To find the area of the surface above the given rectangle, we need to determine the intersection of the cylinder with the plane of the rectangle. The surface area above the rectangle is equal to the area of the rectangle multiplied by the range of the z-coordinate.
Explanation:To find the area of the surface that lies above the given rectangle, we need to determine the intersection of the cylinder with the plane of the rectangle. The equation of the cylinder is y^2+z^2=9, and the vertices of the rectangle are (0,0), (4,0), (0,2), and (4,2). At the x=0 and x=4 cross sections, we can see that the y-coordinate ranges from 0 to 2 and the z-coordinate ranges from -3 to 3. Therefore, the surface area above the rectangle is equal to the area of the rectangle multiplied by the range of the z-coordinate.
The area of the rectangle is (4-0)(2-0) = 8 square units. The range of the z-coordinate is -3 to 3, so the surface area above the rectangle is 8 * (3 - (-3)) = 48 square units.
Tia cut a 4 meter 8 centimeter wire into 10 equal pieces. Marta cut a 540 centimeter wire into 9 equal pieces. how much longer is one of Marta's wires than one of Tia's?
Marta's wire is 19.2 cm longer than Tia's wire.
Further explanation
Given:
Tia 's wire is 4m 8 cm ⇒ cut into 10 equal pieces
Marta's wire 540 cm ⇒ cut into 9 equal pieces
Question:
How much longer is one of Marta's wires then one of Tia's?
1. Tia's wire is in m and cm unit, so we can not divide it straightly into its equal pieces. First step, we are going to convert meter (m) to millimeter (mm):
Tia's wire = 4 m 8 cm
[tex]\boxed {1 m = 100 cm }[/tex]
[tex]\boxed {= (4 m \times \frac{100 cm}{ 1 m}) + 8 cm ) } \\\boxed {= 400 cm + 8 cm }\\\boxed {= 408 }[/tex]
2. Second step, calculate each pieces Tia's wire:
She cut this wire into 10 equal pieces:
[tex]\boxed {= \frac{408}{10} } \\\boxed {= 40.8 cm }[/tex]
Each piece of Tia's s ribbon is is 40.8 cm long
3. Third step, we are going to calculate Marta's wire:
She has 540 cm and cut it into 9 equal pieces
[tex]\boxed {= \frac{540 cm}{9} }[/tex]
[tex]\boxed {=60 cm }[/tex]
Each pieces Marta's wire is 60 cm long
4. Last step, find the difference between Tia's wire and Marta's:
[tex]\boxed {=60 cm -40.8 cm }\\\boxed {=19.2 cm }[/tex]
So, Marta's wire is 19.2 cm longer than Tia's wire
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Keywords: converting, conversion, dividing, subtraction, find the difference, converting meter to centimeter, converting unit of length
(3y)^-2(9y)^2/3y^-4=
Beth sold half of her comic books and then bought nine more. She now has 28. How many did she begin with?
At noon, ship A is 170 km west of ship B. Ship A is sailing east at 35 km/h and ship B is sailing north at 20 km/h. How fast is the distance between the ships changing at 4:00 PM?
The distance between the ships is changing at a rate of 39 km/hr at 4:00 PM. This is calculated using differentiation of the Pythagorean theorem relating distances between the ships.
Explanation:This is a typical
related rates problem
in calculus. Before we start, let's mark the distance between ship A and ship B as C, the distance that A traveled as X (X=35 km/hr*4 hr = 140 km), and the distance B traveled as Y (Y=20 km/hr*4 hr = 80 km). Note that X, Y, and C form a right triangle. By using the Pythagorean theorem, we get C²=X²+Y², which we can differentiate with respect to time (t) to obtain, 2C * dC/dt = 2X * dX/dt + 2Y * dY/dt. As we're solving for dC/dt (rate of change of the distance between the two ships), we get dC/dt = (X * dX/dt + Y * dY/dt) / C. Plugging in the known values (X=140 km, Y=80 km, dX/dt=35 km/hr, dY/dt=20 km/hr, and C=170 km, as it hasn't changed since they started), we get dC/dt = (140*35 + 80*20) / 170 = 39 km/hr. So, the distance between the ships is changing at a rate of 39 km/hr at 4:00 PM.
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Which number is both a factor of 80 and a multiple of 4? Select three that apply.
A. 40
B. 1
C. 2
D. 8
E. 32
F. 16
A family has a monthly income of $3300 and plans to spend 11% of this amount on entertainment. How much will be spent on entertainment?
A pitcher's arm rotates at a speed of 7 degrees per millisecond (degrees/ms)
At what speed does the pitcher's arm rotate in degrees/s?
To solve this problem, all we have to do is to use a conversion factor to convert millisecond into seconds. We know that there are 1000 milliseconds in a second, therefore:
pitcher’s arm rotation = 7 degrees / millisecond * (1000 milliseconds / second)
pitcher’s arm rotation = 7,000 degrees / second
Answer:
7000 Hope this helps and if it does remember to give me a like , please and thank you!
The length of each side of a square increases by 2.5 inches to form a new square with a perimeter of 70 inches. The length of each side of the original square was inches. NextReset
Answer:
The length of each side of the original square was [tex]15[/tex] inches
Step-by-step explanation:
Let
x------> the length side of the original square
we know that
The perimeter of a square is equal to
[tex]P=4b[/tex]
where
b is the length side of the square
In this problem
[tex]b=(x+2.5)\ in[/tex]
[tex]P=70\ in[/tex]
substitute
[tex]70=4(x+2.5)[/tex]
solve for x
[tex]70=4x+10[/tex]
[tex]4x=70-10[/tex]
[tex]x=60/4=15\ in[/tex]
What is the 80th percentile for the average height of 10 men?
It is claimed that in a bushel of peaches, less than 10% are defective. a sample of 400 peaches is examined and 50 are found to be defective. what is the critical value for α = 0.025?
Final answer:
To find the critical value for α = 0.025 in a one-tailed test, we look at the standard normal distribution tables; the critical value is approximately -1.96.
Explanation:
The question pertains to hypothesis testing in the context of proportion analysis. To determine the critical value for a significance level α = 0.025 in a one-tailed test about a proportion, we use the standard normal distribution (Z-distribution). Given that the sample size is large (n=400), it is appropriate to use a Z-test for this calculation. The critical value corresponds to the Z-score that has 0.025 of the distribution's area to its right (since we are checking for 'less than 10% defective').
Referring to standard normal (Z) distribution tables or using statistical software, we can find that the critical value for α = 0.025 for a one-tailed test is approximately -1.96. This is the Z-score such that the area under the normal curve to the right of this value is 0.025. If the calculated Z-score obtained from the sample proportion is less than -1.96, we would reject the null hypothesis that the proportion of defective peaches is less than 10%.
a carpenter goes through 2 3/5 boxes of nails finishing 3 1/2 rooves. How much would he use finishing 8 roves?
What is the apr of a 30 year 300000 mortage with monthly payments of 3000?
What is the slope of the line that passes through th epoints (26, 7) and (-39, 12)?
Answer:
m = (12 - 7) / (-39 - 26) = 5/(-65) = -1/13
Find the product. Simplify if possible. −13⋅(817)
2/3×5/12=reduce lowest form
write the equation then solve to find the number:seventy four less than a number is 98
Solve this equation please !
−2 − (+7) = ?
An equation is formed when two equal expressions are equated together with the help of an equal sign '='. The solution of the given equation,−2 − (+7) is −9.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
What is Addition?The addition is one of the four fundamental mathematical operations, the others being subtraction, multiplication, and division. When two whole numbers are added together, the total quantity or sum of those values is obtained.
Given an equation, −2 − (+7) which is needed to be solved. Therefore, The given equation can be solved as shown below.
−2 − (+7)
Open the brackets,
= −2 − 7
Add the two terms,
= −9
Hence, the solution of the given equation,−2 − (+7) is −9.
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The perimeter of a square is 32 centimeters. What is the length of one side?
A parabola has a vertex at (0,0). The focus of the parabola is located on the positive x-axis. Which part of the graph will the directrix pass through?
Solve for n: a= p(1+nr)
Which is 0.54 (.54 is repeating) converted to a simplified fraction?
A) 27/50
B) 54/100
C) 6/11
D) 54/99
Answer:
B
Step-by-step explanation:
The answer above me ^^
Which statements about the graph of the function f(x) = –x2 – 4x + 2 are true? Check all that apply.
The domain is {x|x ≤ –2}.
The range is {y|y ≤ 6}.
The function is increasing over the interval (–∞ , –2).
The function is decreasing over the interval (−4, ∞).
The function has a positive y-intercept.
Find the inverse of each of the given functions.
f(x) = 4x − 12
f−1(x) = _x + _
f(x) = 4x − 12
f−1(x) =1/4 x + 3
The inverse of the function f(x) = 4x - 12 is f^-1(x) = (x + 12)/4.
Explanation:To find the inverse of the function f(x) = 4x - 12, we need to switch the roles of x and y and solve for y.
Step 1: Replace f(x) with y: y = 4x - 12.
Step 2: Swap x and y: x = 4y - 12.
Step 3: Solve for y: x + 12 = 4y.
Step 4: Divide both sides by 4: (x + 12)/4 = y.
Therefore, the inverse function is f-1(x) = (x + 12)/4.
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Edmundo used a number line to show the solution for the inequality |2x-6|<4 Which number line shows the solution? HURRY PLEASE
To solve the inequality |2x-6|<4, we break it down into two inequalities and solve for the range of values. Then, we can plot the solution on a number line.
Explanation:The given inequality is |2x-6|<4. To solve this inequality, we need to break it down into two separate inequalities:
2x-6<4-(2x-6)<4Solving these inequalities will give us the range of values that satisfy the original inequality. Once we have the solution, we can plot it on a number line.
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Answer:
Step-by-step explanation:
an absolute value has two solutions, one negative and one positive.
so 2x-6<-4
2x<2
x<1
and
2x-6<4
2x<10
x<5
1>x<5
Option A is correct
Javier used the equivalent ratios to find the number of millimeters in 8 inches.
How many millimeters are in 8 inches?
127 mm
163.2 mm
167 mm
203.2 mm
A circle has a radius of 2.5 centimeters and a central angle AOB that measures 90°. What is the area of sector AOB? Use 3.14 for pi and round your answer to the nearest tenth
Are the fractions equivalent? 12/15 and 20/25
Solve each given equation and show your work. Tell whether it has one solution, an infinite number of solutions, or no solutions, and identify each equation as an identity, a contradiction, or neither
(A) 6x+4x-6=24+9x
(B)25-4x=15 -3x+10-x
(C) 4x+8=2x+7 +2x-20
James lives in San Francisco and works in Mountain View. In the morning, he has 3 transportation options (bus, cab, or train) to work, and in the evening he has the same 3 choices for his trip home. If James randomly chooses his ride in the morning and in the evening, what is the probability that he'll take the same mode of transportation twice?
How do you do it??
Answer:
1/3
Step-by-step explanation:
Find the value of a so that the differential equation y ' − xy − 6x = 0 has a solution of the form y(x) = a + bex2/2 for any constant
b.
Answer:
a = -6
Step-by-step explanation: