The volume of 20,000 m³, and the cost of $40/m², $100/m², and
$200/m², give the dimensions that give minimum cost as follows;
The height of the cistern is approximately 20.4 metersThe length is approximately 40.8 metersThe width is approximately 24.029 metersHow can the dimensions of the cistern be found?The dimensions of the cistern = L × W × H
L = 2·H
L × W × H = 20000
2·H² × W = 20000
[tex]W = \mathbf{ \dfrac{20000}{2 \cdot H^2}}[/tex]
Therefore;
A = 40·L·W + 200·L·W + 100·2·L·H + 100·2·W·H
A = 400·H² + 680·W·H
Given that the leading coefficient is positive, the function has a minimum point.
[tex]A = \dfrac{400 \cdot H^4 + 6800000 \cdot H}{H^2}[/tex]
[tex]\dfrac{d}{dH} A = \mathbf{\dfrac{d}{dH} \left( \dfrac{400 \cdot H^4 + 6800000 \cdot H}{H^2} \right)} = 0[/tex]
Which gives;
800·H⁵ - 6800000·H² = 0
800·H⁵ = 6800000·H²
H³ = 6800000 ÷ 800 = 8500
H ≈ 20.4 m
Which gives;
L ≈ 2 × 20.4 m = 40.8 m
[tex]W = \dfrac{20000}{2 \times 20.4^2} \approx \mathbf{24.029}[/tex]
The interior dimensions of the cistern are;
The height, H ≈ 20.4 m.The length, L ≈ 40.8 mWidth of the cistern, W ≈ 24.029 mLearn more about minimum value of a function here:
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I need your help please
Answer:
Answers A C C B A C C A
Step-by-step explanation:
Please help me with this too. Thankyouu!!!
Answer:
Q 4. 69
Step-by-step explanation:
Q 4:-
(37)^2 - 1300 1369 - 130069You ran a 100m race in 10 seconds. How fast did you run?
options:
100 m/s
100 mph
10 mph
10 m/s
Answer:
The answer is 10 mph
Step-by-step explanation:
Divide 100 by 10
The triangles are similar. Find the value of X.
Answer:
C. 18
Step-by-step explanation:
Triangle RST is dilation of 1.33333333 of triangle ACB, and side CA corresponds to angle SR.
24/1.33333333 = 18
Hope this helps :)
suppose a charity received a donation of $12.8 million, if this represents 33% of the charitys donated funds, what is the total amount of its funds
Answer:
Step-by-step explanation:
Restate the problem:
" 29% of x is $28.9 million"
(29/100)x = $28.9 million
[in word (story) problems "of" usually means multiply]
29% may be written as (29/100) or 0.29 as needed by the problem.
x = (100/29)($28.9 million)
x ≅ $99.655 million
x ≅ $100 million [rounded
What is the surface area of the net?
Answer:
150.66
Step-by-step explanation:
Round 822,119 to the nearest ten thousand.
Answer:
820,000
Step-by-step explanation:
2 is lower than 5 so round down to 20
Pls Brainliest If Helps
Answer:
820,000
Step-by-step explanation:
The 10,000 digit is the 2 on the left.
All digits to the right of the left 2 become zero.
820,000
The first digit that is dropped is the right 2.
Since it is not 5 or more, the 2 that is kept does not go up to 3.
Answer: 820,000
Which graph represents the function y = log x + 4?
Answer:
see attached
Step-by-step explanation:
We assume you are looking for the graph of ...
y = log(x) +4
This represents a vertical translation 4 units upward of the graph of log(x). That is, the point (1, 0) that appears on a graph of a log function will be translated to (1, 4).
The only graph shown that goes through the point (1, 4) is the last one, attached.
__
If you are actually looking for the graph of ...
y = log(x +4)
it will be a graph of the log function shifted 4 units to the left. The 2nd offered choice is that graph. The point (-3, 0) will be on that graph.
_____
Additional comment
For a function y = f(x), the transformation ...
y = f(x -h) +k
represents a horizontal shift of h units to the right, and a vertical shift of k units upward. Here, the argument of the log function is not clearly shown, so we cannot tell if the intended shift is to the left or upward.
The cheerleaders at Lake High School launch T-shirts into the crowd every time the Lakers score a touchdown. The height of the T-shirt can be modeled by the function h(x)-16x^2+48x+6, where h(x) represents the height of the T-shirt after x seconds.
the anser is c because i dont know
Which method would be the best to solve the following system of equations? y=1/2x+6 -2x+4y=24
A. None of these methods will work.
B. Elimination
C. Substitution
D. Graphing
Answer:
C. Substitution
But gives you infinity solitions
Solving steps:
Step: Solvey=1/2
x+6for y:
y=1/2x+6
Step: Substitute
1/2
x+6foryin−2x+4y=24:
−2x+4y=24
−2x+4(1/2x+6)=24
24=24(Simplify both sides of the equation)
24+−24=24+−24(Add -24 to both sides)
0=0
if you take Yola's age and subtract Zed's age you get 23. If you double Zeds age and then add Yolas age you get 80. Find both ages
Answer:
Yola is 42, Zed is 19
Step-by-step explanation:
I used a system of equations:
y - z = 23
2z + y = 80
Then I graphed them.
Please answer quick 15 points this is urgent
Answer:
x = 26
Step-by-step explanation:
180 = (5x-10) + (3x-18)
180 = 8x -28
180 + 28 = 8x
208 = 8x
x = 26
In a survey of 2500 registered voters, 1900 of them said that they plan to vote in the next presidential election. Let p denote the proportion of all registered voters who plan to vote. Find the 95% confidence interval for p.
This can alternatively be written as 0.74 < p < 0.78
========================================================
Explanation:
n = 2500 = sample size
x = 1900 = number of successes = number who plan to vote
phat = x/n = 1900/2500 = 0.76
phat is the sample proportion that estimates the population proportion p.
At 95% confidence, the z critical value is roughly z = 1.96 which you use a table or calculator to find this value (or it's something you memorize).
E = margin of error
E = z*sqrt(phat*(1-phat)/n)
E = 1.96*sqrt(0.76*(1-0.76)/2500)
E = 0.016742 approximately
The lower bound (L) of the confidence interval is
L = phat - E
L = 0.76 - 0.016742
L = 0.743258
L = 0.74
The upper bound (U) of the confidence interval is
U = phat + E
U = 0.76 + 0.016742
U = 0.776742
U = 0.78
The values of L and U are approximate.
The confidence interval in the format (L, U) would be (0.74, 0.78) approximately.
Another way to write the confidence interval is to say 0.74 < p < 0.78 as it's in the form L < p < U; showing that we're 95% confident that p is somewhere between 0.74 and 0.78
In other words, we're 95% confident that between 74% and 78% of the population would plan to vote in the next presidential election.
-4 and a y intercept at 3
Answer:
f(x)=-4x+3
Step-by-step explanation:
Assuming you're talking about f(x)=mx+b. b is y intercept. So f(x)=mx+3. You substitute m for -4, as you said, and we get f(x)=-4x+3
y = 9x - 17
y = -5x + 11
Solve each system of equations by substitution
Answer:
[tex]y=1,\:x=2[/tex]
Step-by-step explanation:
[tex]\begin{bmatrix}y=9x-17\\ y=-5x+11\end{bmatrix}[/tex]
[tex]\mathrm{Substitute\:}y=-5x+11[/tex]
[tex]\begin{bmatrix}-5x+11=9x-17\end{bmatrix}[/tex]
[tex]x=2[/tex]
[tex]\mathrm{For\:}y=-5x+11[/tex]
[tex]\mathrm{Substitute\:}x=2[/tex]
[tex]y=-5\cdot \:2+11[/tex]
[tex]\mathrm{Simplify}[/tex]
[tex]y=1[/tex]
[tex]\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}[/tex]
[tex]y=1,\:x=2[/tex]
Find the slope and the y-intercept of the graph of the linear equation.
y = -3x+2
The slope is (Answer here)
and the y -intercept is (Answer here)
Answer:
-3 is the slope
2 is the y intercept
Step-by-step explanation:
always
Mamady is planning a trip. He will stay six nights at a hotel that charges $51.25 a night. What is a good estimate of the total amount he will pay for the hotel? 250, 300, 360, 50.
Answer:
Answer is 300
Step-by-step explanation:
because 51.25x6=307.5 and the closest estimate is 300.
3 times the sum of a number and 5 is 6
Answer:
the number is -3
Step-by-step explanation:
3(x + 5) = 6
let x be the number anyways thooo
we distribute 3
3x + 15 = 6
then solve
3x = 6 - 15
3x = -9
x = -3
Most dogs fail to become service dogs. In a recent training class, only 4 of 15 were certified as service dogs. What percent of dogs, rounded to the nearest whole number, became certified service dogs?
Answer:
27
Step-by-step explanation:
4/15×100 =80/3 =26.6
Rounded to the nearest whole number is 27
Explain how the Multiplication Property of Equality can be used to solve the equation
x ÷ 6 = 7.
Step-by-step explanation:
Multiplication property of equality is when you multiply the same number on both sides of an equation, the equation will still hold true.
In order to have x by itself, you need to multiply by 6. The property states that you can multiply 6 on both sides and the equation will still hold true.
Mark is 8 years older than half Jon's age. If Jon is 20, how old is Mark?
Answer:
18 years old
Step-by-step explanation:
20÷2=10
10+8=18 years old
Mulberry Elementary has a playground in the shape of a rectangle.
The length is 5.5 meters
The width is 3.2 meters
Over the summer, the school will increase both the length and the width of the playground by 40% each.
Part A:
What will be the perimeter, in meters, of the enlarged playground? Enter your answer as a decimal with a hundredths place value.
Part B:
By how many square meters will the area of the playground increase? Enter your answer as a decimal with a thousandths place value.
The perimeter of the enlarged playground is 24.36 meters, and the increase in area is 16.9 m²
What is an area?
An area is the amount of space occupied by a two dimensional shape or object. The area of a rectangle is:
Area = length * width
Given that length = 5.5 m, width = 3.2 m
Hence:
Area = 5.5 * 3.2 = 17.6 m²
Perimeter = 2(length + width) = 2(5.5 + 3.2) = 17.4 m
There is an increase in both the length and the width of the playground by 40% each. Hence:
New length = 1.4 * 5.5 = 7.7 m, new width = 1.4 * 3.2 = 4.48 m
Area = 7.7 * 4.48 = 34.5 m²
Perimeter = 2(length + width) = 2(7.7 + 4.48) = 24.36 m
Increase in area = 34.5 m² - 17.6 m² = 16.9 m²
The perimeter of the enlarged playground is 24.36 meters, and the increase in area is 16.9 m²
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Linda bought 2 sets of 8 apples and each set costs $5.6 how much money does Linda need to pay to the cashier?(giving brainliest!)
Help please(geometry math)
Answer:
No solution
Step-by-step explanation:
By bisector theorem: the relative lengths of the two segments that a triangle's side is divided into by a line that bisects the opposite angle. It equates their relative lengths to the relative lengths of the other two sides of the triangle
y/8 = 8/2
y = 32 .... sum of the length of 2 sides of triangle must be larger than the 3rd side, 8+2+8 = 18 < 32
y can only has a value < 18
If we use Law of Sines also get y = 32 ... not forming a triangle
1/2 + p = -3
PLEASE HELP I DONT UNDERSTAND HOW TO DO THIS
Answer:
p=3.5
Step-by-step explanation:
So minus 1/2 on both sides. p= 3.5
A soccer field is 80 yds wide and 130 yds long. Find the length of the diagonal of such a field. Give an exact answer as a radical expression and an approximation to three decimal places.
[tex] \bf \underline{Given :-}[/tex]
Width of soccer field = 80 ydsLength of soccer feild = 130 yds[tex] \\ \\ [/tex]
[tex] \bf \underline{ To \: find:-}[/tex]
Length of diagonal[tex] \\ \\ [/tex]
[tex] \bf \underline{Solution:-}[/tex]
Strongly recommend to keep up with Digram , as name of sides are based according to Digram.
As we know soccer feild is rectangle , therefore ∠A = ∠B = ∠C = ∠D = 90°
Now as we have to just find value of diagonal AD therefore just focus on triangle ACD.
we know ∠C = 90° , triangle ACD. is a right angled triangle.
[tex] \\ \\ [/tex]
[tex] \bigstar \boxed{ \rm Hypotenuse^2 = Base^2 + Perpendicular^2}[/tex]
Here :-
Hypotenuse = AD
Base = CD
Perpendicular = AC
[tex] \\ [/tex]
Therefore :-
[tex] \\ [/tex]
[tex] \dashrightarrow\sf AD^2 =CD^2 + AC^2 \\ [/tex]
[tex] \\ \\ [/tex]
[tex] \dashrightarrow\sf AD^2 =(130)^2 + (80)^2 \\ [/tex]
[tex] \\ \\ [/tex]
[tex] \dashrightarrow\sf AD^2 =130 \times 130 + (80)^2 \\ [/tex]
[tex] \\ \\ [/tex]
[tex] \dashrightarrow\sf AD^2 =16900+ (80)^2 \\ [/tex]
[tex] \\ \\ [/tex]
[tex] \dashrightarrow\sf AD^2 =16900+80 \times 80 \\ [/tex]
[tex] \\ \\ [/tex]
[tex] \dashrightarrow\sf AD^2 =16900+6400\\ [/tex]
[tex] \\ \\ [/tex]
[tex] \dashrightarrow\sf AD^2 =23300\\ [/tex]
[tex] \\ \\ [/tex]
[tex] \dashrightarrow\sf AD= \sqrt{23300} \\ [/tex]
[tex] \\ \\ [/tex]
[tex] \dashrightarrow\bf AD =152.643 \: yds\\ [/tex]
[tex] \\ \\ [/tex]
Find the perimeter of the semicircle. Let ≈ 3.14. r=17
Answer:
53.38
Step-by-step explanation:
First, find the circumference of the whole circle.
C=2pir
C=2(3.14)(17)
C=106.76
Then, divide by 2 because a semi-circle is half of a circle.
106.76/2 = 53.38
Therefore, the circumference, or the perimeter, of the semicircle is 53.38
18) Solve for x.
A) 42
B) 50
C) 63
D) 75
The correct answer to your question is D
Sure hope this helps you
The triangles ΔDJY and ΔFJS are similar triangles. Then the value of x will be 75. Then the correct option is D.
What is the triangle?A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.
The angle ∠J is common for both triangles.
The triangles ΔDJY and ΔFJS are similar triangles, then we have
DJ/DF = YJ/YS
50/x = 42/63
x = 75
More about the triangle link is given below.
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Justin is evaluating the expression 12.5 + 3.8 x, when x is 7.9.
12.5 + 3.8 (7.9). 16.3 (7.9). 128.77.
What was Justin’s error?
Justin should have multiplied 12.5 and 7.9 first.
Justin should have added 12.5 and 7.9 first.
Justin should have multiplied 3.8 and 7.9 first.
Justin should have added 3.8 and 7.9 first.
Answer:
Justin should have multiplied 3.8 and 7.9 first
Step-by-step explanation:
Multiply before adding
12.5 +3.8(x)x
12.5+3.8x7.9
Answer:Justin should have multiplied 3.8 and 7.9 first
Step-by-step explanation:
I need help I will appreciate the answer.
Solve the system of equations below using substitution. y = 2x + 3y = 23
answer
options-
x+y=3, 2x-8y=19, 2x+y=-2, x+2y=2 hope that helps
Step-by-step explanation: