What is 1+1? Please HELP!!!! Will give brainliest

The volume of the solid obtained by rotating the region bounded by the curve y = 1 - (x - 5)² in the first quadrant about the y-axis is 51π cubic units.

To find the volume of the solid obtained by rotating the region bounded by the curve y = 1 - (x - 5)² in the first quadrant about the y-axis, we can use the method of cylindrical shells.

The formula for the volume using cylindrical shells is:

V = 2π ∫ [a, b] x * h(x) dx

Where:

- V is the volume of the solid

- π represents the mathematical constant pi

- [a, b] is the interval over which we are integrating

- x is the variable representing the x-axis

- h(x) is the height of the cylindrical shell at a given x-value

In this case, we need to solve for x in terms of y to express the equation in terms of y.

Rearranging the given equation:

x = 5 ± √(1 - y)

Since we are only interested in the region in the first quadrant, we take the positive square root:

x = 5 + √(1 - y)

Now we can rewrite the volume formula with respect to y:

V = 2π ∫ [c, d] x * h(y) dy

Where:

- [c, d] is the interval of y-values that correspond to the region in the first quadrant

To determine the interval [c, d], we set the equation equal to zero and solve for y:

1 - (x - 5)² = 0

Expanding and rearranging the equation:

(x - 5)² = 1

x - 5 = ±√1

x = 5 ± 1

Since we are only interested in the region in the first quadrant, we take the value x = 6:

x = 6

Now we can evaluate the integral to find the volume:

V = 2π ∫ [0, 1] x * h(y) dy

Where h(y) represents the height of the cylindrical shell at a given y-value.

Integrating the expression:

V = 2π ∫ [0, 1] (5 + √(1 - y)) * h(y) dy

To find h(y), we need to determine the distance between the y-axis and the curve at a given y-value. Since the curve is symmetric, h(y) is simply the x-coordinate at that point:

h(y) = 5 + √(1 - y)

Substituting this expression back into the integral:

V = 2π ∫ [0, 1] (5 + √(1 - y)) * (5 + √(1 - y)) dy

Now, we can evaluate this integral to find the volume

V = 2π ∫ [0, 1] (5 + √(1 - y)) * (5 + √(1 - y)) dy

To simplify the integral, let's expand the expression:

V = 2π ∫ [0, 1] (25 + 10√(1 - y) + 1 - y) dy

V = 2π ∫ [0, 1] (26 + 10√(1 - y) - y) dy

Now, let's integrate term by term:

\(V = 2\pi [26y + 10/3 * (1 - y)^\frac{3}{2} - 1/2 * y^2]\)] evaluated from 0 to 1

V = \(2\pi [(26 + 10/3 * (1 - 1)^\frac{3}{2} - 1/2 * 1^2) - (26 * 0 + 10/3 * (1 - 0)^\frac{3}{2} - 1/2 * 0^2)]\)

V = 2π [(26 + 0 - 1/2) - (0 + 10/3 - 0)]

V = 2π (25.5)

V = 51π cubic units

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Answer:

Two examples of points that satisfy this condition is (0,5) and (0,-5).

Step-by-step explanation:

Suppose we have two points:

\(A = (x_{1}, y_{1})\)

\(B = (x_{2}, y_{2})\)

The distance between these points is:

\(D = \sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}}\)

In this question:

B(0,0)

A(x,y)

We have to find x and y.

We have that:

\(\sqrt{(x-0)^{2} + (y-0)^{2}} = 5\)

\(\sqrt{x^{2} + y^{2}} = 5\)

\((\sqrt{x^{2} + y^{2}})^{2} = 25\)

\(x^{2} + y^{2} = 25\)

One example of a point:

I will say that x = 0. So

\(0^{2} + y^{2} = 25\)

\(y = \pm \sqrt{25}\)

\(y = \pm 5\)

So two examples of points that satisfy this condition is (0,5) and (0,-5).

The distance formula is a formula that is used to find the distance between two points.

The coordinate of point A is (0, 5)  or   (0, -5).

Let us consider that, coordinate of point A is (x, y).

The distance between (0,0) and (x, y) is computed as by using distance formula.

                 \(Distance=\sqrt{(x-0)^{2}+(y-0)^{2} } \\\\5=\sqrt{(x-0)^{2}+(y-0)^{2} } \\\\x^{2} +y^{2}=25\)

All values that satisfies above equation, will be the coordinate of point A.

When x = 0,  

                \(y=\sqrt{25} =\pm 5\)

The coordinate of point A is (0, 5)  or   (0, -5).

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The critical points for the equation \(f(x)=(x^{2} +64)^{\frac{1}{11} }\) is

\((x,f(x))\) = \((0,2^{\frac{6}{11} })\) = \((0,1.46)\). at x=0

The absolute maximum is at \((x,f(x))\\\) = \((9,\sqrt[11]{145} )\) =  \((9,1.6)\), at x=9.

What is the absolute maximum of an equation?

The highest conceivable values for f are represented by the absolute maximum (sometimes called the global maximum) of a function f(x) (x). Let's imagine the function's critical value, x=c, is present within its domain. If the inequality f(c) \(\geq\) f(x), x is a domain, then the function f(x) is said to satisfy an absolute maximum when x=c.

To find the critical points, we find the value of f'(x) and equate to 0.

\(\frac{d}{dx} (\sqrt[11]{x^{2}+64} )=0\)

we get x=0.

We see that f'(x) exists for all x between [-8,9].

We also find the endpoints, that is -8 and 9.

Then we calculate f(x) at critical points and endpoints.

We calculate f(x) at 0, -8, and 9.

We get,

for x=0, f(x)= \(2^{\frac{6}{11} }\)

for x=-8, f(x)= \(2^{\frac{7}{11} }\)

for x=9, f(x)= \(\sqrt[11]{145}\)

We see that the value is maximum at x=9, and f(x) becomes \(\sqrt[11]{145}\).

Hence we get the absolute maximum is \((x,f(x))\\\) = \((9,\sqrt[11]{145} )\) = \((9,1.6)\)

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The work done by the gas when the gas expands will be 878.89 ft-lb.

The Pressure is inversely proportional to the volume.

Let the initial pressure and initial volume be P₁ and V₁, and the final volume be V₂.

Then the work done by the gas will be

WD = P₁ V₁ ln (V₂ / V₁)

A quantity of the gas with an initial volume of 1 cubic foot and an initial pressure of 400 pounds per square foot.

The gas expands to a volume of 9 cubic feet.

Then the work done by the gas will be

WD = 400 x 1 x ln (9/1)

WD = 400 x 2.197

WD = 878.89 ft-lb

The work done by the gas when the gas expands will be 878.89 ft-lb.

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Answer:

  $28

Step-by-step explanation:

Each round trip will be double the price of a one-way trip, so will be ...

  2 × $3.50 = $7.00

Diego and his 3 friends will require a total of 4 round-trip tickets for a cost of ...

  4 × $7.00 = $28.00

Answer:3/4

Step-by-step explanation: If you weigh a brick at 2/4 lbs, it will weigh less than a brick that weighs 3/4

Answer:

The area of the smaller figure is 126 cm^2.

Step-by-step explanation:

3:7 ratio

Divide 294 by larger ratio.

294/7 = 42

Multiply 42 by the smaller ratio.

42 x 3 = 126

Answer:

10-8

Step-by-step explanation:

The number of years it would it take for there to be one person for every square yard is 108,325.68 years.

When there is one person for every square yard, it means that the population and land area are equal in value.

Number of years = (In FV / PV) / r

(In 19 billion / 4,079,000) / 0.043 = 108,325.68 years

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Answer: Choice D

can be larger, smaller, or equal to the number of degrees of freedom for the denominator.

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

Explanation:

The F distribution is useful to see if two groups have the same variance or not. By extension, we can compare standard deviations between two groups.

Let \(n_1\) and \(n_2\) be the sample sizes of the two groups. Those two n values aren't necessarily equal in value. All that matters is that they are positive whole numbers. The associated degrees of freedom are \(n_1 - 1\) and \(n_2 - 1\). Convention usually has the numerator with the larger variance, but we don't have to worry about that when addressing this particular question.

All we care about is if the quantities \(n_1 - 1\) and \(n_2 - 1\) are either:

It turns out that there aren't any restrictions on the values of n, which in turn means there aren't any restrictions on \(n_1 - 1\) and \(n_2 - 1\). Therefore, the degrees of freedom for the numerator can be larger, smaller, or equal to the number of degrees of freedom for the denominator.

This is why the answer is choice D

Further confirmation of this is to look at a standard F distribution table. Note that any cell is possible and we could have either of the three cases mentioned happen.

Answer:

2

Step-by-step explanation:

Took the test.

Step 1: Isolate the Sin Operator

\(8 sin(\frac{\pi }{6} x)=2\\sin(\frac{\pi }{6} x)=0.25\\\\\)

Step 2: Use Inverse Sin(arcsin) to isolate the term with the x variable

Note that since trig functions have 2 general solutions, this will give us one of our general solutions.

\(x=\frac{6 arcsin(0.25)}{\pi } =0.48\)

x₁= 0.48

Solving for x₂

Use the period identity for Sin Functions

\(sin(x)=sin(\pi -x)\)

X in this case is arcsin(0.25)

\(\frac{\pi }{6} x=\pi -arcsin(0.25) = 5.52\)

So our two general solutions are 0.48 and 5.52

Step 3: Period

Trig Functions have periodic behavior and this function period is

\(\frac{2\pi }{1} (\frac{6}{\pi } )= 12\)

So our general solutions are

0.48±12k, where k is an integer

5.52±12k, where k is an integer

Let k=1, and we get our next set of solutions:

12.48 and 17.52

So our answer is 0.48,5.52,12.48,17.52

Answer:

155

Step-by-step explanation:

Sort them

155 is the median value

The domain is all real numbers, and the range is all real numbers greater than or equal to -4.

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

f(x) = (x + 2)(x + 6)

The above equation is a quadratic function

The rule of this function is that

The domain is the set of all real numbers

For the range, we expand and calculate the vertex

So, we have

f(x) = x² + 8x + 12

The x-coordinate of the vertex is

x = -8/(2 * 1)

x = -4

The x-coordinate of the vertex is

f(-4) = (-4)² + 8(-4) + 12

f(-4) = -4

So, the range is

y ≥ -4

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Hi there!! Your answer would be -0.26933333333.  Depending on what your teacher is looking for, you may want to lessen or keep the other exponents or numbers.

Step-by-step explanation:

1. Use the power rule (ab)^n =a^n b^n to distribute the exponent. S

implify the expression, (-1), (3 1/3),

2. 8 1/3 divided by 125 1/3.

3. Cancel the common factor of 3.

4. Evaluate the exponent

5. implify the numerator and simplify denominator

6. The result can be shown in multiple forms.

Exact Form:

−2/5

Decimal Form:

−0.4.

Hope this helps!! Have a good day!

Given

Find

Evaluate the expression

Explanation

substitute the value of a and b in given expression.

Final Answer

Therefore , the correct option is d.

Answer:

a=11

Step-by-step explanation:

Let's solve your equation step-by-step.

√a+5=4

Solve Square Root.

√a+5=4

a+5=42(Square both sides)

a+5=16

a+5−5=16−5(Subtract 5 from both sides)

a=11

Check answers. (Plug them in to make sure they work.)

a=11(Works in original equation)

Answer: a=11

Step-by-step explanation: What the other person said. :D

Answer:

if the x after the 20 means multiply then the answer is -34/7 or -4 6/7 if the x is a letter then it's 2/11

Step-by-step explanation:

20x2-7x=6

20x2=40

40-7x=6

subtract 40 from 6= 34

-7x=34

34÷-7= -34/7 if needed in a mixed fraction -4 6/7

Answer:

5x = 25|:5

x = 5

9514 1404 393

Answer:

  9 ft, 22 ft, 23 ft

Step-by-step explanation:

Let s represent the length of the shortest side. Then the middle length side is (2s+4) and the longest side is (3s-4). The perimeter is the sum of the side lengths:

  54 = s +(2s +4) +(3s -4)

  54 = 6s . . . . . . . . . . . . . . collect terms

  9 = s . . . . . . . . . . divide by 6

  2s+4 = 2·9 +4 = 22

  3s -4 = 3·9 -4 = 23

The lengths of the three sides are 9 feet, 22 feet, and 23 feet.

To do the synthetic division we need to use the coefficients of the polynomial:

which are: 4, -3, -7, and 6, and the zero of the next polynomial:

which is 2.

Synthetic division

Given that the remainder, 12, is not zero, then (x - 2) is not a factor of the degree 3 polynomial.

Answer: -3

Step-by-step explanation:

Answer: -1331

Step-by-step explanation:

First, we use PEMDAS and add 12 and 15.

(6 - 17)³-2

Next, we subtract 17 from 6 to get -11.

(-11)³-2

then, we cube -11 to get -1331.

-1331 -2

Finally, we add and keep the - sign.

-1333.

Hope This helps!!

P.S I might be wrong lol.

Step-by-step explanation:

70 to 85 % of his maximum

Maximum is estimated to be 220 - age  = 220 - 42 = 178

70% of this is 125

85 % is 89  151  

I believe I would go with the third choice  116-160 bpm

Answer:

  8

Step-by-step explanation:

That total is ...

  (number of possibilities in each location)^(number of locations) = 2^3 = 8

The possible numbers are ...

  444, 449, 494, 499

  944, 949, 994, 999

There are 8 of them.

The graph of g(x) is on the image at the end, and the correct option for the transformation is B.

We define a horizontal dilation of scale factor k as:

g(x) = f(k*x)

if k > 1, we have a stretch.

if  0 < k < 1, we have a shink of scale factor 1/k

Here we have:

g(x) = f (5x) = 5x - 4

We can notice that k = 5, then we have a stretch, thus, the correct option is B.

The graph of function g(x) can be seen in the image at the end.,

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Answer: x=26

set 4x+8=6x-44

then get the x to the left side and make it stand alone by subtracting the other numbers to get them over

Hope this helped a little XD

Answer:

To calculate Fred's power, we can use the formula:

Power = Work / Time

Given that Fred did 600 J of work in 60 seconds, we can substitute the values into the formula:

Power = 600 J / 60 s

Power = 10 W

Therefore, the correct answer is:

D. 10 W

Step-by-step explanation:

Answer:

Power = Work/Time

Power = 600 J/60 s = 10 W

Therefore, the answer is D. 10 W.

Step-by-step explanation: