In both places where you can place point C​ to form the right triangle CDL​ times d times l, the horizontal distance between points D​d and L​l, |x2​−x1​|=​ (blank) blocks, and the vertical distance between points D​d and L​l, |y2​−y1​|=​ (blank) blocks.
Fill the blank and answer

To estimate the area under the graph of f(x) = 3√x from x = 0 to x = 4 using four approximating rectangles, we can divide the interval [0, 4] into four subintervals of equal width and calculate the area of each rectangle using either the right endpoints or the left endpoints.

(a) Using right endpoints:

The width of each rectangle is Δx = (4 - 0) / 4 = 1.

The right endpoints for the four subintervals are x = 1, 2, 3, and 4.

We can calculate the height of each rectangle by evaluating f(x) = 3√x at the right endpoints:

f(1) = 3√1 = 3

f(2) = 3√2

f(3) = 3√3

f(4) = 3√4 = 6

The area of each rectangle is then the product of the width and the height.

R1 = 1 * 3 = 3

R2 = 1 * f(2)

R3 = 1 * f(3)

R4 = 1 * 6

To estimate the total area, we sum up the areas of the four rectangles:

R4 = R1 + R2 + R3 + R4

(b) Using left endpoints:

Similar to part (a), the width of each rectangle is Δx = (4 - 0) / 4 = 1.

The left endpoints for the four subintervals are x = 0, 1, 2, and 3.

We can calculate the height of each rectangle by evaluating f(x) = 3√x at the left endpoints:

f(0) = 3√0 = 0

f(1) = 3√1 = 3

f(2) = 3√2

f(3) = 3√3

The area of each rectangle is the product of the width and the height.

L1 = 1 * 0 = 0

L2 = 1 * f(1)

L3 = 1 * f(2)

L4 = 1 * f(3)

To estimate the total area, we sum up the areas of the four rectangles:

L4 = L1 + L2 + L3 + L4

Now, to determine whether the estimates are underestimates or overestimates, we compare them to the actual area under the curve.

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Answer:

t cannot be -5 or 0 because these cause a 0 in the denominator and you cant divide by 0 that I'm aware of

True, to calculate the average of numeric values in the list, the first step is to get the total of values in the list.

Steps to calculate the Average:

Let’s assume there are 4 numbers having values of 2,8,22,48 respectively.

To find the average we first have to take the total of all values.

2+8+22+48=80.

Our next step will be to divide this total by the number we have in our question i.e., 4.

so, our average will be 80/4= 20.

So, 20 will be our average.

So yes, it is true that to calculate the average of numeric values in the list, the first step is to get the total of all values in the list.

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Given the volume of the cube, the length of each edge of the cube is approximately 2.62ft.

The volume of a cube is expressed as;

V = a³

Where a is the length of the edges.

Given the data in the question;

We substitute the given value into the equation above.

V = a³

18ft³ = a³

Take the cube root of both sides.

a = ∛(18ft³)

a = 2.62ft

Given the volume of the cube, the length of each edge of the cube is approximately 2.62ft.

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Answer:

x=32

Step-by-step explanation:

you have to solve by taking the interior angle of polygon

Answer:

\((4,8)\)

Step-by-step explanation:

\(y=x^2-8x+24 \\ \\ y=(x^2-8x+16)+24-16 \\ \\ y=(x-4)^2+8\)

So, the vertex is \((4,8)\).

The sum of angles in any triangle is 180 degrees.

We are given that;

The line AB parallel to CD

Now,

angle ACD = angle A (alternate interior angles) angle BCD = angle C (corresponding angles) angle ACD + angle BCD + angle B = 180 (sum of angles in a straight line)

Substituting angle A for angle ACD and angle C for angle BCD, we get:

x + z + y = 180

which is equivalent to:

x + y + z = 180

Therefore, by the angles the answer will be 180 degrees.

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The partial derivative \($f_{xyz}$\) of the function

\($f(x, y, z) = e^{x} \cdot sin(yz)$\) is given by

\($f_{xyz} = -y^2 e^x sin(yz)$\)

The given function is \($f(x, y, z) = e^{x} \cdot sin(yz)$\).

We need to compute \($f_{xyz}$\) using the formula of partial differentiation.

The formula of partial differentiation is

\(f_{xyz} = \frac{\partial^3 f}{\partial x \partial y \partial z}\)

We differentiate the given function f(x, y, z) partially with respect to x, then with respect to y, and finally with respect to z. We use the chain rule for differentiation since x, y, and z are functions of t.

We have

\(\frac{\partial f}{\partial x} = \frac{\partial}{\partial x} \left[ e^x \cdot sin(yz) \right] \\= e^x \cdot sin(yz) \cdot \frac{\partial}{\partial x} \left[ x \right] \\= e^x \cdot sin(yz)\)

Next, we differentiate with respect to y,

\(\frac{\partial f}{\partial y} = \frac{\partial}{\partial y} \left[ e^x \cdot sin(yz) \right] \\= e^x \cdot cos(yz) \cdot \frac{\partial}{\partial y} \left[ yz \right] \\= e^x \cdot cos(yz) \cdot z\)

Finally, we differentiate with respect to z,

\(\frac{\partial f}{\partial z} = \frac{\partial}{\partial z} \left[ e^x \cdot sin(yz) \right] \\= e^x \cdot cos(yz) \cdot \frac{\partial}{\partial z} \left[ yz \right] \\= e^x \cdot cos(yz) \cdot y\)

Therefore,

\(\frac{\partial^3 f}{\partial x \partial y \partial z} = \frac{\partial}{\partial z} \left[ e^x \cdot cos(yz) \cdot y \right] \\= e^x \cdot sin(yz) \cdot y \cdot (-y) \\= -y^2 e^x sin(yz)\)

Hence,

f_{xyz} = \frac{\partial^3 f}{\partial x \partial y \partial z} = -y^2 e^x sin(yz)

Conclusion: The partial derivative \($f_{xyz}$\) of the function

\($f(x, y, z) = e^{x} \cdot sin(yz)$\) is given by

\($f_{xyz} = -y^2 e^x sin(yz)$\).

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Answer:

x y

1 2

2 2

3 2

4 2

5 2

To write the equation y = -2x + 6 as a table, we need to substitute different values of x into the equation and solve for y. Here is an example of a table with some values of x and the corresponding values of y:

x y

1 4

2 2

3 0

4 -2

5 -4

Step-by-step explanation:

Hence, the deal of  $\(479\) is best unit price per blender.

What is the equation?

The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.

Here given that,

Oliver is buying equipment for his restaurant. He can buy two blenders for $\(396\) or three blenders for $\(479\).

So,

Oliver buying two blenders at  $\(396\) so the cost of one blender is

i.e., \(\frac{396}{2}=198\)$

Oliver buying two blenders at  $\(479\)  so the cost of three blenders is

i.e., \(\frac{479}{3}=159\)$

Hence, the deal of  $\(479\) is best unit price per blender.

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Answer:

b= 50

Step-by-step explanation:

the entire angle equals 80 degrees and a portion of it equals 30. therefore the portion that equals b = 50 because 30+50=80 hope this helps.

The total number of seeds that Josiah would plant would be = nR×S

To determine the total number of seeds that Josiah will plant will be to add the seeds in the total number of rooms he planted.

Let each row be represented as = nR

Where n represents the number of rows planted by him.

Let the seed be represented as = S

The total number of seeds he planted = nR×S

Therefore, the total number of seeds that was planted Josiah would be = nR×S.

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In the given parallelogram vwxy: x = 3; m∠Y = 65° and ∠YVX = 61° by (alternate interior angle).

A quadrilateral with the opposing sides parallel is called a parallelogram (and thus opposite angles equal).

In the given parallelogram vwxy:

Parallel sides are equal.

So, 2x = 6

x = 6/2 = 3

Opposite pair of angles are also equal.

So,

∠W = ∠Y = 65°

Now,

∠YVX = 61° (alternate interior angle).

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The mathematical comparison of your experimental results to a known value is known as Percentage error.

According to the statement

We have to tell the term about the experimental value and the known value comparison.

So, For this purpose, we know that the

when we compare the known value with the comparison va;ue and by this way we find the percentage error.

So,

Percent error is the difference between estimated value and the actual value in comparison to the actual value and is expressed as a percentage.

And by this way we find that the experimental value is correct or not.

Because when the percentage error is increased then experimental value stated as false values.

So, The mathematical comparison of your experimental results to a known value is known as Percentage error.

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The half-life of radon-222 is 3 days, it will take an additional 3 days for the remaining 42% of the sample to decay, for a total of 6 days for the sample to decay completely.

The half-life of a radioactive is time for 50% of its particles to decay or disintegrate into a new element. The pace at which a radioactive material will decay is predicted using this indicator of an isotope's stability. An element's half-life, which differs substantially across various elements, is based on the unique characteristics of its nucleus.

For instance, the half-life of uranium-238 is 4.5 billion years whereas that of carbon-14 is 5,730 years. This indicates that half of the carbon-14 atoms in a sample will have decayed after 5,730 years, and half of the uranium-238 atoms will have decayed after 4.5 billion years.

How to solve?

(a) After 3 days, the sample has decayed to 58% of its original amount, which means that half of the original amount has already decayed. Therefore, the half-life of radon-222 is 3 days.

(b) Since the half-life of radon-222 is 3 days, it will take an additional 3 days for the remaining 42% of the sample to decay, for a total of 6 days for the sample to decay completely.

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the vector pq is drawn from origin to point (1,-3)

To sketch the vector  p q in the plane, we start at the initial point p (2, -2) and end at the terminal point q (3, -5).

First, draw a coordinate system with x and y axes. Then plot the point p at (2, -2) and the point q at (3, -5).

Next, draw an arrow from point p to point q. The length of the arrow represents the magnitude of the vector, and the direction of the arrow represents the direction of the vector.

The vector p q can be represented as the difference between the coordinates of q and p:

p q = (3, -5) - (2, -2) = (1, -3)

So the vector pq is drawn from origin to point (1,-3)

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Answer:

60%

Step-by-step explanation:

8-5=3

3/5=0.6 and 0.6 = 60%

so 3 is 60% or 5

so 5+3 is a 60% increase

Answer: B.3x

Step-by-step explanation:

- Events A, B, C, and D are exhaustive.
- Events A and B, B and D are not mutually exclusive.
- Events A and C, C and D, A and D are mutually exclusive.

To determine whether the events are exhaustive or mutually exclusive, we need to understand the definitions of these terms:
1. Exhaustive events: Events are considered exhaustive if the union of all the events covers the entire sample space S. In other words, there are no outcomes in the sample space that are not included in any of the events.
2. Mutually exclusive events: Events are considered mutually exclusive if they have no outcomes in common. In other words, the events cannot occur simultaneously.
Now let's analyze the given events:
A = {1, 2, 4}
B = {1, 2, 4, 5, 6}
C = {5, 6}
D = {2, 3, 6}
To determine if the events are exhaustive, we need to check if their union covers the entire sample space S.
The union of A, B, C, and D is {1, 2, 3, 4, 5, 6}, which covers the entire sample space S. Therefore, the events A, B, C, and D are exhaustive.

To determine if the events are mutually exclusive, we need to check if any outcomes are shared between the events.
The outcomes 1, 2, and 4 are shared between events A and B. Therefore, events A and B are not mutually exclusive.
The outcomes 2 and 6 are shared between events B and D. Therefore, events B and D are not mutually exclusive.
No outcomes are shared between events A and C, C and D, or A and D. Therefore, events A and C, C and D, and A and D are mutually exclusive.

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Answer:

6 seconds

Step-by-step explanation:

h(x)=-(x-2)^2+16

We want h(x) to be 0 ( that is when the ball hits the ground)

0 = -(x-2)^2+16

Subtract 16 from each side

-16  = -(x-2)^2+16-16

-16 = -(x-2)^2

Divide by -1

16 = (x-2)^2

Take the square root of each side

sqrt(16) = sqrt((x-2)^2)

±4 = x-2

Add 2 to each side

2±4 = x-2+2

2±4 =x

2+4 = x   2-4 = x

6 =x  -2 =x

Time cannot be negative so x=6

Answer:

X = 6

Step-by-step explanation:

hope it will help you

Answer:

35 average minutes at practice.

Step-by-step explanation:

Answer:

What do I find?

If it's the mean then the answer is 35.

Step-by-step explanation:

34, 30, 45, 30, 40, 38, 28 ==> 7 numbers

34+30+45+30+40+38+28=245

245/7=35

Answer:

All answers below in explanation!

Step-by-step explanation:

1. x / 3 = 15 - 5

2. 2x = 11 + 6

3. x = -12

4. 400 - 20x = 60

Answer:

3734.95

Step-by-step explanation:

Pi = 3.14 to find the radius of a circle we multiply the circumference and Pi. Then square it. So, 34.48x3.14 = 108.2672 then 108.2672² = 3734.94651 which rounds to 3734.95

Answer:

D

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

-2x² + 3x + 10

Step-by-step explanation:

-(2x² - 3x - 7) + 3

-2x² + 3x + 7 + 3

-2x² + 3x + 10