This question has 2 parts:A. Is the relationship between the diameter and the circumference of circles proportional?B. If the relationship between the diameter and the circumference is proportional, give the C.O.P. If it's not, explain why.

ANSWER: y = (1/2)x - 1.

To find the equation of the tangent line to the curve y = √(x - 3) at the point (4, 1), we need to determine the slope of the tangent line and its y-intercept.

First, let's find the derivative of the function y = √(x - 3) using the power rule:

dy/dx = 1/(2√(x - 3))

Now, we can substitute x = 4 into the derivative to find the slope of the tangent line at that point:

m = dy/dx = 1/(2√(4 - 3)) = 1/2

So, the slope of the tangent line is 1/2.

Next, we can use the point-slope form of a line to find the equation of the tangent line. Given the point (4, 1) and the slope m = 1/2, the equation becomes:

y - y1 = m(x - x1)

Substituting the values (x1, y1) = (4, 1):

y - 1 = (1/2)(x - 4)

Simplifying the equation:

y - 1 = (1/2)x - 2

y = (1/2)x - 1

Therefore, the equation of the tangent line to the curve y = √(x - 3) at the point (4, 1) is y = (1/2)x - 1.

Answer:

y = (1/2)x - 1/2

Step-by-step explanation:

Step 1: Find the derivative of the function

The derivative of a function gives the slope of the tangent line to the curve at any point. To find the derivative of the given function y = sqrt(x - 3), we can use the power rule of differentiation which states that:

d/dx (x^n) = nx^(n-1)

Applying this rule to our function, we get:

dy/dx = d/dx sqrt(x - 3)

To differentiate the square root function, we can use the chain rule of differentiation which states that:

d/dx f(g(x)) = f'(g(x)) * g'(x)

Applying this rule to our function, we have:

g(x) = x - 3

f(g) = sqrt(g)

So,

dy/dx = d/dx sqrt(x - 3) = f'(g(x)) * g'(x) = 1/(2*sqrt(g(x))) * 1

Substituting g(x) = x - 3, we get:

dy/dx = 1/(2*sqrt(x - 3))

So, the derivative of y with respect to x is 1/(2*sqrt(x - 3)).

Step 2: Evaluate the derivative at the given point

To find the slope of the tangent line at the point (4, 1), we need to substitute x = 4 into the derivative expression:

dy/dx = 1/(2*sqrt(4 - 3)) = 1/2

So, the slope of the tangent line at the point (4, 1) is 1/2.

Step 3: Use point-slope form to write the equation of the tangent line

Now that we know the slope of the tangent line at the point (4, 1), we can use point-slope form to write the equation of the tangent line. The point-slope form of a line is given by:

y - y1 = m(x - x1)

where (x1, y1) is the point on the line and m is the slope of the line.

Substituting the values x1 = 4, y1 = 1, and m = 1/2, we get:

y - 1 = (1/2)*(x - 4)

Simplifying this equation, we get:

y = (1/2)x - 1/2

So, the equation of the tangent line to the curve y = sqrt(x - 3) at the point (4, 1) is y = (1/2)x - 1/2.

Hope this helps!

nevermind, I got the wrong answer. not sure how to delete my own answers :/

Answer:

Step-by-step explanation:

This shows that 76 cookies will be made with the total pounds of cookies

Fractions are written as a ratio of two integers. Given the following parameters

Total pounds of cookies made = 4 3/4 pounds

Total pounds of cookies made = 19/4 pounds

If he uses 1/16 pound of dough for each cookie, the total amount of cookies made is given;

Number of cookies = 19/4 ÷ 1/16

Number of cookies = 19/4 * 16/1

Number of cookies = 19 * 4

Number of cookies = 76

This shows that 76 cookies will be made with the total pounds of cookies

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Their exam must have been scheduled on Wednesday, allowing them to start hiking on Thursday after the exams.

To determine the day of the week on which Kai and Finley's exam was scheduled, we need to consider the information provided about the trail being closed on Mondays, Wednesdays, and weekends.

If they had planned to hike to the log cabin for two days after the exams, and the trail is closed on weekends, it means they cannot start hiking on Saturday or Sunday.

Since they cannot start hiking on Saturday or Sunday, the two possible options for the exam day would be Monday or Wednesday, as they have not specified whether the hike starts immediately after the exams or the day after.

However, we can conclude that their exam was not scheduled on Monday, as the trail is closed on Mondays, and they had planned to hike immediately after the exams.

Therefore, their exam must have been scheduled on Wednesday, allowing them to start hiking on Thursday after the exams.

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Answer:

33.3

Step-by-step explanation:

You need to divide 200  and 150 to get you 4/3. Then you will have to _____________________________

Step-by-step explanation:

To determine if events are independent, one has to confirm if there's no relationship between the events.

Event A. Not shutting off the water in the kitchen sink.

Event B. Receiving a high water bill.

Both Events are related as Event B is proportional to Event A. This means they are not independent but rather dependent

Answer:

0.9

Step-by-step explanation:

remove all the other digits OR

divide by ten after the d. p.

A²+B²= C²

31²+ 21²= z²

961+441 = z²

1402= z²

z= 37.443290454

The vectors that span the null space of A are given by: null(A) = span {[1 -1 1 0 ] , [-6  -5  0  1]} (in column form)

The null space of a matrix represents the solution to a homogeneous system formed by the given matrix. It may be written in terms of some basis that spans the entire solution.

The null space of the matrix, A, may be obtained from the matrix equation

Ax=0

The equivalent augmented matrix of the matrix equation is shown below.

(refer to the image attached)

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Answer:

The change in elevation is -134 ft

Step-by-step explanation:

Given;

initial depth of the submarine, d₁ = 235 ft

final depth of the submarine, d₂ = 101 ft

The change in the elevation of the submarine is given by;

Δd = d₂ - d₁

Δd = 101 ft - 235 ft

Δd = -134 ft

The change in elevation is negative because the submarine is moving closer to the surface.

Therefore, the change in elevation is -134 ft

Answer:

54

Step-by-step explanation:

If a is 3, then we plug in "a" as 3.

3(6a) is 3(6(3))

3 * 6 * 3 = 54

Answer:

Below

Step-by-step explanation:

(x-10)^2 = 90     sqrt both sides

x-10  =  ± sqrt (90)

x  =   10 ± sqrt (90)

The expressions are simplified to;

1. 72n² + 63n

2. 18t - 18t²

3. -18b² - 18b

4. -56r - 21r²

5. -6m + 9m²

Algebraic expressions are simply described as expressions that are known to consist of coefficients of variables, variables, constants, terms, and factors.

These algebraic expressions are also made up of mathematical or arithmetic operations.

These operations are;

From the information given, we have;

1. -9n (-8n -7)

expand the bracket

72n² + 63n

2. -2t(-9 + 9t)

expand the bracket

18t - 18t²

3. -3b(6b + 6)

expand the bracket

-18b² - 18b

4. -7r(8 + 3r)

expand the bracket

-56r - 21r²

5. 3m(-2 + 3m)

expand the bracket

-6m + 9m²

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Answer:

10,000

Step-by-step explanation:

because 10 times 10 is 100 times 100 equals the answer

sry if i get it wrong  have a great day

Answer:

10 to the fourth power 10^4

Step-by-step explanation:

Answer:

We need to find the first term.  We can use the formula

an = a1 + d(n - 1)

to solve for a1.  We already know the 12th term, a12, common difference, d, and nth sequence, n.

a12 = -36

d = -4

n = 12

-36 = a1 - 4(12 - 1)

-36 = a1 - 44

8 = a1

The first term is 8.  Therefore, your formula is

an = 8 - 4(n - 1)

an = -4n + 12

Then use this formula to graph.

n is the independent variable.

an is the dependent variable.

Your graph will be a line.

n    |       an

___________

1          8

2          4

3          0

4         -4

5         -8

6         -12

Step-by-step explanation:

give me brainliest.

Answer:

19) Domain: - ∞ < x < ∞                    20) Domain:  - ∞ < x < ∞

Range: - ∞ < y < ∞                                  Range: - ∞ < y < ∞

Increases throughout                            Decreases throughout

Step-by-step explanation:

Given the parent function " y = ∛x" we know that the first graph should have a vertical shift down 2 units, and a horizontal shift 4 units to the right. There is no vertical stretch since there is no coefficient. (Check first graph)

Domain: - ∞ < x < ∞

Range: - ∞ < y < ∞

Increases throughout

______________________________

For the second graph there should be a vertical shift down three units, a horizontal shift 1 unit to the left, and a vertical stretch by a factor of - 1. (Check second graph)

Domain: - ∞ < x < ∞

Range: - ∞ < y < ∞

Decreases throughout

INFORMATION:

We know that:

- John sells plain cakes for $8 and decorated cakes for $12.

- On a particular day, John started with a total of 100 cakes, and sold all but 4.

- His sales that day totaled $800.

And we must find the number of plain cakes and decorated cakes that he sold that day.

STEP BY STEP EXPLANATION:

To find them, we can represent the situation using a system of equations

Where, x represents the number of plain cakes that he sold and y represents the number of decorated cakes that he sold.

Now, we must solve the system:

1. We must multiply the equation (1) by -8

2. We must add equations (2) and (3)

3. We must solve equation (4) for y

4. We must replace the value of y in equation (1) and then solve it for x

So, we found that x = 88 and y = 8.

Finally, John sold 88 plain cakes and 8 decorated cakes.

ANSWER:

He sold 88 plain cakes and 8 decorated cakes that day.

9514 1404 393

Answer:

  the correct answer is marked

Step-by-step explanation:

The denominator of a fractional exponent becomes the index of the radical when the power is written using a radical. The fractional power only applies to the y-factor, so that is all that is under the radical.

  \(\displaystyle xy^{\frac{2}{9}}=x\cdot (y^2)^{\frac{1}{9}}=\boxed{x\sqrt[9]{y^2}}\)

The written and solved equation to determine the cost of the desserts, d is  5(9.75 + d) = 63.75; d = 3.00

Five friends ate lunch and spent a total of $63.75.

They each bought the same meal for $9.75, and they each bought the same dessert.

The equation to determine the cost of the dessert, d can be represented as follows:

Hence,

5 (9.75 + d) = 63.75

48.75 + 5d = 63.75

Therefore, let's use the equation to solve for d.

48.75 + 5d = 63.75

subtract 48.75 from both sides of the equation

63.75 - 48.75 = 5d

15 = 5d

divide both sides of the equation by 5

15 / 5 = 5d / 5

d = 3

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The graph is shown below.

We use an open dot at zero because x is only less than 0,

it's not less than or equal to 0.

So we have an open dot at 0 going to the left.

Answer:

Step-by-step explanation:

Identify the number of decimal places in each factor.

    0.47

  × 3.2

The number of decimal places in 0.47 is

✔ 2

.

The number of decimal places in 3.2 is

✔ 1

.

The number of decimal places in the product will be the sum of the factors’ decimal places. So the product will have

✔ 3

decimal places.

Answer:

x=30

Step-by-step explanation:

6x+4x-6=24+9x

combine like terms

10x-6=24+9x

add 6 on both sides

10x=30+9x

subtract 9x on both sides

x=30

Hope this helps! :)

This occurs when the number of $5 price increases is approximately 10.82 or 15.32.

The function given is P(x) = −6x2 + 156x + 1,000, where x is the number of $5 price increases for each solar panel. We are to identify the approximate value of the x-intercept and explain what the x-intercept means in terms of the problem scenario.

The x-intercept is a point where the graph of the function crosses the x-axis. At this point, the value of the function is zero.

We can find the x-intercept by setting P(x) = 0 and solving for x.0 = −6x2 + 156x + 1,0006x2 - 156x - 1000 = 0Dividing by 6, we get:x2 - 26x - 166.67 = 0Solving using the quadratic formula,

we get:x ≈ 10.82 or x ≈ 15.32So, the x-intercepts are approximately 10.82 and 15.32. In terms of the problem scenario, the x-intercept represents the point at which the company breaks even, i.e., the point at which the daily profit is zero.

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Answer:

\( E(100 Y^2) =100 E(Y^2)\)

And we have that :

\( E(Y^2) =\sum_{i=1}^n X^2_i P(X_i)\)

And replacing we got:

\( E(Y^2) =0^2 *0.6 + 1^2 *0.25 +2^2*0.10 +3^2 *0.05 = 1.1\)

And finally we have:

\( E(100 Y^2) =100 *1.1 = 110\)

Step-by-step explanation:

For this case we have the following probability masss function given:

Y         0           1              2             3

p(Y)    0.6        0.25      0.10         0.05

And we can define the surcharge with this expression \( 100Y^2\)

We want to find the expected value for the last expression and we can do it on this way:

\( E(100 Y^2) =100 E(Y^2)\)

And we have that :

\( E(Y^2) =\sum_{i=1}^n X^2_i P(X_i)\)

And replacing we got:

\( E(Y^2) =0^2 *0.6 + 1^2 *0.25 +2^2*0.10 +3^2 *0.05 = 1.1\)

And finally we have:

\( E(100 Y^2) =100 *1.1 = 110\)

Answer: No

Step-by-step explanation:

to be proportional, both numbers have to increase by the same number

because if u multiply 6 by 2 you get 12, but when you multiply 10 by 2 you get 20, not 60 it would be proportional if you said 6 and 10 in to 12 and 20 in

The maximum possible number of parasites for the class containing the value 47 is equal to 50.

In a frequency distribution table, a class width can be defined as the difference between the upper (maximum) and lower (minimum) boundaries of any class in a data set. This ultimately implies that, all classes must all have the same width in a frequency distribution table or histogram.

Mathematically, the class width of a data set can be calculated by using this formula:

Class width = max - min

Where:

Based on the histogram above, the class width with a value of 47 is given by;

Class width = 45 to 50

Therefore, the maximum (upper) possible number is 50.

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Answer:

Step-by-step explanation: well, you will more than likely get it at least 60%-80% of the time! If this doesn't help i can try to explain in a lot more detail unless someone does for me!