Please help!!! Very confused on my homework.
The tank is completely filled with water and then drains completely into the pool. The volume of the cylindrical tank is v1=36pir2/1 where r1 is the radius of the tank in feet.
PROBLEM IS ON THE ATTACHMENT!
Answers
Step-by-step explanation:
we need to use both equations for the volumes.
the only variables in them are r1 and r2.
when we say both results (volumes) are equal, that means we can create an equation with one formula on one side and the other formula on the other side.
and then we can easily transform the equation into "r1 = ..." or "r2 = ..."
and yes, your teacher made a mistake by hinting to solve for r1 in a. and b. it is r1 in a. and r2 in b.
a.
the goal here is an equation in the form
"r1 = ..."
that means r1 is a function of r2.
36×pi×r1² = 1/2 × 4/3 × pi × r2³ = 4/6 × pi × r2³ =
= 2/3 × pi × r2³
36 × r1² = 2/3 × r2³
r1² = (2/3 / 36) × r2³ = (1/(3×18)) × r2³ = 1/54 × r2³
r1 = sqrt(1/54 × r2³) = 1/3 × sqrt(1/6 × r2³)
b.
the goal here is
"r2 = ..."
again
36×pi×r1² = 2/3 × pi × r2³
36 × r1² = 2/3 × r2³
3×36 × r1² = 2 × r2³
3×18 × r1² = r2³
54 × r1² = r2³
[tex]r2 = \sqrt[3]{54 \times {r1}^{2} } = 3 \times \sqrt[3]{2 \times {r1}^{2} } [/tex]
c.
r2 is doubled.
so, we have to go back to our equation of a.
r1 = sqrt(1/54 × r2³).
when r2 is doubled, we get
r1 = sqrt(1/54 × (2×r2)³) = sqrt(1/54 × 8 × r2³) =
= sqrt(8) × sqrt(1/54 × r2³)
so, when r2 doubles, r1 has to grow by the factor of sqrt(8) to keep the equality intact.
Related Questions
i need help asap please
Answers
Step-by-step explanation:
the range is (-32, 28)
note that when the bubble is not filled in it should be an open bracket
a shopper purchased 8 t-shirts and 5 pairs of pants for $220. the next day, he purchased 5 t-shirts and 1 pair of pants for $112.How much does each t shirt and each pair of pants cost?
Answers
Answer:
Step-by-step explanation:
Let the costs of 1 t - shirt and 1 pair of pants be 'x' and 'y' respectively then:
Case 1 --> 8x + 5y = 220 ----------(1)
Case 2 --> 5x + y = 112 ----------(2)
Multiplying equation (2) by 5:
8x + 5y = 220
25x + 5y = 560 ------(3)
Subtracting equation (1) from equation (3) we get :
17x = 340
x = 20
Putting x in (2):
5 x 20 + y = 112
y = 12
therefore, cost of each t-shirt is 20 rupees and the cost of each pair of pants is 12 rupees
How many ways can the train be made up?
Answers
Answer:
16c9
Step-by-step explanation:
First, we will add up the number of different car possibilities. This is:
6 + 7 + 3 = 16.
Then, we need to take 9 of these 16 cars, giving us 16c9.
Hope this helped!
Answer:
4,151,347,200
Step-by-step explanation:
i need help Please will mark brainiest
Answers
The standard form of the polynomial -n²(n² + 5n + 6) is -n⁴ - 5n³ - 6n².
How to represent polynomial in standard form?Polynomials are algebraic expressions that consist of variables and coefficients.
The standard form of a polynomial is expressed by writing the highest degree of terms first then the next degree and so on.
Hence, let's represent the polynomial in standard form as follows:
-n²(n² + 5n + 6)
Open the brackets
-n²(n² + 5n + 6) = -n⁴ - 5n³ - 6n²
Hence,
-n²(n² + 5n + 6) = -n⁴ - 5n³ - 6n²
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What is the domain of the function y √ x?
Answers
The domain of the function y = √ x is x ≥ 0.
The domain of a function is the set of all input values for which the function is defined. The square root function, represented by √, is only defined for non-negative real numbers. This is because the square root of any negative number is not a real number, it becomes an imaginary number. Therefore, the domain of √ x is the set of all real numbers greater than or equal to zero.
This means that any input value less than zero would result in an undefined output for the square root function. In this case, since the square root is the only function, the domain of the function y = √ x is x ≥ 0. This means that the function can only take non-negative real numbers as input and will output a non-negative number.
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Is(1, 7)a solution to the inequality 3x + 11y ≤ 8? IXL
Answers
Answer: No, it is not a solution.
Step-by-step explanation:
We will substitute the point given, and if the inequality is true after simplifying then it is a solution.
Given:
3x + 11y ≤ 8
Substitue:
3(1) + 11(7) ≤ 8
Multiply:
3 + 77 ≤ 8
Add:
80 ≤ 8 ✗
2 2/5 times 1/4 simplest form
Answers
Answer:
37/56
Step-by-step explanation:
Answer: 3/5 = 0.6
Step-by-step explanation:
1. 2 2/5 x 1/4 = 12/20
2. 2 times 5 over 5 + 2/5 = 10 + 2 over 5 = 12/5
3. 12/5 times 1/4 = 12/20
4. 12/20=3/5
PLEASE HELPPPP
(image below)
Answers
Answer:
b
Step-by-step explanation:
I think number B is the answer. because the square becomes root when it crosses the = . So, the answer is B
Answer:
b. ±√60
Step-by-step explanation:
You want to know the solution to x² = 60.
SolutionIn general, the process of solving for a variable's value requires you to "undo" what is done to the variable. This generally means you use inverse operations. The inverse of the squaring operation is the square root operation.
Taking the square root of both sides, we get ...
√(x²) = √60
|x| = √60 . . . . . . simplify the left side
x = ±√60 . . . . . . . write the equivalent without the absolute value bars
__
Additional comment
As with any operation performed on an equation, it must be done to both sides of the equal sign.
You will get a ±(radical) result whenever you take an even-index root: square root, fourth root, sixth root, and so on. Odd-index roots will have the same sign as the value under the radical.
√64 = ±8
∛64 = 4; ∛-64 = -4
Un prisma cuadrangular regular tiene 4 m de arista de la base y 6m de altura Calcula el area y el volumen
Answers
Answer:
El área y volumen del prisma cuadrangular mencionado son respectivamente:
Área = [tex]16m^{2}[/tex] Volumen = [tex]96m^{3}[/tex]Step-by-step explanation:
Para solucionar este ejercicio debes recordar que un prisma cuadrangular tiene como base y como superficie cuadrados, por lo tanto, para calcular el área de dicho cuadrado puedes utilizar la siguiente fórmula:
Área de un cuadrado = [tex]arista^{2}[/tex]Ya que el ejercicio nos da el valor de la arista (4 metros), podemos reemplazarla en la ecuación y calcular:
Área de un cuadrado = [tex](4m)^{2}[/tex]Área de un cuadrado = [tex]16m^{2}[/tex]Por último, para calcular el volumen debes multiplicar el área superficial, el área del cuadrado calculado, por la altura del prisma, cuyo valor dentro del enunciado es de 6 metros, de esta forma:
Volumen de un prisma cuadrangular = área superficial * alturaVolumen de un prisma cuadrangular = [tex]16m^{2}[/tex] * [tex]6 m[/tex]Volumen de un prisma cuadrangular = [tex]96m^{3}[/tex]Como puedes ver tras los cálculos, el área superficial del prisma es de [tex]16m^{2}[/tex] y su volumen es [tex]96m^{3}[/tex].
helpppppppppppppppp!!!!
Answers
Answer:
69π m^2
Step-by-step explanation:
surface area of cylinder= 2πrh+2πr^2
However, the cylinder is open top
Therefore, the outer surface area of the cylinder
=2π(6/2)(10)+π(3)^2 m^2
=60π+9π m^2
=69π
Solve using the quadratic formula. Show all work. Write each solution in simplest form. No decimals.
Answers
-4 +/- √ 16-4(1)(7)
_____________
2
-4 +/- 2i√3
_______
2
x= -2+/- i√3
hat is the product of the least common multiple and the greatest common factor of $22$ and $48$?
Answers
Answer:
1056
Step-by-step explanation:
You want the product of the LCM and the GCF of 22 and 48.
ProductOne way to find the LCM of two numbers is to start with their product, then divide out the extra factor:
LCM(A, B) = (A×B)/GCF(A, B)
Since we want the product of the LCM and the GCF, we can start with this and multiply by the GCF:
LCM(A, B) · GCF(A, B) = ((A×B)/GCF(A, B)) · GCF(A, B)
LCM(A, B) · GCF(A, B) = A×B
Using this for the given numbers, we get ...
LCM(22, 48)·GCF(22, 48) = 22·48 = 1056
__
Additional comment
If you want to go to the trouble of finding the LCM and GCF, you get ...
22 = 2·11
48 = 2·24
LCM(22, 48) = 2·11·24 = 528
GCF(22, 48) = 2
LCM·GCF = 2·528 = 1056
Write a polynomial in intercept form so that P(x)=0 has the given roots.
7. 2, √√3
8. -i, -5
9. i, √7
11. --√6, √3
10. 2i, -i
12. 4DR, VII
Answers
The polynomial in intercept form so that P(x)=0 has the given roots is, x^2 - √3x - 2x + 2√3 = 0.
What is polynomial?
A polynomial is an expression in mathematics that only uses the operations of addition, subtraction, multiplication, and powers of positive-integer variables. It consists of indeterminates and coefficients. The polynomial x^2 4x + 7 is an illustration of one with a single indeterminate x.
We have to find the polynomial in intercept form so that P(x)=0 has the roots 2 and √3.
Let 2 and √3 are the roots of the polynomial so,
x = 2, x = √3
⇒ x - 2 = 0, x - √3 = 0
⇒ (x - 2)(x - √3) = 0
x^2 - √3x - 2x + 2√3 = 0
Hence, the polynomial in intercept form so that P(x)=0 has the given roots is, x^2 - √3x - 2x + 2√3 = 0.
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heyy! i’ll give brainliest help asap pls
Answers
Answer: the answer is A
Step-by-step explanation:
Answer:
4
Step-by-step explanation:
What is the equation of the straight line shown below? Give your answer in the form y = mx + c, where m and c are integers or fractions in their simplest forms. Y 14- 13- 12- 11- 10- 9 8- 97654 MNE 7- 6- 5- 4- 3- 2- 1- -10-9-8-7-6-5-4-3-2 0 1 2 3 4 5 6 7 8 9 10 x -1 -2- -3- بنا -4- 56 -5- -6+
Answers
Answer:
y = 2x + 10
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 5, 0) and (x₂, y₂ ) = (0, 10) ← 2 points on the line
m = [tex]\frac{10-0}{0-(-5)}[/tex] = [tex]\frac{10}{0+5}[/tex] = [tex]\frac{10}{5}[/tex] = 2
the line crosses the y- axis at (0, 10 ) ⇒ c = 10
y = 2x + 10 ← equation of line
1. Find the surface area of the cone in terms of pi.
A. 84pi cm
B. 98pi cm
C. 70pi cm
D. 119pi cm
Answers
The surface area of the cone is 119π
How to find the surface area of a cone?Surface area of a cone = πr(r + l)
where
r = radiusl = lengthTherefore,
r = 7 cm
l = 10 cm
Hence,
Surface area of the cone = 7π(7 + 10)
Surface area of the cone = 7π(17)
Surface area of the cone = 119π
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Answer: option D. 119
Step-by-step explanation:
surface area of cone =[tex]\pi[/tex] x r x l + [tex]\pi[/tex] x r^2
r =7 l =10
pi x 7 x 10 + pi x 7^2
(6.3 x 10") + 2, 700, 000
Scientific notation
Answers
Scientific 2.700063 x 10^6
Identify the independent variable and the dependent variable. A pool store owner wants to determine the effect of algaecide brands on the treatment of pool water with algae. He contacts customers who have purchased the brands of algaecide and asks their opinion of the algaecide.
Answers
The independent variable is the brand of algaecide. The dependent variable is the treatment of pool water with algae.
What is the independent and dependent variable?
In mathematical modeling, statistical modeling, and experimental sciences, there are dependent and independent variables. Dependent variables get their name because, during an experiment, their values are investigated under the presumption or requirement that they are dependent on the values of other variables due to some law or rule.
Here, we have
Given
A pool store owner wants to determine the effect of algaecide brands on the treatment of pool water with algae. He contacts customers who have purchased the brands of algaecide and asks their opinion of the algaecide.
We have to determine the independent variable and the dependent variable.
We concluded that the independent variable is the brand of algaecide and the dependent variable is the treatment of pool water with algae.
Hence, the independent variable is the brand of algaecide and the dependent variable is the treatment of pool water with algae.
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Clare spent $5.17 on apples. How many pounds of apples did Clare buy?
(round to the nearest tenth)
Answers
Answer: complete the question please
Step-by-step explanation:
How much is a pound/lb? Then do 5.17 divided by (however much is a pound/lb)
How much is 2 + 2?
a) 22
b) 44
Answers
neither it is just 4
Step-by-step explanation:
unless this is a joke. 2x11=22.
Answer:
Hold up, wait a minute...
Ummmm A? 22
Step-by-step explanation:
Logic:
2 + 2 (Combined)
= 22
So, the answer is 22.
A map is drawn to a scale 2cm to 100km. On the map the distance between two towns is 2.5cm. What is their true distance apart.
Answers
Answer: 125 km
Step-by-step explanation:
Given
Scale is 2 cm to 100 km i.e. 2 cm of the map is equivalent to 100 k in the true sense
or 1 cm is equivalent to 50 km
If the distance between the two towns is 2.5 cm
so, in their true distance, it is
[tex]\Rightarrow 2.5\ cm=2.5\times 50\\\Rightarrow 125\ km[/tex]
The distance between two towns is 125 km
a club treasurer is solving a problem using the expression shown. -23.50 + 5 which problem is the treasurer MOST LIKELY solving? A. There is a club member who pays 23.50$ in dues each month for 5 months. What is the total amount, in dollars, that the member pays in dues? B. There are 5 club memebers who each owe the club 23.50$ in dues. What is the total balance, in dollars, of the members accounts? C. a total of 23.50$ in dues is owed to the club. There are 5 club memebrs who each owe the same account in dues. What is the amount, in dollars, that each member owes in dues? D. A total of 23.50$ in dues is owed to the club. There are 5 club members who each owe the same amount in dues. What is the balance,in dollars, of each members account?
Answers
When the treasurer is solving a problem using the expression shown. -23.50 ÷ 5, the problem that the treasurer is lost likely solving is D. A total of -$23.50 in dues is owed to the club. There are 5 club members who each owe the same amount in dues. What is the balance,in dollars, of each members account?
How to illustrate the expression?From the information, the club treasurer is solving a problem using the expression shown. -23.50 ÷ 5. An expression show the relationship between the variables.
In this case, a total of $23.50 in dues is owed to the club. There are 5 club members who each owe the same amount in dues.
The correct option is D.
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How do I solve this I don't understand?
Answers
Answer:
The equation for this sequence will be 8 + 17n - 17 with n being replaced with the term number you are trying to find.
so 8 + 17(16) - 17
17 x 16= 272
8 + 272= 280
280- 17= 263
Thus, the 16th term will be 263.
Answer:
16ᵗʰ Term of the sequence is 263
Step-by-step explanation:
Here,
First Term = a₁ = 8
Second Term = a₂ = 25
Third Term = a₃ = 42
Now,
Common Difference (d)
d = a₂ - a₁ = 25 - 8 = 17
d = a₃ - a₂ = 42 - 25 = 17
Here, Common Difference is same everywhere
Now, For 16ᵗʰ term, n = 16
aₙ = a + (n - 1)d
a₁₆ = 8 + (16 - 1) × 17
a₁₆ = 8 + 15 × 17
a₁₆ = 8 + 255
a₁₆ = 263
Thus, 16ᵗʰ Term of the sequence is 263
-TheUnknownScientist
In a bike shop there is a total of 120 bikes. If mountain bikes make up 10% of the total bikes in the shop how many mountain bikes are there
Answers
Answer: There are 12 mountain bikes in the shop
Step-by-step explanation:
Total number of bikes in the bike shop =120
Percentage of mountain bikes =10%
Number of mountain bikes in the shop =10% of 120
=10% x 120
==0.1 x 120=12
6
2/3
15
13
Hit
Miss
2/5
3
5
215
2
Not score
Score
Find the probability that Ryan misses the target and does not score a goal,
(2 marks)
Not score
Answers
Answer:
Step-by-step explanation:
6
2/3
15
13
Hit
Miss
2/5
3
5
215
2
Not score
Score
Find the probability that Ryan misses the target and does not score a goal,
(2 marks)
The ratio of apple juice to cranberry juice in a punch
is 27:51. Which ratio is equivalent to 27:51?
3:7
14 to 26
54:92
9 to 17
Answers
Answer:
9 to 17
Step-by-step explanation:
If you divide 21 by 3 you get 9. So divide 51 by 3 you get 17.
Hope it helps!
Answer: 9 to 17 never got Brandie’s pls give to me
Step-by-step explanation:
PLEASE ANSWER ASAP WILL GIVE BRAINLIEST
Answers
Answer:
Translate(1.3, -1)
Scale Factor: 2/3
Step-by-step explanation:
First, perform a dilation about the origin. This will make the original shape smaller.
From the given diagram, we can see that R'S' is 10 units long. RS is 15 units long. Using this information, we can create this ratio.
[tex]\frac{10}{15}[/tex]
This means that Triangle R'S'T' is 2/3 of Triangle RST. Construct lines from the origin (the center of dilation) to each point on the original triangle. Then, find two thirds of that line. The new point will be the new y-coordinate.
The new coordinates will (approx.) be:
R = (-2, 4.7)
S = (-2, -5.3)
Only two coordinates are necessary to perform this translation. As per the graph, this triangle must shift approximately 1.3 units up and 1 unit to the left. Thus, the final translation is:
Translate(1.3, -1)
Scale Factor: 2/3
Carlos bought 515 Euros for his holiday to Germany. He spent £ 412 to obtain these Euros. How many Euros would Carlos have obtained if he spent £500 ?
Answers
Carlos needs a total of 400 Euros for buying 500 Euros.
The total amount available with Carlos for his holiday to Germany = 515 Euros
Amount spent to obtain these 515 Euros = £ 412
As it is clear that for buying 515 Euros he spent 412 Euros.
So, we will first find the Euros spent on buying 1 Euro.
For that, we will use Unitary Method:
So, the total Euros spent for buying 1 Euro will be = (412/515) = 0.8
So, for finding the total Euros spent for obtaining 500 Euros we will simply multiply the total Euros needed by the Euro spent for buying 1 Euro.
Thar will be equal to (0.8 * 500) = 400 Euros.
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What quadrant is 3 and 4 in a graph?
Answers
Both the x- and y-axes have negative values in this quadrant.
The x-axis in the fourth quadrant has positive values, whereas the y-axis has negative numbers.
A two-dimensional Cartesian system's axes split the plane into four infinite areas called quadrants, each of which is limited by two half-axes. These are frequently numbered from 1st through 4th and marked by Roman numerals: I (+; +), II (; +), III (; ), and IV (+; ).
The intersection of the x-axis (the horizontal number line) and the y-axis divides the coordinate plane into four equal pieces in the cartesian system (the vertical number line). These four regions are known as quadrants because they each account for one-quarter of the coordinate plane.
The third quadrant, known as Quadrant III, is located in the bottom left quadrant.
The fourth quadrant, indicated as Quadrant IV, is in the bottom right quadrant.
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Sarah has 3 bags of marbles. Each bag has 16 marbles. If 3/4 of the marbles are blue, what is the total number of blue marbles in the bags?
Answers
Answer: 12
Step-by-step explanation: 3/4 divid by 3