You measure the height and diameter (of the base) of a right circular cone to be h=20 cm and d=8cm. However, your measuring device is only accurate to the nearest millimeter. Estimate the error in calculating volume of the cone using these measurements by finding the differential dV.

The equation of a circle having endpoints of diameter as (4,9) and (4,-3) is (x - 4)² + (y - 3)² = 36.

The "center" of circle is called as midpoint of diameter.

The "x-coordinate" of "mid-point" is = (4+4)/2 = 4, and

The "y-coordinate" of "mid-point" is = (9+(-3))/2 = 3.

So, center of circle is (4,3),

The radius of circle is half the length of the diameter, which is distance between two endpoints of diameter. We find distance using distance formula:

⇒ distance = √((x₂ - x₁)² + (y₂ - y₁)²), where (x₁,y₁) and (x₂,y₂) are "end-points" of diameter.

⇒ distance = √((4 - 4)² + (9 - (-3))²)

⇒ √(144) = 12.

So, radius is 6.

The equation of circle with center (h,k) and radius "r" is : ⇒ (x - h)² + (y - k)² = r²,

Substituting the values

We get,

⇒ (x - 4)² + (y - 3)² = 6²,

⇒ (x - 4)² + (y - 3)² = 36,

Therefore, the equation of the circle is (x - 4)² + (y - 3)² = 36.

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According to the definition of the inverse function, given a function f

Therefore, regardless of function f(x), f(f^-1(x))=x, we do not even need to know the analytic form of f^-1(x). The answer is x.

9514 1404 393

Answer:

  -8x +12

Step-by-step explanation:

The distributive property can help you simplify the product.

  (4)(-2x +3) = (4)(-2x) +(4)(3) = -8x +12

Answer:

b. To find the probability a customer who ordered pancakes came to thediner late, we need to look at the intersection of the "pancakes" row and the "late" column. This gives us a probability of 0.1, or 10%

c. To determine whether breakfast choice and meal time are independent, we need to see if the probability of one event changes based on the occurrence of the other event. In this case, it seems that breakfast choice and meal time are not independent, as the probability of being late seems to differ based on what breakfast item the customer chose. For example, the probability of being late is higher for customers who ordered pancakes compared to those who ordered cereal. Therefore, the choice of breakfast item appears to be related to the probability of being late, and so breakfast choice and meal time are not independent.

Step-by-step explanation:

Answer:

2. 7/72 it is less than

3. 49/70 it is equal to

Step-by-step explanation:

2. 7*1=7, 8*9= 72. 7/72.

3. 7*7=49, 7*10=70, 49/70

To use a triple integral to find the volume of the solid bounded by the surfaces z and z over the rectangle.

1. Determine the limits of integration for the rectangular region: Let's say the rectangular region is given by x ranges from a to b, y ranges from c to d, and z ranges from f(x, y) to g(x, y).

2. Set up the triple integral: The triple integral will have the form:
  ∫∫∫(dV) = ∫[a, b] ∫[c, d] ∫[f(x, y), g(x, y)] (dz dy dx)

3. Evaluate the innermost integral: Compute the integral with respect to z, keeping x and y constant.
  ∫[f(x, y), g(x, y)] (dz) = g(x, y) - f(x, y)

4. Substitute the result into the original triple integral: Now we have:
  ∫∫∫(dV) = ∫[a, b] ∫[c, d] (g(x, y) - f(x, y)) (dy dx)

5. Evaluate the remaining integrals: Compute the double integral by first integrating with respect to y, then with respect to x.

6. The result of the final integration will be the volume of the solid bounded by the surfaces z and z over the rectangle.

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Answer: The lines are only parallel if these pairs of angles are of equal size:

Angle 1 ≡ Angle 5

Angle 2 ≡ Angle 6

Angle 3 ≡ Angle 7

Angle 5 ≡ Angle 8

Step-by-step explanation:

All these angles follow a rule called corresponding angles. The rule goes that corresponding angles on parallel lines are equal. If the pairs of angles are equal, this must mean that the lines are parallel and vice versa.

Answer: 63 ÷ (7-4) x 2=42

Step-by-step explanation:

Answer:

The answer is 42

Step-by-step explanation:

We can solve this by using Order of Operations

1. Solve whats inside the parentheses (7-4) =3

63÷3×2

2. Now solve from left to right

63÷3 =21

21 ×2= 42

And we get a final answer of 42.

Hope this helps!

The volume of the sphere with radius R is (1/5)R⁵.

In spherical coordinates, x = ρsinφcosθ. Therefore, x² = ρ²sin²φcos²θ. The integral becomes ∫ρ²sin²φcos²θρ²sinφdρdθdφ.

The limits of integration are 0 ≤ ρ ≤ R, 0 ≤ θ ≤ 2π, and 0 ≤ φ ≤ π. Solving the integral gives (1/5)R⁵. This is the volume of a sphere with radius R multiplied by (1/5). The reason for this is that x² is an even function, meaning that it is symmetric across the yz-plane.

Therefore, the integral over the whole sphere will be equal to the integral over half the sphere multiplied by 2. And the integral over half the sphere is just the volume of a hemisphere, which is (2/3)πR³/2.

Multiplying by 2 gives (4/3)πR³/2, which is the volume of a sphere with radius R multiplied by (2/3).

Dividing this by 4π/3, the volume of a sphere with radius R, gives the result of (1/5)R⁵.

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7 organisms

Area of lawn that supplies oxygen for a particular multicellular organism = 625 sq ft

Total area of the lawn = 4,375 sq ft

Number of organisms = 4375/625

Number of organisms = 7

A total of 4,375 sq ft of lawn would provide the daily supplies of oxygen for 7 organisms

Answer:

D. Horizontally compressed by a factor of 1/3

The correct answer is B. The passage states that "The United States forced Japan to strip its emperors of significant power after World War II." This is a clear example of a change in the role of the Japanese emperors.

Answer:

-22

Step-by-step explanation:

Answer:

h(x) = 10y/2

Step-by-step explanation:

6x + y = 4x + 11y

6x - 4x = 11y - y

2x = 10y

divide both side by 2

x = 10y/2

h(x) = 10y/2

Answer: a) 190cm³

              b) 76cm³

(refer to the image to see all the steps and workings I did related to these diagrams)

Answer:

20 days

Step-by-step explanation:

Because to find the number of days that Sonia will have you have to divide total money ($40) by money each day ($2). And $40 divided by $2 is 20, so 20 days is the answer.

Have a most wonderfull day, and I hope you likeee the answer....so yep.

The total perimeter will be 4x^+17 and length be 22.76 cm

As per the data given in the questions,

We have, the shape of the sandwich be rectangular.

We know that, perimeter of the rectangle can be determined by using formula: 2(l+b),

where, l = length of the rectangle

and, b = breadth of the rectangle

The expression for the perimeter of the sandwich would be:

2 (2x^2 + 9) + 2 (2x^2 + 8)

= 4x^2 + 26

Now for finding the length of the crust,

we will put the value of x=1.2,

So, the value of the approximate length of the crust would be:

=4x^2 + 26

= 4 * 1.2^2 + 26

= 22.76 centimetres.

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Answer:

Option A

Step-by-step explanation:

Given the following question:

\(x < -1\)

Keep a few things in mind when graphing the inequality:
. x value is less than -1 (which means the line will go in the direction of the x)
. < is a greater sign not greater than or equal (≤) so it would be a open dot.
. The number line starts at -1.

According to all this information your answer is indeed option A.

Hope this helps.

Answer:

2x+4

3x+15

4x+4

4x-8

Step-by-step explanation:

...............

Answer:

  30 miles per hour

Step-by-step explanation:

We want to know the average speed over a course with one leg run at one speed, and another leg run at a different speed.

To find the average speed, we need to know the total time and the total distance. The relation ...

  time = distance/speed   ⇔   distance = speed × time

can be used to fill in the blanks.

The first leg is a distance of 140 miles. The time for that leg is ...

  t1 = (140 mi)/(28 mi/h) = 5 h

The second leg takes 2 hours at a speed of 35 mph. The distance covered is ...

  d2 = (35 mi/h)(2 h) = 70 mi

The total distance is ...

  d = d1 +d2 = 140 mi +70 mi = 210 mi

The total time is ...

  t = t1 +t2 = 5 h + 2 h = 7 h

The average speed is the ratio of total distance to total time:

  d/t = (210 mi)/(7 h) = 30 mi/h

Susan's average speed for the trip was 30 mph.

Answer:

180 X 2 + 1200 X 2= YOUR ANSWER

Step-by-step explanation:

I can't give you your answer but I hope this helps PLEASE MARK ME AS BRAINLIEST

Answer:

2760

Step-by-step explanation:

first you do 180x2 then 1200x2 and once you got both of those numbers you add them togeterr so 360+2400=2760

Answer:

24

Step-by-step explanation:

Answer:

24

Joke answer: heaven

Step-by-step explanation:

\(3 \frac{3}{5} + 1 \frac{1}{6} = \\ \)

\( \frac{(3 \times 5) + 3}{5} + \frac{(1 \times 6) + 1}{6} = \\ \)

\( \frac{15 + 3}{5} + \frac{6 + 1}{6} = \\ \)

\( \frac{18}{5} + \frac{7}{6} = \\ \)

\( \frac{18 \times 6}{5 \times 6} + \frac{7 \times 5}{6 \times 5} = \\ \)

\( \frac{108}{30} + \frac{35}{30} = \\ \)

\( \frac{108 + 35}{ 30} = \\ \)

\( \frac{143}{30} \\ \)

Answer:

50

Step-by-step explanation:

The sum of angles in a triangle is 180 so the answer is 180 - 90 - 40 = 50.

Also, for your first question, 2 corresponding angles of the triangles must be congruent.

Answer:

B. 50°

Step-by-step explanation:

40°+90°+y = 180°

130°+y°=180°

y° =180°-130°

y = 50° (sum of the interior angles in a triangle=180°)

Answer:

2839.4 meters

Step-by-step explanation:

Given that:

Altitude = 1200 m

Using trigonometry :

The distance from point P to the airplane :

Using trigonometric relation :

Sin θ = opposite / hypotenus

Sin θ = altitude / x

Sin θ = 1200 m / x

Sin 25 = 1200 / x

0.4226182 = 1200 / x

x = 1200 / 0.4226182

x = 2839.4423

Distance from P to airplane = 2839.4 meters

The required original number that June was thinking of is 36.

Let's assume the original number June was thinking of is represented by "x". According to the problem, June doubles the original number (2x) and adds 18 to get an answer of 90. We can write this as the equation:

\(2x + 18 = 90\)

To find the value of x, we need to isolate it on one side of the equation. Let's subtract 18 from both sides:

\(2x = 90 - 18 \\ 2x = 72\)

Now, we divide both sides of the equation by 2 to solve for x:

\(x = 72 / 2 \\ x = 36\)

Therefore, the original number that June was thinking of is 36.

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The true statements are, Line A B and Line C G are parallel, Line C G and Line R S are perpendicular, Line A B and Line R S must intersect and Line segment C G lies in plane X.

Given that Planes X and Y intersect at a right angle. Line AB and CG are on plane X, while line RS is on plane Y. Therefore, line CG lies on plane X.

Since both line AB and CG lie on the same plane, they are parallel to each other.

Since plane X and plane Y are perpendicular to each other and line CG is on plane X while line RS is on plane Y, this means that Line CG and Line RS are perpendicular to each other.

Line AB and Line RS may or may not intersect. They could be skew lines, which do not intersect and are not parallel.

Line segment CG lies on plane X since it is contained within the plane that contains points C, G, and either A or B.

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The question is -

Which statements are true? Select three options.

a. Line A B and Line C G are parallel.

b. Line A B and Line R S are parallel.

c. Line C G and Line R S are perpendicular.

d. Line A B and Line R S must intersect.

e. Line segment C G lies in plane X.

f. Line segment R S lies in plane X.

Answer: ace

Step-by-step explanation:

Answer: 43.98cm

Step-by-step explanation:  C=2πr^2