Let f be a differentiable function such that f (2) = 4 and f (2) = − 1/2 . What is the approximation for f (2.1) found by using the line tangent to the graph of f at x = 2 ?

Answer:

16.74

Step-by-step explanation:

-1.8 times -9.3 will have a positive answer because 2 negative numbers will have a positive sum

  -1.8

x -9.3

---------

    5 4

1 6 2 0

---------

1 6 7 4 ||| add two decimal spaces

16.74

The final answer is

∭E (xy + yz + xz) dV = **1 + 3z**, where E={(x,y,z)∣0≤x≤1,−x^2≤y≤x^2,0≤z≤9}. the upper bound of integration in the region E. This result reflects the contribution of the variables xy, yz, and xz over the bounded region E={(x,y,z)∣0≤x≤1,−x^2≤y≤x^2,0≤z≤9}.

The evaluation of the triple integral ∭E (xy + yz + xz) dV over the bounded region E={(x,y,z)∣a≤x≤b,h1(x)≤y≤h2(x),e≤z≤f} is as follows:

To evaluate the given triple integral, we need to express the bounds of integration in terms of x, y, and z. In this case, we are given the region E={(x,y,z)∣0≤x≤1,−x^2≤y≤x^2,0≤z≤9}. Let's break down the integral into its individual components.

The bounds for x are given as 0≤x≤1. This means x varies from 0 to 1.

The bounds for y are −x^2≤y≤x^2. This indicates that y lies between the curves y = −x^2 and y = x^2.

The bounds for z are 0≤z≤9, which means z ranges from 0 to 9.

Now, let's set up the triple integral using these bounds:

∭E (xy + yz + xz) dV = ∫₀¹ ∫₋ˣ² ˣ² ∫₀⁹ (xy + yz + xz) dz dy dx.

We start by integrating with respect to z, as the bounds for z are constant. The integral becomes:

∭E (xy + yz + xz) dV = ∫₀¹ ∫₋ˣ² ˣ² [(xy + yz + xz)z]₀⁹ dy dx.

Simplifying further:

∭E (xy + yz + xz) dV = ∫₀¹ ∫₋ˣ² ˣ² (9xy + 9yz + 9xz) dy dx.

Next, we integrate with respect to y. The integral becomes:

∭E (xy + yz + xz) dV = ∫₀¹ [3ˣ⁴ + 6ˣ²z + 3ˣ⁴z]₋ˣ² dx.

Finally, we integrate with respect to x:

∭E (xy + yz + xz) dV = [x⁵ + 2x³z + x⁵z]₀¹.

Evaluating the integral at the upper and lower limits:

∭E (xy + yz + xz) dV = (1⁵ + 2(1³)z + 1⁵z) - (0⁵ + 2(0³)z + 0⁵z).

Simplifying:

∭E (xy + yz + xz) dV = 1 + 2z + z - 0.

Therefore, the final answer is:

∭E (xy + yz + xz) dV = **1 + 3z**, where E={(x,y,z)∣0≤x≤1,−x^2≤y≤x^2,0≤z≤9}.

By evaluating the given triple integral, we obtained a final result of 1 + 3z, where z represents the upper bound of integration in the region E. This result reflects the contribution of the variables xy, yz, and xz over the bounded region E={(x,y,z)∣0≤x≤1,−x^2≤y≤x^2,0≤z≤9}.

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The projection of (1+2v) onto the given vectors is (5 + 9v). The projection of vector 3 is -2, and the projection of vector 2v is 9v.

To find the projection of a vector onto another vector, we use the formula proj(u) = ((u · v) / ||v||^2) * v, where u is the vector being projected and v is the vector onto which the projection is being made.

In the given question, we are provided with proj1 and proj2, which are the projections of vectors 1 and 2, respectively. We need to find the projections of (1+2v), 3, and 2v.

For proj(1+2v), we can substitute the given values into the projection formula. Since proj1 = 3 - 5 and proj2 = 2 + 7, we have proj(1+2v) = 3 - 5 + (2 + 7)v. Simplifying this expression gives us proj(1+2v) = 5 + 9v.

For proj3, we are given that proj3 = 3 - 5. Simplifying this expression gives us proj3 = -2.

For proj2v, we can use the same projection formula. Since proj2 = 2 + 7, we have proj(2v) = (2 + 7)v. Simplifying this expression gives us proj(2v) = 9v.

Therefore, the projections of (1+2v), 3, and 2v are (5 + 9v), -2, and 9v, respectively.

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Answer:

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

Let the amount deposited be x. It is assumed we are talking about simple interest.

After 4 years the interest amount is:

95% of this amount is Rs 4940:

Mrs Majhi deposited Rs 20000.

Mrs. Majhi deposited Rs 20000 in her bank account. This was calculated by first finding the total interest (before tax) and then using the formula for simple interest to determine the principal amount.

The question is based on the concepts of Simple Interest and taxation. We know that Mrs Majhi received Rs 4940 as net interest after 4 years and this amount is 95% of the total interest (since 5% was paid as income tax). The total interest can be calculated as (4940 / 95) * 100 = Rs 5200.

The rate of interest is given as 6.5% per annum. Thus, the money deposited (Principal) by her can be calculated using the formula for simple interest (I = PRT/100), where P is the Principal, R is the rate of interest, and T is the time. Re-arranged to calculate the Principal (P), it becomes P = I / (R*T) = 5200 / (6.5*4) = Rs 20000.

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Answer:

78.909877

Step-by-step explanation:

89.0987

Answer: 1/4 or 0.25 cups

Step-by-step explanation: I looked it up

This is pseudo-trig.  It has a trig function but it's irrelevant.

Let y = cos X

y + 1/y = 40

Squaring,

y² + 2(y)(1/y) + 1/y² = 1600

y² + 2 + 1/y² = 1600

y² + 1/y² = 1598

cos² X + 1/cos²X = 1598

Answer: 1598

total days = 3+5+2+2 = 12

Sunny days = 3

Divide the sunny days by the total number of days

P = 3/12 = 0.25

Answer:(-4,3)

Step-by-step explanation:

Here, Every equation has same slope (-4) and same y-intercept (3), so we don't need to calculate those.

Now, as coordinates are in left-portion, and also touches the line, it would be: y ≥ -4x + 3

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where,

\( \star \sf{ \pink{x_1 = -2 , x_2 = 4}}\)

\( \star \sf{ \color{hotpink}y_1 = 6 , y_2 = -2}\)

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[ divide by 2 ]

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hope it helps ⸙

The third quartile in a box-and-whisker plot represents the score below which 75% of the data falls. It is a measure of central tendency.

In a box-and-whisker plot, the third quartile (also known as the upper quartile or Q3) represents the score below which 75% of the data falls. It is a measure of central tendency that indicates the boundary between the highest 25% and the lowest 75% of the scores. To determine the third quartile, follow these steps:

1. Order the scores from smallest to largest.

2. Divide the data into two halves: the lower half and the upper half.

3. Locate the median of the upper half, which is the value where 50% of the data falls above and 50% falls below.

4. This value is the third quartile and represents the score below which 75% of the data falls.

The third quartile provides insights into the performance of students on the math test, indicating the score that is relatively higher than most of the scores achieved.

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Answer:5/8

Step-by-step explanation:

\(\begin{gathered} \boxed{ \sf \frac{3}{4} - \frac{1}{8}} = \\ \\ \sf \frac{8 \div 4 \times 3 - 8 \div 8 \times 1}{8} = \\ \\ \sf\frac{6 - 1}{8} = \\ \\ \sf \boxed{ \sf\frac{5}{8}} \end{gathered}\)

Therefore, the result of this subtraction of fractions is five eighths.

How to subtract unlike fractions:

Heterogeneous fractions are fractions that have different denominators.

To subtract heterogeneous fractions we follow these steps:

Answer:

$10

Explanation:

If you only have to pay $5 of the $15 you gave him, he has to pay you 15-5 or $10 back.

Answer:

−5z−21

Step-by-step explanation:

If factored it is :-5z-21

Answer:

-21-5z

Step-by-step explanation:

-1+(-10)+(-10)-5z

-1-10-10-5z

-1-20-5z

-21-5z

`x > 0`, `f''(x) > 0`.∴ `f(x)` is concave upwards for `x > 0`.So, `(0, f(0))` is the point of inflection of `f(x)`.

Given function is `f(x) = e^(-32x²)`.So, `f'(x) = -64xe^(-32x²)`.

Put `f'(x) = 0` to get the critical points of `f(x)`.

∴ `-64xe^(-32x²) = 0`

⇒ `-64x = 0` or `e^(-32x²) = 0`

⇒ `x = 0` is the critical point.

So, the first derivative is negative for `x < 0` and positive for `x > 0`.

Hence, `f(x)` is decreasing for `x < 0` and increasing for `x > 0`.

So, `x = 0` is the point of relative minimum of `f(x)`.

Again, `f''(x) = (-64e^(-32x²))² - 64xe^(-32x²) * (-64xe^(-32x²))

`= `4096x²e^(-64x²)`

So, `f''(0) = 0`.

Now, for `x < 0`, `f''(x) > 0`.∴ `f(x)` is concave upwards for `x < 0`.

Again, for `x > 0`, `f''(x) > 0`.∴ `f(x)` is concave upwards for `x > 0`.So, `(0, f(0))` is the point of inflection of `f(x)`.

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Answer:

15

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

google .

divide the length by 36 basically

Answer:

y = -2/3x + 13/3

Step-by-step explanation:

y = mx + c

m = -2/3

y = -2/3x + c

Put in your point (2,3):

3 = -2/3 (2) + c

3 = -4/3 + c

3 + 4/3 = c

13/3 = c

so

y = -2/3x + 13/3

At TD Bank, after five years the amount would be $941.37.

What is amount?

Amount is a word used to describe the total of something, typically money, that is due, owed, or paid. It is used to represent a numerical value, usually in terms of currency, but it can also refer to any other kind of quantitative representation. Amount is often used to refer to a specific amount of money, or the sum of multiple elements. In accounting, the term is also used to refer to the total of all transactions, or the sum of all debits and credits in an account.

TD Bank:

5.3% compounded continuously for 5 years

Amount = $712 x e^(5.3% x 5) = $934.57

Wells Fargo:

6.4% compounded quarterly for 5 years

Amount = $712 x (1 + (6.4% / 4))^(4 x 5) = $941.37

At Wells Fargo, after five years the amount would be $945.15. This means that Wells Fargo offers a higher rate of return than TD Bank. Therefore, if the goal is to maximize the total amount of money saved, the teenager should go with Wells Fargo.

The higher rate of return offered by Wells Fargo is due to the fact that the interest is compounded more frequently. Compounding interest more often allows the amount to grow faster than if the interest were compounded less frequently. Therefore, a higher rate of return can be achieved with Wells Fargo.

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At TD Bank, after five years the amount would be $934.57 while at Wells Fargo the amount would be $941.37. As Wells Fargo Bank offers more profitable options we should go with Fargo.

Amount is a word used to describe the total of something, typically money, that is due, owed, or paid. It is used to represent a numerical value, usually in terms of currency, but it can also refer to any other kind of quantitative representation. Amount is often used to refer to a specific amount of money, or the sum of multiple elements. In accounting, the term is also used to refer to the total of all transactions, or the sum of all debits and credits in an account.

TD Bank:

5.3% compounded continuously for 5 years

Amount = $712 x e^(5.3% x 5) = $934.57

Wells Fargo:

6.4% compounded quarterly for 5 years

Amount = $712 x (1 + (6.4% / 4))^(4 x 5) = $941.37

At Wells Fargo, after five years the amount would be $945.15. This means that Wells Fargo offers a higher rate of return than TD Bank. Therefore, if the goal is to maximize the total amount of money saved, the teenager should go with Wells Fargo.

The higher rate of return offered by Wells Fargo is due to the fact that the interest is compounded more frequently. Compounding interest more often allows the amount to grow faster than if the interest were compounded less frequently. Therefore, a higher rate of return can be achieved with Wells Fargo.

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Solution:

Given that a committee of 4 teachers and 3 students is to be formed from 12 teachers and 35 students, we have

Recall that:

This gives:

Hence, the number of committees that can be formed is

Answer: To find out how much Moira would have been paid after working for 18 weeks, we need to multiply her fortnightly pay by the number of fortnights in 18 weeks.

Since there are 26 fortnights in a year, 18 weeks is equivalent to 18/26 = 9/13 of a year.

So, Moira's total pay after 18 weeks would be:

891.60 * 9/13 = $584.40

So, Moira would have been paid $584.40 after working for 18 weeks.

Step-by-step explanation:

Answer:

The missing fraction is 6/12

(you can further simplify this but the question requires that you don't do that)

Step-by-step explanation:

To add fractions easily, their denominators should have the same value, so the denominator should be 12,

Then, to get 16 in the numerator, we need to find a number that on adding to 10, gives 16, or,

10 + x = 16

x = 16 - 10

x = 6

So, the numerator should be 6

so we get the fraction, 6/12

We can also solve it in an alternate way,

\(10/12 + x = 16/12\\x = 16/12 - 10/12\\x = (16-10)/12\\x = 6/12\)

The cost for renting shoes is represented by the number 3.

The cost per game is represented by the number 2.5.

The given equation is a linear one. One variable with a power of one makes up a linear equation.

y= 2.5x + 3

2.5 in the above calculation stands for the extra cost for each game played. Each game played sees an increase in this number.

When:

The additional cost is 2.5 x 1 = 2.50 for 1 game played.

If 10 games are played, the extra cost is 2.5 times 10 games, or $25.

The base rate to rent the shoes is $3. It is an ongoing expense that stays the same regardless of how many games are played.

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The perimeter measures around 36 metre.

The perimeter refers to the area surrounding an object. For instance, your house has a fenced-in yard. The perimeter is the length of the fence. If the yard is 50 feet by 50 feet, your fence is 200 feet long.

While 12.74 rounds up to 13, 5.45 rounds down to 5. Recatangle created a total of four sides, two of which are identical in length to the other two (which is a poor way to explain it). There are two sides that are 13 inches long and two sides that are 5 inches long, which is the solution to this question. When added together, the perimeter would be 13+13+5+5.

As an expression,

2(13)+2(5)

=26+10

=36.

The perimeter is approximately 36 meters.

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Answer:

D) 10x - 24

Step-by-step explanation:

Bc I know maths a lot

Answer:

The material cost for December = $356,000

Step-by-step explanation:

The manufacturing overhead is the sum of the indirect costs that come from the manufacturing process except labor and materials

Hence, whereby the cost per liter = $0.47, we have;

Total volume produced = 4.0 million liters

Manufacturing overhead = $1,435,000

Total cost = Cost per liter × Total volume produced

∴ Total cost = 4 × 10⁶ × $0.47 = $1,880,000

Hence the cost of labor + materials = Total cost - Manufacturing overhead

the cost of labor + materials = $1,880,000 - $1,435,000 = $445,000

Labor cost = 25% material cost = 0.25 × material cost

∴ 0.25 × material cost + material cost = $445,000

1.25 × material cost = $445,000

material cost = $445,000/1.25 = $356,000

Which gives labor cost = 0.25 × $356,000 = $89,000

The material cost for December = $356,000.

To find the vector function r(t) given r'(t) = 8t'i + 10t^0j + tk and r(1) = i + j

Follow these steps:
Step 1: Integrate each component separately. For r'(t) = 8t'i + 10t^0j + tk, integrate each component with respect to t:

∫(8t'i) dt = 4t^2i + C1i
∫(10t^0j) dt = 10tj + C2j
∫(tk) dt = 0.5t^2k + C3k

Step 2: Find the constant vector C. We know that r(1) = i + j, and by substituting t=1 into the integrals, we get:

r(1) = 4(1)^2i + C1i + 10(1)j + C2j + 0.5(1)^2k + C3k = i + j

Comparing the two equations, we can solve for C1, C2, and C3:

4 + C1 = 1 => C1 = -3
10 + C2 = 1 => C2 = -9
0.5 + C3 = 0 => C3 = -0.5

Step 3: Combine the results to find the general form of r(t):

r(t) = (4t^2 - 3)i + (10t - 9)j + (0.5t^2 - 0.5)k

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To find out how far Jacky walks every day, we need to divide the total distance he walks every week (220 1/2 m) by the number of days he walks.

Assuming he walks every day, there are 7 days in a week. So,

220 1/2 m ÷ 7 = 31 1/2 m

Therefore, Jacky walks 31 1/2 meters every day.