The circumference of the equator of a sphere was measured to be 82 82 cm with a possible error of 0.5 0.5 cm. Use linear approximation to estimate the maximum error in the calculated surface area to 4 decimal places.
Answer:
The maximum error in the calculated surface area is approximately 8.3083 square centimeters.
Step-by-step explanation:
The circumference ([tex]s[/tex]), in centimeters, and the surface area ([tex]A_{s}[/tex]), in square centimeters, of a sphere are represented by following formulas:
[tex]A_{s} = 4\pi\cdot r^{2}[/tex] (1)
[tex]s = 2\pi\cdot r[/tex] (2)
Where [tex]r[/tex] is the radius of the sphere, in centimeters.
By applying (2) in (1), we derive this expression:
[tex]A_{s} = 4\pi\cdot \left(\frac{s}{2\pi} \right)^{2}[/tex]
[tex]A_{s} = \frac{s^{2}}{\pi^{2}}[/tex] (3)
By definition of Total Differential, which is equivalent to definition of Linear Approximation in this case, we determine an expression for the maximum error in the calculated surface area ([tex]\Delta A_{s}[/tex]), in square centimeters:
[tex]\Delta A_{s} = \frac{\partial A_{s}}{\partial s} \cdot \Delta s[/tex]
[tex]\Delta A_{s} = \frac{2\cdot s\cdot \Delta s}{\pi^{2}}[/tex] (4)
Where:
[tex]s[/tex] - Measure circumference, in centimeters.
[tex]\Delta s[/tex] - Possible error in circumference, in centimeters.
If we know that [tex]s = 82\,cm[/tex] and [tex]\Delta s = 0.5\,cm[/tex], then the maximum error is:
[tex]\Delta A_{s} \approx 8.3083\,cm^{2}[/tex]
The maximum error in the calculated surface area is approximately 8.3083 square centimeters.
Can someone please help
Answer:
6^7
Step-by-step explanation:
6^8 x 6^-1
6^{8-1}
6^7
1.5 x 10 to the power of 11
Answer:
150000000000
Step-by-step explanation:
1.5x10¹¹
= 150000000000
You can think about scientific notations by moving the position of the 'dot' 11 times to the right
A relay microchip in a telecommunications satellite has a life expectancy that follows a normal distribution with a mean of 90 months and a standard deviation of 3.5 months. When this computer-relay microchip malfunctions, the entire satellite is useless. A large London insurance company is going to insure the satellite for 50 million dollars. Assume that the only part of the satellite in question is the microchip. All other components will work indefinitely.
A. For how many months should the satellite be insured to be 94% confident that it will last beyond the insurance date?
B. If the satellite is insured for 84 months, what is the probability that it will malfunction before the insurance coverage ends?
C. If the satellite is insured for 84 months, what is the expected loss to the insurance company?
D. If the insurance company charges $3 million for 84 months of insurance, how much profit does the company expect to make?
Answer:
a) The insurance should be of 84.6 months, that is, approximately 85 months.
b) 0.0436 = 4.36% probability that it will malfunction before the insurance coverage ends.
c) The expected loss to the insurance company is of 2.18 million.
d) The company should expect to make a profit of $689,200.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
A relay microchip in a telecommunications satellite has a life expectancy that follows a normal distribution with a mean of 90 months and a standard deviation of 3.5 months.
This means that [tex]\mu = 90, \sigma = 3.5[/tex]
A. For how many months should the satellite be insured to be 94% confident that it will last beyond the insurance date?
The 100 - 94 = 6th percentile, which is X when Z has a pvalue of 0.06. So X when Z = -1.555.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.555 = \frac{X - 90}{3.5}[/tex]
[tex]X - 90 = -1.555*3.5[/tex]
[tex]X = 84.6[/tex]
The insurance should be of 84.6 months, that is, approximately 85 months.
B. If the satellite is insured for 84 months, what is the probability that it will malfunction before the insurance coverage ends?
This is the pvalue of Z when X = 84. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z= \frac{84 - 90}{3.5}[/tex]
[tex]Z = -1.71[/tex]
[tex]Z = -1.71[/tex] has a pvalue of 0.0436
0.0436 = 4.36% probability that it will malfunction before the insurance coverage ends.
C. If the satellite is insured for 84 months, what is the expected loss to the insurance company?
0.0436 probability of losing 50 million. So
0.0436*50 = 2.18
The expected loss to the insurance company is of 2.18 million.
D. If the insurance company charges $3 million for 84 months of insurance, how much profit does the company expect to make?
1 - 0.0436 = 0.9564 probability of making 3 million.
0.0436 probability of losing 50 million
So
[tex]E = 0.9564*3 - 0.0436*50 = 0.6892[/tex]
The company should expect to make a profit of 0.6892 million, that is, $689,200.
Howdy!
I am here with a handful of geometry questions today. Please answer the question based off the image(s) below.
If you are not sure of the answer please leave a comment, DO NOT ANSWER THE QUESTION UNLESS YOU KNOW THE ANSWER. Please don't take me points! Thanks for understanding.
Anyways, please show all of your work and explain your thinking! Thanks!
Answer:
Right square pyramid
Volume:
V = 1/3a²h = 1/3*3²√(4² - (3/2)²) = 11.1 ft³Surface area:
A = a² + 2al = 3² + 2*3*4 = 33 ft²A, B and C are points on a circle with diameter AB.
ABC is a right-angled triangle.
Calculate the area of the circle.
Give your answer correct to 3 significant figures. *
Answer:
area is approximately 36.56
Step-by-step explanation:
9
10
11
12
A rectangular garden is 16 ft
by 30 ft. Victoria wants to
build a fence along the
diagonal of the garden.
How long does the fence
need to be?
13
14
15
16
17
18
30
19
20
16
X
21
22
23
24
Answer:
rectangles opposite sides are equal.
the diagonal of rectangle is hypotenuse of the right angle triangle.
30²+16²=x²
900+256=x²
1156=x²
1156½=x²
34=x
so, the fence need to be 34ft
What kind of angels are 1 and 2 ?
Four friends all give each other presents.
The total cost of the presents is £80.52
Work out the mean cost of a present in pounds (£).
Answer:
20.13
Step-by-step explanation:
Four friends all give each other presents. The total cost of the presents is £80.52.
We need to find the mean cost of a present in pounds.
Mean = sum of observations/total no of observation
[tex]M=\dfrac{80.52}{4}\\\\=20.13[/tex]
So, the mean cost of a present is equal to 20.13 .
simplify the following expression
(x+y)²
Answer:
[tex] {x}^{2} + 2xy + {y}^{2} [/tex]
Step-by-step explanation:
1) Use square sum: (a + b)² = a² + 2ab + b².
[tex] {x}^{2} + 2xy + y^{2} [/tex]
Therefor, the answer is x² + 2xy + y².
Factor 70q+60. Write your answer as a product with a whole number greater than 1.
Answer:
10(7q + 6)
Step-by-step explanation:
Find the GCF of 70 and 60: 10Divide each number by 10 (steps shown below)70q ÷ 10 = 7q60 ÷ 10 = 6Re-write the expression with 10: 10(7q + 6)I hope this helps!
please help me please i really need help please
Answer:
d metamorphosis
Step-by-step explanation:
1/3 How many minutes does April jump rope 1 day? 1 week. Please tell the answer for 1 day and 1 week
Answer:
1/3
i don't know laughing out loud
Does anyone know how to do this?
Answer: 53
Step-by-step explanation:
Hope this helps!
Hey!
I am here with a handful of geometry questions today. Please answer the question based off the image(s) below.
If you are not sure of the answer please leave a comment, DO NOT ANSWER THE QUESTION UNLESS YOU KNOW THE ANSWER. Please don't take me points! Thanks for understanding.
Anyways, please show all of your work and explain your thinking! Be sure to answer all 3 and be clear which answer goes to the question. Thanks!
9514 1404 393
Answer:
A) JM = 30
B) x = 11
C) x = 18
Step-by-step explanation:
A) Chords the same distance from the circle center have the same length.
KL = 2×15 = 30 = JM
__
B) Tangents from the same point have the same length.
2x -14 = x -3
x = 11 . . . . . . . . . add 14-x to both sides
__
C) No x is shown. We presume it is the length of the tangent segment. The product of lengths to the near and far circle intercepts is the same for both secants. A tangent is a degenerate secant having both intercepts at the same point.
x² = 12(12 +15) = 324
x = √324
x = 18
Sahak pays 11% sales tax on a trumpet that costs 750 dollars. How much does the sales tax add to the purchase price?
Answer:
$82.50
Step-by-step explanation:
Please help me click the picture to see
The table shows the pricing for four different types of apples.
Which type costs the least per kilogram?
A $4 for 1.5 kg
B $5 for 2.0 kg
C $7 for 2.5 kg
D $8 for 3.5 kg
Write the following:
a) 16 as a fraction of 152
b) 15 as a fraction of 210
Answer:
[tex]\frac{16}{152}[/tex]
[tex]\frac{15}{210}[/tex]
Step-by-step explanation:
The scale drawing of a room in a hotel is shown below. If 3 in. = 12 ft, what are the actual dimensions of the room?
15 in.
20 in
A length = 40 feet, width = 39 ft.
B length = 60 feet, width = 45 feet
C length = 75 feet, width = 60 feet
D length = 80 feet, width = 60 feet
Answer:
B length = 60 feet, width = 45 feet
Step-by-step explanation:
If you divide the scale drawing (15 in) by length by the scale of of the same dimension (3 in) and multiply what you get (5) by what the larger scale is (12 ft) you get the answer (60 ft)
What is the percent of change from 50,000 to 80,000?
Answer:
Percentage Calculator: What is the percentage increase/decrease from 50000 to 80000? = 60
Step-by-step explanation:
four hundred twenty is 3/5 of what number
700 is the answer to your problem
solve the system of equations
y=-3/2x+9
2x+2y=16
Answer:
x=2 and y=6
Step-by-step explanation:
Look at the sections between the whole numbers on the number line below. How many equal parts are in each section? What fraction does each part show? Each mark on the number line represents a fraction. What denominator will all the fractions have? Write the missing labels on the number line.
Please help me with this
You multiply two two-digit numbers and the product is close to 2,600.What two numbers did you multiply?
Step-by-step explanation:
the answer would be 26 and 10 because is you multiply 26×10 your answer will be 2600
Answer:
52 and 50
Step-by-step explanation:
Break it down into smaller numbers in this case 3 numbers.
26 * 10 * 10 = 2600
By multiplicative rule,
we can break 10 into 5 * 2,
giving 26 * 10 * 5 *2,
because multiplication is commutative and associative
group them up as (26 * 2) * (10 * 5) = ( 52 * 50) = 2600
SOMEONE PLEASE HELP ME ASAP ILL GIVE BRAINLIEST
Answer:
for first one
√8²+4²=24
6²=36 not right angled triangle
so it is obtuse TRAINGLE
Step-by-step explanation:
for second one
it is acute TRAINGLE
Help me
Rearrange this equation that "0" is the subject.
You have 50 cups. 10 cups are blue, 20 cups are red, and 20 cups are white. What percentage of cops are blue?
Answer:
10% or 5%
Step-by-step explanation:
13=2m+5
what does m equals ?
Answer:
m=4
Step-by-step explanation:
First subtract 5 from 2m and 13. This gives you 2m=8. Then divide by 2 on both sides. This gives you m=4
Answer:
m=4
Step-by-step explanation:hope it helps
5-13=2m+5-5
2/2m=8/2
m=4