Answers
In the picture we have to solve the individual variables A=2πr²+2πrh. We got function with r as subject is[tex]\frac{-h}{2} \pm\sqrt{\frac{h^{2}}{4 } +\frac{a}{2\pi} }[/tex]
Given that,
In the picture we have to solve the individual variables
A=2πr²+2πrh
We have to find function with r as subject.
Taking A to left side we get
2πr²+2πrh-A=0
We can see the equation is in the form of quadratic equation with variable r.
So, The factor we find by using the formula
That is [tex]\frac{-b\pm\sqrt{b^{2}-4ac } }{2a}[/tex]
Here, a=2π,b=2πh and c=-A
r=[tex]\frac{-2\pi h\pm\sqrt{(2\pi h)^{2}-4(2\pi)(-a) } }{2(2\pi)}[/tex]
r=[tex]\frac{-2\pi h\pm\sqrt{(4\pi^{2}h^{2} +8\pi a) } }{4\pi}[/tex]
r=[tex]\frac{-h}{2} \pm\frac{\sqrt{(4\pi^{2}h^{2} +8\pi a )} }{4\pi}[/tex]
r=[tex]\frac{-h}{2} \pm\sqrt{\frac{4\pi^{2}h^{2}+8\pi a }{16\pi^{2} } }[/tex]
r=[tex]\frac{-h}{2} \pm\sqrt{\frac{h^{2}}{4 } +\frac{a}{2\pi} }[/tex]
Therefore, We got function with r as subject is[tex]\frac{-h}{2} \pm\sqrt{\frac{h^{2}}{4 } +\frac{a}{2\pi} }[/tex]
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Related Questions
Show (3 steps) that the function is either continuous or discontinuous at the given value of x
1. f(x) = 1/x at x = 3
2. f(x) = |x+1|/x at x = 2
3. f(x)= [x] at x = 2
Answers
Using the continuity concept, the functions are classified as follows:
1) Continuous.
2) Continuous.
3) Discontinuous.
What is the continuity concept?A function f(x) is continuous at x = a if it is defined at x = a, and:
[tex]\lim_{x \rightarrow a^-} f(x) = \lim_{x \rightarrow a^+} f(x) = f(a)[/tex]
For functions 1 and 2, the functions are given by simple definitions, hence they are continuous, the limits and the numeric value will al be equal.
In item 3, the function will be discontinuous. This is because the function [x] returns the greatest integer less than x, hence:
[1.999999999999] = 1.[2.000000000001] = 2.Thus:
[tex]\lim_{x \rightarrow 2^-} f(x) = 1[/tex][tex]\lim_{x \rightarrow 2^+} f(x) = 2[/tex]Due to different lateral limits, the function is not continuous at x = 2.
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During a job interview, Pam Thompson is offered a salary of $50,000. The company gives annual raises of 12 percent. What will be
Pam's salary during her fifth year on the job? Use Exhibit 1-A. (Round time value factor to 3 decimal places and final answer to the
nearest whole number.)
Answers
Answer:
$78 700
Step-by-step explanation:
Four time periods year 2 3 4 and 5
50 000 ( 1.12 )^4 = 50 000 ( 1.574) = 78700
( 1.574 is from the table for 12 % and 4 periods )
Standard form of y=(X+3)^2-10
Answers
Please help me please In your own words
Answers
A line segment has two endpoints, whereas a ray has one endpoint and extends infinitely in the other direction, and a line extends infinitely in both directions.
What's the solution set of –4x + 1 ≤ 9 or x∕5 + 2 < 3?
Question 3 options:
A)
All real numbers
B)
x ≥ –2 or x < 5
C)
2 ≤ x < 5
D)
There is no solution.
Answers
Answer:
B) x ≥ –2 or x < 5
Step-by-step explanation:
We can immediately rule out A) All real numbers, since that will almost never be true for an inequality like this. We can also rule out C) 2 ≤ x < 5, since this is not a compound inequality.
Let's see if B) x ≥ –2 or x < 5 works by plugging in an x value greater than -2 and then, plugging in an x value less than 5.
Plug -1 into x
–4(-1) + 1 ≤ 9
4 + 1 ≤ 9
Combine like terms
5 ≤ 9
This is true, 5 is less than 9, so x ≥ –2 works.
Plug 4 into x
4∕5 + 2 < 3
Combine like terms
2.8 < 3
This is true, 2.8 is less than 3.
It can't be D) no solution now that B works, so B) x ≥ –2 or x < 5 is your answer.
Take care and Have a lovely rest of your day! :)
K
Find the lateral surface area and volume of the solid
object shown below.
9.5"
9"
11"
11"
The base of the pyramid is an equilateral triangle.
...
Answers
Answer: 209 square inches, 182 cubic inches
Step-by-step explanation:
The lateral surface area is the sum of the areas each of the four faces.
The area of one face is [tex](1/2)(11)(9.5)[/tex]. Multiplying this by 4, we get 209 square inches.
To find the volume, we use the formula [tex]V=\frac{1}{3}Bh[/tex]. This gives us that the volume is [tex](1/3)[(1/2)(11)(11)](9)[/tex], or about 182 cubic inches.
Write the equation in slope-intercept form.
1. Slope = 1/3; y-intercept = -1
2. Slope = -2/5; y-intercept = 0
3. Slope = 1; y-intercept = 8
Answers
Answer:
[tex]1. \;\;y = \dfrac{1}{3}x - 1\\\\2.\;\;y = -\dfrac{2}{5}x\\\\3.\;\;y = x + 8[/tex]
Step-by-step explanation:
The slope intercept form equation is y = mx + b
where m = slope and b = y-intercept
So for each case, substitute for slope(m) and y-intercept(b)
Answer:
1. y = 1/3x + (-1)
2. y = -2/5x
3. y = 1x + 8 = 1x + 8 or y = x + 8
Step-by-step explanation:
1. First of all, we need to know the slope-intercept form. The formula is y = mx + b. M represent the slope and b represents the y-intercept. So the question asked for the slope-intercept form for the slope that is 1/3 and the interception of -1. So we need figure out how to write it. It asked for -1/3 and -1 and we use the formal y = mx + b and it'll help us on figuring out how to write it. So far we have y = 1/3x + b, b is the intercept. The intercept would be -1. So the way we'd right it out is y = 1/3x + (-1). But first you have to multiply the + with -1. When we would multiply the signs you do it like this: (+) (+) = + and (-) multiplied by (-) is +. As well as (-) multiplied by (+) is -.
So for 1 the slope would be 1/3 and the (0, -1) . But we have to write it in the given form: y = mx + b ... m = slope, b = y intercept. So the way we'd right it is y = mx + b and m = slope, b = y intercept. Therefore the answer for this one is y = 1/3x - 1.
2. First we should know that we have the slope of -2/5 and the y-intercept is 0. The right form for this is y = -2/5x +. So for this one we got y = -2/5x because we said that the first one is 1/3 and -1. As well as the second is -2/5 and 0. The third is 1 and 8 as we wrote it earlier. So that's how we got our answer y = -2/5x for this question. Therefore our answer to this question is y = -2/5x.
3. For this one we first know slope = 1 and intercept =8. This equation is easier than both number 1 and 2 all we need to do is just put every given number in the right place. So we'll need to write the y as it is then add the = sign. Then write the slope which is given above. Then we have to write the x. We'll need to add the + sign and write the intercept given above next to it. After doing these steps you we'd have the answer because this is the general formula. So we would write 1 instead of m and the intercept is 8 so you need to write it instead of b. Therefore our answer would be y = 1x + 8 = 1x + 8 or another way we could write it is y = x + 8 either way would be correct.
I hope this helps, have a blessed day! :)
A scientist mixes water (containing no salt) with a solution that contains 35% salt. She wants to obtain 210 ounces of a mixture that is 15% salt. How many ounces of water and how many ounces of the 35% salt solution should she use?
Answers
The scientist should use 90 ounces of 35 percent solution and 120 ounces of water.
Percent is defined as the amount for a hundred units. Percentage is calculated by dividing the given amount by the total amount and multiplying by 100.
Let the scientist uses x ounces water.
Therefore the 35 percent solution is 210 - x.
Therefore the amount of salt in the 35 percent solution is 0.35 (210 - x )
The resulting mixture contains 15 percent salt.
Amount of salt = 15% of 210 =0.15 × 210 = 31.5 ounces.
Now 31.5 = 0.35 ( 210 - x )
or, 90 = 210 - x
or, x = 120 ounces
Therefore the 35 percent solution needed = 210 - 120 =90 ounces
Hence the scientist should use 90 ounces of 35 percent solution and 120 ounces of water.
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Correct the errors and fill in the blanks by completing the square.
Answers
Answer:
x = 2 - 5[tex]\sqrt{3}[/tex], x = 2 + 5[tex]\sqrt{3}[/tex]
Step-by-step explanation:
x² - 4x = 71
to complete the square
add ( half the coefficient of the x- term )² to both sides
x² + 2(- 2)x + 4 = 71 + 4
(x - 2)² = 75 ( take the square root of both sides )
x - 2 = ± [tex]\sqrt{75}[/tex] = ± 5[tex]\sqrt{3}[/tex] ( add 2 to both sides )
x = 2 ± 5[tex]\sqrt{3}[/tex]
then
x = 2 - 5[tex]\sqrt{3}[/tex] , x = 2 + 5[tex]\sqrt{3}[/tex]
A line segment has the endpoints V(7, 2) and W(3, 10). Find the coordinates of its midpoint M.
Answers
The coordinates of the midpoint M of the line segment VW are M = (5, 6)
In this question,
We have been given a line segment having endpoints V(7, 2) and W(3, 10)
We need to find the coordinates of the midpoint M of the line segment VW.
We know that the midpoint of points (x1, y1) and (x2, y2) is
M = (x1 + x2 / 2, y1 + y2 / 2)
Using midpoint formula,
M = ((7 + 3) / 2, (2 + 10) / 2)
M = (10/2, 12/2)
M = (5, 6)
Therefore, the coordinates of the midpoint M of the line segment VW are M = (5, 6)
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Math homework due in 30 min
Answers
The missing values are x = 45, t = 90, n = 60, p = 75, m = 30, s = 15, k = 135, w = 30, f = 60 and y = 45.
How to determine the values of the missing angles
Herein we have a geometrical system formed by six triangles, one of them is a equilateral triangle and other one is a right triangle. By geometry we know that the sum of the measures of a triangle is equal to 180°, the angles in a equilateral triangle have the same measure and one of the angles in a right triangle is a right angle.
Then, we have following system of linear equations:
t = 90 (1)
t + 2 · x = 180 (2)
3 · n = 180 (3)
2 · p + m = 180 (4)
p + f + y = 180 (5)
(t + 5) + w + n = 180 (6)
s + k + m = 180 (7)
x + n + p = 180 (8)
f + w = 90 (9)
m + n = 90 (10)
p + s = 90 (11)
By (1) and (2):
x = 45
By (3):
n = 60
By (8):
p = 180 - 45 - 60
p = 75
By (4):
m = 180 - 2 · 75
m = 30
By (11):
s = 90 - 75
s = 15
By (7):
k = 180 - 15 - 30
k = 135
By (6) and (1):
w = 180 - 60 - 90
w = 30
By (9):
f = 90 - 30
f = 60
By (5):
y = 180 - 75 - 60
y = 45
The missing values are x = 45, t = 90, n = 60, p = 75, m = 30, s = 15, k = 135, w = 30, f = 60 and y = 45.
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A company makes pens. They sell each pen for $9.
Their revenue is represented by R = 9 x.
The cost to make the pens is $3 each with a one time start up cost of $6000.
Their cost is represented by C = 3 x + 6000.
a) Find the profit, P, (P = R - C) when the company sells 1000 pens.
0
9000
-9000
15000
-3000
b) Find the number of pens they need to sell to break even (when R = C).
667
1000
1100
2000
Answers
Answer:
a) 0
b) 1000
Step-by-step explanation:
revenue = R = 9x
cost = C = 3x + 6000
profit = P = R - C
(a)
P = R - C
P = 9x - (3x + 6000)
P = 9x - 3x - 6000
P = 6x - 6000
For 1000 pens, x = 1000.
P = 6(1000) - 6000
P = 6000 - 6000
P = 0
Answer: 0
(b)
R = C
9x = 3x + 6000
6x = 6000
x = 6000/6
x = 1000
Answer: 1000
Each shape in the diagram below stands for a number.
000
Work out the value of each shape.
50/51 Marks
Total 90
-Total 66
Answers
By using the method of division, circle=20 , triangle= 35.
What is division?One of the four fundamental mathematical operations, along with addition, subtraction, and multiplication, is division. Division is the process of dividing a larger group into smaller groups so that each group contains an equal number of things. It is a mathematical operation used for equal distribution and equal grouping. In this post, let's study more about the division operation in math. One of the fundamental mathematical operations is division, which involves breaking a bigger number into smaller groups with the same number of components.
Given that,
The circles are 3
Which have the total of 60.
So, the total value divided by total number of circles.
60/3= 20
20 is the value of each circle.
The triangles are 2 including one circle
Which have the total of 90
90 - 20(circle)= 70
So, the total value divided by total number of triangles.
70/2= 35.
35 is the value of each triangle.
Therefore, circle=20 , triangle= 35
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Farmer Brown is making a garden 14 1/2 feet long and 8 3/4 feet wide. He puts up a fence 23 1/2 feet long and 17 3/4 feet wide. What is the distance from the fence to the edge of the garden?
Answers
The distance from the fence to the edge of the garden using the center as reference point is 4 1/2 feet.
Given data
garden 14 1/2 feet long and 8 3/4 feet wide
Fence 23 1/2 feet long and 17 3/4 feet wide
How to find the distance from the fence to the edge of the garden.We assume:
the fence has no thickness,
the distance considered is in the side of the length
the reference point for the distance is the center
Therefore:
Using the mid points we solve as follows:\
garden length / 2 - fence length / 2
= ( 23 1/2 ) / 2 - ( 14 1/2 ) / 2
= 11.75 - 7.25
= 4.5
= 4 1/2 feet
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Analyze the diagram below and complete the instructions that follow.
Answers
Similar triangles are triangles which have the same corresponding angle measures and proportional side lengths. The value of x is 17.5.
What are similar Triangles?Similar triangles are triangles which have the same corresponding angle measures and proportional side lengths.
Let PQ be the line between RS and RT.
Now PQR and RST are similar triangles.
RT/RP=RS/RQ
14/8=x/10
Use cross multiplication
14(10)=8x
140=8x
Divide both sides by 8.
17.5=x
Therefore x is 17.5.
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What is the area of a circle with a diameter of 10 inches?
a.
78.5 in2
c.
314 in2
b.
62.8 in2
d.
100 in2
Answers
Answer:
area is 3.14 r2
Step-by-step explanation:
here r = 5 inch
area = 3.14 × 25
so 78.5 in2
Write an equation of the line that passes through point (−3, 8) and has the slope m=−2.
Answers
SOMEBODY HELP WITH THIS PLEASE
Answers
To find the average height over each coaster, we must first add the height of each one together
109+135+115+365+126 = 850
Now divide 850 by the total amount of coasters, 5
850
------- = 170 Feet
5
Since the amusement park claimed their average height was 170 ft, it is not misleading. It is a good strategy because it is an honest statistic, which gives the amusement park more liability.
Pls help BD bisects LABC. Find m LABD, m m LABC = (25x + 34) °
Answers
Answer: ABD=67 degrees
CBD=67 degrees
ABC=134 degrees
Step-by-step explanation:
ABC=ABD+CBD
25x+34=ABD+11x+23
14x+34=ABD+23
ABD=14x+11
ABD=CBD ==> Bisected angles are equal to each other since angle ABC is divided into two equal angles when bisected.
14x+11=11x+23
3x+11=23
3x=12
x=4
ABD=14x+11
ABD=14(4)+11
ABD=56+11
ABD=67 degrees
CBD=11x+23
CBD=11(4)+23
CBD=44+23
CBD=67 degrees
ABC=25x+34
ABC=25(4)+34
ABC=100+34
ABC=134 degrees
Answer:
∠ ABD = 67° , ∠ CBD = 67° , ∠ ABC = 134°
Step-by-step explanation:
since BD bisects ∠ ABC , then
∠ ABD = ∠ CBD = 11x + 23
∠ ABC = ∠ ABD + ∠ CBD ( substitute values )
25x + 34 = 11x + 23 + 11x + 23
25x + 34 = 22x + 46 ( subtract 22x from both sides )
3x + 34 = 46 ( subtract 34 from both sides )
3x = 12 ( divide both sides by 3 )
x = 4
Then
∠ ABD = 11x + 23 = 11(4) + 23 = 44 + 23 = 67°
∠ CBD = ∠ ABD = 67°
∠ ABC = 25x + 34 = 25(4) + 34 = 100 + 34 = 134°
Q 32. If the length of the adjacent sides of a parallelogram is 16 cm and 30 cm, and the angle between them is 45°, then find
the area of the parallelogram.
Ops: A. 0240,2 sq.cm
B. 022542 sq.cm
C. 0270,2 sq.cm
D. 0180/2 sq.cm
Answers
Answer:
Option A
Step-by-step explanation:
When adjacent sides and angle between the adjacent sides are given, then,
[tex]\sf \boxed{\text{\bf Area of Parallelogram = a*b * $Sin \ \theta$}}[/tex]
Here, a and b are the adjacent sides and [tex]\sf \theta[/tex] is the angle between them.
a = 16 cm ; b = 30 cm ; [tex]\sf \theta = 45^\circ[/tex]
Area of parallelogram = 16 * 30 * Sin 45
[tex]\sf = 16 * 30 * \dfrac{\sqrt{2}}{2}\\\\= 8*30*\sqrt{2}\\\\= 240\sqrt{2} \ sq.cm[/tex]
The price of petrol rose by 650% in the past decade. If the original price was 1 dollar per liter, find the final price
Answers
Answer: $ 6.50 per liter of petrol rose
Step-by-step explanation:
Do these decorations always come off of jokers or end up falling off when they get old answer asap for brainlist?
Yes or no
Answers
Answer:
Step-by-step explanation:
Answer:
yes
Step-by-step explanation:
Find the distance between the pair of points, Use the distance formula.
Show your work.
(-12,20) and (-22,16)
Answers
Answer:
10.770
Step-by-step explanation:
You want the distance between points (-12,20) and (-22,16) using the distance formula.
Distance between pointsThe distance formula gives you the distance (d) between points (x1, y1) and (x2, y2).
d = √((x2 -x1)² +(y2 -y1)²)
For the given points, the distance is ...
d = √((-22-(-12))² +(16 -20)²) = √((-10)² +(-4)²) = √(100+16)
d = √116 = 2√29 ≈ 10.770330
The distance between the given points is about 10.77 units.
Aisha is three years older than Mpho . Together their ages add up to 17 years. How old is Aisha
Answers
Answer:
Aisha is ten years old and Mpho is seven
The age of Aisha is 10 years old and the age of Mpho is 7 years old.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
Aisha is three years older than Mpho. Together their ages add up to 17 years.
Let x be the age of Aisha and y be the age of Mpho. Then the equations are given as,
x = y + 3 ...1
x + y = 17 ...2
From equations 1 and 2, then we have
y + 3 + y = 17
2y = 14
y = 7
Then the value of 'x' is given as,
x = 7 + 3
x = 10
The age of Aisha is 10 years old and the age of Mpho is 7 years old.
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Give 5 different names for this line.
Answers
Answer:
post a pic, OP, to get specific answer
Step-by-step explanation:
You can use any two points, usually uppercase letters, that are on the line, in any order. Also, lines are named with a single script or italicized lowercase letter that is written beside one end of the line. See image for example.
I am confused on how → 0 to $9875 at 10% = 987.50
and,
→ $9876 to $29600 at 12% = 2,367.00 was figured out? I never done my own taxes before! I got the first step down, but can someone please explain this to me
Answers
Answer:
$2367
Step-by-step explanation:
You want to know how to figure the 12% tax due on the amount that falls in the bracket $9876 to 29600.
ApplicationTax tables are often written in a somewhat misleading way. This one seems to tell you
0 to 9875 . . . . 10% tax rate
9876 to 29600 (and up to 40,125) . . . . 12% tax rate
What this means is that every dollar between (and including) the 9876th dollar and the 29600th dollar will have a $0.12 tax applied. It is figured by subtracting 9875 from the amount that falls in this bracket, and multiplying that difference by 12%.
(29600 - 9875) × 12%
= 19725 × 0.12
= 2367 . . . . . . . . tax due on the amount in the 9876 to 29600 bracket
Tax due
If your taxable amount is $29,600, the total tax due is ...
(amount in first bracket) × 10% + (amount in second bracket) × 12%
= 9875 × 0.10 + (29600 -9875) × 0.12
= 987.50 +2367.00
= $3,354.50 . . . . . . . . . . . total due on $29,600
__
Additional comment
It can be easier to write a new tax table that simplifies the computation. For taxable amounts up to $40,125, this table can be simplified to ...
10% . . . . for taxable income at or below $9,875.(12% of income) - $197.50 . . . . for taxable income at or below $40,125Using this last entry for $29,600, we find the total tax due to be ...
$29,600 × 0.12 - 197.50
= $3,552.00 -197.50
= $3,354.50 . . . . . . . same as above.
The amount $197.50 is (12% -10%)×9875.
Along the same lines, the rest of the tax table can be simplified to ...
(22% of income) - $4,210.00(24% of income) - $5,920.50(32% of income) - $18,984.50(35% of income) - $25,205.00(37% of income) - $35,573.00It turns out that the tax due is the maximum of the values computed using these equations. (You don't actually have to know what bracket applies to your income. Knowing the bracket does simplify the process by choosing the applicable formula.)
Note that this is a tax table for 2020. The rates for 2021 are different.
what are the length and width in meters of the actual court
Answers
The real court is 9 by 18 meters in length and width.
In arithmetic, what does length mean?The length of something is its width or size measured across its entire surface. Or, to put it another way, it is the larger of a geometric shape's higher two or three dimensions.
This statement implies that the court's original dimensions have been reduced by 22.5 for every 1 centimeter in the size of the current drawing, which is 40 cm by 80 cm. To get the original dimension, we will multiply the required dimension by each 22.5 cm as shown. Original length for a 40-cm length = 40 * 22.5 originally 900 cm long 100 cm equals one meter in metres. Multiply 900cm by x to get 9m: 100x = 900*1x = 900/100x Therefore, 900cm = 9m For the 80-cm width: Original width is equal to 80 * 22.5, or 1800 cm. 100 cm equals one meter in metres. multiplying 1800cm by x yields 100x, 1800*1, 1800/100x, and 18m. So 1800cm = 9m. As a result, the real court is 9 meters long and 18 meters wide.
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V
The length of a rectangle is six times its width.
If the area of the rectangle is 600 ft², find its perimeter.
Answers
Answer:
140
Step-by-step explanation:
→ Find an expression for the area
6x × x = 6x²
→ Equate to area
6x² = 600
→ Solve
x = 10
→ Find length and width
Length = 60 and width = 10
→ Find perimeter
60 + 60 + 10 + 10 = 140
Step-by-step explanation:
you can ask questions for clarification
Write a number in which the value of the 3 is ten times greater than the value of the 3 in 135,864
Answers
A number in which value of 3 is ten times greater than the value of 3 is 375,786.
Here,
We have to find a number in which the value of the 3 is ten times greater than the value of the 3 in 135,864.
What is Place value?
Place value can be defined as the value represented by a digit in a number on the basis of its position in the number.
Now,
The value of 3 in 135,864 is 30,000.
And, We want to write a number that is ten times greater than 30,000.
Hence, We have to write any other number in which the value of 3 is 300,000.
Since, There are infinitely many numbers that we can write.
Some numbers are:
375,786
2,345,576
9,387,988 ........ and so on.
Therefore, A number in which value of 3 is ten times greater than the value of 3 is 375,786.
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The area of a rectangular wall of a barn is 119 square feet. its length is 10 feet longer than the width find the length and the width. Find the length and width of wall of the barn
Answers
The length of the rectangular wall of a barn is 7 and the width is 17 feet
Area of the rectangular wall of a barn = 119 square feet
Length of the wall of the barn = width of barn + 10 feet
Let the width of the wall of the barn be x feet
So, the length of the wall of the barn will be x + 10 feet
The area of the rectangular wall of the barn is given by:
Area of the rectangular wall of the barn = Length of the barn * Width of the barn
119 = x*(x+10)
119 = x^2 +10x
0 = x^2 +10x - 119
Using splitting the middle term method
0 = x^2 + 17x - 7x - 119
0 = x(x + 17) - 7(x + 17)
x = 17 or 7.
Since the width is 10 feet more than the length
Therefore, the length of the rectangular wall of a barn is 7 and the width is 17 feet
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