The following scatterplot shows the percentage of the vote a candidate received in the 2016 senatorial elections
according to the voter's income level based on an exit poll of voters conducted by a news agency. The income
levels 1-8 correspond to the following income classes:
1 = Under $15,000; 2 = $15-30,000; 3 = $30-50,000; 4 = $50-75,000; 5 = $75-100,000;
6 = $100-150,000; 7 = $150-200,000; 8 = $200,000 or more.
Use the election scatterplot to the find the critical values corresponding to a 0.01 significance level used to test
the null hypothesis of ρs = 0.
A) -0.881 and 0.881
B) -0.881
C) -0.738 and 0.738
D) 0.881

Using proportions, it is found that you would expected the white counter to be chosen 128 times.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

From the table, the proportion of the white counter is given as follows:

p = 32/(32 + 18) = 32/50 = 0.64.

Hence, out of 200 trials, the number of trials in which the white counter is expected to be chosen is given by:

0.64 x 200 = 128 times.

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Answer:

160 cm × 120 cm

Step-by-step explanation:

this means 1 cm turns into 20 cm.

so, 8 cm × 6 cm becomes

8×20 = 160 cm × 6×20 = 120 cm

The Evaluating expression √6 +√6+√27-√12 become √3(2√2+ 1) after simplification.

According to the statement

We have given that one evaluating expression which is √6 +√6+√27-√12

And we have to simplify this expression by evaluating it.

So, Given expression is:

√6 +√6+√27-√12

√6 +√6+√(9*3)-√(4*3)

√6 +√6+3√(3)-2√(3)

√6 +√6+√3( 3-2)

After evaluating the expression it become

√6 +√6+√3(1)

√(3*2) +√(3*2) +(1)√3

Take common from above expression then

√3(√2 +√2 ) +√3

√3(2√2) +√3

√3(2√2+ 1)

Now the expression √6 +√6+√27-√12 become √3(2√2+ 1) after simplification.

So, The Evaluating expression √6 +√6+√27-√12 become √3(2√2+ 1) after simplification.

Disclaimer: This question was incomplete. Please find the full content below.

Question:

Which choice is equivalent to the expression below?

√6 +√6+√27-√12

A. √3(2√2+ 1)

B. 2√3-√21

C. 3√3+√6

D. 5√3

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The next three numbers here would be 0, 10, 1011, 1031, 102113, 10311213, 10411223, 1031221314, 1041222314.

The term number sequence is used to refer to the list of numbers that have the relationship of having a linked rule. The number that follows in the sequence has to be worked out from the previous numbers in that particular sequence. You have to follow the particular rule to be able to work out the number that has to follow in the sequence.

For example we have these numbers 1, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34 etc. We would have to understand the pattern of numbers that are in the sequence. We can see that there is a difference of 3 between the number that succeeds the previous one in the sequence.

The first value here is given to be 0

Next we have the 1 0 = 10

The next that we have is 1 0 and 1 1 written as 1011

Next is 1 zero and three one = 1031

We continue to follow the pattern till we arrive at 1041222314. This is where the sequence would then have to stop.

Hence we have to conclude that the next numbers are 10411223, 1031221314, 1041222314.

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Answer: a) $ 6,487.47

b) $ 1,487.47

Step-by-step explanation:

Marketing-oriented firms focus more on what the market needs above every other aspects.

Marketing-oriented firms can be described as firms that major in identifying the needs and wants of customers and then creating specific products that are designed to meet the wants of such customers. One of the important elements of marketing-oriented firms is to ensure there is a demand for whatever products or services they offer.

Some examples of marketing-oriented firms are:

A product-oriented firm focus more resources on and focus on researching and developing quality products rather than focusing more on the market to discover the wants of customers.

Sales-oriented firm tend to focus more on developing its sales force that will promote their products and services.

Marketing-oriented firms stand out and are different from the other two types of firms because they focus more on what the market needs above every other aspects.

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the minimum amortization is given as 20300 dollars

We have the value of A to be $3235000

while we have the value of B to be $3474000

Of these two values the greatest or the highest is that of the option B.

Next we have to find the corridor value using 10 percent

0.10 * 3474000

= 347400

$505740 -  347400

= 158340

The number of years = 7.8

minimum amortization = 158340/7.8

= 20300 dollars

Hence the minimum amortization is given as 20300 dollars

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Answer: [tex]4(x+2\sqrt{2})(x-2\sqrt{2})[/tex]

Step-by-step explanation:

We can first take out the common factor of 4, as both 4x² and -32 are divisible by 4.

[tex]4(x^2-8)[/tex]

From here, we can assume that x²-8 is a difference of two squares even though 8 is not a perfect square.

For review, a difference of two squares [tex]a^2-b^2[/tex] can be factored into [tex](a+b)(a-b)[/tex].

[tex]4(x^2-8)\\4(x+\sqrt{8})(x-\sqrt{8})\\4(x+2\sqrt{2})(x-2\sqrt{2})[/tex]

The answer is p = -8/15


Proportion can simply be defined as equating two ratios

The proportion of 3/2 = 4/p +9 can be calculated as follows

3/2 - 9/1 = 4/p

-15/2 = 4/p


cross multiply both sides together to find the value of p

-15×p= 4×2

-15p= 8

p= -8/15

Hence the answer is p= -8/15

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Answer:

[tex]\huge\boxed{\sf v = 45 \ km/hr}[/tex]

Step-by-step explanation:

Distance = S = 162 km

Time = t = 3hr 36/60 min = 3 hr 0.6 hr = 3.6 hr

Average Speed = v = ?

[tex]\displaystyle v = \frac{S}{t}[/tex]

Put the givens in the above formula

[tex]\displaystyle v = \frac{162}{3.6} \\\\v = 45 \ km/hr\\\\\rule[225]{225}{2}[/tex]

Answer:

  f(x) = x³ -4x² +9x +164

Step-by-step explanation:

When a function has a zero at x=p, it has a factor (x-p). When a polynomial function with real coefficients has a complex zero, its conjugate is also a zero.

Given the two zeros and the one we can infer, we can factor our 3rd-degree polynomial function as ...

  f(x) = a(x -(-4))·(x -(4+5i))·(x -(4-5i))

Using the factoring of the difference of squares, we can combine the complex factors to make a real factor.

  f(x) = a(x +4)((x -4)² -(5i)²) = a(x +4)(x² -8x +16 +25)

The value of this at x=1 is ...

  f(1) = a(1 +4)(1 -8 +41) = 170a

We want f(1) = 170, so ...

  170 = 170a   ⇒   a=1

The factored polynomial function is ...

  f(x) = (x +4)(x² -8x +41)

Expanding this expression, we have ...

  f(x) = x(x² -8x +41) +4(x² -8x +41) = x³ -8x² +41x +4x² -32x +164

  f(x) = x³ -4x² +9x +164

The attached graph verifies the real zero (x=-4) and the value at x=1. It also shows that the factor with complex roots has vertex form (x -4)² +25, exactly as it should be.

Answer:

[tex]f(x) = (x+4)(x^2-8x+41)[/tex]

Step-by-step explanation:

Ok, so there are a couple of things to note here. The first thing is that there is a complex solution

Complex Conjugate Root Theorem:

    if [tex]a-bi[/tex] is a solution then [tex]a+bi[/tex] is a solution and vice versa

Fundamental Theorem Of Algebra:

   Any polynomial with a degree "n", will have "n" solutions. Those solutions can be real and imaginary numbers

So since we're given the root: [tex]4+5i[/tex], we can use the Complex Conjugate Root Theorem to assert that: [tex]4-5i[/tex] is also a solution.

So now we know 3 solutions/zeroes, and since n=3 (the degree), we can know for a fact that we have all the solutions due to the Fundamental Theorem of Algebra.

So using these roots, we can express the polynomial as it's factors. When you express a polynomial as factors it'll look something like so: [tex]f(x) = a(x-b)(x-c)(x-d)...[/tex] where a, b, and d are zeroes of the polynomial. Also notice the "a" value? This will affect the stretch/compression of the polynomial.

So let's express the polynomial in factored form:

[tex]f(x) = a(x-(-4))(x-(4+5i))(x-(4-5i))[/tex]

Simplify the x-(-4)

[tex]f(x) = a(x+4)(x-(4+5i))(x-(4-5i))[/tex]

Now let's distribute the negative sign to the complex roots

[tex]f(x) = a(x+4)(x-4-5i)(x-4+5i))[/tex]

Now let's rewrite the two factors (x-4-5i) and (x-4+5i) so the (x-4) is grouped together

[tex]f(x) = a(x+4)((x-4)-5i)((x-4)+5i))[/tex]

If you look at the two complex factors, this looks very similar to the difference of squares: [tex](a-b)(a+b) = a^2-b^2[/tex]

In this case a=(x-4) and b=5i. So let's use this identity to rewrite the two factors

[tex]f(x) = a(x+4)((x-4)^2-(5i)^2)[/tex]

Let's expand out the (x-4)^2

[tex]f(x) = a(x+4)(x^2+2(-4)(x)+(-4)^2-(5i)^2)[/tex]

Simplify

[tex]f(x) = a(x+4)(x^2-8x+16-(5i)^2)[/tex]

Now simplify the (5i)^2 = 5^2 * i^2

[tex]f(x) = a(x+4)(x^2-8x+16-(-25))[/tex]

Simplify the subtraction (cancels out to addition)

[tex]f(x) = a(x+4)(x^2-8x+41)[/tex]

So just to check for the value of "a", we can substitute 1 as x, and set the equation equal to 170

[tex]170 = a(1+4)(1^2-8(1)+41)\\170 = a(5)(1-8+41)\\170 = a(5)(34)\\170 = 170a\\a=1[/tex]

In this case it's just 1, so the polynomial can just be expressed as:
[tex]f(x) = (x+4)(x^2-8x+41)[/tex]

Answer:

x=10 and x=-4

Step-by-step explanation:

When the absolute value is all by itself on one side of the equation, the next step is to remove the absolute value bars. This will create TWO separate equations.

| x - 3 | = 7

x-3 = 7 This is one of the equations. Just straight up copied the equation but without the bars.

Here is the second equation:

x - 3 = -7

It is the left side copied, without the bars, but the right side has the opposite sign.

Solve these both separately to find the answers.

x-3=7 and x-3=-7

x=10 and x=-4

The probability of occurrence for the events A, B and C is; 1/4.

For the first event A in which case, there's no odd number on the first two rolls, the possible events are; EEE and EEO. Consequently, the required probability is;

Event A = 2/8 = 1/4.

For the event B in which case, there's an even number on both the first and last rolls; the possible events are; EEE and EOE. Consequently, the required probability is;

Event B = 2/8 = 1/4.

For the event C in which case, there's an odd number on each of the first two rolls; the possible events are; OOO and OOE. Consequently, the required probability is;

Event C = 2/8 = 1/4.

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The number of ways the program can be arranged for this segment is 8, 648, 640 ways

It is important to note that the formula for finding the permutation or arrangement of a set of dats is given as;

Permutation = [tex]\frac{n!}{(n-r)!}[/tex]

where

Let's substitute the values into the formula for permutation, we have

Permutation = [tex]\frac{13!}{13 - 7!}[/tex]

Find the difference of the denominator

Permutation = [tex]\frac{13!}{6!}[/tex]

Find the factorial of the values

Permutation = [tex]\frac{6,227,020,800}{720}[/tex]

Divide the numerator by the denominator

Permutation = 8, 648, 640 ways

Thus, the number of ways the program can be arranged for this segment is 8, 648, 640 ways

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Answer:

400$

Step-by-step explanation:

Let C.P. of the watch = Rs. 100

When profit =5%; S.P. = Rs. (100+5)

= Rs. 105

and when profit = 11%;

S.P. = Rs. (100+11)

=Rs.111

Difference of two selling prices

= Rs. 111-Rs.105 = Rs.6

When watch sold for Rs. 6 more; then C.P. of the watch = Rs.

100

6

When watch sold for Rs. 24 more; then C.P. of the watch = Rs.

100

6

×

24

= Rs.

100

×

24

6

=400

The stages to utilize to construct a frequency distribution table utilizing Sturge's approximation are as follows:

The steps to create a frequency distribution table utilizing Sturge's approximation exist as follows;

Step 1: Estimate the range of the data:

This exists simply by finding the difference between the biggest and the least values.

Step 2: Decide on the inaccurate number of classes in which the provided data exist to be grouped. The formula for this is;

K = 1 + 3.322logN

where; K= Number of classes

logN = Logarithm of the whole number of observations.

Step 3: Specify the approximate class interval size:

This exists acquired by splitting the range of data by the number of classes and exists symbolized by h class interval size.

Step 4: Find the starting point:

The lower class limit should take care of the least value in the raw data.

Step 5: Determine the remaining class boundaries:

When you have reached the lowest class boundary, then you can count the class interval size to the lower class boundary to obtain the upper-class boundary.

Step 6: Circulate the data into separate classes.

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Answer:

8

Step-by-step explanation:

-32/-4 the minus takes out the second minus then we are left with 32/4which makes the answer a positive 8

Answer:

100 miles and 5.5 inches

[tex]\stackrel{\textit{\LARGE Line A}}{(\stackrel{x_1}{-8}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{-5}~,~\stackrel{y_2}{4})} ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{4}-\stackrel{y1}{5}}}{\underset{run} {\underset{x_2}{-5}-\underset{x_1}{(-8)}}} \implies \cfrac{4 -5}{-5 +8}\implies -\cfrac{1}{3} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{\LARGE Line B}}{(\stackrel{x_1}{0}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{-1})} ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-1}-\stackrel{y1}{1}}}{\underset{run} {\underset{x_2}{4}-\underset{x_1}{0}}} \implies \cfrac{-1 -1}{4 +0}\implies -\cfrac{1}{2}[/tex]

keeping in mind that perpendicular lines have negative reciprocal slopes, and that parallel lines have equal slopes, well, those two slopes above aren't either, so since they're neither, and they're different, that means that lines A and B intersect.

Answer:

No, she is wrong

Step-by-step explanation:

[tex]\frac{60}{36} = \frac{5}{3}[/tex] {Simplification}

[tex]\frac{5}{3} \neq \frac{1}{6}[/tex]

Answer:

2 1/8

Step-by-step explanation:

I counted from 29 to 31 and then saw that for 29 it was 3/8 and for 31 it was 2/8 so i knew that the answer would be 2 1/8

Answer: a.

Step-by-step explanation:

46 is subtracted by n to get -21 so the equation is 46 - n = -21

Add n on both sides; 46 - n + n = -21 + n; 46 = -21 + n

Add 21 on both sides; 46 + 21 = -21 + n + 21; 67 = n

So n = 67

(730.72, 4569.53) is the confidence interval for the population variance σ² given that c = 0.98, s = 39 and n = 15. This can be obtained by using formula for confidence interval and using statistical table for values.

The formula for finding the confidence interval for population variance is:

[tex]\frac{(n-1)s^{2} }{\chi^{2} _{\frac{\alpha }{2} } } < \sigma^{2} < \frac{(n-1)s^{2} }{\chi^{2} _{1-\frac{\alpha }{2} } }[/tex]

where n is the size of the sample, (n - 1) is the degrees of freedom, s is the standard deviation, α is the significance level.

Here it is given that,

α/2 = 0.02/2 = 0.01

1 - α/2 = 1 - 0.01 = 0.99

For (n - 1) degrees of freedom,

[tex]\chi^{2}_{\frac{\alpha}{2} }[/tex] = 29.141 , and  [tex]\chi^{2}_{1-\frac{\alpha}{2} }[/tex] = 4.660 (Using statistical table)

Using the formula we get,

[tex]\frac{(n-1)s^{2} }{\chi^{2} _{\frac{\alpha }{2} } } < \sigma^{2} < \frac{(n-1)s^{2} }{\chi^{2} _{1-\frac{\alpha }{2} } }[/tex]

[tex]\frac{(14)39^{2} }{29.141} < \sigma^{2} < \frac{(14)39^{2} }{4.660}[/tex]

[tex]730.72 < \sigma^{2} < 4569.53[/tex]

The confidence interval for the population variance is (730.72, 4569.53)

Hence (730.72, 4569.53) is the confidence interval for the population variance σ² given that c = 0.98, s = 39 and n = 15.

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The volume of the rectangular box is the product of the base area and the height 3x - 1

The given parameters are:

Length = 3x + 4

Width = 3x

Height = 3x - 1

The base area of the rectangular box is calculated as

Base area = Length * Width

Substitute the known values in the above equation

Base area = 3x(3x + 4)

This means that the volume of the rectangular box is the product of the base area and the height 3x - 1

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a. Recall that in polar coordinates, we can parameterize [tex]x=r\cos(\theta)[/tex] and [tex]y=r\sin(\theta)[/tex]. So, doing as the hint suggests, we have

[tex]r = 6\cos(\theta) + 8 \sin(\theta)[/tex]

[tex]\implies r^2 = 6r\cos(\theta) + 8r\sin(\theta)[/tex]

[tex]\implies \boxed{x^2 + y^2 = 6x + 8y}[/tex]

b. By completing the square, we get

[tex]x^2 + y^2 = 6x + 8y[/tex]

[tex]x^2 - 6x + y^2 - 8y = 0[/tex]

[tex]x^2 - 6x + 9 + y^2 - 8y + 16 = 25[/tex]

[tex](x-3)^2 + (y-4)^2 = 5^2[/tex]

which is the equation of the circle centered at (3, 4) with radius 5. Thus the area bounded by [tex]C[/tex] is [tex]\pi\cdot5^2 = \boxed{25\pi}[/tex].

c. This is made easier if you can consult a plot (attached). In the first quadrant, we have [tex]0\le\theta\le\frac\pi2[/tex], while the radial coordinate [tex]r[/tex] runs uninterrupted from the origin [tex]r=0[/tex] to the circle [tex]r=6\cos(\theta)+8\sin(\theta)[/tex]. So the area is

[tex]\displaystyle \int_0^{\pi/2} \int_0^{6\cos(\theta) + 8\sin(\theta)} r\,dr\,d\theta = \boxed{\frac12 \int_0^{\pi/2} \left(6\cos(\theta) + 8\sin(\theta)\right)^2 \, d\theta}[/tex]

d. Evaluate the integral.

[tex]\displaystyle \frac12 \int_0^{\pi/2} \left(36\cos^2(\theta) + 96\sin(\theta)\cos(\theta) + 64 \sin^2(\theta)\right) \, d\theta[/tex]

Simplify the integrand with the help of the identities

[tex]\cos^2(x) + \sin^2(x) = 1[/tex]

[tex]\sin(x)\cos(x) = \dfrac12 \sin(2x)[/tex]

[tex]\sin^2(x) = \dfrac{1 - \cos(2x)}2[/tex]

[tex]\displaystyle \frac12 \int_0^{\pi/2} \left(50 + 48\sin(2\theta) - 14 \cos(2\theta)\right) \, d\theta[/tex]

The rest is easy. You should end up with

[tex]\displaystyle \frac12 \int_0^{\pi/2} \left(6\cos(\theta) + 8\sin(\theta)\right)^2 \, d\theta = \boxed{24 + \frac{25\pi}2}[/tex]

a) The Cartesian equation that described curve C is x² + y² = 6 · x + 8 · y.

b) The area inside C is A = π · 5² = 25π square units.

c) The integral that computed the area inside curve C within the first quadrant is A = (1 / 2)∫ (6 · cos θ + 8 · sin θ)² dθ, for θ ∈ [0, 0.5π].

d) The integral evaluated at the given limits is equal to an area of 20.139π square units.

In this question we find a polar equation in explicit form. a) To find the equivalent form in rectangular coordinates, we must apply the following substitutions x = r · cos θ, y = r · sin θ:

r = 6 · cos θ + 8 · sin θ

r² = 6 · r · cos θ + 8 · r · sin θ

x² + y² = 6 · x + 8 · y       (1)

The Cartesian equation that described curve C is x² + y² = 6 · x + 8 · y.

b) Perhaps the equation represents a conic section, possibly a circunference. To prove this assumption, we must apply algebraic handling until standard form is obtained:

x² - 6 · x + y² - 8 · y = 0

x² - 6 · x + 9 + y² - 8 · y + 16 = 25

(x - 3)² + (y - 4)² = 5²          (1b)

Which indicates a circumference centered at point (h, k) = (3, 4) and with a radius of 5 units. By the area formula for a circle we find that the area inside C is A = π · 5² = 25π square units.

c) The polar form of the area integral is presented herein:

A = ∫ ∫ r dr dθ, for r ∈ [0, r(θ)] and θ ∈ [0, 0.5π]  

A = (1 / 2)∫ [r(θ)]² dθ, for θ ∈ [0, 0.5π]  

A = (1 / 2)∫ (6 · cos θ + 8 · sin θ)² dθ, for θ ∈ [0, 0.5π]  

The integral that computed the area inside curve C within the first quadrant is A = (1 / 2)∫ (6 · cos θ + 8 · sin θ)² dθ, for θ ∈ [0, 0.5π].

d) By algebraic handling, trigonometric formulas and integral properties:

A = 25 ∫ dθ  + 24 ∫ sin 2θ dθ - 14 ∫ cos 2θ dθ, for θ ∈ [0, 0.5π]  

A = 25 · θ - 12 · cos 2θ - 7 · sin 2θ, for θ ∈ [0, 0.5π]  

A = 20.139π

The integral evaluated at the given limits is equal to an area of 20.139π square units.  

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Answer:

68?

Step-by-step explanation:

multiples of 5 end in 5 or 0

_ _ _

last digit has 2 choices ( 5 and 0 )

1,3,5,7,9 are odd

so tens digit has 5 choices but we see that 5 is repeated so we split into more cases

when last digit is 0, tens digit has 5 choices then hundreds digit has 8 choices so 1*5*8=40

when last digit is 5, tens digit has 4 choices and hundreds digit has 7 choices (0 can't be first digit) 1*4*7=28

40+28=68

The Lateral area of the cube = 900 in.²

The Surface area of the cube = 1,350 in.².

A cube's lateral area is the area covered by the lateral surfaces of the cube shape. The formula for the lateral area of a cube is given as: LA = 4a², where:

a = edge length of cube.

The surface area of a cube is the total area of all its 6 surfaces. The formula for finding the surface area of a cube is: 6a², where:

a = edge length of cube.

Edge length of cube (a) = 15 in.

Lateral area = 4a² = 4(15²)

Lateral area = 4(225)

Lateral area of the cube = 900 in.²

Surface area = 6a² = 6(15²)

Surface area = 6(225)

Surface area of the cube = 1,350 in.².

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The answer to the questions of volumes are given as follows

a) [tex]v=128 \pi[/tex]

b) [tex]v=\frac{128}{3} \pi[/tex]

 c)[tex]v=\frac{1024}{5} \pi[/tex]

d)[tex]V=\frac{13568}{15} \pi[/tex]

Generally, the questions are  mathematically solved below

[tex]y=\sqrt{x}, y=4, x=0[/tex]

a) x-axis

if $y=4, x=16, x=0$

Using disk method

[tex]} v=\pi \int_{0}^{16}(\sqrt{x})^{2} d x \\[/tex]

[tex]v=\pi\left(\frac{x^{2}}{2}\right)_{0}^{16} \\[/tex]

[tex]v=\frac{\pi}{2} \times 16 \times 16 \\[/tex]

[tex]v=128 \pi[/tex]

b)  line y=4

if x=0, y=0 ;

[tex]y=\sqrt{x} \Rightarrow x=y^{2}[/tex]

Using shell method

[tex]v = \int_{0}^{4} 2 \pi(4-y) \cdot y^{2} d y \\[/tex]

[tex]v=2 \pi \int_{0}^{4}\left(4 y^{2}-y^{3}\right) d y[/tex]

[tex]v=2 \pi\left[\frac{4 y^{3}}{3}-\frac{y^{4}}{4}\right]_{0}^{4} \\[/tex]

[tex]v=\frac{2 \pi}{12}[1024-768] \\[/tex]

[tex]v=\frac{512 \pi}{12} \\[/tex]

[tex]v=\frac{128}{3} \pi[/tex]

c) y-axis

0 ≤ y ≤ 4

x=y^2

Using disk method

volume

[tex]v=\pi \int_{0}^{4} y^{4} d y$[/tex]

[tex]v=\pi\left(\frac{y 5}{5}\right)_{0}^{4} \\[/tex]

[tex]v=\frac{1024}{5} \pi[/tex]

d) line x=-1

y=√x, y=4, x=0

0 ≤ x ≤ 6

Using shell method

volume is

[tex]V=\int_{0}^{16} 2 \pi(1+x) \sqrt{x} d x$[/tex]

[tex]V=2 \pi\int_{0}^{16}(x^{1 / 2}+x^{3 / 2}\right) )d x\right. \\[/tex]

[tex]V=2 \pi\left[\frac{x^{3 / 2}}{3 / 2}+\frac{x^{5 / 2}}{5 / 2}\right]_{0}^{16} \\[/tex]

[tex]V=2 \pi\left[2 / 3 \cdot\left(4^{2}\right)^{3 / 2}+2 / 5\left(4^{2}\right)^{5 / 2}\right] \\[/tex]

[tex]V=4 \pi / 3 \cdot 4^{3}+4 \pi / 5 \cdot 4^{5} \\[/tex]

[tex]V=4 \pi\left(\frac{1}{3}+\frac{4^{2}}{5}\right)[/tex]

[tex]V=\frac{256}{15}(5+48) \pi \\[/tex]

[tex]V=\frac{256 \times 53}{15} \pi \\[/tex]

[tex]V=\frac{13568}{15} \pi[/tex]

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