The maximum error in the calculated surface area is 24.19cm² and the relative error is 0.0132.
Given that the circumference of a sphere is 76cm and error is 0.5cm.
The formula of the surface area of a sphere is A=4πr².
Differentiate both sides with respect to r and get
dA÷dr=2×4πr
dA÷dr=8πr
dA=8πr×dr
The circumference of a sphere is C=2πr.
From above the find the value of r is
r=C÷(2π)
By using the error in circumference relation to error in radius by:
Differentiate both sides with respect to r as
dr÷dr=dC÷(2πdr)
1=dC÷(2πdr)
dr=dC÷(2π)
The maximum error in surface area is simplified as:
Substitute the value of dr in dA as
dA=8πr×(dC÷(2π))
Cancel π from both numerator and denominator and simplify it
dA=4rdC
Substitute the value of r=C÷(2π) in above and get
dA=4dC×(C÷2π)
dA=(2CdC)÷π
Here, C=76cm and dC=0.5cm.
Substitute this in above as
dA=(2×76×0.5)÷π
dA=76÷π
dA=24.19cm².
Find relative error as the relative error is between the value of the Area and the maximum error, therefore:
[tex]\begin{aligned}\frac{dA}{A}&=\frac{8\pi rdr}{4\pi r^2}\\ \frac{dA}{A}&=\frac{2dr}{r}\end[/tex]
As above its found that r=C÷(2π) and r=dC÷(2π).
Substitute this in the above
[tex]\begin{aligned}\frac{dA}{A}&=\frac{\frac{2dC}{2\pi}}{\frac{C}{2\pi}}\\ &=\frac{2dC}{C}\\ &=\frac{2\times 0.5}{76}\\ &=0.0132\end[/tex]
Hence, the maximum error in the calculated surface area with the circumference of a sphere was measured to be 76 cm with a possible error of 0.5 cm is 24.19cm² and the relative error is 0.0132.
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A portion of the Quadratic Formula proof is shown. Fill in the missing reason.
Statements Reasons
ax2 + bx + c = 0 Given
ax2 + bx = −c Subtract c from both sides of the equation
x squared plus b over a times x equals negative c over a Divide both sides of the equation by a
x squared plus b over a times x plus the quantity b over 2 times a squared equals negative c over a plus the quantity b over 2 times a squared Complete the square and add the quantity b over 2 times a squared to both sides
x squared plus b over a times x plus the quantity b over 2 times a squared equals negative c over a plus b squared over 4 times a squared Square the quantity b over 2 times a on the right side of the equation
x squared plus b over a times x plus the quantity b over 2 times a end quantity squared equals negative 4 times a times c over 4 times a squared plus b squared over 4 times a squared Find a common denominator on the right side of the equation
x squared plus b over a times x plus the quantity b over 2 times a squared equals b squared minus 4 times a times c all over 4 times a squared Add the fractions together on the right side of the equation
quantity x plus b over 2 times a end quantity squared equals b squared minus 4 times a times c all over 4 times a squared ?
Rewrite the perfect square trinomial as a binomial squared on the left side of the equation
Take the square root of both sides of the equation
Multiply both sides of the equation by 2
Square the left side of the equation
The quadratic equation ax²+bx+c = 0 is given and this is illustrated below.
How to illustrate the equation?ax²+bx+c = 0
Step 1: Subtract c from both sides
ax²+bx+c-c = 0-c
ax²+bx = -c
Step 2: Divide both sides of the equation by a
ax²/a + bx/a = -c/a
x² + bx/a = -c/a
Step 3: Complete the square and add the quantity (b/2a)² times a squared to both sides
x² + bx/a + (b/2a)² = -c/a + (b/2a)²
Step 4: Square the quantity b/2a on the right side of the equation
x² + bx/a + (b/2a)² = -c/a + b²/4a²
Step 5: Find a common denominator on the right side of the equation which is 4a²
x² + bx/a + (b/2a)² = -4ac/4a² + b²/4a²
Step 6: Add the fractions together on the right side of the equation
x² + bx/a + (b/2a)² = (-4ac+ b²)/4a²
Step 7: The equation on the left is to be written as a perfect square as shown
(x+b/2a)² = (-4ac+ b²)/4a²
Step 8: Take the square root of both sides
√(x+b/2a)² = √ (-4ac+ b²)/4a²
(x+b/2a) = √(-4ac+ b²)/2a
Step 9: subtract b/2a from both sides
x+b/2a - b/2a = -b/2a + √(-4ac+ b²)/2a
x = -b/2a + √(-4ac+ b²)/2a
Step 10: Add the fractions together on the right-hand side
x = -b±√(-4ac+ b²)/2a
This will then gives the required equation.
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A(n) _____ is a line drawn from one part of a circle's circumference to another without passing through the center.
Answer:
chord
Step-by-step explanation:
a chord is a line drawn from one part of a circle's circumference to another without passing through the centre.
If the line passed through the centre then it would be a diameter
Which of the following are not polynomials?
A. x² +2√x+1
B.x²+x+1
C. 2/3x2+x+1
D. x2+√2x+1
E. x-2+x+1
Answer: A, C, E
Step-by-step explanation:
These are not polynomials because there is one term where the variable has an exponent that is not a positive integer.
I need help with question 11-21 show your work please and thank you!
The computation shows that the thickness of the beam is 3.75 inches.
How to calculate the values?11. The thickness of the beam will be:
= 3/4 inch × 5
= 3.75 inches.
12. The length of the board will be:
= 7 5/8 × 5
= 38.125 inches.
13. The total height of the stairs will be:
= 8 3/16 × 13
= 106.4375 inches.
14. The height of the stack will be:
= 55 × 3/8in
= 20.625 inches.
15. The length of the board will be:
= 3/4 × 86 1/4
= 64.6875 inches.
16. The number of hours that it'll take to replace the trim will be:
= 37 1/2 × 1/4
= 9.375 hours.
17. The height of the will required will be:
= 22 × 5/12
= 9.167 feet
18. The inches removed from the wood will be:
= 1/16 × 7
= 0.4375 inches.
19. The shortest finish stock will be:
= 3/16 × 15
= 2.8125 feet.
20. The total amount of board wasted will be:
= 3/16 × 11
= 2.0625 inches.
21. The total rise in the staircase will be:
= 22 × 7 3/8
= 162.25 inches.
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The Torrey family was on vacation. One day, they spent $140 for a motel room, $130 for meals, and $200 at a park. How much money did they spend that day?
Answer:
$470
Step-by-step explanation:
Add all the amounts given.
200+140+130=470
They spent $470 that day.
Hope this helps!
If not, I am sorry.
Answer:
470
Step-by-step explanation:
140+130+200= 470
They said that day, which means all together. So we add.
Write the standard form of the line that passes through the given points. include your work in your final answer. (-1, -3) and (2, 1)
The standard form of a line passing through the points (-1, -3) and (2, 1) is 4x - 3y = 5.
The slope of the given line, m = (1 - (-3))/(2 - (-1)) = (1 + 3)/(2 + 1) = 4/3.
Computed using the formula for the slope of a line, m = (y₂ - y₁)/(x₂ - x₁), when a line passes through the points (x₁, y₁) and (x₂, y₂).
The point intercept form of a line is y - y₁ = m(x - x₁) when the line passes through the point (x₁, y₁) and has the slope m.
Thus, the given line in the point intercept form can be written as:
y - 1 = (4/3)(x - 2).
The standard form of a line is ax + by = c.
To convert the point intercept form to the standard form, we do as follows:
y - 1 = (4/3)(x - 2),
or, 3(y - 1) = 3(4/3)(x - 2) {Multiplying both sides by 3},
or, 3y - 3 = 4x - 8 {Simplifying},
or, 8 - 3 = 4x - 3y {Rearranging},
or, 4x - 3y = 5 {Rearranging and simplifying}.
Thus, the standard form of a line passing through the points (-1, -3) and (2, 1) is 4x - 3y = 5.
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The coordinates of CD are C (-7,-2) and D (-3,-5). Point E is the midpoint of CD. What are the coordinates of the midpoint E?
The coordinates of the midpoint of CD with endpoint at C(-7,-2) and D(-3,-5) is E(-5, -3.5)
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Let (x, y) represent the coordinate of the midpoint E. Point E is the midpoint of CD, hence:
x = [(-7) + (-3)] / 2 = -5
y = [(-2) + (-5)] / 2 = -3.5
The coordinates of the midpoint of CD with endpoint at C(-7,-2) and D(-3,-5) is E(-5, -3.5)
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The cost of a gallon of gas increased from $3.54 to $3.87 over the weekend. What is the percent increase for the cost of gas, rounded to the nearest whole percent?
Answer:
9%
Step-by-step explanation:
percent increase is calculated as
[tex]\frac{increase}{original}[/tex] × 100%
increase = $3.87 - $3.54 = $0.33 , then
% increase = [tex]\frac{0.33}{3.54}[/tex] × 100% ≈ 9% ( to the nearest whole percent )
Answer:
9 % (rounded to the nearest whole percent)
Step-by-step explanation:
the amount of increase:
3.87 - 3.54 = 0.33
Then
the percent increase for the cost of gas :
[tex]=\frac{0.33}{3.54} \times 100\\\\= 0.093220338983 \times 100\\\\=9.3220338983 \ \%[/tex]
write each polynomial in standard form. Then give the leading coefficient. You may need to combine like terms before writing the polynomial in standard form.
10-3x²+x^5 + 4x³
Step-by-step explanation:
To write a polynomial in standard form, put the degree that are the greatest first
So here it would be
[tex] {x}^{5} + 4 {x}^{3} - 3 {x}^{2} + 10[/tex]
Remember constant are numbers that you learned back in elementary,
Numbers like 10,90,4,1,0,-3 etc.
Remember that constant are basically represented like this
[tex]k \times {x}^{0} [/tex]
For example, 10 is represented like
[tex]10 \times {x}^{0} [/tex]
Since 0 is the smallest degree possible, for a polynomial, constants are the last term of a polynomial in standard form
find the are of the rectangle
Answer:
126 ft^2
Step-by-step explanation:
The area of a rectangle is just its length times its width. We are given that the length is 14 ft, and the width is 9 ft. If we multiply the two quantities, we get that the area is 14*9 or 126 ft^2
Answer: 126ft^2
Step-by-step explanation:
area of rectangle=length*width
here
length=14 ft
width=9ft
area=14*9
area= 126 ft^2
Select all of the options which are examples of expenditure.
what is the length of EF?
The length of EF is 3.8
How to solve for EF?To do this, we make use of the following law of sines
EF/sin(D)= DE/sin(F)
So, we have:
EF/sin(75)= 3/sin(50)
This gives
EF = sin(75) * 3/sin(50)
Evaluate the product
EF = 3.8
Hence, the length of EF is 3.8
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Which set of ordered pairs has the same slope as the given set: (2,9) (1,12)?
The slope(m) of the given set is -3.
What is the slope of a pair of the ordered set?The slope(m) of a pair of the given ordered set is the change in the rise over the run. The rise is the y-axis while the run is the x-axis.
Mathematically;
[tex]\mathbf{Slope(m) = \dfrac{\Delta y}{ \Delta x}}[/tex]
[tex]\mathbf{Slope(m) = \dfrac{y_2-y_1}{x_2-x_1} }[/tex]
Here:
x_1 = 2y_1 = 9x_2 = 1y_2 = 12[tex]\mathbf{Slope(m) = \dfrac{12-9}{1-2} }[/tex]
[tex]\mathbf{Slope(m) = \dfrac{3}{-1} }[/tex]
Slope (m) = -3
Therefore, we can conclude that the slope of the given set is -3. From the given option, kindly find out which of the slope is equivalent to -3.
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For the following exercises, solve each inequality and write the solution in interval notation.
30. 2| v − 7 | − 4 ≥ 42
Answer:
The solution to the inequality [tex]$2|v-7|-4 \geq 42$[/tex] in interval notation is given by [tex]$-16 \leq v \leq 30$[/tex].
Step-by-step explanation:
An absolute value inequality [tex]$2|v-7|-4 \geq 42$[/tex] is given.
It is required to solve the inequality and write the solution in interval form.
To write the solution, first solve the given absolute value inequality algebraically and then write it in interval notation.
Step 1 of 4
The given absolute value inequality is [tex]$2|v-7|-4 \geq 42$[/tex].
Add on both 4 sides,
[tex]$$\begin{aligned}&2|v-7|-4 \geq 42 \\&2|v-7|-4+4 \geq 42+4 \\&2|v-7| \geq 46\end{aligned}$$[/tex]
Step 2 of 4
Divide by 2 on both sides,
[tex]$$\begin{aligned}&\frac{2|v-7|}{2} \geq \frac{46}{2} \\&|v-7| \geq 23\end{aligned}$$[/tex]
The inequality can be written as [tex]$v-7 \leq 23$[/tex] and [tex]$v-7 \geq-23$[/tex]
Step 3 of 4
First solve the inequality, [tex]$v-7 \leq 23$[/tex].
Add 7 on both sides,
[tex]$$\begin{aligned}&v-7 \leq 23 \\&v-7+7 \leq 23+7 \\&v \leq 30\end{aligned}$$[/tex]
Step 4 of 4
Solve the inequality [tex]$v-7 \geq-23$[/tex].
Add 7 on both sides,
[tex]$$\begin{aligned}&v-7 \geq-23 \\&v-7+7 \geq-23+7 \\&v \geq-16\end{aligned}$$[/tex]
The solution of the inequality in interval notation is given by [tex]$-16 \leq v \leq 30$[/tex].
What is the equation of the line shown above?
Answer:
[tex]a.) y=\frac{1}{4} x+3[/tex]
Step-by-step explanation:
Any two points along the line are (4,4) and (0,3),
[tex]Gradient= \frac{4-3}{4-0}=\frac{1}{4}[/tex]
we know the y intercept is 3
Therefore equation of the line is : [tex]y=\frac{1}{4} x+3[/tex]
Suppose g(x)=f(x+2)-3
The transformations which map f(x) to g(x) according to the equation are; Translation of f(x) 2 units to the left and 3 units upwards.
Which translations maps f(x) to g(x)?The equation given in the task content is as follows;
g(x)=f(x+2)-3It therefore follows that the transformations which would produce function g(x) from f(x) involves a 2 units translation to the left and a 3 units translation upward.
Remarks:
The complete question requires that the transformations from f(x) to g(x) be identified.
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The volume of a square pyramid is 50 inches. The length of the base of the pyramid is 5 inches. What is the height of the pyramid?
Answer: the height of the pyramid is 6 inch.
Step-by-step explanation:
V=50 inch³ a=5 inch H=?
Formula of volume square pyramid is:
[tex]\boxed {V=\frac{1}{3}*S_{base}*H },[/tex]
where: Sbase - pyramid base area;
H - pyramid height.
Hence,
[tex]H=\frac{3*V}{S_{base}}\\[/tex].
Since the pyramid is square, its base is a square. ⇒
[tex]S_{base}=a^2\\S_{base}=(5\ inch)^2\\S_{base}=25\ inch^2\\H=\frac{3*50}{25} \\H=3*2\\H=6\ (inch).[/tex]
Good luck!
Which of the following lines will have a negative slope? Select all that apply
Everyday Math
424. House Paint April wants to paint the exterior of her house. One gallon of paint covers about 350 square feet, and the exterior of the house measures approximately 2000 square feet. How many gallons of paint will she have to buy?
Answer:
If the exterior of the house is 2000 square feet and each gallon of paint covers 350 square feet.
Then she needs to buy 6 gallons of paint.
Step-by-step explanation:
Dividing the total area by the area that each gallon of paint covers we get,
[tex]$\frac{2000}{350} \times \frac{50}{50}=\frac{40}{7}$$[/tex]
Now, performing long division we get,
[tex]$7\overset{5}{\overline{\left){\begin{align} & 40 \\ & \underline{35} \\ & \underline{05} \\ \end{align}}\right.}}$$[/tex]
She needs five gallons of paint fully and some amount of the sixth gallon because we get a remainder.
She can't buy paint in fraction, hence she has to buy 6 gallons of paint.
What is the TV's length?
Answer:
32.75 inches
Step-by-step explanation:
Pythagoras' theorem. The long length squared minus the short length squared gives you the answer squared, so square root it :)
Which graph shows the solution to the system of linear inequalities?
y> x+3
ys-x+2
VO
Next
Submit
The solution to the inequality y > x + 3 and y < -x + 2 is the dark green region shown in the graph.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Inequality shows the non equal comparison of two or more numbers and variables.
Given the inequality y > x + 3 and y < -x + 2.
The solution to the inequality y > x + 3 and y < -x + 2 is the dark green region shown in the graph.
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A girl has 3 shirts (red, yellow, blue) and 6 pairs of socks (red, blue, green, orange, white, black). What is the probability her socks will be orange and her shirt will be red?
Answer:
1/18
Step-by-step explanation:
P(Orange AND Red)
= P(Orange socks)*P(Red shirt)
= 1/3*1/6
= 1/18
Show all work to identify the asymptotes and end behavior of the function f(x)= 5x/x-25.
Considering the given function and the asymptote concept, we have that:
The vertical asymptote is of x = 25.The horizontal asymptote is of y = 5.The end behavior is that as [tex]x \rightarrow \infty, f(x) \rightarrow 5[/tex].What are the asymptotes of a function f(x)?The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator.The horizontal asymptote is the value of f(x) as x goes to infinity, as long as this value is different of infinity. Hence it also gives the end behavior of the function.In this problem, the function is:
[tex]f(x) = \frac{5x}{x - 25}[/tex].
The vertical asymptote is found as follows:
x - 25 = 0 -> x = 25.
The horizontal asymptote is found as follows:
[tex]y = \lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow \infty} \frac{5x}{x - 25} = \lim_{x \rightarrow \infty} \frac{5x}{x} = \lim_{x \rightarrow \infty} 5 = 5[/tex].
Hence the end behavior is that as [tex]x \rightarrow \infty, f(x) \rightarrow 5[/tex].
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15 brainlist coins. ASAP. What type of function is f(x) = 2^x –14?
This is an exponential function due to the presence of exponent
What are exponential functions?Exponential functions are inverse of logarithmic functions. Given the function below;
f(x) = 2^x - 14
This is an exponential function due to the presence of exponent and since the standard form of an exponential function is y = ab^x
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Based off this picture, what would the length of AC- be?
The length of AC- is?
(Giving 70 points!)
Answer:
AC = 9
Step-by-step explanation:
Set the negative value into absolute as length cannot be negative.
⇒ AC = AB + BC
⇒ AC = |-5| + 4
Formula: |-a| = a
⇒ AC = 5 + 4
⇒ AC = 9
Answer: I think the length is 9 units
Step-by-step explanation:
The president of a company create a graph of the price of the company stock over one year he describes the graph as following the price of the stock Rose two about $17 before falling to about three dollars they have only been two periods during which the price of the stock decrease the price of the stock is expected to increase in the long run which graph correctly shows the price of the stock
The price of the stock is expected to increase in the long run correctly describes it and is denoted as option D.
What is a Graph?This is defined as the pictorial representation of date or variables in an organized manner.
From the graph provided , we can infer that after a while the stock began to rise which is the same as it increasing in the long run.
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In the triangle below, what is the measure of ZZ?
OA. 65°
B. 7°
O C. 90°
D. 50°
65
7
2. Jill makes a blend of brownies for the bake sale. The double-chocolate brownies are $5.50 per plate, and the chocolate-mint brownies are $4.00 per plate. Jill sells more than 11 plates total. Jill also sells less than $66.50 worth of brownies. Using this information, choose the solution set that would be found in the overlapping areas of a graph of Jill's sales. 2. Jill makes a blend of brownies for the bake sale . The double - chocolate brownies are $ 5.50 per plate , and the chocolate - mint brownies are $ 4.00 per plate . Jill sells more than 11 plates total . Jill also sells less than $ 66.50 worth of brownies . Using this information , choose the solution set that would be found in the overlapping areas of a graph of Jill's sales .
By using a graphing calculator, the solution set that would be found in the overlapping areas of a graph of Jill's sales is (15, -4).
How to determine the solution set?First of all, we would assign variables to the blend of brownies that were made by Jill for the bake sale as follows:
Let x be the double-chocolate brownies.Let y be the chocolate-mint brownies.Since Jill sold more than 11 plates in total, we have:
x + y > 11.
Also, Jill sold less than $66.50 worth of brownies:
5.50x + 4.00y < 66.50.
By using a graphing calculator, the solution set that would be found in the overlapping areas of a graph of Jill's sales is (15, -4).
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Help asap pleaseeeeeeeeee its due 5 and its 4 for me right now
Answer:
The answer would be A
Step-by-step explanation:
1^2=1×1= 1
2^2 =2×2=4
3^2=3×3=9
4^2=4×4=16
Therefore,
√11 lies between 3 and 4
Answer:
A
Step-by-step explanation:
[tex]since 3 is \sqrt{9} and 4 is \sqrt{16} then it follows that \sqrt{11} is between the two[/tex]
Durante una venta de liquidación, el Sr. Pablo, un profesor particular, compró un total de 12 libros de asesoría de Secundaria 4 y Secundaria 1 por S/82. El precio de un libro de asesoría de Secundaria 4 era de S/ 8 y el precio de un libro de asesoría de
Secundaria 1 era de S/ 6. Que el número de los libros de asesoría de Secundaria 1 comprados sea “k”.
a) Expresa el número de libros de asesoría de Secundaria 4 comprados en términos de “k”.
b) Forma una ecuación en “k' y resuélvela, calculando la cantidad de libros de cada tipo que compró el Sr.Pablo
Resolviendo un sistema de ecuaciones, vemos que se venden 6 libros de secundaria 4 y 6 libros de secundaria 1.
¿Como escribir un sistema de ecuaciones?
Primero definimos dos variables:
x = numero de libros de secundaria 4 vendidos.k = número de libros de secundaria 1 vendidos.Sabemos que se venden 12 libros en total, entonces:
x + k = 12
Tambien sabemos que se recauda un total de $82, entonces:
x*$8 + k*$6 = $82
Entonces tenemos dos ecuaciones.
a) Usando la primer ecuacion, podemos aislar x para tener:
x = 12 - k
b) Ahora podemos reemplazar eso en la otra ecuación para solucionar el sistema.
(12 - k)*$8 + k*$6 = $82
$96 - $2*x = $82
$2*x = $12
x = $12/$2 = 6
Es decir se venden 6 libros de secundaria 4, y como se venden 12 libros en total, los otros 6 libros vendidos son de secundaria 1.
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