1

f'(x) = -sin(x) = 0 (at x = 0)

Therefore, the linearized function is f(x) ≈ 1 + 0(x - 0) = 1.

d) f(x) = sin(x)(cos(x) - 4), around x = 0

To linearize this function, we evaluate the function and its derivative at x = 0:

f(0) = sin(0)(cos(0) - 4) = 0

f'(x) = cos(x)(cos(x) - 4) - sin(x)(-sin(x)) = \(cos^2\)(x) - 4cos(x) + \(sin^2\)(x) = 1 - 4cos(x)

Therefore, the linearized function is f(x) ≈ 0 + (1 - 4cos(0))(x - 0) = 5x - 5.

To compare the linearized functions with the actual functions, we can use MATLAB's "taylor" and "plot" commands. Here is an example of how to perform the comparison for the given functions:

% Part (a)

syms x;

f = x^1 + diff(\(x^1\), x)*(x - 2);

taylor_f = taylor(f, 'Order', 1);

x_vals = -0.5:0.2:0.5;

actual_f = double(subs(f, x, x_vals));

linearized_f = double(subs(taylor_f, x, x_vals));

disp("Part (a):");

disp("Actual f(x):");

disp(actual_f);

disp("Linearized f(x):");

disp(linearized_f);

% Part (b)

syms x;

f = exp(x);

taylor_f = taylor(f, 'Order', 1);

x_vals = -0.5:0.2:0.5;

actual_f = double(subs(f, x, x_vals));

linearized_f = double(subs(taylor_f, x, x_vals));

disp("Part (b):");

disp("Actual f(x):");

disp(actual_f);

disp("Linearized f(x):");

disp(linearized_f);

% Part (c)

x_vals = 0:0.1:1;

actual_f = cos(x_vals);

linearized_f = ones(size(x_vals));

disp("Part (c):");

disp("Actual f(x):");

disp(actual_f);

disp("Linearized f(x):");

disp(linearized_f);

figure;

plot(x_vals, actual_f, 'r', x_vals, linearized_f, 'b');

title("Comparison of Actual and Linearized f(x) for Part (c)");

legend('Actual f(x)', 'Linearized f(x)');

xlabel('x');

ylabel('f(x)');

grid on;

% Part (d)

syms x;

f = sin(x)*(cos(x) - 4);

taylor_f = taylor(f, 'Order', 1);

x_vals = 0:0.1:1;

actual_f = double(subs(f, x, x_vals));

linearized_f = double(subs(taylor_f, x, x_vals));

disp("Part (d):");

disp("Actual f(x):");

disp(actual_f);

disp("Linearized f(x):");

disp(linearized_f);

This MATLAB code snippet demonstrates the calculation and comparison of the actual and linearized functions for each part (a, b, c, d). It also plots the actual and linearized functions for part (c) using the "plot" command with the "hold" command to combine the graphs in one plot.

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The volume of the solid generated when the region in the first quadrant is: V ≈ 183.78

The disc method, the shell method, and Pappus' centroid theorem can all be used to calculate volume. In many academic disciplines, such as engineering, medical imaging, and geometry, revolution volumes are used. Integration can be used to determine the area of a region bounded by a known curve.

Because we are only revolving the region in the first quadrant, the x values range from x = 0 to x = 3.

Because of the rotation is about the vertical line x = -1, the radius of the cylindrical shell at x is r = x + 1.

The height of the cylindrical shell at x is h = \(x^{2}\)

We can now create our integral equation to find the volume:

\(V =2\pi\int\limits^a_b {rh} \, dx =2\pi\int\limits^3_0 {(1+x)x^2} \, dx \\\\V =2\pi\int\limits^3_0 {(x^{2} +x^3)} \, dx\)

We can now integrate and evaluate to find the volume of the solid.

\(V=2\pi(\frac{x^3}{3}+\frac{x^4}{4} )|^3_0\\\\V = 2\pi(\frac{27}{3}+\frac{81}{4} )\\\\V=\frac{117\pi}{2}\)

V ≈ 183.78

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The given question is incomplete, complete question is:

Find the volume of the solid generated by revolving the region in the first quadrant bounded above by the curve y =\(x^{2}\), below by the x-axis, and on the right by the line x = 3, about the line x = −1

Answer:

Below

Step-by-step explanation:

Similar triangles due to A - A - A

Set up ratios

QR is to RS   as  QP is to TS

(x+2) / (2x-5) = 3/5       Cross multiply to get

5x+10 = 6x-15               subtract 5x from both sides of the equation

10 = x - 15                     add 15 to both sides

25 = x

The price vectors a. p₁ = 3 and p₂ = 2, Mary will consume only good 1.

Here we have the Utility function as

U(x₁ , x₂) = 3x₁ + x₂

From the given utility function we can clearly see that these goods are substitutes for each other

Now,

δU/δx₁ = 3

δU/δx₂ = 1

Hence we get the Marginal Rate of Substitution or MRS

\(=- \frac{\delta U/ \delta x_1 }{\delta U/ \delta x_2}\)

= -3

The MRS signifies that for every additional unit of 1, Mary is willing to give up 3 units of good 2

|MRS| = 3

For Mary to only consume good 1, |MRS| > p₁/p₂

Hence here we get the p/p ratio for the 4 price vectors to be

a. 3/2 = 1.5

b. 10/3 = 3.33

c. 4

d. 15.4 = 3.75

Hence we can clearly say that for the price vectors p₁ = 3 and p₂ = 2, Mary will consume only good 1.

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Answer:

f = 40

Step-by-step explanation:

Rewrite 35% as 0.35, the equivalent decimal fraction.

Now let f be the original amount.  35% of this amount is 14:

0.35f = 14

Dividing both sides by 0.35, we get:

f = 14/0.35 = 40

f is 40

Therefore, the area of the quarter circle of radius 8 cm is 16π square centimeters (or approximately 50.2655 square centimeters if we use a decimal approximation for π).

A circle is a two-dimensional shape that is defined as the set of all points that are a fixed distance (called the radius) from a central point (called the center) in a plane. It is one of the most basic geometric shapes and is often used in a variety of mathematical and scientific contexts. One important thing to note about circles is that they are symmetrical: any line passing through the center of a circle divides the circle into two halves that are mirror images of each other. Circles are commonly used in a variety of contexts, including geometry, trigonometry, physics, engineering, and many other fields. They are also used in everyday life, such as in the design of wheels and other circular objects, the calculation of the areas of circular fields or gardens, and the measurement of circular objects like plates and bowls.

Here,

The formula for the area of a quarter circle is given by:

A = (1/4)πr²

where A is the area of the quarter circle, r is the radius of the circle, and π is the mathematical constant pi (approximately 3.14159).

In this case, the radius of the quarter circle is 8 cm, so we can substitute this value into the formula and simplify as follows:

A = (1/4)π(8 cm)²

A = (1/4)π(64 cm²)

A = 16π cm²

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Answer:

3 hundredths or .03

Step-by-step explanation:

We will use the fact that the quotient between height and shadow length must be a constant, we will find that the height of the tree is 7.14ft

If we assume the sun is at a constant height, then the quotient between the height and the length of the shadow needs to be a constant.

Then we can write the relation:

(height of the tree)/(shadow of the tree) = (height of Diego)/(shadow of diego).

Here we can define:

Height of the tree = h

Shadow of the tree = 10ft

Height of Diego = 5ft

Shadow of Diego = 7ft

Replacing that in the equation above we get.

h/10ft = (5ft/7ft)

Solving for h:

h = 10ft*(5/7) = 7.14 ft

The height of the tree is 7.14 ft.

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