1 Evaluate lim X x+3 (x - 3)2 09 O3 O 0 O-3 No Limit 2 Let f(x) = x + 2x, xs1 X>1 2x, Evaluate lim fex) X + 1 03 02 © 1 0 No Limit

The volume is equal to : V = 512pi/3 - (40√15)pi.

First let's imagine how the solid looks like.

Let's rearrange the equation of the ellipsoid to find semi-axes:

4x² + 4y² + z² = 64

x²/16 + y²/16 + z²/64 = 1

So semi-axes are a=4, b=4, c=8. So x varies (-4, 4), y from(-4,4) and z from (-8, 8). So ellipsoid is much wider than the cylinder.

Cylinder defines region in xy plane and the ellipsoid bounds solid from bellow and from above.

Let's find the region in the xy plane. (You may skip this part if you understand from above that the region in xy plane is a disk x² + y² ≤ 1)

The region R is bounded by the cylinder x² + y² = 1 (1) and projection of the ellipsoid in the xy plane:

z=0 and 4x² + 4y² + z² = 64

4x² + 4y² = 64

x² + y² = 16...(2)

So the region in xy plane is bounded by two circles (1) and (2) and actually is inside both of them:

Introduce polar coordinates

x = r cost, y = r sint

Then integration limits for thr region R:

0<= t <= 2pi

0 <= r <= 1

Next let's find the limits for z from the equation of the ellipsoid:

4x² + 4y² + z² = 64

4(x² + y²) + z² = 64

4r² + z² = 64

z² = 64 - 4r²

z² = 4 (16 - r²)

z = +/- 2 √(16 - r²)

So the integration limits for z : -2 √(16 - r²) <= z <= 2 √(16 - r²).

But as the solid is symmetrical we can take just a half and double the volume:

V = 2* (0, 2pi) ∫ (0, 1)∫ (0, 2 √[16 - r²]) ∫ r dz dr dt

After integration the volume is equal to

V = 512pi/3 - (40√15)pi.

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Answer:

True

Step-by-step explanation:

Bc its true do the math

Answer:

1ab

Step-by-step explanation:

Hope this helps! Pls give brainliest!

Answer:

1ab or just ab

Step-by-step explanation:

All 3 parts of the equation have the variables ab at the end, meaning that the solution will also end with ab.

Let's first solve by doing the first property, subtraction:

3ab-9ab=-6ab

Now, we add that sum to 7ab:
-6ab+7ab=1ab

Depending on what they ask, you can either write 1ab or ab, they are the exact same thing.

Answer:

26

Step-by-step explanation:

you square both 10 and 24

you then will get 100 and 576

you then will add them together

and get 676

since 676 is not a whole number

you then will dive the number by 4

to get the numbers

13 and 4

13 \(\sqrt{4} \\\)

13*2 because the square root of 4 is 2

13*2 =26

Around 1950, family sociologists described a standard marriage pattern at about age 20 for women and age a) 22 for men.

The standard marriage pattern today, based on the time a couple marries, is mid-to-late twenties.  Some marriages are contracted very late, with some in the forties.

Sociologists have pointed out that the current delay in marriages is caused by the higher priority placed on education and career by youths.

However, marriage patterns based on the type of arrangement include:

Traditionally, marriages have served two societal purposes:

Thus, around 1950, family sociologists described a standard marriage pattern at about age 20 for women and age  22 for men.

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Answer:

Step-by-step explanation:

Given the solution to the equation y to be cos⁻¹(1)

y = cos⁻¹(1)

y =0°

In trigonometry identity, the general solution for cosine function is expressed as θ = 2kπ ± n, where n is any integer.

Substituting the solution gotten to the equation above into the general formula θ = 2kπ ± n, will give;

y = 2kπ ± n

since we have just one solution, we will find the value of y at n = 0

y = 2kπ ± 0

y = 2kπ

Answer: -34

Step-by-step explanation:

66 minus 100 is negative 34.

hey <3

negative exponentials can be written as a power of a fraction

for example, 4^-2 can be written as 1/(4^2)

thus, your answer would be 1/(5^2)

hope this helps :)

Answer:

\(\frac{1}{25}\)

Step-by-step explanation:

Using the rule of exponents

\(a^{-m}\) = \(\frac{1}{a^{m} }\) , then

\(5^{-2}\) = \(\frac{1}{5^{2} }\) = \(\frac{1}{25}\)

Answer: Jenna multiplied both numbers by 5 and added the products of the two equations into her answer. Mia added the numbers then multiplied by 5 to get her answer. However, in some situations, this isn't the case. take 5(9+6) for example. You multiply both by 5 to get 45+30=75. That's correct. And when you add both to get 15, then multiplied by 5, you also get 75. But in certain scenarios, such as dividing, that won't be the case. 5(9/3)=15. (Dividing the 9 by 3 first) 5(9/30) [not dividing first] gets you 3.

The cost of one sandwich is $4.25

Given data

number of sandwiches = 3

number of drinks = 1

cost of drink = $1.75

tip = $5

total pay = $20.66

sales tax = 8% = 0.08

let the cost of sandwich be x, so that:

1.75 + 0.08*1.75 + 5 + 3x + 3*(0.08 * x) = 20.66

6.89 + 0.24x + 3x =20.66

3.24x = 13.77

x = 4.25

cost of one sandwich is $4.25

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Answer:

- 7

Step-by-step explanation:

d = a₂ - a₁ = a₃ - a₂ = - 2 - 5 = - 9 - (- 2) = - 7

The  system of equations that could be used to determine the price of each pound of raspberries and the price of each pound of grapes is:  44 x + 43 y = 217 , 45x + 18y = 144 .  Each pound of peaches cost $2 and each pound of grapes cost $3

x = price of each pound of peaches

y = price of each pound of grapes.

Given that yesterday,  he sold 44 pounds of peaches and 43 pounds of grapes for a total revenue of $217

So 44 x + 43 y = 217 be equation 1.

Also given that today he sold 45 pounds of peaches and 18 pounds of grapes for a total revenue of $144.

So 45x + 18y = 144 equation 2.

Multiplying equation 1 with 18 gives us,

792x +774y = 3906

Multiplying equation 2 with 43 gives us,  

1935x+774y = 6192

Solving these,

792x +774y = 3906

1935x+774y = 6192

---------------------------------------------

-1143 x=- 2286

x = 2286/ 1143

x = 2

Plug this value of x in equation 1 and solve for y, to get,

44 x + 43 y = 217

44 (2) + 43 y = 217

43 y = 217 − 88

43 y =129

y = 129/43

y = 3

Therefore each pound of peaches cost $2 and each pound of grapes cost $3

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The equation of the line in slope-intercept form, through Z that is parallel to XY is: C. y = 2/3(x) + 1

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of line XY;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (4 - 2)/(8 - 5)

Slope (m) = 2/3

At data point Z (6, 5) and a slope of 2/3, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 5 = 2/3(x - 6)  

y = 2/3(x) - 4 + 5

y = 2/3(x) + 1

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Answer: See explanation

Step-by-step explanation:

From the question, we are informed that Yuvika bought books for Rs.465 and she paid Rs.500 to the bookstore.

To calculate the correct amount of change that she will get back will be:

= Rs 500 - Rs 465

= Rs 35

Answer:

Y= - 8x+47/7

X= -7y+47/8

Y= x+1/4

X= 3y

In order to depict alchemy and the philosopher's stone, which is the ultimate goal of alchemy, a sign of a circle within a square within a triangle within a larger circle started to be used in the 17th century.

What do the symbols for a circle, triangle, and square mean?

It has deep philosophy where a circle symbolizes heaven and represents number one, a square represents earth and represents number two, and a triangle represents people and represents number three.

An enduring representation of good fortune, the triangle enclosed within a circle was thought to stave off evil spirits. It was accepted by Alcoholics Anonymous as a symbol of a person's transition from an alcohol preoccupation to a life saturated with the triangle of Recovery, Unity, and Service.

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The explicit formula for the given geometric sequence is \(a_n=5\times(-5)^{n-1}\).

The given sequence is 5, -25, 125,.......

Here, the common ratio is -25/5 = -5 and 125/(-25) = -5.

We know that, the explicit formula for an geometric sequence is \(a_n=ar^{n-1}\).

Where, a = first term of the sequence, r= common ratio and n = number of terms.

Substitute, a=5 and r=-5 in \(a_n=ar^{n-1}\), we get

\(a_n=5\times(-5)^{n-1}\)

Therefore, the explicit formula for the given geometric sequence is \(a_n=5\times(-5)^{n-1}\).

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Answer:

50 inches

Step-by-step explanation:

Given that

5 equal sized square shelves arranged in a column.

Total area of five shelves = 500 sq inches

To find:

Length of shelving unit = ?

Solution:

First of all, let us find the area of each shelving unit.

Area of each shelving unit = Total area of five shelved divided by 5

Area of each shelving unit = 500 \(\div\) 5 = 100 sq units.

Each shelving unit is of square shape and area of a square is given as:

Area = \(Side^2\)

100 = \(Side^2\)

So, side of shelve = 10 inches

Now, there are 5 squares in the shelving unit.

So, length of shelving unit = \(10 \times 5 = \bold{50 \ inches}\)

The part of the graph that would show no change in distance is when Mary stopped and waited for the traffic light to turn green.

Statement B is correct.

We know that during this time, Mary did not move forward or cover any distance. Hence, the graph would show a flat line at this point, indicating no change in distance.

Distance is described as a numerical or occasionally qualitative measurement of how far apart objects or points are.

In physics or everyday usage, distance may refer to a physical length or an estimation based on other criteria.

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By AA similarity Triangle PQR and TQS are similar.

Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles. Similar figures are described as items with the same shape but varying sizes, such as two or more figures.

Given:

As, PR || TS then

<RPQ = <TSQ (Alternate Interior Angle)

< <QTS = <QRP (Alternate Interior Angle)

So, Triangle PQR and TQS are similar by AA similarity criteria.

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Answer:

(0-8)

Step-by-step explanation:

the z represents a unknown number.=, and because it equals y it starts at 0. so (0-8)

23 lies between the two perfect squares 16 and 25 which are the squares of 4 and 5 respectively.

The value of √23 lies between 4 and 5.

What in mathematics is a perfect square?

Informally: A square number, perfect square, or simply "a square" is the result of multiplying an integer (a "whole" number), positive, negative, or zero, times itself. Therefore, 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, and so on are all square numbers.

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The value of x from the given equation is 9/2

The given equation is

log₂(2x - 1) = 3

The general form of logarithm with base 2 is

          log₂ N = x

Conversion of the logarithm to exponential form is

            2ˣ = N

where x is the log₂ of N

           x is the number of times number '2' should be multiplied by intself to obtain n

Using this conversion in the above equation,

log₂(2x - 1) = 3

       (2x - 1)  = 2³    

       (2x - 1)  = 8

        2x - 1 = 8

        2x = 8 +1

        2x = 9

          x = 9/2

Therefore the value of x is 9/2

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Answer:

24.49

Step-by-step explanation:

16.00

8.49

____

24.49

Answer:

3 19/24

Step-by-step explanation:

Answer:

285.28571429 minutes

Step-by-step explanation:

Let us represent

The number of minutes you talk = t

C1 = Cost in dollars of the first plan

C2 = Cost in dollars of the second plan

First plan

The first plan charges a rate of 26 cents per minute

Converting cents to dollars

100 cents = 1 dollars

26 cents =

26/100 cents

=$ 0.26

C1 = $0.26 × t

C1 = 0.26t .......... Equation 1

Second Plan

The second plan charges a monthly fee of $39.95 plus 12 cents per minute

Converting 12 cents to dollars

100 cents = 1 dollars

12 cents =

12/100

= $0.12

C2 = $39.95 + 0.12t........Equation 2

Find the number of talk minutes that would produce the same cost for both plans

We would Equate C1 to C2

C1 = C2

0.26t = $39.95 + 0.12t

Collect like terms

0.26t - 0.12t = $39.95

= 0.14t = $39.95

Divide both sides by 0.14

= t = $34.95/0.14

t = 285.28571429 minutes

Therefore, the number of talk minutes that would produce the same cost for both plans is 285.28571429 minutes.

The 90% confidence interval for the proportion of district residents in favor of starting the school day 15 minutes later is (0.392, 0.548). The true proportion is estimated to lie within this interval with 90% confidence.

To calculate the 90% confidence interval for the true proportion of district residents who are in favor of starting the school day 15 minutes later, we can use the following formula:

CI = p ± z*(√(p*(1-p)/n))

where:

CI: confidence interval

p: proportion of residents in favor of starting the day later

z: z- score based on the confidence level (90% in this case)

n: sample size

First, we need to calculate the sample proportion:

p = 94/200 = 0.47

Next, we need to find the z- score corresponding to the 90% confidence level. Since we want a two-tailed test, we need to find the z- score that cuts off 5% of the area in each tail of the standard normal distribution. Using a z-table, we find that the z- score is 1.645.

Substituting the values into the formula, we get:

CI = 0.47 ± 1.645*(√(0.47*(1-0.47)/200))

Simplifying this expression gives:

CI = 0.47 ± 0.078

Therefore, the 90% confidence interval for the true proportion of district residents who are in favor of starting the school day 15 minutes later is (0.392, 0.548). We can be 90% confident that the true proportion lies within this interval.

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The required operating time, total expense and receipt are 33hours, $759 and $759 respectively.

How to get hours in operation?

It is time taken by worker or operator to operate particular work.

We have given,

Spend money = $594

Average hourly operating cost = $5.

Average hourly receipt = $23

Let time taking in operation be h,

594 + 5h = 23h

18h = 594

h = 33 hours.

and

Total expense = 23h =$23(33) =$ 759

receipt =594 + 5h = 594 + 5(33) = 594 + 165 =$ 759  

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The area of the pool increasing at the rate of 753.98 cm²/min when the radius is 5 cm

Given:

radius of the pool increases at a rate of 24 cm/min

To Find:

How quickly does the pool's area grow when the radius is 5 cm?

Solution:

we are given with the circular pool

hence the area of the circular pool =

A = πr²-----------------------------(1)

The area of the pool os increasing at the rate of 24 cm/min, meaning that the area of the pool is changing with respect to time t

so differentiating eq (1)  with respect to t , we have

dA/dt =π 2r dr/dt

we have to find  dA/dt    with  dr/dt  = 24 cm/min and  r =  5cm

substituting the values

dA/dt = π 2(5)24

dA/dt =  π 26*8

dA/dt =  π 240

dA/dt =240π

dA/dt = 753.98

The area of the pool increasing at the rate of 753.98 cm²/min when the radius is 5 cm

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