Final answer:
The approximate length of a pendulum that takes 2.4 pi seconds to swing back and forth is about 14.7 meters.
Explanation:
To find the approximate length of a pendulum that takes 2.4 pi seconds to swing back and forth, we can use the formula for the period of a pendulum:
T = 2π √(L/g)
Where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity.
Given that the period is 2.4 pi seconds, we can substitute this value into the formula:
2.4 pi = 2π √(L/g)
Simplifying the equation, we can divide both sides by 2π:
1.2 = √(L/g)
Squaring both sides of the equation, we get:
1.44 = L/g
Since we don't have the value of g, we cannot solve for L exactly. However, if we assume that g is approximately 9.8 m/s², which is the average acceleration due to gravity on Earth, we can estimate the value of L:
1.44 = L/9.8
Multiplying both sides by 9.8, we find:
L ≈ 14.7 m
Find the pattern, then write the next two numbers.
0, 2, 6, 12, 20,
Answer:
30, 42
Step-by-step explanation:
You add 2 to the additional 2 you started with
0+2=2
2+(2x2)=6
6+(2x3)=12
The required next two-term of the sequence is 30 and 42.
Given that,
To determine the pattern and next two-term of numbers 0, 2, 6, 12, 20.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
Here,
The given sequence is,
0, 2, 6, 12, 20,
a0 = 0,
a1 = 2
nth term an = a(n - 1) + 2(n - 1)
For 6th term
n = 6
6th term = a(6 - 1) + 2(6 - 1)
a6 = a5 + 10
a6 = 20 + 10
a6 = 30
7th term,
an = a(n -1) + 2 (n - 1)
a7 = a6 + 2*6
a7 = 30 + 12
a7 = 42
Thus, the required next two-term of the sequence is 30 and 42.
Learn more about arithmetic here:
brainly.com/question/14753192
#SPJ2
what is the area of the composite figure ? enter your answer in the box . use 3.14 for pi
Answer:
The area of the composite figure = 12.785 square units
Step-by-step explanation:
The figure composite of :
A ⇒ Rectangle with coordinates (0,0) , (0,5) , (2,5) and (2,0)
B ⇒ Rectangle with coordinates (2,0) , (2,1) , (4,1) and (4.0)
C ⇒ Quarter of a circle with coordinates (2,1) , (2,2) and (3,1)
Area of A: Length = 5 and Width =2
Area of A = Length times the width = 5*2 = 10 square units
Area of B: Length = 2 and Width =1
Area of B = Length times the width = 2*1 = 2 square units
Area of C: radius = 1
Area of C = 0.25 * pi * r² = 0.25 * 3.14 * 1² = 0.785 square units
Total Area = 10 + 2 + 0.785 = 12.785 square units
Answer:
the answer is 12.785
Step-by-step explanation:
i took the test
The sum of two numbers is 39 and their difference is 5. Which is the larger number?
Answer:
22
Step-by-step explanation:
Let x be a number
Other number = 39 -x
x - (39 - x) =5
x - 39 + x = 5
2x = 5 + 39 = 44
x = 44/2
x = 22
Other number = 39 - 22 = 17
Answer:
The larger number = 22
Step-by-step explanation:
Let the two number x and y
The sum of two numbers is 39 can be represented as:
x + y = 39----------------1
The difference of two numbers is 5 can be represented as:
x - y = 5------------------2
x + y = 39----------------1
x - y = 5------------------2
Using Elimination Method and subtracting 2 from 1
x-x + y-(-y) = 39 - 5
0+y+y=34
2y=34
y=34/2
y=17
substituting y=17 in 1
x+17=39
x=39-17
x=22
∴ The larger number = 22
11. The perimeter of a rectangle is 60 cm. The length is four times the width. What
are the length and the width of the rectangle?
Answer:
Length = 24 cm
Width = 6 cm.
Step-by-step explanation:
The formula to compute the perimeter of a rectangle is,
[tex]Perimeter=2(length+width)[/tex]
Given:
Perimeter = 60 cm
width = w
length = 4w
Determine the value of width as follows:
[tex]Perimeter=2(length+width)\\60=2\times(4w+w)\\60=10w\\w=6[/tex]
The value of length is:
[tex]length(l)=4\times w\\l=4\times6\\l=24[/tex]
Thus, the length and the width of the rectangle are 24 cm and 6 cm respectively.
Find the value of the expression:
a
p^2q^2+pq–q^3–p^3 for p=1 and q=−1
Answer:
0
Step-by-step explanation:
Put the numbers where the letters are and do the arithmetic.
(1)^2(-1)^2 +(1)(-1) -(-1)^3 -(1)^3
= 1·1 -1 -(-1) -1
= 1 - 1 + 1 - 1 = 0
The value of the expression is 0.
Which equation represents the line of best fit for the scatter plot?
A. y=x+10
B. y=2x+10
C. y=-x+10
D. y=-2x+10
the equation line of the scatter plot is y = ×+10
what is 8,473 divided by 7? I need the actual work shown to see if I did it right. I have a calculator but I'm helping my kid with her homework and I want to make sure we did it right
Answer:
1210 r3
Step-by-step explanation:
7000/7=1000
1400/7= 200
73/7= 10 r3
8473/7=1210 r3
How many cubic feet of concrete are needed to pour 4 cylindrical pillars 5 feet high with a diameter of 4 inches?
Answer: 1.75 cubic feet concrete is needed.
Step-by-step explanation:
Alright, lets get started.
The volume of the pillar is : [tex]\pi r^2h[/tex]
We have given the height is 5 feet.
We have given the diameter is 4 inches.
So the radius will be : [tex]\frac{4}{2}=2 \ inches[/tex]
Converting inches into feet.
The radius will be : [tex]\frac{2}{12} \ feet[/tex] [tex]= 0.167 feet[/tex]
So the volume of the cylinder will be : [tex]\pi * 0.167^2*5[/tex]
So the volume of the cylinder will be : [tex]0.4380 \ cubic \ feet[/tex]
As there are 4 pillars, so total volume will be : [tex]4*0.4380[/tex]
So, total volume will be : [tex]1.75 \ cubic \ feet[/tex]
Hence 1.75 cubic feet concrete is needed. : Answer
Hope it will help :)
Answer:
1.75 cubic feet
Step-by-step explanation:
Measure the diameter of the cylinder. ...
Hope this helps
In right triangle PQR PR=17 RQ=15 PQ =8 What is tan P
What is the answer
Answer:
The value of tan P = 1.875
Step-by-step explanation:
Given:
PR=17
RQ=15
PQ =8
To find:
tan P = ?
Solution:
In trigonometric ratio
tan = [tex]\frac{opposite}{adjacent}[/tex]
Now on substituting the given values(refer the figure)
tan (P) =[tex]\frac{15}{8}[/tex]
tan (P) = 1.875
Rectangle 25 feet long. It has a perimeter of 130 feet. What is the area of the basement?
Final answer:
To find the area of the basement, we started with the given perimeter of 130 feet and the known length of 25 feet and solved for the missing width. Once we determined the width was 40 feet, we used the formula for the area of a rectangle (Area = length × width) to calculate that the basement's area is 1000 square feet.
Explanation:
To solve the question regarding the area of a rectangle where the length is 25 feet and the perimeter is 130 feet, we must first deduce the width of the rectangle using the perimeter formula: P = 2l + 2w (where P is the perimeter, l is the length, and w is the width). Since we know the perimeter (P) and the length (l), we can rearrange this formula to solve for the width (w).
The perimeter formula is expressed as:
130 = 2(25) + 2w
130 = 50 + 2w
2w = 130 - 50
2w = 80
w = 40 feet
Now that we have both the length and the width, we can calculate the area of the rectangle using the formula Area = length × width.
Therefore, the area of the rectangle is:
Area = 25 feet × 40 feet
Area = 1000 square feet
A store sells cantaloupes at a price of 6 for $9.00. Henry wants to send 24 cantaloupes to his grandmother. How much will Henry spend if he buys the cantaloupes at the store?
Answer: $36
Step-by-step explanation:
Each cantaloupe is $1.5.
Answer:
he will spend 36 dollars because 24 ÷ 6 = 4 and 9$ times 4 = 36$
GIVING BRAINLIEST. Write a proportion that could be used to solve for each variable. Then solve. 12 balls in 2 boxes 78 balls in x boxes a. 12/2 = 78/x; x = 13 c. 12/2 = 78/x; x = 12 b. 2/12 = 78/x; x = 468 d. 12/2 = x/78; x = 458
Answer:
B. 2/12 = 78/x ; x = 468
Step-by-step explanation:
12/2 = 78/x
6 = 78/x
6 x 78 = x
468
An arc of a circle of radius 7cm subtends an eagle of 120degree at the centre. Find its perimeter.
Answer:
[tex]\dfrac{14\pi }{3}\ cm[/tex]
Step-by-step explanation:
The circumference of the circle with radius of 7 cm is
[tex]C=2\pi r\\ \\C=2\pi \cdot 7=14\pi \ cm[/tex]
An arc of a circle o subtends an angle of [tex]120^{\circ}[/tex] at the centre.
The circle has the full angle of [tex]360^{\circ},[/tex] then
[tex]14\pi \ cm - 360^{\circ}\\ \\x\ cm - 120^{\circ}[/tex]
Write a proportion:
[tex]\dfrac{14\pi }{x}=\dfrac{360}{120}\\ \\\dfrac{14\pi }{x}=\dfrac{3}{1}\\ \\14\pi =3x\\ \\x=\dfrac{14\pi }{3}\ cm[/tex]
Alice is planning her next vacation. She budgeted 110 for travel expenses, and she expects to spend 120 each day for food and lodging. Her total budget for the trip is 710 . How many days can Alice have for her vacation without exceeding her budget?
Answer:
5 days to spend exactly $710
Step-by-step explanation:
Answer:
5 days
Step-by-step explanation:
5 x 120 = 600
600 + 110 = 710
Which is the solution of the quadratic equation (4y – 3)= 72?
Answer:
[tex]y = 18.75[/tex]
hope that is what you need
Step-by-step explanation:
[tex](4y - 3) = 72[/tex]
[tex]4y - 3 = 72[/tex]
[tex]4y = 72 + 3[/tex]
[tex]4y = 75[/tex]
[tex] \frac{4y}{4} = \frac{75}{4} [/tex]
[tex]y = \frac{75}{4} [/tex]
[tex]y = 18.75[/tex]
9 pounds for $1.50 how many pounds for $1.00
1. Find how much one pound is.
- to do this, divide 1.50 by 9. This will give you one pound.
2. Figure out how many times 1 pound can go in a dollar.
proportion
[tex]\frac{9}{1,5} = \frac{x}{1} \\[/tex]
1.5x=9*1
1.5x=9
x=[tex]\frac{9}{1.5}[/tex]
x=6
at dinner jermey and his friend spent $24. They left a 20% tip and then slpit the cost? How much did eacj person pay
Answer: They each paid $2.40.
The length of a rectangle is twelve inches more than its width. The perimeter of the rectangle is 276 inches. What are the dimensions of the rectangle?
Answer: The dimensions of the rectangle are
Length = 75 and Width = 63
Step-by-step explanation: We would start with the information about the sides of the rectangle which states that the length is twelve inches more than it's width. In other words, if the width is represented by the letter w, then the length will be w + 12.
Also the perimeter of a rectangle is given as
2(L + W) where L is the length and W is the width of the rectangle
Therefore
Perimeter = 2( {w +12} + w)
276 = 2(2w + 12)
276 = 4w + 24
Subtract 24 from both sides of the equation
252 = 4w
Divide both sides of the equation by 4
63 = w
Therefore the width of the rectangle is 63 and the length is 75 (63 + 12).
L = 75 inches
W = 63 inches
Which statement proves that quadrilateral UWXY is a parallelogram? A. Diagonals UX and WY bisect each other B. Diagonals UX and WY are perpendicular C. Sides UW and XY are congruent D. Sides UW and XY are parallel (there was no given figure just this)
Answer: It’s D, i got it right!!
Step-by-step explanation:
5. The measures of the angles of a triangle are in the extended ratio 17:16:12. What is the measure of the (1 point)
largest angle?
O 34
O45
O48
068
Factor this expression 36a2x
Answer:
The answer is (6a√x) * (6a√x)
Step-by-step explanation:
Let's factor this expression 36a²x:
Let's use √, this way:
36a² = 6a * 6a
x = √x * √x
Therefore, we can factor, this way:
(6a * 6a) * (√x * √x)
(6a√x) * (6a√x)
How do you solve X+10y=-9 X=5y+21
Answer:
Step-by-step explanation:
Identify an equation in point-slope form for the line perpendicular to y = - 1/3 * x - 6 that passes through (- 1, 5)
A)y - 5 = 3(x + 1)
B)y - 5 = - 1/3 * (x + 1)
C)y + 5 = 1/3 * (x - 1)
D)y + 1 = 3(x - 5)
Answer:
A
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = - [tex]\frac{1}{3}[/tex] x - 6 ← is in slope- intercept form
with slope m = - [tex]\frac{1}{3}[/tex]
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-\frac{1}{3} }[/tex] = 3
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
here m = 3 and (a, b) = (- 1, 5), thus
y - 5 = 3(x - (- 1)), that is
y - 5 = 3(x + 1) → A
Find the equation of a line that is parallel to line g that contains (P, Q).
the coordinate plane has a line g that passes through the points (-3,2) and (0,5).
3x − y = 3P − Q
3x + y = Q − 3P
x − y = P − Q
x + y = Q − P
Correct option:
[tex]\boxed{x-y=P-Q}[/tex]
Explanation:
Given that the line we are looking for is parallel to g, then the slope of that line and g is the same, therefore:
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ \\ (x_{1},y_{1})=(-3,2) \\ \\ (x_{2},y_{2})=(0,5) \\ \\ \\ m=\frac{5-2}{0-(-3)}=1[/tex]
So we can write the point-slope form of the equation of the line as follows:
[tex]y-y_{0}=m(x-x_{0}) \\ \\ (x_{0},y_{0})=(P,Q) \\ \\ \\ y-Q=1(x-P) \\ \\ y-Q=x-P \\ \\ \\ Arranging: \\ \\ P-Q=x-y \\ \\ \boxed{x-y=P-Q}[/tex]
Learn more:Graphying systems of linear equations: https://brainly.com/question/13799715
#LearnWithBrainly
A linear equation is in the form:
y = mx + b
where y, x are variables, m is the slope and b is the y intercept.
Line g passes through (-3,2) and (0,5). hence:
[tex]Slope\ of\ line\ g=\frac{y_2-y_1}{x_2-x_1}=\frac{5-2}{0-(-3)}=1[/tex]Two lines are parallel if they have the same slope. Hence:
Line parallel to line g has a slope of 1. Since it passes through (P, Q), hence:
[tex]y-y_1=m(x-x_1)\\\\y-Q=1(x-P)\\\\y-Q=x-P\\\\x-y=P-Q[/tex]
The equation of a line that is parallel to line g that contains (P, Q) is x - y = P - Q
Find out more on linear equation at: https://brainly.com/question/14323743
2 to the 3rd power times 4 divided by 2 plus 2
Answer: 18
Step-by-step explanation: 2 x 2 x 2= 8
8 x 4 = 32
32 / 2 = 16
16 + 2 = 18
A circle and a square each have a perimeter of 160 feet. Which has the greater area and by how much
Answer:
[tex]The \: circle \: has \: a \: bigger \: area \: by \approx 438 \: {ft}^{2} [/tex]
Explanation:
[tex]Diameter \: of \: circle:160 \div 3.14 \approx 51 \: ft \\ Area \: of \: circle : \frac{3.14 \times {51}^{2} }{4} \approx 2038 \: {ft}^{2} \\ Sides \: of \: square:160 \div 4 = 40 \: ft \\
Area \: of \: square: \: {40}^{2} = 1600 \: {ft}^{2} \\ 2038 - 1600\approx 438 \: {ft}^{2} [/tex]
Final answer:
Comparing the areas of a circle and a square with the same perimeter of 160 feet, the circle has a greater area by approximately 435.75 square feet.
Explanation:
We are comparing the areas of a circle and a square which both have a perimeter of 160 feet. For the square, since the perimeter (P) is 160 feet, each side (s) will be P/4, which gives us s = 40 feet. The area of the square (Asquare) is s², so Asquare = 40² = 1600 square feet.
For the circle, the perimeter is the circumference (C), which is 160 feet. The formula for the circumference of a circle is C = 2πr, where r is the radius. So, 160 = 2πr, giving us r = 160/(2π). The area of the circle (Acircle) is πr², so Acircle = π(160/(2π))². After calculation, we find that Acircle ≈ 2035.75 square feet.
Comparing the two areas, the circle has a greater area than the square by Acircle - Asquare ≈ 2035.75 - 1600 ≈ 435.75 square feet.
use limits to find the area of the region bounded by the graph f(x)=4-2x^3 , the x-axis , and the vertical lines x=0 and x=1
A) 7
B) infinity
C) 7/2
D) 7/4
Answer:
[tex]\frac{7}{2}[/tex] square units.
Step-by-step explanation:
We have to use limits to find the area of the region bounded by the graph [tex]f(x) = 4 - 2x^{3}[/tex] , the x-axis, and the vertical lines x=0 and x=1.
So, the area will be
A = [tex]\int\limits^1_0 {(4 - 2x^{3})} \, dx[/tex]
= [tex][4x - \frac{x^{4}}{2} ]^{1} _{0}[/tex]
= [tex]4 - \frac{1}{2}[/tex]
= [tex]\frac{7}{2}[/tex] square units. (Answer)
PLEASE HELP ME :'(
The Memphis Pyramid is in Tennessee is a building that is in the shape of a square pyramid. The base area of the building is 349,281 square feet and the height of the pyramid is 321 feet. If you were to roll a marble from the very top of the building, how many feet would it travel to reach the bottom? Round your answer to the nearest tenth.
Answer:
321.1 ft
Step-by-step explanation:
Linear Distance
Let's imagine a square-based pyramid of side L and height H. Please refer to the image provided below where a simplified drawing of the pyramid shows the diagonal distance D that the marble has to travel to reach the base of the pyramid from the very top of it, assuming it rolls by the very center of one of the sides.
The distance can be calculated by
[tex]\displaystyle D=\sqrt{\left(\frac{L}{2} \right)^2+H^2}[/tex]
We need to find the length of the side of the square base. We know its area is [tex]349,281 ft^2[/tex]. The area of a square is
[tex]A_s=L^2[/tex]
We solve for L
[tex]L=\sqrt{A}=\sqrt{349,281 }=18.9\ ft[/tex]
Now we compute D
[tex]\displaystyle D=\sqrt{\left(\frac{18.9}{2} \right)^2+321^2}[/tex]
[tex]\boxed{D=321.1\ ft}[/tex]
This should be easy I hope
Answer:
two to the power of one multiply by two hundred twenty seven to the power of one.
Step-by-step explanation:
456÷2=227
227 can not be divided any further so it would be two to the power of one multiply by two hundred twenty seven to the power of one.
You are supposed to find prime factorization by dividing the number by prime numbers.
Solve for x.
3x = 6x – 2
Answer:
x = [tex]\frac{2}{3}[/tex]
Step-by-step explanation:
Given
3x = 6x - 2 ( subtract 6x from both sides )
- 3x = - 2 ( divide both sides by - 3 )
x = [tex]\frac{-2}{-3}[/tex] = [tex]\frac{2}{3}[/tex]
Answer:
x=2/3
Step-by-step explanation:
Its just right