5 find the missing length

Answer:

6.2 is an integer

Step-by-step explanation:

Answer

6.2

Step-by-step explanation:

The first part of the question asks to draw and set up the integrals for finding the area enclosed by the y-axis, the curve y = (x + 1)¹/2, and y = 2. It needs to be determined whether the region is a type I or type II region.

The second part of the question asks to set up the integrals (without computation) for finding the volumes of solids of revolution by revolving the region enclosed by the x-axis, y = ln(x), and the line x = e about y = 3. The washer method and cylindrical shell method are to be used, and the formulas for radii and heights need to be shown.

For the first part of the question, to find the area enclosed by the y-axis, y = (x + 1)¹/2, and y = 2, we need to determine the type of region. By analyzing the given curves, it can be observed that the region is a type II region. The integral for calculating the area can be set up as ∫[a, b] (f(x) - g(x)) dx, where f(x) represents the upper curve (y = 2), and g(x) represents the lower curve (y = (x + 1)¹/2).

For the second part of the question, to find the volumes of solids of revolution by revolving the region enclosed by the x-axis, y = ln(x), and x = e about y = 3, two methods are mentioned: the washer method and the cylindrical shell method. For the washer method, the integral can be set up as ∫[a, b] π(R² - r²) dx, where R represents the outer radius and r represents the inner radius. For the cylindrical shell method, the integral can be set up as ∫[a, b] 2πrh dx, where r represents the radius of the cylinder and h represents the height.

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Answer:

20 pounds

Step-by-step explanation:

250% = 2.5

8 times 2.5 = 20 pounds

So, a one-year-old baby weighs 20 pounds.

The integral in spherical coordinates becomes:

∫(c to d) ∫(0 to 2π) ∫(a to b) 3√(9 - ρ²sin²(φ)) ρ²sin(φ) dρ dθ dφ

We have,

To change the given integral to spherical coordinates, we need to express the differential volume element dV in terms of ρ, θ, and φ. In spherical coordinates, the differential volume element is given by ρ²sin(φ) dρ dθ dφ.

Now let's change the integral ∫∫∫ 3√(9 - x²) dV to spherical coordinates:

∫∫∫ 3√(9 - x²) dV

= ∫∫∫ 3√(9 - ρ²sin²(φ)cos²(θ) - ρ²sin²(φ)sin²(θ)) ρ²sin(φ) dρ dθ dφ

= ∫∫∫ 3√(9 - ρ²sin²(φ)(cos²(θ) + sin²(θ))) ρ²sin(φ) dρ dθ dφ

= ∫∫∫ 3√(9 - ρ²sin²(φ)) ρ²sin(φ) dρ dθ dφ

The limits of integration for the spherical coordinates are:

For ρ: a ≤ ρ ≤ b

For θ: 0 ≤ θ ≤ 2π

For φ: c ≤ φ ≤ d

Therefore,

The integral in spherical coordinates becomes:

∫(c to d) ∫(0 to 2π) ∫(a to b) 3√(9 - ρ²sin²(φ)) ρ²sin(φ) dρ dθ dφ

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The complete question:

Change the integral ∫∫∫ 3√(9 - x²) dV to spherical coordinates, where the limits of integration are as follows:

For ρ: a ≤ ρ ≤ b

For θ: 0 ≤ θ ≤ 2π

For φ: c ≤ φ ≤ d

The total current bid by Empire design is 300b + 60l while the total current bid by the Build Em- Up co. is 320b + 40l.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

Here,
According to the condition,
The amount of the bid is given by the expression of the arithmetic sum of the individual charges for the bridge length b and the number of beams l.
So,
(a) The total current total bid by Empire design is 300b + 60l in dollars,
(b) the total current bid by the Build Em- Up co. is 320b + 40l. in dollars,

Thus, the current total bid by Empire design is 300b + 60l while the total current bid by the Build Em- Up co. is 320b + 40l.

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Step-by-step explanation:

step 1. we will denote the average rate of change as r.

step 2. r = (f(5) - f(3))/(5 - 3)

step 3. r = (375 - 81)/2

step 4. r = 294/2

step 5. r = 147.

step 6. note: this is just like finding m. m = (y2 - y1)/(x2 - x1)

The angle of depression of the fish from the given height to the bottom of the lake is 60° .

The bird caught the fish at site A, flew it 100 yards to location B, and then dropped it off at location C. (which is horizontally 50 yards from A).

The right angled triangle BAC is equal to the length of the perpendicular and base .

The angle the bird creates with the water piques our interest (horizontal). This angle is BAC. We can claim to be knowledgeable about the "hypotenuse" and "adjacent" side of the right triangle to angle BAC. Since the cosine relationship between the hypotenuse and its neighbors exists, we can write:

cos BAC = 50/100

BAC = cos ⁻¹ 1/2

BAC = 60 °

Here, our goal is to determine the length (distance) of segment BC. We can say that BC is "opposite" to the angle BAC, which we discovered to be 60 degrees. The hypotenuse is known to be 100. So let's utilize sine since sine is the ratio of the hypotenuse's opposite.

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Answer:

D is the correct answer i think

Step-by-step explanation:

Domain of the function is option (D) {2, 4, 6, 8}

The domain of a function is the set of inputs accepted by the function.

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

From the given table,

Domain of the function is {2, 4, 6, 8}

Because the domain of a function is the set of inputs accepted by the function.

Hence, Domain of the function is option (D) {2, 4, 6, 8}

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Answer:

-1024

Step-by-step explanation:

multiply each number by 2

Answer:

The evening temperature is 4° F

Step-by-step explanation:

6° F below 0 =  -6.

15° F. -6 + 15 is 9.

9° F. 5° F. 9 - 5 = 4

Answer:

CAUSE I FEEL THE BREK FEEL THE BREK FELLLLLLL THE BREKK

Step-by-step explanation:

Answer:

1a 1/4  1b 1/4  2a 5  2b40  

Step-by-step explanation:

Answer:

x  = 0

  y  = -2

Step-by-step explanation:

The given system of equation are:

   5x + y = -2

   2x - 2y = 4  

The problem here is to find x and y from the expression

   5x + y = -2     ----- i

   2x - 2y = 4    ---- ii

 So;

i x 2 :  10x + 2y  = -4     ----  iii

ii x 5 :  10x - 10y  = 20    ----- iv

   iii - iv;   12y  = -24

                  y  = -2

    Now find x;

             5x + y  = -2

             5x  - 2  = -2

                  x  = 0

Answer:

24) 23.79

25)1.79

These answers are rounded

Step-by-step explanation:

The formula which shows how to calculate the number of tires, t, needed if they produce c cars per day is t = 5c. option D

Total tires needed by each car = 4 + 1

= 5

Total number of tires, t needed for c cars.

Number of tires needed, t = Total tires needed by each car × Number of cars produced per day

t = 5 × c

t = 5c

For instance,

if 5 cars are produced per day

Number of tires needed, t = Total tires needed by each car × Number of cars produced per day

t = 5c

= 5 × 5

t = 25 tires

Therefore, the formula which shows how to calculate the number of tires, t, needed if they produce c cars per day is t = 5c. option D

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Answer:

$18.4

Step-by-step explanation:

40oz=2.5lb

10lb=4*2.5lb=4*4.6=18.4

The desired fuel efficiency of a car two years from now would ideally be improved compared to the current fuel efficiency.

There are several reasons why we would want the fuel efficiency of a car to be better in the future:

Environmental Concerns: Improving fuel efficiency helps reduce carbon emissions and minimize the environmental impact of vehicles. As the world becomes more conscious of climate change and the need to reduce greenhouse gas emissions, enhancing fuel efficiency plays a vital role in mitigating environmental damage.

Energy Conservation: Better fuel efficiency means using less fuel to travel the same distance. With finite energy resources and the need to conserve them, improving fuel efficiency helps reduce the overall energy consumption in transportation, leading to better resource management.

Cost Savings: Increasing fuel efficiency directly translates to lower fuel consumption and reduced expenses for car owners. With rising fuel prices, having a more fuel-efficient car can significantly cut down on fuel costs, saving money for individuals and businesses.

Technological Advancements: As technology progresses, advancements in engine design, aerodynamics, lightweight materials, and alternative energy sources enable the development of more fuel-efficient vehicles. Striving for improved fuel efficiency encourages innovation in the automotive industry, leading to the creation of more sustainable and eco-friendly transportation options.

Government Regulations: Many governments worldwide have implemented fuel efficiency standards and regulations to reduce fuel consumption and emissions. By meeting or exceeding these standards, car manufacturers contribute to a cleaner and more sustainable transportation sector.

Ultimately, aiming for improved fuel efficiency two years from now aligns with the global push for environmental sustainability, energy conservation, cost savings, technological advancements, and adherence to regulatory standards. It benefits both individuals and society as a whole by promoting a greener and more efficient approach to transportation.

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The dimensions of the lightest open-top right circular cylindrical can that will hold a volume of 1331 cm³ are a radius of √(1331/π) cm and a height of 2√(1331/π) cm.

The volume V of a right circular cylindrical can is given by V = πr²h, where r is the radius and h is the height of the can. We are given that the volume of the can is 1331 cm³.

To find the dimensions of the lightest can, we need to minimize the surface area of the can, which corresponds to minimizing the sum of the lateral surface area and the top surface area. Since the can is open-top, we can ignore the bottom surface area.

The lateral surface area A of a right circular cylindrical can is given by A = 2πrh, and the top surface area is given by A_top = πr².

By substituting the volume equation into the lateral surface area equation, we can express the lateral surface area as A = 2V/h.

To minimize the surface area, we need to minimize the sum of A and A_top. Since A_top = πr², we can rewrite the sum as A_total = 2V/h + πr².

To find the dimensions that minimize A_total, we can differentiate A_total with respect to r and h, set the derivatives equal to zero, and solve the resulting equations. However, since we are only interested in the dimensions, we can substitute the given volume and radius into the equations and simplify.

By substituting V = 1331 cm³ and r = √(1331/π) cm, we find that h = 2√(1331/π) cm.

Therefore, the dimensions of the lightest open-top right circular cylindrical can that will hold a volume of 1331 cm³ are a radius of √(1331/π) cm and a height of 2√(1331/π) cm.

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k = 13The smallest zero or root is x = -10

===============================

Steps:

note: you can write "x^2" to mean "x squared"

f(x) = x^2+3x-10

f(x+5) = (x+5)^2+3(x+5)-10 ... replace every x with x+5

f(x+5) = (x^2+10x+25)+3(x+5)-10

f(x+5) = x^2+10x+25+3x+15-10

f(x+5) = x^2+13x+30

Compare this with x^2+kx+30 and we see that k = 13

Factor and solve the equation below

x^2+13x+30 = 0

(x+10)(x+3) = 0

x+1 = 0 or x+3 = 0

x = -10 or x = -3

The smallest zero is x = -10 as its the left-most value on a number line.

Please mark brainliest

Hope this helps.

Answer:

\(\dfrac{3}{85}\)

Step-by-step explanation:

It is given that a small town’s raffle has 85 entries and 3 gift baskets that three different people could win.

Total number of entries = 85

Total number of gift baskets = 3

We need to find the probability of winning a gift basket.

\(\text{Required probability}=\dfrac{\text{Total number of gift baskets}}{\text{Total number of entries}}\)

\(\text{required probability}=\dfrac{3}{85}\)

Therefore, the required probability is \(\dfrac{3}{85}\).

Answer:

2 n - 2 = n - 38

Step-by-step explanation:

Two fewer than "a number doubled"

2n-2 = n-38

Answer:

The mode of the age is 8 so their will be 3 birds with the age of 8 and 1 bird with the age of 14 and one bird with the age of  12 and another bird with the age of 10.

Step-by-step explanation:

Work Shown:

\(V = \pi*r^2*h\\\\V \approx 3.14*(5.1)^2*2.8\\\\V \approx 228.67992\\\\V \approx 228.68\\\\\)

The volume is approximately 228.68 cubic feet.

The result is approximate because pi = 3.14 is approximate.

Answer:

Step-by-step explanation:

Answer:

X=140

Step-by-step explanation:

Firstly, any Quadrilateral has a total sum of its angle equal to 360 degrees

The attachment you are showing us shows that we already know two angles

(70)&(60) degrees. I am assuming the line DC is a tangent, so angle ADC must be 90 degrees since a full angle on a tangent is equal to 180 degrees and there is 90 from the other side (180-90=90). Now we know 3 angles and what you have to do is find X so that when you add them all up they make a sum of 360.

X+70+60+90=360

X=360-70-60-90

X=140

To find the distance between two parallel planes, we can use the formula:
distance = |(d - c) / ||n|||

where d and c are the distances of the two planes from the origin, and ||n|| is the magnitude of the normal vector of the planes.

In this case, both planes have the same normal vector (7, 5, 5), so we only need to find the distances from the origin.

For the first plane, 7x + 5y + 5z = 28, we can find the distance by dividing the constant term by the magnitude of the normal vector:
distance1 = |28 / ||(7, 5, 5)|||

                = |28 / sqrt(99)| ≈ 2.87

For the second plane, 7x + 5y + 5z = 42, we can find the distance in the same way:
distance2 = |42 / ||(7, 5, 5)|||

                  = |42 / sqrt(99)| ≈ 4.35

Therefore, the distance between the two planes is:
distance = |(42 / sqrt(99)) - (28 / sqrt(99))| ≈ 1.48

So the distance from the plane 7x + 5y + 5z = 28 to the plane 7x + 5y + 5z = 42 is approximately 1.48 units.

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Answer:

y = -3x + 13

Step-by-step explanation:

For slope-intercept form, you need the slope and the y-intercept.  To find the slope, you need to rearrange the given equation to slope-intercept form.

x - 3y = 9

-3y = -x + 9

y = 1/3x - 3

The slope for the given equation is 1/3.  The slope of a perpendicular line will be the negative reciprocal.  This means that the slope of the perpendicular line will be -3.

You can now solve for the y-intercept (b) using the slope (m) and the given point in slope-intercept form.

y = mx + b

1 = (-3)(4) + b

1 = -12 + b

13 = b

b = 13

Now that you have both the slope and y-intercept, you can find the equation.

y = -3x + 13

The equation of the line is y = -3x + 13

The equation of a line is an algebraic form of representing the set of points, which together form a line in a coordinate system.

The slope intercept form is given by:

y = mx + b

m = slope and b = y-intercept

We have,

A line perpendicular to line x - 3y = 9 and the line passes through the point (4, 1).

Make the line x - 3y = 9 in slope-intercept form.

-3y = 9 - x

y = (9 - x) / -3

y = (1/3)x - 3

The slope of the line x - 3y = 9 is:

m1=  1/3

Since the line required to find is perpendicular to the line x - 3y = 9

Let the required line slope be m2

m1 x m2 = -1

m2 = -1 / (1/3) = -3

The required line passes through the point (4, 1).

Let the required line be y = mx + b

we have,

1 = (-3)4 + b

1 = -12 + b

b = 13

We can write as:

y = -3x + 13

Thus the equation of the line is y = -3x + 13

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Answer:

smack her or washout her mouth with soap than

Step-by-step explanation:

The mean of the given set of group numbers is 6.6

Given,

In the question:

The Group of numbers are as follows:

6.1, 5.9, 4.2, 5.9 and 10.7

To find the mean of the given set of group of numbers.

Now, According to the question:

Given is the following data:

6.1, 5.9, 4.2, 5.9 and 10.7

We can find the mean of the given set of data using the formula-

Mean (M) = Σ a[i]/n = (Sum of all the elements)/(total number of elements)

Now, n = 5

and Σ a[i] = 6.1 + 5.9 + 4.2+ 5.9 + 10.7 = 32.8

Putting the values in the formula, we get:

M = 32.8/5 = 6.56 = 6.6

Hence, The mean of the given set of group numbers is 6.6

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