Answer:
[tex]W=22652.98ft-lb[/tex]
Step-by-step explanation:
We are given that
Height of tank=6feet
Diameter of tank=8 feet
Radius of cone,r=d/2=8/2=4 feet
Let a layer of thickness dy at distance yr from the bottom at origin
y=6 feet
Using similar triangle property
[tex]\frac{r}{y}=\frac{4}{6}=\frac{2}{3}[/tex]
[tex]r=\frac{2}{3}y[/tex]
Weight of water=62.4 pounds per cubic foot
Now,
Weight of layer=[tex]62.4\times \pi r^2 h=62.4(\frac{4}{9}\pi y^2 dy[/tex]
Now, work done to fill the tank from a depth of 4 feet to a depth of 6 feet is given by
[tex]W=\int_{a}^{b}62.4\times \frac{4}{9}\pi y^2(y) dy=\int_{4}^{6}62.4\times \frac{4}{9}\pi y^3 dy[/tex]
[tex]W=\frac{62.4\times 4\pi}{9}[\frac{y^4}{4}]^{6}_{4}[/tex]
[tex]W=\frac{249.6\pi}{36}(6^4-4^4)[/tex]
[tex]W=22652.98ft-lb[/tex]
Naron is 3 times older than his sister. In 2 years, Naron will be twice as old as his sister. How old is each now?
Answer:
A possible answer is that Naron is 6 yrs old and his sister is 2 yrs old.
Step-by-step explanation:
6 is 3 times as much as 2
(6+2)/2=2+2
8/2=4
Answer:
Naron is 6 years old and his sister is 2 years old
Step-by-step explanation:
Algebra 1 unit 4 mid quiz
The inequality that represents this graph is y < 2x + 2.
What are inequalities and their types?Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.
The symbol a < b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
a is less than or equal to b when a notation like a ≤ b.
a is bigger or equal value of an is indicated by the notation a ≥ b.
The dotted line represents strictly less than or greater than.
From the graph, we can conclude that when x = 0, y = 2, and when x = 1 y = 4, and values of y are strictly less.
∴ The inequality that represents this graph is y < 2x + 2.
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if x=-3 is the only x-incercept of the graph of a quadratic equation which statement best describes the discrinant of the equation
Answer:
The discriminant must be zero.
Step-by-step explanation:
Quadratic Equation
The standard representation of a quadratic function is:
[tex]f(x)=ax^2+bx+c[/tex]
where a,b, and c are constants.
The zeros, roots, or x-intercepts can be found by solving the equation:
[tex]ax^2+bx+c=0[/tex]
We can use the quadratic formula to find the roots:
[tex]\displaystyle x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
Note this formula gives us two different roots if the square root is non-zero.
The only way there can be only one x-intercept is because the square root is zero.
If the square root is zero, then
[tex]b^2-4ac =0[/tex]
The expression is called the discriminant.
Thus, if x=-3 is the only x-intercept of the graph of a quadratic function, then the discriminant must be zero.
Which postulate or theorem proves that these two triangles are
congruent?
HL Congruence Theorem
SAS Congruence Postulate
ASA Congruence Postulate
AAS Congruence Theorem
Answer:
ASA
Step-by-step explanation:
Took the test.
I used 1/3 of a bottle of wax to wax 3/4 of a car. How many cars can I wax with one bottle? Please helppp
Answer:
2.25 cars are waxed with one bottle
Step-by-step explanation:
1/3 * 3 = 1
3/4 * 3 = 9/4
9/4 = 2.25
I NEED HELP
(-8, 6); slope = 1/4
6 = 1/4(-8) +b
6 = -2 +b
8 = b
y = 1/4x +8The equation of this line having slope 1/4 and points (-8,6) is y = (1/4)x + 8.
What is slope ?Slope is the rate of change.It can also be thought of as rise over run.
According to the given question slope(m) is 1/4 and point is (-8,6).
We know equation of a line in slope intercept form is y = mx + b, where b is the y intercept.
∴ 6 = (-8)1/4 + b.
6 = - 2 + b.
b = 8.
Now the equation of this line in slope intercept from can be written as
y = (1/4)x + 8.
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Help math hv 30 minutes
Answer:
ACD
Step-by-step explanation:
(0,0) shows that the cost is 0 when the weight is 0,
(0.5,2) shows that when the weight is 0.5 pounds the cost is 2 dollars
same concept for D
A line is drawn on the coordinate plane that passes through the point (10,1) and has a slope of -0.5. The y-intercept of the line is
Find the value of x:
To find the value of x, bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to find the result. There you go!
How my calories are in 48 oz if tea
Answer:
2 calories
Step-by-step explanation:
yes
Answer:
The answer you are looking for is 2 calories.
Step-by-step explanation:
1 serving 8 fl oz cup (238 g)
Can anybody help and get this right I keep getting it wrong ..
Answer:its d
Step-by-step explanation:
Convert the fraction to a decimal: 1/6 =
Answer:
1/6 as a decimal is 1.66 or 1.6 repeating.
40% of 250 is equal to 60% of what number
Answer:
24
Step-by-step explanation:
250% × ? = 60
? =
60 ÷ 250% =
60 ÷ (250 ÷ 100) =
(100 × 60) ÷ 250 =
6,000 ÷ 250 =
24
Si tienes 5 manzanas para comer durante la semana y te comes el 20% el primer día cuántas manzanas quedan para el resto de la seman?
Answer: El o Ella tiene 4 manazanas izquierda comer para el semana
Step-by-step explanation: Si necesitas ayuda con algo más estoy disponible generalmente de 9 a.m. a 3:50 p.m.
The number of apples left to eat are equivalent to 4.
What is percentage?In mathematics →
a percentage is a number or ratio expressed as a fraction of 100.it is often denoted using the percent sign "%".Given is that you have 5 apples to eat during the week and you eat 20% on the first day.
Assume the number of apples left are {x}. So, we can write -
{x] = 5 - 20% of 5
{x} = 5 - (20/100) x 5
{x} = 5 - 1
{x} = 4
Therefore,
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{Question in english -
If you have 5 apples to eat during the week and you eat 20% on the first day, how many apples are left for the rest of the week?}
A recipe calls for 3 3/4 cups of flour. How many cups will you need if you are preparing 5 batches of the recipe?
Answer:
18.75 cups of flour
Step-by-step explanation:
The answer is 18.75 cups of flour as you have to multiply 5 by 3 3/4. The result will be 18.75. Hope it helps!
You need 18 3/4 cups of flour, to make 5 batches of the recipe.
What is a fraction?An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.
If one batch of the recipe calls for 3 3/4 cups of flour, then 5 batches of the recipe will require:
5 × 3 3/4 cups
To multiply a whole number by a mixed number, we first convert the mixed number to an improper fraction:
3 3/4 = (4 × 3 + 3) / 4 = 15/4
Now we can multiply:
5 × 15/4 = (5 × 15) / 4 = 75/4
To convert this fraction to a mixed number, we divide the numerator by the denominator and write the remainder as a fraction:
75 ÷ 4 = 18 remainder 3
So, 75/4 is equal to 18 3/4.
Therefore, 5 batches of the recipe will require:
18 3/4 cups of flour.
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Find the slope of (2,-3) (-4,7)
Answer:
m = 139167 / 329 = 423 / 1 = 423
Step-by-step explanation:
\displaystyle\int_{-\infty}^\infty e^{-x^2}dx = \sqrt{\pi}
\displaystyle \sum_{n} \frac{1}{n^s} = \prod_{p} {\frac{1}{1 - \frac{1}{p^s}}}
\displaystyle n! = \int_{0}^{\infty} {x^n e^{-x} \,dx}
F(n) = \frac{(\varphi)^n - (-\frac{1}{\varphi})^n}{\sqrt{5}}
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whats the degree of the polynomial 5a-2b^2+1
Answer:
hope it helps..
Step-by-step explanation:
PLEASE THANK MY ANSWER
45 degrees+2k+k=180
can you help me with this?
Answer:
k=45
Step-by-step explanation:
45+2k+k=180
Step 1: Simplify both sides of the equation.
45+2k+k=180
(2k+k)+(45)=180(Combine Like Terms)
3k+45=180
3k+45=180
Step 2: Subtract 45 from both sides.
3k+45−45=180−45
3k=135
Step 3: Divide both sides by 3.
3k/3=135/3
k=45
Which expression is another way to write 10,000,000? 10 × 10 × 10 × 10 × 10
10 × 10 × 10 × 10 × 10 × 10
10 × 10 × 10 × 10 × 10 × 10 × 10
10 × 10 × 10 × 10 × 10 × 10 × 10 × 10
Answer:
Step-by-step explanation:
10^6
Answer:
10^6
Step-by-step explanation:
Help ASAP). Which relation is a function. Where the hand is at thats graph A across is graph B. The graph under graph a is ( graph C). Under graph B is (graph D). Need answer now please and thank you. [ I chose B but not 100% sure]
If martha is walking 9meters south and turns and walks 10meters west how far is she from her starting point?
Answer:
She is 13.45 meters from her starting point.
Step-by-step explanation:
Use Pythagorean Theorem (a^2+b^2=c^2) so 9^2+10^2=c^2. Solve it algebraically and you get c= 13.45 (rounded to nearest hundredth).
Point A is at (-2, 4) and point M is at (2.5, 3.5).
Point M is the midpoint of point A and point B.
What are the coordinates of point B?
Answer:
Coordinates of point B: (7, 3)
Step-by-step explanation:
Given M(2.5, 3.5) as midpoint of AB, and A(-2, 4),
let [tex] A(-2, 4) = (x_2, y_2) [/tex]
[tex] B(?, ?) = (x_1, y_1) [/tex]
[tex] M(2.5, 3.5) = (\frac{x_1 +(-2)}{2}, \frac{y_1 +(4)}{2}) [/tex]
Rewrite the equation to find the coordinates of B
[tex] 2.5 = \frac{x_1 - 2}{2} [/tex] and [tex] 3.5 = \frac{y_1 + 4}{2} [/tex]
Solve for each:
[tex] 2.5 = \frac{x_1 - 2}{2} [/tex]
[tex] 2.5*2 = \frac{x_1 - 2}{2}*2 [/tex]
[tex] 5 = x_1 - 2 [/tex]
[tex] 5 + 2 = x_1 - 2 + 2 [/tex]
[tex] 7 = x_1 [/tex]
[tex] x_1 = 7 [/tex]
[tex] 3.5 = \frac{y_1 + 4}{2} [/tex]
[tex] 3.5*2 = \frac{y_1 + 4}{2}*2 [/tex]
[tex] 7 = y_1 + 4 [/tex]
[tex] 7 - 4 = y_1 + 4 - 4 [/tex]
[tex] 3 = y_1 [/tex]
[tex] y_1 = 3 [/tex]
Coordinates of point B: (7, 3)
Answer:
Coordinates of point B: (7, 3)
Step-by-step explanation:
Given M(2.5, 3.5) as midpoint of AB, and A(-2, 4),
Rewrite the equation to find the coordinates of B
Coordinates of point B: (7, 3)
Question
Example
Step by Step
Jennifer is saving money to buy a bike. The bike costs
$213. She has $123 saved, and each week she adds $18
to her savings.
How long will it take her to save enough money to buy
the bike?
It will take her
weeks _____to save for the bike.
Answer:
5
Step-by-step explanation:
18x5=90+123=213.
An acre is a unit of measure for area. One acre ie equal to 43,560 square feet. Often, an acre is a rectangle that measures 660 feet by 66 feet. However, the length and width of the rectangle can vary. An acre can actually have any shape, as long as it measures exactly 43,560 square feet. Rachel purchased 1/5 acre of land in the shape of an isosceles triangle. What is the area of the land Rachel purchased?
Answer:
area of land purchased =247
The area of the land Rachel purchased is approximately 10,055.64 square feet.
How to calculate the area?We can start by finding the area of one acre in square feet, which is given as 43,560 square feet.
To find the area of 1/5 acre, we can divide 43,560 by 5, which gives us 8,712 square feet.
Since Rachel's land is in the shape of an isosceles triangle, we need to find the base and height of the triangle in order to calculate its area. Let's call the length of the base "b" and the height "h".
We know that the area of a triangle is given by the formula:
Area = (1/2) x base x height
So, we can rearrange this formula to solve for the height:
height = 2 x Area / base
Now we can substitute in the values we know:
Area = 8,712 square feet
base = unknown
height = unknown
We also know that the triangle is isosceles, which means that two of the sides are equal in length. Let's call the length of one of these sides "s". Then the length of the base can be expressed in terms of s as:
base = 2s
We can use the Pythagorean theorem to find the height in terms of s:
s² + (h)² = (2s)²
s² + h² = 4s²
h² = 3s²
h = s x √(3)
Now we can substitute this expression for the height in terms of s into the formula we derived for the area:
Area = (1/2) x base x height
Area = (1/2) x 2s x s x √(3)
Area = s² x √(3)
We know that the area of the triangle is 1/5 of an acre or 8,712 square feet, so we can set this equal to the expression we just derived for the area and solve for s:
s² x √(3) = 8,712
s² = 8,712 / √(3)
s = √(8,712 / √(3))
Now that we know the length of one of the equal sides of the isosceles triangle, we can find the length of the base by multiplying by 2:
base = 2s
base = 2 x √(8,712 / √(3))
Finally, we can substitute in the values we just found for the base and height into the formula for the area of the triangle:
Area = (1/2) x base x height
Area = (1/2) x 2 x √(8,712 / √(3)) x √(3) x √(8,712 / √(3))
Area = 2 x 8,712 / √(3)
Area = 17,424 / √(3)
Therefore, the area of the land Rachel purchased is approximately 10,055.64 square feet.
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Perry is responsible for distributing soccer balls to the kids at soccer camp. During practice, Perry would like each group of 5 children to share two soccer balls. How many soccer balls does Perry need if 25 kids attend camp?
Q: Perry is responsible for distributing soccer balls to the kids at soccer camp. During practice, Perry would like each group of 5 children to share two soccer balls. How many soccer balls does Perry need if 25 kids attend camp?
A: 20 soccer balls
Hope this helped!
y - 5 = 1/10 (x – 10)
How do you rewrite the equation in slope-intercept form?
Answer.
Y=|10x-100|+5
Select each transformation that carries a square onto itself.
a reflection over one of the square's sides
3 rotation of 180' clockwise about the square's center
a rotation of 90: clockwise about the squares center
a rotation of 180: clockwise about one of the squares vertices
: reflection over one of the souare s diagonals
Answer:
1. a reflection over one of the square's sides
2. a rotation of 90: clockwise about the squares center
3. a rotation of 180' clockwise about the square's center
Step-by-step explanation:
I did a test :)
The wind is blowing N 35.0 degrees W at 1.60 * 10^2 mph. A plane has an engine speed of 3.20 * 10^2 mph. Where should the pilot point the plane in order to fly straight W?
Answer: 24.2° SouthWest
Step-by-step explanation:
First step: DRAW A PICTURE of the vectors from head to tail (see image)
I created a perpendicular from the resultant vector to the vertex of the given vectors so I could use Pythagorean Theorem to find the length of the perpendicular. Then I used that value to find the angle of the plane.
Perpendicular (x):
cos 35° = adjacent/hypotenuse
cos 35° = x/160
→ x = 160 cos 35°
Angle (θ):
sin θ = opposite/hypotenuse
sin θ = x/320
sin θ = 160 cos 35°/320
θ = arcsin (160 cos 35°/320)
θ = 24.2°
Direction is down (south) and left (west)
translation is the point (2, −6). At what coordinates is the image of point (−3, −2) located under the same translation?
Answer:
hey
Step-by-step explanation:
A truck requires 1 gallon of gas to cover a distance of 10 miles. How many gallons of gas will it take to cover 200 miles?
Answer: 20
Step-by-step explanation:
Answer:
20 gal of gas
Step-by-step explanation:
200÷10=
20