(a) Find the differential dy. y = tanz dy (b) Evaluate dy for the given values of and da. 2 = 7/4 and dx -0.05 dy Question Help: Video Message instructor Submit Question

Answer:

In Example 2, the relationship between the dependent variable a, the amount still owed, and the independent variable w, the number of weeks Ethan pays $5, is given by the equation:

a = 100 - 5w

If we increase the value of w by 1, then the new value of w becomes w + 1. To find out what happens to the value of the dependent variable a, we substitute w + 1 for w in the equation:

a = 100 - 5(w + 1)

a = 100 - 5w - 5

Simplifying this expression, we get:

a = 95 - 5w

Comparing this expression to the original equation, we see that the value of the dependent variable a decreases by 5 when the value of the independent variable w is increased by 1. Therefore, if Ethan pays $5 for one more week, the amount still owed will decrease by $5.

Answer:

0.3

Step-by-step explanation:

Answer: If x represents the number of hours that Ryan rides his bike, and y represents the total number of miles that he rides, we can write the equation relating x and y as:

y = 12x + 5

This is a linear equation in slope-intercept form, where the slope is 12 (the rate at which Ryan rides, in miles per hour) and the y-intercept is 5 (the number of miles Ryan has already ridden).

To predict how many minutes it will take for Ryan to ride a total of 60 miles, we can substitute y = 60 into the equation and solve for x:

60 = 12x + 5

55 = 12x

x = 55/12

To convert this to minutes, we need to multiply by 60, since there are 60 minutes in an hour:

x (in minutes) = (55/12) * 60

x (in minutes) ≈ 275

Therefore, it will take Ryan approximately 275 minutes (or 4 hours and 35 minutes) to ride a total of 60 miles.

Step-by-step explanation:

the missing TR amount for Group 1 is $200 and the missing MR amount is $30.

To calculate the missing TR (total revenue) and MR (marginal revenue) amounts for Group 1, we need to use the given data in the table.

Total revenue (TR) is calculated by multiplying the price (P) with the quantity (Q), while marginal revenue (MR) is the change in total revenue resulting from selling an additional unit of output.

Looking at the table for Group 1, we see that the price (P) is $10 and the quantity (Q) is 20. Therefore, the TR for Group 1 can be calculated as:

TR = P x Q = $10 x 20 = $200.

To calculate MR, we need to compare the change in total revenue when the quantity increases from 20 to 30 units. From the table, we see that the total revenue for Group 1 when the quantity is 30 is $230.

Therefore, the marginal revenue for Group 1 can be calculated as:
MR = TR2 - TR1 = $230 - $200 = $30.

So, the missing TR amount for Group 1 is $200 and the missing MR amount is $30.

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Beginning and intermediate algebra encompass the foundational aspects of mathematics, introducing students to the language and symbolism used in mathematical expressions and equations.

Beginning and intermediate algebra courses serve as stepping stones in a student's mathematical education, providing them with essential skills and knowledge in algebraic concepts.

These courses emphasize the language and symbolism of mathematics, teaching students to translate real-world problems into mathematical expressions and equations.

In these courses, students learn to work with variables, which represent unknown quantities, and manipulate algebraic expressions using operations such as addition, subtraction, multiplication, and division. They learn how to solve equations and inequalities, simplifying expressions and finding solutions that satisfy given conditions.

Furthermore, beginning and intermediate algebra introduce students to important mathematical concepts like functions, graphing, exponents, and factoring.

These topics help develop critical thinking and problem-solving skills, laying the foundation for more advanced mathematical disciplines. By learning the language and symbolism of mathematics in beginning and intermediate algebra.

Students gain a solid understanding of mathematical concepts and acquire the necessary skills to tackle more complex mathematical problems in higher-level courses and real-world applications.

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the absolute extrema of the linear equation f(x) =  12x^2 -11x +2 are 27 (absolute maximum) for x = - 8 and - 9 (absolute minimum) for x = 4. (- 8, 27) and (4, - 9).

What are the absolute extrema of a linear equation within a closed interval?

According to the functions theory, linear equations have no absolute extrema for all real numbers, but things are different for any closed interval as absolute extrema are the ends of linear function. Now we proceed to evaluate the function at each point:

Absolute maximum

f(- 8) =   12x^2 -11x +2

f(- 8) = 27

Absolute minimum

f(4) = - 3 · 4 + 3

f(4) = - 9

By means of functions theory and the characteristics of linear equations, the absolute extrema of the linear equation f(x) = 12x^2 -11x+2  are 27 (absolute maximum) for x = - 8 and - 9 (absolute minimum) for x = 4. (- 8, 27) and (4, - 9).

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The answer is a measure of gravitational force

Answer:

(3, 4)

Step-by-step explanation:

Using elimination method:

3x + 8y = 41

-3(x + 2y = 11)

-3x -6y = -33

2y = 8

y = 4

x = 3 (plug y back into the equation)

(3, 4)

Answer:

\(3x + 8y = 41 - - (1) \\ x + 2y = 11 - - (2) \\ (2) \: x + 2y = 11 \\ x = 11 - 2y - (3) \\ (3)in(1) is \: \: 3(11 - 2y) - 8y = 41 \\ 33 - 6y + 8y = 41 \\ 33 + 2y = 41 \\ 2y = 41 - 33 \\ 2y = 8 \\ y = \frac{8}{2} \\ y = 4 \\ y = 4 \: in \: (2) \: is \: x + 2(4) = 11 \\ x + 8 = 11 \\ x = 11 - 8 \\ x = 3\)

Answer: 3 Factors

Step-by-step explanation:

Answer:

Step-by-step explanation:

2x squared, denoted (2x)2, is equal to 4x2. In general, we can raise a product to a power using the following product rule for exponents: (ab)n = an

Answer:

(x + 3)² + (y - 6)² = 9

Step-by-step explanation:

the equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k ) are the coordinates of the centre and r is the radius

here (h, k ) = (- 3, 6 ) and r = 3 , then

(x - (- 3 )² + (y - 6)² = 3² , that is

(x + 3)² + (y - 6)² = 9

Let's change it by multiplying by 10^6.

So, the number is:

82,840,000 [82 million, 840 thousand]

Now,

For scientific notation, we have to take the decimal point until there is 1 digit to its left.

Thus it will be:

8.284

This number will be multiplied by a power of 10. This power will be the number of digits we went left to have 8.284 instead of 82,840,000...

Well, that's 7 digits. Thus, the scientific notation would be:

Step-by-step explanation:

Use distributive property to rewrite 6m(3n+1) in its equivalent form

Answer:

Sate why the measure of angle d is 120 degrees

Answer: 4.70020754

Hope this helps :)

The value of y as x tends to 2 is infinity since the curve progresses to infinity at this point that is \(\lim_{x \to 2} f(x) = \infty\)

Find the graph attached. From the graph, we can see that the range of the function is the values along the y-axis and is from the minimum point on the curve (y = -2) to infinity

From the graph, we can deduce that the value of y as x tends to 2 is infinity since the curve progresses to infinity at this point.

Therefore we can conclude that \(\lim_{x \to 2} f(x) = \infty\)

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Answer: (43,5)

Step-by-step explanation: did the assignment myself.

Answer:

43, 5

Step-by-step explanation:

Tok the test

Answer:

96

Step-by-step explanation:

We simply need to plug in a = 4 so 6a² = 6 * 4² = 6 * 16 = 96.

Answer: f(-5)= -5

Step-by-step explanation:

If f(x)=x then f is one and 1 times -5 is -5

The total number of white tiles that Paul used is 54

From the question, we have the following parameters that can be used in our computation:

Length of the entire floor = 9 feet

Width of the entire floor = 12 feet

The total number of white tiles used is calculated as

Total number of white tiles used = Length of the entire floor * Width of the entire floor/2ft²

Substitute the known values in the above equation, so, we have the following representation

Total number of white tiles used = 9ft * 12ft/2ft²

Evaluate

Total number of white tiles used = 54

Hence, the white tiles are 54

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Answer:

A = 500(1+6%/2)^2t

Step-by-step explanation:

Given the general compound interest formula A = P(1+r/n)^nt. With an initial investment of $500, and percent interest of 6% compounded semi annually(every six months/half a year/twice in one year). A = 500(1+6%/2)^2t .

i.e if given two years of compound interest, t=2. A = 500(1+6%/2)^2(2), 500(1+0.03)^4, 500(1.03)^4, 500(1.12550881), 500(≈1.1255) = 562.75

A = 562.75$ for two years

The area of a circle can be found using the formula A = πr^2, where r is the radius of the circle. Since the diameter is given as 18 units, the radius would be half of that, which is 9 units. Now, substitute the value of the radius into the formula: A = π(9^2) = 81π units^2. Therefore, the correct answer is option b) 81π units^2.


1. Use the formula A = πr^2, where A is the area and r is the radius of the circle.
2. The diameter is given as 18 units, so the radius would be half of that, which is 9 units.
3. Substitute the value of the radius into the formula: A = π(9^2) = 81π units^2.

Therefore, the area of the circle with a diameter of 18 units is 81π units^2.

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Answer: A greater percentage of second-lunch students (39%) eat outside.

Step-by-step explanation: i just did it

Answer:

Step-by-step explanation: 12 ft just had a test on this

Answer:

x<-4

Step-by-step explanation:

MARK AS BRAINLIST!!

Answer:

the range is {-2, 6, 22}

Step-by-step explanation:

Use " ^ " to indicate exponentiation:  f(x) = x^2 - 3.

For each value in the domain {1, 3, 5}, calculate f(x) = x^2 - 3:

f(1) = 1^2 - 3 = -2

f(3) = 3^2 - 3 = 9 - 3 = 6

f(5) = 5^2 - 3 = 25 - 3 = 22

Thus, the range is {-2, 6, 22}

There are a total of 12 choices for a small cup and 12 choices for the flavor, resulting in 12 possible selections. For the large cup, there are 12 choices for the first scoop and 11 choices for the second scoop (excluding the flavor already chosen), resulting in 132 possible selections.

The number of possible selections, we consider the choices for each cup size separately.

For a small cup, there are 12 flavors to choose from, so there are 12 possible selections.

For the large cup, we need to choose two different flavors. We have 12 choices for the first scoop, and once we have chosen a flavor, there are 11 remaining flavors for the second scoop (since it must be different from the first). This gives us a total of 12 * 11 = 132 possible selections.

Therefore, combining the possibilities from the small cup (12) and the large cup (132), there are a total of 12 + 132 = 144 possible selections at Cold Cup o' Cream.

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Answer:

4 1/2

Step-by-step explanation:

Answer:

No solution

Step-by-step explanation:

First we would have to see if anything has to be distributed and yes the 4 in the expression 4(x + 1) has to be distributed to the x and 1. So we would multiply the 4 by x and 1. Now we have 4x + 4 = 4x + 10. We have to get the x's on 1 side of the equation so we would do the inverse of one of the x's and we can only subtract. So we can subtract 4x on both sides. So now we have

4 = 10. That isn't a correct statement so there is no solution.

4 does not equal 10.

Answer:

150

Step-by-step explanation:

300-150

Answer:

y=-6/5x -8

Step-by-step explanation:

slope is the same as gradient(m) so find the c in the equation y=mx+c using the point (-5,-2) which gives u -8 then substitute values of m and c in that very equation

Answer:

\(y=-\frac{6}{5}x-8\)

Step-by-step explanation:

Same process as the other two lol

y= -(6/5)x+b

solve for b by plugging in the required coordinates

-2= -(6/5)(-5)+b

-2= 6+b

-8=b

put it all together