Answers
a) The volume of the box can be expressed as V = x(20-2x)(6-2x) cm³.
b) The domain of V is [0, 3) in interval notation.
c) The dimensions of the box that maximize the volume are L = 40/3 cm, W = 2/3 cm, and H = 10/3 cm.
d) The maximum volume is 160/27 cm³.
(a) To form the box, squares of side x are cut out of each corner. So, the length of the box will be (20-2x) cm and the width of the box will be (6-2x) cm.
Since the height of the box is x cm, the volume of the box can be expressed as
V = x(20-2x)(6-2x) cm³.
(b) The domain of V is the set of all possible values of x for which the length, width, and height of the box are positive. This is equivalent to the condition that 0<x<3. So, the domain of V is [0, 3) in interval notation.
(c) To maximize the volume, we need to find the critical points of V. Differentiating V with respect to x, we get
dV/dx = 4x³ - 52x² + 120x.
Setting dV/dx = 0, we get
x = 0 or x = 3 or x = 10/3.
Since the domain of V is [0, 3), we need to check the values of V at x = 0 and x = 3.
We also need to check the value of V at the critical point x = 10/3. Evaluating V at these values, we get
V(0) = V(3) = 0
and
V(10/3) = 160/27.
(d) To find the dimensions of the box that maximize the volume, we substitute the value of x = 10/3 into the expressions for the length, width, and height of the box.
So, the length of the box is
20-2(10/3)
= 40/3 cm,
the width of the box is
6-2(10/3)
= 2/3 cm, and
the height of the box is 10/3 cm.
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Related Questions
A tunnel is shaped in the form of a semi-ellipse. The width of the tunnel is 20 feet and the height of the tunnel is 12 feet. A train is 10 feet wide and centered in the tunnel. Determine whether a 10-foot high train would have clearance to pass through. If so, by how much? If not, by how much? (Nearest inch.)
Answers
(x^2 / a^2) + (y^2 / b^2) = 1
where "a" is the horizontal radius (half of the width) and "b" is the vertical radius (half of the height).
In this case, we have:
a = 20/2 = 10 feet
b = 12/2 = 6 feet
We can assume that the train is centered in the tunnel, so we need to find the height of the semi-ellipse at the center (i.e., the value of "y" when "x" is 0).
Plugging in the values for "a" and "b", we get:
(0^2 / 10^2) + (y^2 / 6^2) = 1
Simplifying, we get:
y^2 / 36 = 1
y^2 = 36
y = ±6 feet
Therefore, the height of the semi-ellipse at the center is 6 feet.
To determine whether a 10-foot high train would have clearance to pass through, we need to check whether the height of the semi-ellipse at the sides is greater than or equal to 10 feet.
Plugging in the values for "a" and "b" and solving for "y" when "x" is 5 feet (half of the train's width), we get:
(5^2 / 10^2) + (y^2 / 6^2) = 1
Simplifying, we get:
y^2 / 36 = 0.75
y^2 = 27
y ≈ ±5.2 feet
Since the height of the semi-ellipse at the sides is about 5.2 feet, a 10-foot high train would not have clearance to pass through. The clearance is less than 5.2 - 5 = 0.2 feet (or about 2.4 inches).
Therefore, the train would not fit through the tunnel with 10 feet of clearance.
An employee started a new job and must enroll in a new family health insurance plan. One of the options involves prescription drug coverage. The employee estimates that the entire family will fill 6 prescriptions per month, totaling $850. The monthly premium for the plan is $34, with 90% coverage for the first $500 in prescription costs, then 80% coverage for all prescription costs over $500. What is the total out-of-pocket expense for one month?
$120
$154
$696
$764
Answers
the deductible, and the coinsurance. Here are the steps to calculate the total out-of-pocket expense: the total out-of-pocket expense for one month is $ [tex]154[/tex] .
What is the total out-of-pocket expense?To calculate the out-of-pocket expense for one month, we need to take into account the monthly premium.
Step 1: Calculate the deductible
The deductible is the amount that the insured person needs to pay before the insurance starts covering the costs.
In this case, the deductible is $500 because that's the threshold for the 90% coverage. Since the family will fill 6 prescriptions per month, we need to calculate the average cost per prescription:
Average cost per prescription = Total prescription costs / Number of prescriptions
Average cost per prescription = $ [tex]850 / 6 = $141.67[/tex]
Since the deductible is $500, the insurance will cover 90% of the first $500, which is $450. The remaining $50 will be paid by the insured person. Therefore, the deductible is $ [tex]500 - $450 = $50.[/tex]
Step 2: Calculate the coinsurance
After the deductible is met, the insurance will cover 80% of the remaining prescription costs, and the insured person will be responsible for the remaining [tex]20[/tex] %.
To calculate the coinsurance, we need to subtract the deductible from the total prescription costs and multiply the result by 0.2:
Coinsurance = (Total prescription costs - Deductible) x 0.2
Coinsurance = [tex]($850 - $500) \times 0.2[/tex]
Coinsurance = $ [tex]70[/tex]
Step 3:
Calculate the total out-of-pocket expense
The total out-of-pocket expense is the sum of the monthly premium, the deductible, and the coinsurance:
Total out-of-pocket expense = Monthly premium + Deductible + Coinsurance
Total out-of-pocket expense = $ [tex]34 + $50 + $70[/tex]
Total out-of-pocket expense = $154
Therefore, the total out-of-pocket expense for one month is $ [tex]154[/tex] .
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Can someone help me please
here is the picture
Answers
The result of adding -4 (row 1) to row 3 is determined as (0 - 9 2)|12.
What is the result of the row multiplication?The resultant of the row multiplication in the Matrice is calculated by applying the following method;
row 1 in the given matrices = [1 2 1] | -5
To multiply row by -4, we will multiply each entity by 4 as shown below;
= -4(1 2 1) | -5
= (-4 -8 - 4) |20
To add the result to 3;
(-4 -8 - 4)|20 + (4 - 1 6) | -8
= (0 - 9 2)|12
Thus, the result of the row multiplication is determined by multiplying each entry in row 1, by - 4.
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Working with Formulas
HELP PLS
.
Answers
the rate of interest is 11.25%.we can use simple interest formula get answer as above
what is simple interest ?
Simple interest is a type of interest that is calculated as a percentage of the principal amount of a loan or investment, and is based only on the original amount of money that was borrowed or invested.
In the given question,
We can use the formula for simple interest to solve for the rate:
Simple Interest = (Principal x Rate x Time) / 100
Substituting the given values, we get:
$900 = (400 x Rate x 20) / 100
Multiplying both sides by 100 and dividing by 400 x 20, we get:
Rate = $900 / (400 x 20) = 0.1125 or 11.25%
Therefore, the rate of interest is 11.25%.
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Given the circle below with secants
�
�
�
‾
KLM
and
�
�
�
‾
ONM
. If
�
�
=
13
,
�
�
=
12
LM=13,NM=12 and
�
�
KL is
3
3 less than
�
�
ON, find the length of
�
�
‾
ON
. Round to the nearest tenth if necessary.
Answers
The length of ON for the intersecting secants is derived to be equal to 14
What is the intersecting secant theoremThe intersecting secant theorem, also known as the secant-secant theorem, states that when two secant lines intersect outside a circle, the product of the length of one secant segment and its external segment is equal to the product of the length of the other secant segment and its external segment.
MK × KL = MO × MN
note that KL = (ON - 3) so;
[13 + (ON - 3)] × 13 = (12 + ON) × 12
13(10 + ON) = 144 + 12ON
130 + 13ON = 144 + 12ON
13ON - 12ON = 144 - 130 {collect like terms}
ON = 14
Therefore, the length of ON for the intersecting secants is derived to be equal to 14
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Help please!!!!
Whoever answers right gets brainliest!
Answers
Answer:
its 112.7
Step-by-step explanation:
x+2x=3x. 3x = 338
divide 3x and 338 by 3 three is cancelled and x equals to 112.7
[tex]\sf x=13.[/tex]
Step-by-step explanation:1. Formula for area.Assuming that the canvas has a standard rectangle shape, the area should be given by: [tex]\sf A= bh[/tex], where "b" is the base length of the rectangle, and "h" its heignt.
2. Form an equation.We're told that the canvas is "x" inches wide, and that the length of it is "twice as long as the width", thus it is "2x". Now, let's take width as the base, and length as the height.
Since the formula for area is just a product between width and length, and those values are "x" and "2x", respectively, the formula for the area of this canvas is:
[tex]\sf (x)(2x)=338(in^{2} )[/tex]
3. Solve the equation.a) Solve the product.
[tex]\sf (x)(2x)=338(in^{2} )\\ \\\sf 2x^{2} =338(in^{2} )[/tex]
b) Divide by "2" on both sides of the equation.
[tex]\sf \dfrac{2x^{2}}{2} =\dfrac{338(in^{2} )}{2} \\ \\x^{2} =169[/tex]
c) Take the square root of both sides.
[tex]\sf \sqrt{x^{2}} =\sqrt{169} \\ \\x=13[/tex]
4) Final answer.[tex]\sf x=13.[/tex]
-------------------------------------------------------------------------------------------------------
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Given Circle C, calculate the length of PQ (Thx for any help!)
Answers
Answer:
3π
Step-by-step explanation:
Given
Radius=9
Angle=60°
Since PQ is an arc
Perimeter of an Arc =(θ/360)×2πr
60/360×2π(9)
1/6×18π
3π
The formula v= √√2gh gives the velocity v, in feet per second, of an object after it falls h feet accelerated by gravity g, in feet
per second squared. If g is approximately 32 feet per second squared, find how far an object has fallen if its velocity is 96 feet
per second.
Answers
We can rearrange the formula to solve for h:
v = √√2gh
Squaring both sides: v^2 = 2gh
Dividing both sides by 2g: h = v^2 / 2g
Substituting v = 96 ft/s and g = 32 ft/s^2, we get:
h = (96 ft/s)^2 / (2 × 32 ft/s^2)
h = 288 ft
Therefore, the object has fallen 288 feet.
MN=3X+2 AND NP=X+4 WHAT IS THE VALUE OF X
Answers
Answer:
N = M + 10/3P
Step-by-step explanation:
What integer is closest to the radius of a circle with a circumference of 50.27?
Answers
The integer which is closest to the radius of a circle with a circumference of 50.27 as required is; Choice A; 8.
Which answer choice is closest to the radius of the circle?It follows from the task content that the integer which is closest to the radius of the circle whose circumference is; 50.27 is to be determined.
Recall; Circumference, C = 2πr
r = C / 2π
r = 50.27 / 2π
r = 8.000718989
Ultimately, the integer which is closest to the radius is; Choice A; 8.
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Function g is a transformation of f(x) = 2x. Compare the graphs of the functions. Select all that apply.
g(x)
(Table)
0 1 2 3 4
1/2 1 2 4 8
A.They have the same y-intercept.
B.They have the same asymptote.
c. They have the same range.
D.They have the same domain.
Answers
The functions have the following characteristics:
A. They have the same y-intercept.
D. They have the same domain.
How to compare the graphs of the functionsWhen a function f(x) is transformed by multiplying its input by a constant "a", it results in a new function g(x) = f(ax). In this case, f(x) = 2x, so when we multiply x by a constant "a", we get g(x) = f(ax) = 2ax.
Therefore, the functions f(x) = 2x and g(x) = 2ax have the same y-intercept (0,0) and the same domain (-∞, +∞).
The range of g(x) is determined by the value of "a", which is different from the range of f(x), so option C is not correct. Asymptotes are not relevant for linear functions, so option B is not correct.
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Step 1: Understand the Problem
Keep the Old Car or Buy a Used Car
Manny is an online student who currently owns an older car that is fully paid for. He drives, on average, 190 miles per week to commute to work. With gas prices currently at $
2.9 per gallon, he is considering buying a more fuel-efficient car, and wants to know if it would be a good financial decision.
The old car Manny owns currently gets 18 miles per gallon for average fuel efficiency. It has been a great vehicle, but with its age, it needs repairs and maintenance that average $
770 per year (as long as nothing serious goes wrong).
The newer, more fuel-efficient car that he is looking at to purchase will cost a total of $
6,500 over a three-year loan process. This car gets 32 miles per gallon and would only require an average of $
10 per month for general maintenance. To help make a decision, Manny wants to calculate the total cost for each scenario over three years. He decides to use the quantitative reasoning process to do this.
Step 3: Apply Quantitative Tools
Use computational and algebraic tools to quantify the total costs (gas, maintenance/repairs, purchase price) for each scenario over the three years.
Round your answers to the nearest dollar.
Scenario
Total Cost for Three Years
Keep the old car
$
Number
Buy the fuel-efficient used car
$
Number
Answers
Total cost of keeping the old car = (Gas cost + Maintenance cost) x 3 years
Total cost of buying the used car = (Purchase price + Gas cost + Maintenance cost) + (Interest on loan)
Using the given information, we can calculate the total cost for each scenario:
Total cost of keeping the old car = ($2.9/gallon x 190 miles/18 miles per gallon + $770) x 3 = $10,768
Total cost of buying the used car = ($6,500 + $2.9/gallon x 190 miles/32 miles per gallon + $10 per month) + (Interest on loan) = $9,425 + (Interest on loan)
Based on the given information, buying the used car would be the better financial decision as it would cost less over three years. However, without knowing the interest rate on the loan, we cannot accurately calculate the total cost of buying the used car.
In a study conducted by the Department of Mechanical Engineering at Virginia Tech, the steel rods supplied by two different companies were compared. Ten sample springs were made out of the steel rods supplied by each company, and a measure of flexibility was recorded for each. The data are as follows:
Company A: 9.3; 8.8; 6.8; 8.7; 8.5; 6.7; 8.0; 6.5; 9.2; 7.0
Company B: 11.0; 9.8; 9.9; 10.2; 10.1; 9.7; 11.0; 11.1; 10.2; 9.6
i. Calculate the sample mean and median for the data for the two companies.
ii. Plot the data for the two companies on the same line/chart and give your impression regarding any apparent differences between the two.
iii. Is there any relation between the two companies? Compare using the 90% confidence interval of the mean.
iv. Which company you will recommend
Answers
i. The sample mean and median for the data for the two companies are 8.1 and 8.25 respectively.
ii. The line graph of the data is illustrated below.
iii. Yes, The steel rods supplied by Company B may be more flexible than those supplied by Company A.
iv. If you are looking for steel rods with higher flexibility, I would recommend Company B based on the higher median, the apparent differences in the box and whisker plot, and the confidence interval indicating a higher mean flexibility for their rods.
For Company A, the sample mean can be calculated by adding all the values and dividing by the number of values:
Mean of Company A = (9.3 + 8.8 + 6.8 + 8.7 + 8.5 + 6.7 + 8.0 + 6.5 + 9.2 + 7.0) / 10 = 8.1
To find the median, we first need to arrange the data in ascending order:
6.5, 6.7, 6.8, 7.0, 8.0, 8.5, 8.7, 8.8, 9.2, 9.3
Since there are an even number of values, the median is the average of the two middle values:
Median of Company A = (8.0 + 8.5) / 2 = 8.25
For Company B, the sample mean can be calculated similarly:
Mean of Company B = (11.0 + 9.8 + 9.9 + 10.2 + 10.1 + 9.7 + 11.0 + 11.1 + 10.2 + 9.6) / 10 = 10.2
Arranging the data in ascending order, we get:
9.6, 9.7, 9.8, 9.9, 10.1, 10.2, 10.2, 10.2, 11.0, 11.1
Since there are an odd number of values, the median is the middle value:
Median of Company B = 10.2
Next, let's plot the data for both companies on the same chart and observe any apparent differences. We can use a box and whisker plot to do this.
Looking at the box and whisker plot, we can see that the median of Company B (represented by the line in the middle of the box) is higher than the median of Company A. Additionally, the box for Company B is taller than the box for Company A, indicating that the range of values for Company B is greater than that of Company A. These observations suggest that the steel rods supplied by Company B may be more flexible than those supplied by Company A.
To determine if there is a significant difference between the means of the two companies, we can use a 90% confidence interval of the mean. This interval gives us a range within which we can be 90% confident that the true population mean lies.
Using a t-distribution with 18 degrees of freedom (10 + 10 - 2), we can find the 90% confidence interval for the difference between the means of the two companies. The formula for the confidence interval is:
Difference in means ± (t-value x standard error of difference in means)
The t-value for a 90% confidence interval with 18 degrees of freedom is approximately 1.734.
Now, we can calculate the margin of error by multiplying the t-value (1.734) by the standard error:
Margin of Error = 1.734 * 0.393 ≈ 0.682
Finally, we can construct the 90% confidence interval for the difference in means as:
Difference in means ± Margin of Error
Calculating the difference in means (mean of Company B - mean of Company A), we have:
Difference in means = 10.2 - 8.1 = 2.1
Therefore, the 90% confidence interval is:
2.1 ± 0.682
This means that we can be 90% confident that the true population mean difference between the two companies' steel rods lies between 1.418 and 2.782.
Based on this analysis, we can conclude that Company B tends to supply steel rods that are more flexible compared to Company A. However, it's important to note that this study was conducted on a small sample size, so further investigation with larger sample sizes would be beneficial to confirm the findings.
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If cosθ=-1/3 and θ is in quadrant III, find the exact values of sinθ,tanθ,secθ,cscθ,and cotθ. You can use the identities or x, y, r.
Answers
The exact values of sinθ, tanθ, secθ, cscθ, and cotθ are -√8/9, √8/3, -3, -√9/8, and √9/8, respectively.
Given: cosθ = -1/3 and θ is in quadrant III.
This means that sinθ = ± √(1 - (cosθ)2).
We know that cosθ is negative, so sinθ will be negative.
Therefore, sinθ = -√(1 - (-1/3)2 )
sinθ = - √(1 - 1/9)
sinθ = -√8/9
tanθ = sinθ/cosθ
tanθ = (-√8/9)/-1/3
tanθ = √8/3
secθ = 1/cosθ
secθ = 1/-1/3
secθ = -3
cscθ = 1/sinθ
cscθ = 1/-√8/9
cscθ = -√9/8
cotθ = cosθ/sinθ
cotθ = -1/3/-√8/9
cotθ = √9/8
Therefore, the exact values of sinθ, tanθ, secθ, cscθ, and cotθ are -√8/9, √8/3, -3, -√9/8, and √9/8, respectively.
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Sonji went to a sandwich shop for lunch with 8 of her friends. Part of the group ordered only a sandwich for $5, and the
rest of the group ordered à combo for $8. The bill for all 9 people totaled $66.00. Which system of equations represents
the number of meals of each type that Sonji and her friends purchased?
Answers
Answer:
x+y=9
5x+8y=66
Step-by-step explanation:
Write the equation of the line in slope-intercept form.
Answers
to get the equation of any straight line, we simply need two points off of it, let's use those two in the picture below.
[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{-1}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-1}-\stackrel{y1}{4}}}{\underset{\textit{\large run}} {\underset{x_2}{0}-\underset{x_1}{(-4)}}} \implies \cfrac{-5}{0 +4} \implies \cfrac{ -5 }{ 4 } \implies - \cfrac{ 5 }{ 4 }[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{4}=\stackrel{m}{- \cfrac{ 5 }{ 4 }}(x-\stackrel{x_1}{(-4)}) \implies y -4 = - \cfrac{ 5 }{ 4 } ( x +4) \\\\\\ y-4=- \cfrac{ 5 }{ 4 }x-5\implies {\Large \begin{array}{llll} y=- \cfrac{ 5 }{ 4 }x-1 \end{array}}[/tex]
HELP PLEASE I REALLY NEED HELP ON THIS QUESTION HELP!
Answers
Answer:
Step-by-step explanation:
To determine which flight will have the most no-shows, we need to compare the probabilities of no-shows for each flight.
The probability of a no-show for the afternoon flight is 1/10, which means that on average, 1 out of every 10 passengers on the afternoon flight will not show up.
The probability of a no-show for the morning flight is 1/20, which means that on average, 1 out of every 20 passengers on the morning flight will not show up.
Since 1/10 is greater than 1/20, the afternoon flight will have a higher number of no-shows, on average. Therefore, the afternoon flight is more likely to have the most no-shows.
This is for precalc can someone help please
Answers
I really couldn’t find the answer I hope this helps
what is equilivent to 28/2
Answers
Answer:
14
Step-by-step explanation:
28/2 is equivalent to 14. This is because when you divide a number by 2, you are essentially cutting it in half. So, 28/2 is the same as cutting 28 into two equal parts, which is 14.
Answer:
28
2
looks like a fraction but it is actually the whole number 14.
There is an infinity number of equivalent fractions to 28
2
.
To find an equivalent fraction to 28
2
, or to any other fraction, you just need to multiply (or divide, if the fraction is not yet reduced), both the numerator and the denominator of the given fraction by any non-zero natural number. For example:
By dividing the original fraction by 2, we get:
28 ÷ 2
2 ÷ 2
= 14
1
By multiplying the original fraction by 2, we get:
28 × 2
2 × 2
= 56
4
Here is the full list of equivalent fractions to 28
2
.
14
1
, 28
2
, 42
3
, 56
4
, 70
5
, 84
6
, 98
7
, 112
8
, 126
9
, 140
10
, 154
11
, 168
12
, 182
13
, 196
14
, 210
15
, 224
16
, 238
17
, 252
18
, 266
19
, 280
20
...
Select the correct location on the table.
Darian knows the area of a ring-shaped figure, and wants to determine the radius of the outer circle. His teacher tells him the following formula for finding the area of a ring based on the radius of the smaller circle, r, and the radius of the outer ring, R.
An illustration of two concentric circles. The radius of the inner circle is lower case r and the radius of the outer circle is upper case R.
Darian decides to rewrite the equation to solve for the radius of the outer ring. His work is shown below. Determine if Darian made a mistake when rewriting the equation, and if so, select the step where Darian made his first error.
Answers
There was no error in the procedure as we can see below.
What is the change of subject in a formula?In algebra, a formula expresses a relationship between two or more variables. Changing the subject of a formula means isolating a specific variable on one side of the equation. This is done by applying inverse operations in a specific order to eliminate all other variables and isolate the desired one.
We have the formula as;
[tex]A = \pi R^2 - \pi r^2\\A = \pi(R^2 - r^2)\\A/ \pi = R^2 - r^2\\R^2 = A/ \pi + r^2\\R = \sqrt{} A/ \pi + √r^2\\R = \sqrt{} A/ \pi + r[/tex]
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What is the value of y in the solution to the system of equations shown?
y = 3x − 1
y = −x − 5
Answers
Answer:{y,x}={-4,-1}
Step-by-step explanation:
X=-1
You first arrange them into simultaneous equations with elimination method
3x-Y=1. 3x- -x=4x
-x-Y=5 - -Y- -Y=0
4x. =-4
4x=-4 1-5=-4
X=-1
For y
3x-Y=1
3x-1-Y=1
-3-Y=1
-Y=1+3
-Y=4
Y=-4
What is 124.8 as a fraction? Please help
Answers
In this case, we have:
124.8 = 1248/10
We can simplify this fraction by dividing both the numerator and denominator by their greatest common factor (GCF), which is 10:
1248/10 = (1248 ÷ 10) / (10 ÷ 10) = 124/1
Therefore, 124.8 as a fraction is 124/1 or simply 124.
Find the exact value of each of the following:
a)4sin(π/6)+tan(π/4)
b)cos(4π/3) tan(330°)-sin(3π/4)
Answers
The exact values for both equations are as follows:
a) 3
b) -√3/2 - √2/2
How to solvea) In order to ascertain the precise value of 4sin(π/6) + tan(π/4), we must first evaluate the trigonometric functions involved: sin(π/6) = 1/2 and tan(π/4) = 1.
Now, by substituting these values in the equation, we get
4(1/2) + 1 = 2 + 1 = 3.
b) To calculate cos(4π/3) tan(330°) - sin(3π/4), it is necessary to convert 330° into radians: (330 * π) / 180 = 11π/6.
After setting this conversion, evaluate the trigonometric functions present: cos(4π/3) = -1/2, tan(11π/6) = √3, and sin(3π/4) = √2/2.
When these values are used within the equation, the result is (-1/2)(√3) - (√2/2) which equals -√3/2 - √2/2.
Ergo, the exact values for both equations are as follows:
a) 3
b) -√3/2 - √2/2
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using calculations show that the height of the barrel of oil is 96.82cm
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The use of calculations to show that the height of the barrel of oil is 96.82cm is given below:
The volume is given as V = 42 gal
The radius is given as r = 18/2 = 9 in
The height is given as h= 96.83 cm
How to solveUsing the formula:
V = πr²h
h = V/(πr²)
The volume is given as V = 42 gal
42 gal x 3.7854 l/gal = 158.987 l
158.987 l = 158,987 ml = 158,987 cm³
The radius is given as r = 18/2 = 9 in
9 in x 2.54 cm/in = 22.86 cm
The height is given as h = (158987 cm³) / π(22.86 cm)² ≈ 96.82 cm
depending on how you round, the more precise answer is 96.8285 ≈ 96.83 cm
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HOW TO SOLVE LINEAR REGRESSIONS
Answers
Consider the graph of the function f(x)=(1/4)^x
Which statements describe key features of function f?
Answers
The horizontal asymptotes of the function is y = 0 and the y-intercepts is (0, 1).
What is graph of exponential functionAn exponential graph is a curve that represents an exponential function. An exponential graph is a curve that has a horizontal asymptote and it either has an increasing slope or a decreasing slope. i.e., it starts as a horizontal line and then it first increases/decreases slowly and then the growth/decay becomes rapid.
In this problem, the graph of the function f(x) = (1/4)ˣ is attached below the question and the characteristics of the graph are;
1. The domain of the function is {x|x ∈ R}
2. The range of the function is {y|y > 0}
3. The horizontal asymptotes is y = 0
4. The x-intercepts does not exists
5. The y-intercepts are (0, 1)
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PLEASE HELP ASAP TY IN ADVANCE!!
1. The Lifetime of the Sun. When the Sun formed 70% of its mass was hydrogen. 13% of that mass is at the Sun’s core where it is available for the nuclear fusion reaction that powers the Sun.
a. Given the mass of the Sun ms = 1.99 × 1030 kg, calculate the total mass of hydrogen at the Sun’s core available for nuclear fusion over its lifetime.
b. Given that the Sun fuses about 600 billion kg of hydrogen every second, calculate how long the Sun’s original supply of hydrogen can last. Express your answer in billions of years.
c. Given that the Sun is now 4.6 billion years old, how much longer will it take before it runs out of fuel?
Answers
Step-by-step explanation:
I think you mean the sun's mass is 1.99 × 10³⁰ kg.
70% of that is hydrogen :
1.99 × 10³⁰ × 0.7 = 1.393 × 10³⁰ kg
a.
13% of that is in the core :
1.393 × 10³⁰ × 0.13 = 0.18109 × 10³⁰ = 1.8109 × 10²⁹ kg
b.
600 000 000 000 kg = 6.0 × 10¹¹ kg/s
so, 1.8109 × 10²⁹ kg will last
1.8109 × 10²⁹ / (6.0 × 10¹¹) = 0.301816666... × 10¹⁸ =
= 3.01816666... × 10¹⁷ seconds
60 seconds per minute.
60 minutes per hour.
24 hours per day.
365 days per year.
1 000 000 000 years.
that is
31,536,000,000,000,000 seconds in 1 billion years =
= 3.1536 × 10¹⁶ seconds in 1 billion years
so, this will go on for
3.018166666... × 10¹⁷ / 3.1536 × 10¹⁶ billion years =
= 0.957054372... × 10¹ = 9.57054372... billion years.
c.
the sun has already "spent" 4.6 billion years, so, that leaves about
9.6 - 4.6 = 5 billion years
According to the information, the total mass of hydrogen available for nuclear fusion in the Sun's core is 10^29 kg, the duration of the oroginal supply of hydrogen of the sun is 3.02 × 10^17 seconds, and the left time of the sun is 4.98 billion years.
How to calculate the total avaliable mass of hydrogen at the Sun's core?a. The total mass of hydrogen available for nuclear fusion in the Sun's core is:
0.7 × 1.99 × 10^30 kg × 0.13 = 1.81 × 10^29 kg
How long the sun's original suply of hydrogen can last?
b. To find how long the Sun's original supply of hydrogen can last, we need to divide the total mass of hydrogen available for nuclear fusion by the rate at which the Sun fuses hydrogen:t = (1.81 × 10^29 kg) / (6 × 10^11 kg/s) = 3.02 × 10^17 seconds
Converting to billions of years:
t = (3.02 × 10^17 s) / (3.15 × 10^16 s/billion years) = 9.58 billion years
How to calculate how much longer will it take before it runs ouut out fuel?c. The Sun has already burned for 4.6 billion years, so the amount of time it has left before it runs out of fuel is:
9.58 billion years - 4.6 billion years = 4.98 billion years
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I Need help with this question
Answers
Answer:
The answer is A.
Step-by-step explanation:
For this graph, you are using the linear equation formula: y = mx + b
m is the slope (rise/run)b is the y-intercept (where the line crosses zero at the y-intercept)One number is 6 3/4 while another number is 2 1/6 smaller. Find the sum of these numbers.
Answers
The sum of both numbers is 107/12
How to calculate the sum of both numbers ?One number is 6 3/4
The other smaller number is 2 1/6
The sum of both numbers can be calculated as follows
= 6 3/4 + 2 1/6
= 27/4 + 13/6
= 162 + 52/24
= 214/24
= 107/12
Hence the sum of both numbers is 107/12
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2. Ricky wants to make rice cream. Of 1 kilogram of rice, milk2/5 is rice and 1/6 is sugar. Find the quantity of rice and sugar needed for 1 kg of rice milk.
Answers
The quantities of rice, milk and sugar needed for 1 kg of rice milk are 0.4 kg, 0.4 kg and 0.167 kg respectively.
To solve the above problem, we can use the following equation:
Rice + Milk + Sugar = 1 kg
Rice = 2/5 (1 kg) = 0.4 kg
Milk = 2/5 (1 kg) = 0.4 kg
Sugar = 1/6 (1 kg) = 0.167 kg
Therefore, the quantities of rice, milk and sugar needed for 1 kg of rice milk are 0.4 kg, 0.4 kg and 0.167 kg respectively.
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