The dimensions that minimize the cost of building the tank are r ≈ 6.5 ft and h ≈ 26 ft
What do you mean by cost?
The cost is the sum of money that a business spends on the development or manufacturing of goods or services. It excludes the profit margin markup. The sum of money spent to create a good or product, as seen from the seller's perspective, is the cost.The total cost becomes
T = ucSc + 2ucSh
= 2ucπrh + 8ucπr²
We need to eliminate h . The volume from the question gives a way out.
4640 = 4/3πr³ + πr²h
h = 4640/πr² - 4r/3
substitute into the formula for total cost gives, after simplifying
T = 16ucπr²/3 + 9280uc/r²
differentiating with respect to r , we get
dT/dr = 32/3Ucπr - 9280Uc/r²
at extrema
dT/dr = 0
⇒ 32/3Ucπr = 9280Uc/r²
r = ∛870/π ≈ 6.5 ft
To confirm that r is a minimum value, carry out the second derivative test
d²T/dr² = 32Ucπ/3 + 18560/r³
substituting ∛870/π, we get that d²T/dr² > 0 confirming that minimum value
To find h , recall that
h = 4640/πr² - 4r/3
substituting r , we get h ≈ 26.0 ft as the corresponding minimum height.
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A veterinarian has been asked to prepare a diet, x ounces of Brand A and y ounces of Brand B, for a group of dogs to be used in a nutrition study at the School of Animal Science. It has been stipulated that each serving should be no larger than 8 oz and must contain at least 29 units of Nutrient I and 20 units of Nutrient II. The vet has decided that the diet may be prepared from two brands of dog food: Brand A and Brand B. Each ounce of Brand A contains 3 units of Nutrient I and 4 units of Nutrient II. Each ounce of Brand B contains 5 units of Nutrient I and 2 units of Nutrient II. Brand A costs 5 cents/ounce, and Brand B costs 7 cents/ounce. Determine how many ounces of each brand of dog food should be used per serving to meet the given requirements at a minimum cost. (x,y)=... What is the minimum cost? (Round your answer to the nearest cent.) ..... cents per serving
To meet the given requirements 3 ounces of Brand A and 4 ounces of Brand B should be served , the minimum cost is $43 .
In the question ,
it is given that ,
the each serving should not be larger than 8oz .
let the number of Ounces of Brand A food = x , and
let the number of ounces of brand B = y ,
So , x + y ≤ 8
Brand A has 3 units of Nutrient 1 and 4 units of Nutrient 2 , and
Brand B has 5 units of Nutrient 1 and 2 units of Nutrient 2 ,
So , 3x + 5y ≥ 29 ,
and 4x + 2y ≥ 20,
and x , y ≥ 0 .
given, that
cost of Brand A = 5 cents/ounce
cost of Brand B = 7 cents/ounce
So , the cost equation is c(x) = 5x + 7y ,
drawing the given inequalities on the graph ,
From the graph given below , we find that the vertices of the feasible region are ,
(2,6) , (5.5,2.5) , (3,4)
Substituting the points in the cost equation , we get
For point (2,6) , C = 5(2) + 7(6) = 10 + 42 = 52
For point (3,4), C = 5(3) + 7(4) = 15 + 28 = 43
For point (5.5,2.5) , C = 5(5.5) + 7(2.5) = 45 ,
the minimum cost is at point (3,4) ,
So , 3 ounces of Brand A and 4 ounces of Brand B should be used .
Therefore , To meet the given requirements 3 ounces of Brand A and 4 ounces of Brand B should be served , the minimum cost is $43 .
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34.7 divided by 0.7
round answer to 2 decimal places
Answer:
49.57
Step-by-step explanation:
0.7 can go into 34.7 49 times. 0.7*49=37.3
34.7-34.3=0.4 and 0.4/0.7 is 4/7 or 0.57...
So 49+.57=49.57
On Monday, jake could lift 25lbs. One month later he could lift 45lbs. What is the percent change in the number of pounds he can lift? Round to the nearest whole number.
what Is the answer
The percent change in the number of pounds that Jake can lift is 80%.
How to calculate the percentage?From the information illustrated, Jake could lift 25lbs and one month later he could lift 45lbs.
The percentage change will be:
= Change in pounds / Original pounds × 100
= (45 - 25) / 25 × 100
= 20 / 25 × 100
= 4 / 5 × 100
= 80%
The percentage change is 80%.
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what substance do you drink to get strong bones
Answer:
milk
Step-by-step explanation:
What is the answer to this problem ?
The three ordered pairs for the equation y = -4x+3 are (0,3), (1,-1) and (2,-5).
According to the question,
We have the following equation:
y = -4x+3
We have to find the three ordered pairs when the values of x are given in the table.
When x = 0, we have the following value of y:
y = -4*0+3
y = 3
When x = 1:
y = -4*1+3
y = -4+3
y = -1
When x = 2:
y = -4*2+3
y = -8+3
y = -5
Hence, the three ordered pairs for the equation y = -4x+3 are (0,3), (1,-1) and (2,-5).
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Determine the distance between the points (−4, −5) and (8, 0). 13 units 12 units 8 units 29 units
The distance between the points (-4, -5) and (8, 0) is 13 units
The coordinates of the first point = (-4, -5)
The coordinates of the second point = (8, 0)
The distance between the two points d = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Where d is the distance between two points
[tex](x_1,y_1)[/tex] is the coordinates of the first point
[tex](x_2,y_2)[/tex] is the coordinates of the second point
Substitute the values in the equation
The distance between the two points = [tex]\sqrt{(8--4)^2+(0--5)^2}[/tex]
= [tex]\sqrt{12^2+5^2}[/tex]
Find the square of each term
= [tex]\sqrt{144+25}[/tex]
Add the terms together
= [tex]\sqrt{169}[/tex]
Find the square root of the number
= 13 units
Hence, the distance between the points (-4, -5) and (8, 0) is 13 units
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Find the x- and y-intercepts of the graph of -2x + y = 22. State each answer as an
integer or an improper fraction in simplest form
The x- and y- intercepts of then graph of; -2x + y = 22 as required in the task content are; -11 and 22 respectively.
What are the x- and y-intercepts of the graph of the given equation?It follows from the task content that the x- and y-intercepts of the graph of the equation; -2x + y = 22 are to be determined.
Recall that the y-intercept of a graph refers to the value of y when x = 0.
Therefore; we have;
-2(0) + y = 22;
y = 22.
Recall that the x-intercept of a graph refers to the value of x when y = 0;
-2x + 0 = 22
x = 22/-2
x = -11.
On this note, it follows that the x-intercept of the graph is at x = -11 while the y-intercept is at; y = 22.
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what is the square rout of 9
Answer:3
Step-by-step explanation: 3x3=9
Answer:
3
Step-by-step explanation:
√9
=√3²
=√(3²)
=3
{as square root =1/2, 2*1/2 = 1}
P is the point (0,-1) and Q is the point (5,9) find the equation of the line through P that is perpendicular to PQ
Answer:
Step-by-step explanation:
Find the slope of PQ
[tex]\frac{9 - (-1)}{5-0}=\frac{10}{5}[/tex] or just [tex]2[/tex]
The perpendicular slope is the negative reciprocal
Use a slope of [tex]-\frac{1}{2}[/tex]
Use the point-slope form of a equation and point P to find a new equation in slope-intercept form
[tex](y- (-1))=-\frac{1}{2}(x-0)[/tex]
[tex]y+1=-\frac{1}{2} x[/tex]
Subtract the 1 from both sides of the equation
[tex]y=-\frac{1}{2}x-1[/tex]
A triangle has side lengths of (7x-4)(7x−4) centimeters, (x+3)(x+3) centimeters, and (3y+2)(3y+2) centimeters. Which expression represents the perimeter, in centimeters, of the triangle?
The perimeter of the triangle is, 8x + 3y +1.
What is perimeter?
A perimeter is a closed path that encloses, surrounds, or delimits a one-dimensional length, a two-dimensional shape, or both. The circumference of a circle or an ellipse is its perimeter. There are numerous practical uses for calculating the perimeter.
Let, the side lengths of the triangle are (7x - 4), (x + 3) and (3y + 2).
Since the perimeter is the sum of all side lengths.
So,
Perimeter = (7x - 4) + (x + 3) + (3y + 2)
= 7x - 4 + x + 3 + 3y + 2
Perimeter = 8x + 3y + 1
Hence, the perimeter of the triangle is, 8x + 3y + 1.
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2 half dollars = how many dimes
2 half dollars just mean a dollar. In that case, that's 10 dimes. (10*10=100)
Answer:
10 dimes
Step-by-step explanation:
So in order to get this answer we first must know that...
1 half dollar = 50 cents
1 dime = 10 cents
So...
5 dimes = 50 cents
2 half dollars = 100 cents aka $1
10 dime = 100 cents aka $1
Therefore we can use our common sense to figure out that 2 half dollars is 10 dimes.
Based on the time recorded for 500 attendees at an amusement park, the average amount of time spent at the park was 6.75 hours with a margin of error of ±1.45 hours. if 2,000 people attended the park on a given day, what is the estimated range of total hours the attendees spent in the park? 2,725 to 5,375 total hours spent in the park 3,842 to 4,893 total hours spent in the park 10,600 to 16,400 total hours spent in the park 13,600 to 19,400 total hours spent in the park
Answer:10,600 to 16,400
Step-by-step explanation:
First you subtract the margin of error to find the least amount of hours.
6.75 - 1.45 = 5.3 x 2,000(people) = 10,600 (least amount of hours)
Then you add the margin of error to find the most amount of hours.
6.75 + 1.45 = 8.2 x 2,000(people) = 16,400 (most amount of hours)
The margin of error just shows that people spent at least 5.3 and at most 8.2 hours at the park.
You multiply those numbers with how many people went to the park. 2,000
That means the answer is C: 10,600 TO 16,400.
Plus.....I took the test and got it right!
Find the solution(s) to the equation sine (startfraction x over 2 endfraction) cosine x minus 1 = 0 on the interval 0 ≤ x 2π. check all that apply. 0 startfraction pi over 3 endfraction startfraction pi over 6 endfraction startfraction 3 pi over 2 endfraction startfraction 5 pi over 3 endfraction
All apply values to the equation are:
0 ⇒ A
π/3 ⇒ B
5π/3 ⇒ E
What is an equation?
A formula known as an equation shows the equality of two expressions by joining them with the equals sign =.
Main Body:
∵ 0 ≤ x ≤ 2π is the domain for angle x
∴ 0 ≤x/2 ≤ π is the domain of angle
∵ sin(x/2) + cos(x) - 1 = 0
→ To solve the equation we should use the rule of cosine double angle
∵ cos(x) = 1 - 2 sin²(x/2)
→ Substitute it in the equation above
∴ sin(x/2) + (1 - 2 sin²(x/2) = 0
∴ sin(x/2) + 1 - 2 sin²(x/2) = 0
→ Add the like terms
∴ sin(x/2) + (1 - 1) - 2 sin²(x/2) = 0
∴ sin(x/2) - 2 sin²(x/2) = 0
→ Take sin(x/2) as a common factor
∴ sin(x/2) [1 - 2sin(x/2)] = 0
→ Equate each factor by 0
∵ sin(x/2) = 0
→ The value of sine equal zero on the x-axis
∴ x/2 = 0, π, 2π
∵ The domain of x/2 is 0 ≤ (x/2) ≤ π
∴ x/2 = 0 and π ⇒ 2π refused because ∉ the domain
→ Multiply both sides by 2 to find x
∴ x = 0 and 2π
∵ 1 - 2sin(x/2) = 0
→ Subtract 1 from both sides
∴ - 2sin(x/2) = -1
→ Divide both sides by -2
∴ sin(x/2) = 1/2
→ The sine is positive in the 1st and 2nd quadrants
∴ (x/2) lies on the 1st OR 2nd quadrants
∵ (x/2) = sin⁻¹(1/2)
∴ (x/2) = π/6 = ⇒ 1st quadrant
→ Multiply both sides by 2
∴ x = π/3
∵ (x/2) = π -π/6 = 5π/6 ⇒ 2nd quadrant
→ Multiply both sides by 2
∴ x = 5π/3
∴ The values of x are 0,π/3 , 5π/3 , 2π
Hence apply values are:
0 ⇒ A
π/3⇒ B
5π/3⇒ E
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Which equation represents the graph below?
-10
Oy = ²r + 10
Oy - 2x + 5
O y = 5x + 2
O y
=
-5
=
x+5
-10
0
-5-
5
y = -1/3 x + 5 this equation represents the given graph.
How do you plot points on graph ?
The horizontal axis is called the x-axis. And the vertical one is the y-axis. Points are written as xy pairs in parentheses, like so: (x, y).Now, just locate the position on x-axis as well as in y-axis and finally plot where these points meet.Proof :
(0, 5) and ( 15, 0) these are the points where the graph is plotted.
y = -1/3 x + 5
put x= 0 and find y
y = 0 + 5
y = 5
put y = 0 and find x
0 = -1/3 x + 5
-5 = -1/3 x
x = 15
So, now we get the same points i.e, (0, 5) and ( 15, 0) as plotted in the given graph.
Hence, we can say that y = -1/3 x + 5 this equation represents the given graph.
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four cards are selected at random without replacement from a well-shuffled deck of 52 playing cards. find the probability of the given event. (round your answer to four decimal places.) four cards of the same suit are drawn.
The probability of selecting four cards of the same suit is 0.0106.
What is probability?A probability is a number that reflects the chance or likelihood that a particular event will occur.
Given that, four cards are selected at random without replacement from a well-shuffled deck of 52 playing cards
No. of cards for each suit = 13
Total types of four suits = 4(hearts, spades, diamond, clubs)
Probability = (conditional case)/(total case)
So, total number of conditional case = No. of case of selecting all 4 cards of hearts suit + no. of case of selecting all 4 cards of spades suit + no. of case of selecting all 4 cards of clubs suit + no. of case of selecting all 4 cards of diamonds suit
= 13C4 + 13C4 + 13C4 + 13C4
= 4*13C4 = 4*13!/9!4! = 4*13*12*11*10*9!/9!*4*3*2*1 = 2860
Total number of cases = 52C4 = 52!/48!4! = 270725
So, probability of getting all 4 cards of the same suit =
2860/270725
= 0.0106.
Hence, The probability of selecting four cards of the same suit is 0.0106.
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I inserted a picture so it can be more clear. This is for Algebra 2, Unit 2
Answer: x=-16
Step-by-step explanation:
g^-1 is the inverse of the g(x) graph meaning that the x and g(x) values of the g(x) graph switch places. So in the table when x=-2 g(x)=-16
The string of a kite is 120 m long and makes an angle of 70° with the horizontal. What is the height of the kite? show work!
The height of the kite is approximately 112.763 meters above the ground.
How to determine the height of a kite above the ground
The situation is represented by the following geometric diagram, a right triangle with a known hypotenuse (r), in meters, and a known acute angle (θ), in degrees. The height of the kite (h), in meters, is represented by the leg opposite to the acute angle and can be found by trigonometric functions:
sin θ = h / r
h = r · sin θ
h = 120 · sin 70°
h ≈ 112.763 m
The height of the kite is approximately 112.763 meters.
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Please help quick thanks
Answer:
Step-by-step explanation:
( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] )
( [tex]x_{2}[/tex] , [tex]y_{2}[/tex] )
d = [tex]\sqrt{(x_{2} -x_{1} )^2+(y_{2} -y_{1} )^2}[/tex]
~~~~~~~~~~~~~~~
A ( 3 , 6 )
B ( 0 , 1 )
C ( 4 , 0 )
AB = [tex]\sqrt{(0-3)^2 + (1-6)^2}[/tex] = 3√5 ≈ 6.71
AC = [tex]\sqrt{(4-3)^2 + (0-6)^2 }[/tex] = √37 ≈ 6.08
BC = [tex]\sqrt{(4-0)^2 + (0-1)^2 }[/tex] = √17 ≈ 4.12
AB ≠ AC ≠ BC ⇒ Δ ABC is a scalene triangle
A number reduced by two, then multiplied by 9
(x-2)9
9x-18
good luck <33
You have $14 in your pocket. A bike rental costs $5 plus $2.50 per hour. What is maximum amount of time you can rent a bike for without spending all of your money?
Answer:
3 hours
Step-by-step explanation:
3 hours will cost 2.50*3 which is 7.50 + the base price of 5.
So that would be $12.5 leaving you with $1.5
A regular polygon has 16 sides. If one of its angles measures (5h − 29)°, what is the value of h?
h=56.5
h=37.3
h=33.6
h=9
PLEASE HELP
The value of h in a regular polygon of 16 sides is 37.3.
According to the question,
We have the following information:
A regular polygon has 16 sides. And one of its angles measures (5h − 29)°.
We know that following formula is used to find the sum of interior angles of a polygon:
(n-2)*180 where n is the number of sides of a polygon
(16-2)180
14*180
2520°
Now, in this polygon, there are 16 sides. So, there will be 16 angles.
Now, to find the measurement of one angle, we will divide total sum by number of angles.
One angle = 2520/16
One angle = 157.5°
Now, we have the following expression:
5h-29 = 157.5
5h = 157.5+29
5h = 186.5
h = 186.5/5
h = 37.3
Hence, the correct option is B (the second one).
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HELP ME PLSSSS I NEED HELP OR ELSE I WILL CRY
The length of the segment BD is 2.4 units and that of AB is 4 units.
According to the question,
We have the following information:
We have a figure of triangle in which there are two right-angled triangles.
Now, we can find the length of the segment BD and AB using the Pythagoras theorem.
Using it in triangle BDC:
[tex]BC^{2} = CD^{2} + BD^{2}[/tex]
Putting the values of BC and CD:
3*3 = 1.8*1.8+[tex]BD^{2}[/tex]
9 = 3.24+[tex]BD^{2}[/tex]
Subtracting 3.24 from both sides:
9-3.24 = [tex]BD^{2}[/tex]
[tex]BD^{2}[/tex] = 5.76
BD = 2.4 units
Now, using the same theorem in triangle BDA:
[tex]AB^{2} = BD^{2}+ AD^{2}[/tex]
[tex]AB^{2}[/tex] = 5.76+3.2*3.2
[tex]AB^{2}[/tex] = 5.76+10.24
[tex]AB^{2}[/tex] = 16
AB = 4 units
Hence, the length of the segment BD is 2.4 units and that of AB is 4 units.
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1) Solve the following equations for 0° ≤ θ ≤ 360°.
(i) 2 sin 2 θ = cos θ
(ii) tan 2θ=4 tan θ
Triangle ABC is congruent to triangle XYZ. Side BC corresponds to what side in triangle XYZ?
Answer:
Side YZ
Step-by-step explanation:
think of the triangles as mirrors of each other
and pay attention to the symbols that correspond from side to side, and angle to angle
A cyclist rode 5.83 miles in 0.4 hours.
How fast was she going in miles per hour?
At that rate, how long will it take her to go 5.5 miles?
Answer:
Its 12.5 miles per hour.
Step-by-step explanation:
Distance covered by cyclist=3.75 miles. Time =0.3 hours. Speed =3.75÷0.3=12.5
hope this helps
Answer:
0.4 miles per hour
Step-by-step explanation:
Distance covered= 5.83 miles
Time taken to cover the distance =0.4 hours
[tex] speed \: = \frac{distance}{time} [/tex]
[tex] = \frac{5.83}{0.4} [/tex]
=14.575 ~=14.5 miles per hour
If the rate (speed) = 14.575 miles per hour
Distance = 5.5 miles
[tex]time = \frac{distance}{speed} [/tex]
[tex] = \frac{5.5}{14.575} [/tex]
=0.337 ~= 0.4 hours
42 km of 120 km help pls
Answer: 42 km of 120km is 35%
Step-by-step explanation: 42 ÷ 120 is 0.35 then you move decimal 2 places right to get percent.
Find the quotient (x³ + 2x² − x − 2) ÷ (x + 2)
Answer: The quotient is x²- 1
Carlos harvests cassavas at a constant rate. he needs 353535 minutes to harvest a total of 151515 cassavas. write an equation to describe the relationship between t, the time, and ccc, the total number of cassavas.
Carlos harvests cassavas at a constant rate. He needs 353535 minutes to harvest a total of 151515 cassavas.
The ratio of the change in dependent values or outputs to the change in independent values or inputs is known as the rate of change. The change, which also refers to the function's slope, represents the shift in values between two points on a coordinate plane. The formula for the rate of change is (y2 - y1)/, where y stands for the dependent variable and x for the independent variable (x2 - x1).
Given:
Carlos gives 353535 minutes to harvest a total of 151515 cassavas.
Find:
We have to find the total number of cassavas.
Solution:
Carlos harvests cassava at constant rate is 353535 minutes per 151515 cassavas
= 151515/353535
= 0.429
A formula for the quantity of cassava (C) that Carlos harvests each time (T).
This means that after 353535 minutes, 151515 cassavas have been harvested, after 700000 minutes, 300000 cassavas, and so on.
Hence, the required constant rate is 0.429T.
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If a = 7 and b equals 13 what is the value of C round your answer to the nearest hundredth
Answer:
c ≈ 14.76
Step-by-step explanation:
In right triangle ABC, you have short sides a=7 and b=13. You want the length of the hypotenuse, 'c'.
Pythagorean theoremThe Pythagorean theorem tells you the relationship between the sides of a right triangle is ...
c² = a² +b²
ApplicationFilling in the given values, we have ...
c² = 7² +13² = 49 +169 = 218
c = √218 ≈ 14.7648
Rounding to hundredths, we have ...
c ≈ 14.76
__
Additional comment
Your posted question asks for the value of C (capitalized). That refers to the right angle, so its value is C = 90°. It is always helpful if you ask for what you really want to know.
Gabriel is designing a rectangular planter box for their garden. It needs to cover an area of
15 1/2 m
Gabriel wants it to be 7- m long.
4
How wide does the planter box need to be?
Answer:
2m Wide
Step-by-step explanation:
