In general, a variable to any even power is a perfect square.
So for example, x² is a perfect square and so is y¹⁴.
A common made by students is not in factoring the difference of two squares, but just failing to recognise that the difference of two squares exist.
It will also help to review your perfect squares
for the numbers between 1 and 16.
1) The region enclosed by the x-axis, the line x=3 and the curve y = sq. Rt x is rotated about the x-axis. What is the volume of the solid generated? *
Using the disk method, the volume would be
[tex]\displaystyle \pi \int_0^3 (\sqrt x)^2 \,\mathrm dx=\pi \int_0^3 x\,\mathrm dx=\frac\pi2 x^2\bigg|_0^3=\boxed{\frac{9\pi}2}[/tex]
That is, you split up the solid into disks of some small height ∆x, and each disk has radius at point x equal to the distance (√(x)) from the axis of revolution (the x-axis, y = 0) to the curve y = √(x). The volume of such a disk is then π (√(x))² ∆x. Take the sum of these volumes to get the total volume, then as the heights get smaller and smaller, replace ∆x with dx and the sum with the integral.
In this exercise we have to use the knowledge of the integral to calculate the volume of the disk that will correspond to:
[tex]V= \frac{9\pi }{2}[/tex]
That is, you split up the solid into disks of some small height ∆x, and each disk has radius at point x equal to the distance (√(x)) from the axis of revolution (the x-axis, y = 0) to the curve y = √(x). The volume of such a disk is then π (√(x))² ∆x. Take the sum of these volumes to get the total volume, then as the heights get smaller and smaller, replace ∆x with dx and the sum with the integral. Using the disk method, the volume would be:
[tex]\pi \int\limits^3_0 {(\sqrt{x})^2} \, dx = \pi \int\limits^3_0 {x} \, dx = \frac{\pi x^2}{2} = \frac{9 \pi }{2}[/tex]
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please help me i need it
Answer:
-27
Step-by-step explanation:
Draw a big X over the equal sign, then cross multiply the terms to get:
6(p) = 9(p+9)
Then you want to get p by itself.
Multiply the 9 out:6p = 9p+81Subtract 9p from both sides:-3p = 81Divide -3 both sides to get p by itself:p = -27Decide which of the two points lies on the graph of the line.
1. X + Y = 8
A. (2,4) B. (2,6)
2. X = 4
A.(4,2) B. (2,4)
3. Y = X - 2
A. (4,6) B. (6,4)
Answers:
B) (2,6)A) (4,2)B) (6,4)===========================================
Explanations:
For this problem, the x and y coordinates must add to 8. In choice A, we have x+y = 2+4 = 6, which doesn't work. But choice B does work since x+y = 2+6 = 8. Therefore, the point (2,6) is located on the line x+y = 8. The equation x+y = 8 is equivalent to y = -x+8.The x coordinate must be equal to 4. The y coordinate can be anything you want. The point (4,2) is on this line, while (2,4) is not. Another point on this line is (4,1). The line is completely vertical.If we plugged the x & y coordinates of choice A into the equation, we get 6 = 4-2 which then becomes 6 = 2 and that's a false statement. That rules out choice A. If we try choice B, then we get 4 = 6-2 which becomes 4 = 4. We get a true statement so choice B is the answer.Sargento cheese slices $2.48 for 10 slices or Velveeta cheese slices $3.18 for 12 slices find the unit rate for each and choose the better deal.
Answer:
Sargento cheese slices are the better deal
Sargento cheese slices $2.48 for 10 slices = 0.248 per slice
Velveeta cheese slices $3.18 for 12 slices = 0.265 per slice
Step-by-step explanation:
The unit rate for each cheese slice is $0.24 per piece for Sargento cheese slices and for Velveeta cheese slices is $0.26, and Sargento cheese slices is the better deal.
Given that,
Sargento cheese slices $2.48 for 10 slices or Velveeta cheese slices $3.18 for 12 slices.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
According to the question,
Sargento cheese slices, unit rate = 2.48/10 = $0.24
Velveeta cheese slices , unit rate = 3.18/12 = $0.26
From above Sargento cheese slices, is cheaper than Velveeta cheese slices.
Thus, the unit rate for each cheese slice is $0.24 per piece for Sargento cheese slices and for Velveeta cheese slices is $0.26, and Sargento cheese slices is the better deal.
Learn more about simplification here:
https://brainly.com/question/12501526
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A plot of land is 25 feet in length and 20 feet wide, and it is in the shape of a parallelogram. The perpendicular distance from the long side to the opposite long side is 18 feet. What is the area of the piece of land?
Given:
Length of the parallelogram = 25 feet
Width of the parallelogram = 20 feet
Perpendicular distance from the long side to the opposite long side = 18 feet.
To find:
The area of the piece of land which is a parallelogram.
Solution:
Area of a parallelogram:
[tex]Area=Base\times height[/tex]
Let the longer side, 25 feet is the base, then the height of the parallelogram is 18 feet. So, the area of the parallelogram is
[tex]Area=25\times 18[/tex]
[tex]Area=450[/tex]
Therefore, the area of the piece of land is 450 square feet.
Answer this for me please!
need help asap will give brainly
i’ll mark the brainliest for the correct answer, please just help me
Answer:
B, A.
Step-by-step explanation:
Find the simple Interest
I=?
P=$1300
R= 5%
T=6 years
$390
$1690
O $39000
i need help...
Answer:
$390 is the correct answer
Answer:
390
Step-by-step explanation:
(1300)(.05)(6) = 390
Determine if the two triangles are congruent. If they are, state how you know.
Answer:
d) AAS
Step-by-step explanation:
The angles shared where the triangles share a vertex are equal. Thus Angle-Angle-Side proves congruency.
Which value of h make the equation true?
2.3 + h = 7.8
Answer:
h = 5.5
Step-by-step explanation:
2.3 + h = 7.8
-2.3 -2.3
h = 5. 5
I need the answer ASAP
Can someone help me with this. Will Mark brainliest.
Answer:
(in degrees)
x = 15.09478709
Step-by-step explanation:
sin(x) = 25/96
Can anybody help me with this question i really need help on
Answer: 4
Step-by-step explanation:
10 x 4 = 40
11 x4 = 44
18 x 4 = 72
Mr.Richardson would like to build a planter surrounded by a brick path (shown in gray). How many square feet of brick does Mr.Richardson need?
Answer:
128 square feet
Step-by-step explanation:
Horizontal Gray parts:
12 - 8 = 4 ÷ 2 = 2
2 * 24 = 48 * 2 = 96
Vertical gray parts:
24 - 20 = 4 ÷ 2 = 2
2 * 8 = 16 * 2 = 32
All together:
96 + 32 = 128 square feet
Use similar triangles △EFG and △IHG to find the missing distance d
Factorize (4y-5)²+80y
Answer:
16y^2+40y+25
Step-by-step explanation:
[tex] {16y}^{2} + 40y + 25[/tex]
Step-by-step explanation:
(4y−5)^2+80y
Use binomial theorem (a−b)^2=a^2−2ab+b^2 to expand (4y−5)^2.
16y^2−40y+25+80y
Combine −40y and 80y to get 40y.
16y^2+40y+25
circle O has a circumference of 88piecm.
what is the length of the radius of the circle
Answer:
radius = 9.38 cm or 7(sq rt 2) cm
Step-by-step explanation:
sq rt 88(Pi) = radius
radius = 9.38 cm or 7(sq rt 2) cm
What's the area and the perimeter of rectangle ABDC shown in the coordinate plane?
Question 2 options:
A)
Area = 32 square units; perimeter = 24 units
B)
Area = 24 units; perimeter = 32 square units
C)
Area = 24 square units; perimeter = 32 units
D)
Area = 32 units; perimeter = 24 square units
Can someone help me with this I don’t understand
Answer:
the fastest is 12 meters every 4 seconds
slowest is 8 meters every 6 seconds
Step-by-step explanation:
A ladder leaning against a wall makes a 60° angle with the ground. The base of the ladder is 3 m from the building. How high above the ground is the top of the ladder?
Answer:
The distance is 5.20m
Step-by-step explanation:
Here, we want to get the height of the ladder
To get this, we need to understand that we have a right triangle, with the base of the triangle as 3 m, the angle at the downward part is 60, and we want to get the height of the triangle
The angle here faces the height we want to calculate
This height is known as the opposite
What we have is the adjacent
Now, the trigonometric identity that relates the opposite and the adjacent is the tan
The tangent of an angle is the ratio of the opposite to the adjacent
Mathematically;
tan 60 = h/3
h = 3 tan 60
h = 5.20 m
The ladder is at a height of 5.20 m above the ground
Can some one please help me with this
Answer:
I think the answer is B. I hoped I helped a little
analisis School 4 out of 10 students choose basketball as a sport like to watch and three out of five students choose football is the ratio of students who choose basketball for 2 to 10 equivalent to the ratio of students who chose football 3 to 25. Yes or No
Answer:
Pos sabe aaaaaaaaaaaaaaaaaaaaaaaa
67% of what is 119.2?
Step-by-step explanation:
[tex] \frac{67}{100} \times x = 119.2 \\ x = \frac{11920}{67} = 117.9 = 178[/tex]
i need help with this question can anyone please help me
PLEASE HELP ME
HAPPY FRIDAY!!!
Answer:
52.365
Step-by-step explanation:
53.715 + 51.3 + 52.62 = 157.635
210 - 157.635 = 52.365
HELP ! In right triangle RST, measure of angle S = 90° and measure of angle R ≠ measure of angle T. If cos(R) = a and sin(R) = b, which is equal to cos(T)/sin(T)?
The choices are
a+b
a-b
b-a
ab
a/b
b/a
Plzzzzzzz helppp i will give brainliest if right
Answer:
1.) 20 square inches
2.) 4.16
3.) (-1, -5) (2, -5)
Step-by-step explanation:
Write the equation of each line in slope-intercept form and identify the slope. 4x=2+y
Answer:
y = 4x - 2
Step-by-step explanation:
Given: 4x=2+y
First, subtract 2 on both sides to isolate out y. (Slope-intercept form is y=mx+b)
Once subtracted, you get: 4x-2=y
Rearrange it, and you get: y=4x-2
7a+3b=27
6a+3b=24
Solve in simultaneous
A=
B=
Answer:
A= 3,B = 2
Hope it helps you
if yes mark me brainliest
Answer:
hence, a = 3
b = 2
Step-by-step explanation:
from the given pair of linear equation we get,
7a + 3b = 27 - ( 1 )
6a + 3b = 24 - ( 2 )
now, subtract equation 2 from equation 1
=》7a + 3b - 6a - 3b = 27 - 24
=》a = 3
now put the value of a in equation 1
=》7a + 3b = 27
=》( 7 × 3 ) + 3b = 27
=》21 + 3b = 27
=》3b = 27 - 21
=》b = 6 ÷ 3
=》b = 2