Answer:
a) the work done in propelling a five-ton satellite to a height of 100 miles above Earth is 487.8 mile-tons
b) the work done in propelling a five-ton satellite to a height of 300 miles above Earth is 1395.3 mile-tons
Step-by-step explanation:
Given the data in the question;
We know that the weight of a body varies inversely as the square of its distance from the center of the earth.
⇒F(x) = c / x²
given that; F(x) = five-ton = 5 tons
we know that the radius of earth is approximately 4000 miles
so we substitute
5 = c / (4000)²
c = 5 × ( 4000 )²
c = 8 × 10⁷
∴ Increment of work is;
Δw = [ ( 8 × 10⁷ ) / x² ] Δx
a) For 100 miles above Earth;
W = ₄₀₀₀∫⁴¹⁰⁰ [ ( 8 × 10⁷ ) / x² ] Δx
= (8 × 10⁷) [tex][[/tex] [tex]-\frac{1}{x}[/tex] [tex]]^{4100}_{4000[/tex]
= (8 × 10⁷) [tex][[/tex] [tex]-\frac{1}{4100}[/tex] [tex]+\frac{1}{4000}[/tex] [tex]][/tex]
= (8 × 10⁷ ) [ 6.09756 × 10⁻⁶ ]
= 487.8 mile-tons
Therefore, the work done in propelling a five-ton satellite to a height of 100 miles above Earth is 487.8 mile-tons
b) For 300 miles above Earth.
W = ₄₀₀₀∫⁴³⁰⁰ [ ( 8 × 10⁷ ) / x² ] Δx
= (8 × 10⁷) [tex][[/tex] [tex]-\frac{1}{x}[/tex] [tex]]^{4300}_{4000[/tex]
= (8 × 10⁷) [tex][[/tex] [tex]-\frac{1}{4300}[/tex] [tex]+\frac{1}{4000}[/tex] [tex]][/tex]
= (8 × 10⁷ ) [ 1.744186 × 10⁻⁵ ]
= 1395.3 mile-tons
Therefore, the work done in propelling a five-ton satellite to a height of 300 miles above Earth is 1395.3 mile-tons
The mean birth weight for children born in a certain country at full term (after 40 weeks) is 3500grams; the standard deviation for birth weight is 500 grams. The shape of the distribution is symmetric and unimodal. About 34% of the weights are between what two values?
Answer:
About 34% of the weights are between 3280 grams and 3720 grams.
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 z-score 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 p-value, we get the probability that the value of the measure is greater than X.
Mean of 3500 grams, standard deviation of 500 grams.
This means that [tex]\mu = 3500, \sigma = 500[/tex]
About 34% of the weights are between what two values?
Between the 50 - (34/2) = 33rd percentile and the 50 + (34/2) = 67th percentile.
33rd percentile:
X when Z has a p-value of 0.33, so X when Z = -0.44.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-0.44 = \frac{X - 3500}{500}[/tex]
[tex]X - 3500 = -0.44*500[/tex]
[tex]X = 3280[/tex]
67th percentile:
X when Z has a p-value of 0.67, so X when Z = 0.44.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]0.44 = \frac{X - 3500}{500}[/tex]
[tex]X - 3500 = 0.44*500[/tex]
[tex]X = 3720[/tex]
About 34% of the weights are between 3280 grams and 3720 grams.
examples of addition of three fractions ( between 0-1) with a common denominator. IN STEPS ALL WORK, I need two examples.
Answer:
1/6 + 2/6 + 3/6 = 6/6 = 1
1/7 + 2/7 + 4/7 = 7/7 = 1
1/8 + 2/8 + 3/8 = 6/8 = 0.75
1/9 + 2/9 + 3/9 = 6/9 = 2/3 = 0.66 (repeater dot above first 6)
1/10 + 2/10 + 3/10 = 6/10 = 3/5 = 0.6
1/12 + 2/12 + 3/12 = 6/12 = 1/2 = 0.5
All numerators in consecutive form 1, 2, 3 adds up to 6
Where 7/7 as a numerator is easier to work with than 6/7 as 6/7 does not leave a whole number as easy as 7/7 does leave whole number = 1.
We notice just 8 and 9 does not leave to 1 decimal point when adding the first consecutive numerators of that whole.
Where 10.and 12 does leave to 1dp as these numbers are not prime numbers like co prime numbers 7 and 11.
Step-by-step explanation:
Sudoku ayúdeme por fa resolviendo
Answer:
7
Step-by-step explanation
v:numero de mi dios vegetta
five times the sum of the digits of a two digit number is 9 less than the number formed by reversing its digits . if four times the value of the digit at ones place is equal to half of the place value of the digit at tens place, find the numbers
9514 1404 393
Answer:
45
Step-by-step explanation:
Let x and y represent the tens and ones digits, respectively. The 5 times the sum of digits is 5(x+y). The value of the digit-reversed number is (10y+x), so the required relation is ...
5(x +y) = (10y +x) -9
The other relationship between the digits is given as ...
4y = 1/2(10x)
A graphing calculator shows the solution to these equations is (x, y) = (4, 5).
The two-digit number is 45.
__
Additional comment
You can solve these equations in any of a variety of ways. Using a graphing calculator to find integer solutions is fast and easy, so is one of my favorites. Here, the coefficients on one equation are not easy multiples of those in the other, so substitution and/or elimination can get messy. In this situation, I like to use the "cross-multiplication" method, which starts with the equations in general form:
4x -5y +9 = 05x -4y +0 = 0From the coefficients of these equations, differences of cross products are formed:
d1 = 4(-4) -(5)(-5) = 9d2 = -5(0) -(-4)(9) = 36d3 = 9(5) -0(4) = 45Then the solutions are the solutions to 1/d1 = x/d2 = y/d3:
x = d2/d1 = 36/9 = 4y= d3/d1 = 45/9 = 5(x, y) = (4, 5) ⇒ the number is 45.
__
This method is one of several variations of Cramer's Rule, the general solution of systems of linear equations using matrix methods.
Give an example of reciprocals?
Answer:
1/6 = 6
1/7 = 7
1/8 = 8
24/5 = -1/5 or 5
Step-by-step explanation:
What is the common ratio of the sequence?
-2, 6, -18, 54,...
-3
-2
3
8
Answer:
-3
Step-by-step explanation:
Solve for x. Round to the nearest hundredth.
A. 0.02
B. 25.17
C. 0.03
B. 12.27
Work Shown:
cos(angle) = adjacent/hypotenuse
cos(64) = x/28
x/28 = cos(64)
x = 28*cos(64)
x = 12.2743921100941
x = 12.27
if 4 men can do a piece of work in 12 days, how many days will 6 men take.
Answer: 2 days
Step-by-step explanation:
M D W
4 3 12
6 2 12
What are the coordinates of B’ if the figure is reflected across the x-axis?
What is the mapping rule for finding the coordinates of a figure reflecting across
A) the x-axis (x,y) ->
B) the y-axis (x,y) ->
Answer:
Step-by-step explanation:
B( 3, -3) given the figure
B' ( 3, 3) because the x-axis intersects the mid point between B and B'
A) (x, y) reflected across x-axis becomes ( x, -y)
B) (x, y) reflected across y-axis becomes ( -x, y)
What is 2/3 – (-2/3)
?A.-4/3
B.4/3
C.0
D.2/3
Answer:
It's C, they both cancel each other out
Calculus3 - Infinite sequences and series ( URGENT!!)
Answer:
Limit=0
Converges
Absolutely converges
Step-by-step explanation:
If [tex]a_n=\frac{2^n n!}{(3n+4)!}[/tex]
then [tex]a_{n+1}=\frac{2^{n+1} (n+1)!}{(3(n+1)+4)!}[/tex].
Let's rewrite [tex]a__{n+1}[/tex] a little.
I'm going to hone in on (3(n+1)+4)! for a bit.
Distribute: (3n+3+4)!
Combine like terms (3n+7)!
I know when I have to find the limit of that ratio I'm going to have to rewrite this a little more so I'm going to do that here. Notice the factor (3n+4)! in [tex]a_n[/tex]. Some of the factors of this factor will cancel with some if the factors of (3n+7)!
(3n+7)! can be rewritten as (3n+7)×(3n+6)×(3n+5)×(3n+4)!
Let's go ahead and put our ratio together.
[tex]a_{n+1}×\frac{1}{a_n}[/tex]
The second factor in this just means reciprocal of [tex]{a_n}[/tex].
Insert substitutions:
[tex]\frac{2^{n+1} (n+1)!}{(3(n+1)+4)!}×\frac{(3n+4)!}{2^nn!}[/tex]
Use the rewrite for (3(n+1)+4)!:
[tex]\frac{2^{n+1} (n+1)!}{(3n+7)(3n+6)(3n+5)(3n+4)!}×\frac{(3n+4)!}{2^nn!}[/tex]
Let's go ahead and cancel the (3n+4)!:
[tex]\frac{2^{n+1} (n+1)!}{(3n+7)(3n+6)(3n+5)}×\frac{1}{2^nn!}[/tex]
Use 2^(n+1)=2^n × 2 with goal to cancel the 2^n factor on top and bottom:
[tex]\frac{2^{n}2(n+1)!}{(3n+7)(3n+6)(3n+5)}×\frac{1}{2^nn!}[/tex]
[tex]\frac{2(n+1)!}{(3n+7)(3n+6)(3n+5)}×\frac{1}{n!}[/tex]
Use (n+1)!=(n+1)×n! with goal to cancel the n! factor on top and bottom:
[tex]\frac{2(n+1)×n!}{(3n+7)(3n+6)(3n+5)}×\frac{1}{n!}[/tex]
[tex]\frac{2(n+1)}{(3n+7)(3n+6)(3n+5)}×\frac{1}{1}[/tex]
Now since n approaches infinity and the degree of top=1 and the degree of bottom is 3 and 1<3, the limit approaches 0.
This means it absolutely converges and therefore converges.
I NEEED HELPPPPP PLEASEEEE UM BEGGING SOMEONE PLEASEEEEEEEEEEEE
Answer:
p = 28.56
Step-by-step explanation:
Circumference of circle
c = 2πr
Since this is a semicircle the perimeter is half the circumference
p = πr
p = 3.14 * 4
p = 12.56
---------------------------
Triangle
the outer perineter is just the two outer sides
p = 6 + 10
p = 16
-------------------------
total outer perimeter
p = 12.56 + 16
p = 28.56
Inflation is running 1.1% per year when you deposit $5,000 in an account earning 4.4% compounded continuously. In constant dollars, how much money will you have 6 years from now?
a. $6439.80
b. $6097.01
c. $1169.51
d. $6510.64
The value of the money including inflation after 6 years will be $6510.64.
What is inflation?The rate at which prices grow over a specific time period is known as inflation. Inflation is often measured in broad terms, such as the general rise in prices or the rise in a nation's cost of living. But it may also be computed more precisely for some products, like food, or for services, like a haircut, for instance. In any situation, inflation refers to how much more costly the pertinent collection of products and/or services has grown over a predetermined time frame, most frequently a year.
Given that, Inflation is running at 1.1% per year when you deposit $5,000 in an account earning 4.4% compounded continuously.
deposit amount (P) = $ 5000
Rate (r) = 4.4 %
Time (t) = 6 years
Compound continuously
Amount (A)= 5000 e⁰°⁰⁴⁴ˣ ⁶
A = $ 6,510.64098
A = $ 6510.64
Total accumulated money after 6 years = $ 6,510.64
value of money decreases due to inflation
The real value of money after n years with the rate of inflation i = 1.1%
yₙ = A( 1 / (1+i) )ⁿ
y₆ = 6510.64 (1 / ( 1 + 0.011))⁶
y₆ = 6,097.008
Real value of money = $ 6,097.01
Therefore, after 6 years real value of the money including inflation will be $ 6,097.01.
Learn more about inflation here:
https://brainly.com/question/29308595
#SPJ5
The waiting times between a subway departure schedule and the arrival of a passenger are uniformly distributed between and minutes. Find the probability that a randomly selected passenger has a waiting time minutes.Find the probability that a randomly selected passenger has a waiting time minutes.
Answer:
Incomplete question, but the concepts of the uniform distribution needed to solve this question are given here.
Step-by-step explanation:
Uniform probability distribution:
An uniform distribution has two bounds, a and b.
The probability of finding a value of at lower than x is:
[tex]P(X < x) = \frac{x - a}{b - a}[/tex]
The probability of finding a value between c and d is:
[tex]P(c \leq X \leq d) = \frac{d - c}{b - a}[/tex]
The probability of finding a value above x is:
[tex]P(X > x) = \frac{b - x}{b - a}[/tex]
The waiting times between a subway departure schedule and the arrival of a passenger are uniformly distributed between a and b minutes.
From here, we get the values of a(smallest value) and b(highest value).
Question of the probabilities:
In the two probability questions, you will get the value of x, and will apply one of the three formulas given above, depending on the question, to find the desired probability.
can anyone help me in this questions
Step-by-step explanation:
3.
1.4191919... = 1405/990
4.
√(2/5) and √(1/2)
tan ydx - x ln xdy=0
Answer:
Uuuzu7ggijjrudidjdiwisiwiwieie
Solve for k:
6=7k+1
K=
Answer:
5/7
Step-by-step explanation:
6=7k+1
-1 -1
--------------
5= 7k
Divide both sides by 7k
k= 5/7
[tex]\huge\color{purple}\boxed{\colorbox{black}{k=0.714}}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\orange{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]
[tex]➺ \: 6 = 7k + 1[/tex]
[tex]➺ \: 7k = 6 - 1[/tex]
[tex]➺ \: 7k = 5[/tex]
[tex]➺ \: k = \frac{5}{7}\\ [/tex]
[tex]➺ \: k = 0.714[/tex]
Therefore, the value of [tex]k[/tex] is [tex]0.714[/tex].
[tex]\large\mathfrak{{\pmb{\underline{\blue{To\:verify}}{\blue{:}}}}}[/tex]
[tex]➺ \: 6 = 7k + 1[/tex]
[tex]➺ \: 6 = 7 \times 0.714 + 1[/tex]
[tex]➺ \: 6 = 5 + 1[/tex]
[tex]➺ \: 6 = 6[/tex]
➺ L. H S. = R. H. S.
Hence verified.
[tex]\bold{ \green{ \star{ \orange{Mystique35}}}}⋆[/tex]
-2 1/2 - (-1 3/4) ?
Answer:
- 3/4
Step-by-step explanation:
-2 1/2 - (-1 3/4)
Subtracting a negative is like adding
-2 1/2 + (1 3/4)
Get a common denominator of 4
-2 2/4 + 1 3/4
The signs are different so we subtract and take the sign of the larger
2 2/4 - 1 3/4
Borrowing from the 2
1 4/4 + 2/4 - 1 3/4
1 6/4 - 1 3/4
3/4
2 2/4 was larger and it was negative so we add a negative sign
- 3/4
Marina is given a rectangular piece of paper. If the length of Marina’s piece of paper is represented by 3x -6 and the width is represented by 2x -5, then the paper has a total area represented by
plsssss help it’s timed!!!!!!
Answer:
the answer to this question is 36.86989°
What’s the answer to this question?
Answer:
f(x) = x/8
Step-by-step explanation:
f(x) = y
y = 8x
switch the x and y
x = 8y
solve for y
Amy has 2437 stamps and Maria had 1347 stamps. Amy gave some stamps to Maria. In the end, Maria had 3 times as many stamps as Amy. How many stamps did Amy have in the end?
Answer:
946
Step-by-step explanation:
Let :
Amy's stamp = 2437
Maria's stamps = 1347
Let Number of stamps Amy gave to Maria = x
After Giving stamps to Maria ; we have the equation :
Amy's stamps = 2437 - x
Maria's stamps = 1347 + x
(1347 + x) = 3(2437 - x)
1347 + x = 7311 - 3x
x + 3x = 7311 - 1347
4x = 5964
x = 5964 / 4
x = 1491
Number of stamps Amy has in the end :
2437 - 1491 = 946
A burger place sells vanilla and chocolate shakes in two sizes, small and large. If 62% of shakes sold are vanilla flavor, 46% are size large, and 23% are large vanilla shakes which size/flavor combination is the most popular? (i.e. has the highest percentage)
Answer:
25 gfstuhfujjjjjgredeetuu
You have some marbles. When you make a shape of an equilateral triangle, you either have 4 extra, or you need 28 more to complete the shape. How many marbles do you have? How long is a side of the biggest equalateral triangle that you can make make with your marbles?
Answer:
You have 500 marbles.
The longest side of the biggest equalateral triangle that you can make with your marbles is 31
Step-by-step explanation:
28 + 4 = 32
So our equation is:
TR(32) - 28
Now find Triangular Number 32: (32 *33)/2=528
528 - 28 = 500
So, we have 500 marbles
Now we need to find the longest side of the biggest equalateral triangle that you can make make with your marbles
Let's go back to 28 + 4 = 32
One row above 32 is 31
So the longest side of the biggest equalateral triangle that you can make with your marbles is 31
Hope this helps!
A plane travels a distance of 22,000 km in a time of 3.6 hours.
What is its average speed rounded to the nearest whole number?
in km/h
Answer:
6111 km/hr
Step-by-step explanation:
Given
Distance travels by plane d=22,000 km
time taken t=3.6 hours
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
create an equation to solve for x then solve for x.
Answer:
Step-by-step explanation:
In parallelogram adjacent angles are supplementary
∠U +∠V = 180
9x + 15 + 6x + 15 = 180
Combine like terms
9x + 6x + 15 + 15 = 180
15x + 30 = 180
Subtract 30 from both sides
15x = 180 - 30
15x = 150
Divide both sides by 15
x = 150/15
x = 10
∠U = 9x + 15
= 9*10 + 15
= 90 + 15
∠U = 105
∠V = 6x + 15
= 6*10 + 15
= 60 + 15
∠V = 75
Answer:
Equation: [tex]2(9x + 15 + 6x + 15) = 360[/tex]
x = 10°
∠U = 105°
∠V = 75°
Step-by-step explanation:
Hello!
The sum of angles in a parallelogram is 360°. The opposite angles of a parallelogram are congruent.
Part AEquation: [tex]2(9x + 15 + 6x + 15) = 360[/tex]Solve[tex]2(9x + 15 + 6x + 15) = 360[/tex][tex]9x + 15 + 6x + 15 = 180[/tex][tex]15x + 30 = 180[/tex][tex]15x = 150[/tex][tex]x = 10[/tex]The value of x is 10°.
Part BTo find the measures of each angle, simply plug in 10° for x in each equation.
∠U[tex]9x + 15[/tex][tex]9(10) + 15[/tex][tex]90 + 15[/tex][tex]105[/tex]Angle U is 105°.
∠V[tex]6x + 15[/tex][tex]6(10) + 15[/tex][tex]60+15[/tex][tex]75[/tex]Angle V is 75°.
CAN SOMEONE HELP WITH THE STEPS THXX
There is a study on exercise and health: a group of women who have been exercising regularly for 5 years are grouped and given a wellness exam and compared to a group of women who have not exercised in the past five years. What kind of data collection is this?
Experiment
Survey
Simulation
Observational Study
Answer:
Survey Data Collection.
Step-by-step explanation:
This is a survey because there are survey questionnaires (wellness exam).
Answer:
Observational Study Is the Answer
find the value of c to the nearest tenth
9514 1404 393
Answer:
x ≈ 9.3
Step-by-step explanation:
The relevant trig relation is ...
Cos = Adjacent/Hypotenuse
cos(50°) = 6/x
Solving for x gives ...
x = 6/cos(50°) ≈ 9.3343
x ≈ 9.3
__
There is no 'c' to find the value of.
Answer:
x ≈ 9.3
Step-by-step explanation:
Since , this is right triangle, we can use trigonometry functions;
cos θ = Adjacent side / Hypotenuse
Where, θ = 50°
Hypotenuse = xAdjacent side = 6Solve for x
cos 50° = 6 / x
Multiply both side by x
cos 50° × x = 6 / x × x
cos 50° × x = 6
divide cos50° by both sides
cos 50° / cos 50° × x = 6 / cos 50°
x = 6 / cos 50°
x ≈ 9.33434296
Nearest tenth :- x ≈ 9.3
expression 6 times 50
Answer:
6x50=300
Step-by-step explanation:
because math
Answer:
6*50
HOPE THIS HELPS
- Todo ❤️
Step-by-step explanation:
6*5=30*10=300