lim x→25 x−25 /√x−5
Final answer:
The solution involves multiplying by the conjugate of the denominator to simplify the expression, leading to the finding that the limit as x approaches 25 of (x-25)/(√x-5) equals 10.
Explanation:
The question asks to evaluate the limit lim x→25 (x−25)/(√x−5). At first glance, directly substituting x = 25 into the equation would lead to a 0/0 form, indicating a need for algebraic manipulation to resolve the indeterminate form.
To simplify, we can multiply the numerator and the denominator by the conjugate of the denominator, which is (√x + 5). This approach is helpful in dealing with limits that involve square roots.
Following this step:
Multiply both the numerator and denominator by (√x + 5).
The numerator becomes (x - 25)(√x + 5).
The denominator turns into x - 25 after applying the difference of squares.
Simplify to get (√x + 5), since (x - 25) in numerator and denominator cancel out.
Finally, substitute x = 25 into the simplified form to get 10 as the answer. Therefore, lim x→25 (x−25)/(√x−5) = 10
Use the equation v=10/p to determine the pressure when the volume is 12 liters
7x300=7x blank hundreds
Find the surface area of the surface given by the portion of the paraboloid z=3x2+3y2 that lies inside the cylinder x2+y2=4. (hint: convert to polar coordinates after setting up the integral)
To find the surface area of the specified area in the paraboloid, convert the original cartesian coordinates to polar coordinates. Then set up and solve the appropriate double integral over the region defined by the circle in polar coordinates.
Explanation:To find the surface area of a paraboloid z=3x²+3y² inside the cylinder x²+y²=4, you first set up the integral and then convert to polar coordinates. As per the given paraboloid equation, we know that dz/dx = 6x and dz/dy = 6y. Therefore, the differential of surface area in polar coordinates can be given as √(1+(6r*cosø)²+(6r*sinø)²) rdrdø.
Next, integrate this over the area of a circle in polar coordinates, from r=0 to r=2 and ø=0 to ø=2π. The limits of 2 and 2π come from the given cylinder equation x²+y²=4, which represents a circle of radius 2 in polar coordinates.
The final integral in terms of r and ø should yield the desired surface area of the paraboloid which lies inside the cylinder.
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What is the slope and y intercept of y=-27.4x
It's the holiday season and you are working for a packing company that specializes in holiday fruit cakes. For Christmas this year, the number of clients requesting fruit cakes has more than tripled and orders need to be shipped prior to the New Year. Your supervisor has asked you to work 15 hours more than a normal 40 hour work week, including Christmas day, which falls on a Friday. Therefore, one of your regular 8 hour days will be paid at the holiday rate. You get paid $10.00 per hour plus you get time and a half for overtime and double pay for the holidays. What will your gross base pay be for the week?
Normal rate: $10/hr
Time and a half= $15/hr
Double pay: $20/hr
Hours to be paid at $10/hr =32 hours
$10/hr x 32hrs= $320
$20/hr x 8hrs= $160
$15/hr x 15hrs=$225
Total gross pay: $705
To calculate your gross base pay for the week working extra hours including a holiday, you need to consider regular pay, overtime pay, and holiday pay. The gross base pay for the week will be $785.00.
Explanation:To calculate your gross base pay for the week, you need to consider your regular hours, overtime hours, and holiday pay. Here's how you can calculate it:
Calculate your regular pay for the 40 hours of work at the regular rate: $10.00 per hour x 40 hours = $400.00.Calculate your overtime pay for the 15 additional hours of work at time and a half: $10.00 per hour x 1.5 = $15.00 per hour. $15.00 per hour x 15 hours = $225.00.Calculate your holiday pay for the 8-hour day at double the regular rate: $10.00 per hour x 2 = $20.00 per hour. $20.00 per hour x 8 hours = $160.00.Add up your regular pay, overtime pay, and holiday pay: $400.00 + $225.00 + $160.00 = $785.00.Therefore, your gross base pay for the week will be $785.00.
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What is 120.571 in expanded form?
Megan Mei is charged 2 points on a $120,000 loan at the time of closing. The original price of the home before the down payment was $140,000. How much do the points in dollars cost Megan? A. $4,200 B. $2,800 C. $8,200 D. $2,400
Answer: Option 'A' is correct.
Step-by-step explanation:
Since we have given that
Amount of original price of the home before the down payment = $140000
Amount of loan at the time of closing = $120000
Megan Mei is charged 2 points on that amount means
[tex]2\%\ on\ \$120000\\\\=\frac{2}{100}\times 120000\\\\=0.02\times 120000\\\\=\$2400[/tex]
Hence, Option 'A' is correct.
Evaluate 5 c - 3 d+11 when c= 7 and d= 8
What is the like term for 4m+(-3n)+n? What is the like term for c+2c+c-5c+1
a) The three terms have variables m, n, n. The two like terms are the last two terms, which both have variable n: -3n, n.
b) The 5 terms have variables c, c, c, c, -. The like terms are the first four, which all have variable c: c, 2c, c, -5c.
Are all rectangles similar
Which number sentence shows the correct placement of the decimal point in the product, based on the two factors?
7.98 × 45.67 = 3,644.466
12.3 × 3.8 = 467.4
0.45 × 2.3 = 1.035
14.22 × 2.8 = 398.16
Answer:
Option 3 - [tex]0.45\times2.3= 1.035[/tex]
Step-by-step explanation:
To find : Which number sentence shows the correct placement of the decimal point in the product, based on the two factors?
Solution :
The correct placement of decimal in product is based on the number of digits after decimals as the number of digits after decimal of one number added to number of digits after decimal of second number is the required place in the result a decimal place.
1) [tex]7.98\times 45.67 = 3,644.466[/tex]
Not correct, decimals are 4 so place after 4 numbers.
2) [tex]12.3\times3.8= 467.4[/tex]
Not correct, decimals are 2 so place after 2 numbers.
3) [tex]0.45\times2.3= 1.035[/tex]
Correct, decimals are 3 so place after 3 numbers.
4) [tex]14.22\times2.8= 398.16[/tex]
Not correct, decimals are 3 so place after 3 numbers.
Therefore, option 3 is correct.
If two non collinear segments in the coordinate plane have slope 3 what can you conclude
90,175,087,309 in expanded form
Sue uses the expression ( 8 x 3,000) + ( 8 x 200) + (8 x 9) to help solve a multiplucation problem what is Sue's multiplucation problem?
Answer:
Sues problem would be - 8×3,209 :8×3,209
on monday 2/3 of the team practiced tuesday 7/8 wednesday 1/2 and thurday 3/4 on which day were the most team memebers present at practice
Graph parallelogram ABCD on a coordinate plane with vertices A(3,4) B(6,1) C(0,-2) and D(-3,1).
Find the slope of each side.
What do you notice about the slopes?
A parallelogram, the opposite sides have equal slopes.
To graph the parallelogram ABCD on a coordinate plane, we can plot the given points A(3,4), B(6,1), C(0,-2), and D(-3,1), and then connect them in order to form the parallelogram.
Here are the steps to find the slope of each side:
Plot the Points:
Plot the points A(3,4), B(6,1), C(0,-2), and D(-3,1) on the coordinate plane.
Connect the Points:
Connect the points in order (A to B to C to D to A) to form the parallelogram.
Find the Slope:
The slope of a line passing through two points
(x_1 ,y_1 ) and (x_2 ,y_2 ) is given by the formula m= y_2 -y_1/ x_2- x_1
Calculate the slope for each pair of consecutive points:
Slope of AB: mAB = 1−4/6−3
Slope of BC: mBC = −2−1/0−6
Slope of CD: mCD = 1−(−2)/−3−0
Slope of DA: mDA = 4−1/ 3−(−3)
Now, observe the slopes:
mAB and mCD
are the slopes of opposite sides. They should be equal for a parallelogram.
mBC and mDA are the slopes of the other pair of opposite sides. They should also be equal for a parallelogram.
So, for a parallelogram, the opposite sides have equal slopes.
you are lying 120 ft away from a tree that is 50 feet tall you look up at the top of the tree approxmaelty how far is your head from the top of the tree in a straight line
For the data in the table does y vary directly with x? X=16,32,48-Y=4,16,36
26×107 What is the value of the second partial product
Which of the following give an equation of a line that passes through the point (6/5,-19,5) and is parallel to the line that passes through the organ and point (-2,-12)
A. y= 6x-11
B. y= 6x-19/5
C. y= 6x-6/5
D. y= 6x+1
christie decided to make bracelets for her class. two-fifths of the bracelets were done on Monday and three-sevenths were done on Tuesday what part of the bracelets are finished?
3.5 x 10^4 write the following number in standard form (decimal).
Answer:
35,000
Step-by-step explanation:
URGENT PLEASE HELP!!! I want to know HOW to solve this as well.
What is the solution to the equation?
4(3 + 7) = 4 · x + 4 · 7
A.
x = 3
B.
x = 4
C.
x = 7
D.
x = 10
A is your anwser. Hope this Helps
jody has 2 red marbles 6 blue marbles and yellow marbles what is the ratio to red to blue
Solve the equation V=1/3 Bh for B
To solve the equation V = 1/3 Bh for B, multiply both sides by 3 to eliminate the fraction and then divide by h, resulting in B = 3V/h.
The equation given is V = 1/3 Bh, where V represents volume, B is the area of the base of the three-dimensional figure, and h is the height. To solve for B, the area of the base, you need to isolate B on one side of the equation. Follow these steps:
Multiply both sides of the equation by 3 to get rid of the fraction on the right-hand side, resulting in 3V = Bh.Next, to solve for B, divide both sides of the equation by h, which gives you B = 3V/h.Therefore, the formula B = 3V/h is used to calculate the base area B given the volume V and height h of the figure.
Arlan needs to create a box from a piece of cardboard. The dimensions of his cardboard are 10 inches by 8 inches. He must cut a square from each corner of the cardboard, in order to form a box. What size square should he cut from each corner, in order to create a box with the largest possible volume?
A. 0.5 inches
B. 1 inch
C. 1.5 inches
D. 2 inches
Where does the graph of the linear equation, y = 1/2 x - 3, cross the y-axis?
negative 2 is where it crosses
For commission as a realtor, Michelle earns $349 plus 3% of the purchase price for each home she helps buy or sell. If she earned $8,965 in commission on a certain home, find its purchase price.
ANSWER:
$8965- $349= $8616
3/100x= 8616
8616 x 100/ 3= $287,200.
I'm posting this because somebody inboxed me asking for help and before I even got to help them, they deleted the inbox and i couldn't remember their name. I hope you see this and benefit from it, sorry!
Well, let us solve this step by step.
We know that Michelle earns 349 plus 3% of the Purchase price. Let us call the Purchase price as P, so that:
Earnings, E = 349 + 0.03 P
So if she earns 8,965 (E = 8,965) so we can find P:
8,965 = 349 + 0.03 P
0.03 P = 8,616
P = $287,200
Michelle's total commission from a house sale was $8,965, from which $349 is a fixed commission. The rest, $8616, represents the 3% of the selling price of the house. By solving the simple equation $8616 = 0.03 * X, we find that the home price is $287,200.
Explanation:This problem is a simple, but common, practice in the world of linear equations. The first step is to understand that the base commission of $349 is a constant that Michelle earns every time, whilst the remaining part of her commission comes from the 3% percentage of the sale price. After subtracting the base commission from the total commission, we get a value of: $8965 - $349 = $8616. This value is equal to 3% of the house price.
We can express this as: 8616 = 0.03 * X, where X is the value of the house. By isolating X (the house price), we divide both sides by 0.03 to get the house price. Therefore, the home price would be $8616 / 0.03 = $287,200.
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Don't understand how to do the graph