A cone has a volume of 12 cubic inches. What is the volume of a cylinder that the cone fits exactly inside of?
Answers
notice, the volume of a cylinder which is the same height(h) and radius(r) as a cone, is three times as much of that of the cone's.
Related Questions
A rectangle is 6 centimeters longer than is wide and has an area of 280 square centimeters if l represent the length,in centimeters of the rectangle solving which of the following formulas will give the correct value for l?
Answers
W = L - 6
280 = L(L - 6) or 280 = L^2 - 6L
a = 280 = w*(w+6)
280 = w^2+ 6w.
0 = w^2 + 6w - 280
w^2 + 20w - 14w - 280
(w^2 + 20w) - (14w-280)
w(w + 20) - 14(w + 20)
0 = w - 14 OR 0 = w + 20
-20=w OR 14=w
14 must be the answer, you cannot have negative width. Ergo, length = 20.
Width + 6, 14 + 6, 20 = length
Madison deposited a total of $5,000 between two saving accounts bearing simple interest. One of the accounts has an interest rate of 4% while the other rate is 5%. If the total interest earned after one year is $220, find the amount deposited into each of the accounts.
Answers
Solve for x to find the amount invested at 4%
0.04x+250-0.05x=220
0.04x-0.05x=220-250
-0.01x=-30
X=30÷0.01
X=3,000 invested at 4%
5000-3000=2000 invested at 5%
James wants to tile his floor using tiles in the shape of a trapezoid. To make the pattern a little more interesting he has decided to cut the tiles in half along the median. The top base of each tile is 15 inches in length and the bottom base is 21 inches. How long of a cut will John need to make so that he cuts the tiles along the median?
Answers
Answer:18 inches
Step-by-step explanation:
The answer would be 18 inches.
What is the median of a trapezoid?The median of a trapezoid is the segment that connects the midpoints of the non-parallel sides.
The length of the median is the average of the length of the bases.
The top base of each tile is 15 inches in length and the bottom base is 21 inches,
Add the top base and bottom base,
So, 15+21=36
Now, divide that by 2
⇒ 18
Hence, the answer would be 18 inches.
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2(8+h) simplify using distrubtive property
Answers
2(8 + h)
The Distributive Property allows us to multiply any number/variable outside of the parenthesis by all numbers/variables inside the parenthesis.
For example;
2(1 + 2)
2(1) + 2(2)
2 + 4
6.
Let's try this with our current problem.
2(8 + h)
2(8) + 2(h)
16 + 2h (This is your simplified expression)
I hope this helps!
Find the area of the shaded region. The units are in millimeters.
Use 3.14 for π. Round your answer to two decimal places.
Answers
Area of circle=pi*r^2
The radius here is 3 because the diameter is 6.
3.14*3^2
3.14*9=28.26mm^2
The shaded region is 36-28.26=7.74
Final answer: 7.74 mm^2
4 students equally share 3/4 of a pizza. How much of the pizza does each student get?
Answers
3/4 divided by four means you have to take the reciprocal of 3/4 to give you 4/3 and then multiply that by 4 to get 16/3.
To find out how much pizza each of 4 students gets when they equally share 3/4 of a pizza, we divide the amount of pizza (3/4) by the number of students (4). The result is 3/16, which means each student gets 3/16 of the pizza.
Explanation:The question asks how 4 students can equally share 3/4 of a pizza. In mathematics, to divide a quantity equally amongst a group, we perform division. So, in this scenario, we need to divide 3/4 (the pizza) by 4 (the students).
Step 1: Represent the given scenario as a division problem: 3/4 ÷ 4. Step 2: Convert the division into multiplication by the reciprocal. This changes our problem into a multiplication problem: 3/4 * 1/4. Step 3: Multiply the numerators together to get the numerator of the answer: 3 * 1 = 3. Step 4: Multiply the denominators together to get the denominator of the answer: 4 * 4 = 16.
So, the answer of 3/4 ÷ 4 is equal to 3/16. Therefore, each student gets 3/16 of the pizza.
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The formula can be used to find the velocity v in feet per second of an object that has fallen h feet. Find the velocity of an object that has fallen 23 feet. Round your answer to the nearest hundredth.
Answers
v = u +gt
where
u = initial velocity (=0 for a falling object)
g = acceleration due to gravity, 32.2 ft/s²
t = time, s
In terms of distance fallen,
v² = u² + 2gh
where h = distance fallen, ft.
Because h = 23 ft and u = 0, therefore
v² = 2*32.2*23 = 1481.2
v = 38.486 ft/s
Answer: 28.49 ft/s (nearest hundredth)
which algebraic expression represents the phase
Answers
A product is the result when multiplying.
Therefore, the answer here is B.
Find the work done by a force fâ =1.8i^+2.2j^n as it acts on an object moving from the origin to the point râ =56i^+31j^m.
Answers
[tex]W=\mathbf F\cdot\mathbf r=(1.8\,\mathbf i+2.2\,\mathbf j)\cdot(56\,\mathbf i+31\,\mathbf j)[/tex]
[tex]W=169\,\text{Nm}[/tex]
The work done by the force is found by taking the dot product of the force vector and the position vector. This is achieved by multiplying corresponding components of the vectors and then adding the results together.
Explanation:To find the work done by the force, we use the formula Work = Force . Displacement, where the '.' signifies a dot product. In this case, the force vector is fâ = 1.8i^ + 2.2j^ and the position vector, râ = 56i^ +31j^. The dot product between force fâ and the displacement (position vector) râ is calculated by multiplying corresponding i and j components and then adding them together. Therefore, Work = (1.8i^.56i^) + (2.2j^.31j^). Perform the multiplication for both components and then add the results to get the total work done by the force.
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The function g(x) = 3(x - 3)2 + 2 will translate 3 units to the right. True or False?
Answers
A set of data with a mean of 45 and a standard deviation of 8.3 is normally distributed. Find the value that is +1 standard deviation away from the mean.
Answers
Answer:
53.3
Step-by-step explanation:
Add one standard deviation to the mean:
45 +1(8.3) = 53.3
Answer:
53.3
Step-by-step explanation:
+1 standard deviation away from the mean is 45+1(8.3)
which property of congruence would prove that BD ≈ BD?
the reflexive property of congruence
the symmetric property of congruence
the transitive property of congruence
None of the choices are correct.
Answers
Use appropriate algebra and theorem 7.2.1 to find the given inverse laplace transform. (write your answer as a function of t.) −1 s (s − 5)(s − 6)(s − 30)
Answers
Based on the given, the useful transformation equation is shown in the attached picture. The given equation is
[tex] \frac{-1}{s(s-5)(s-6)(s-30)} [/tex]
Breaking it into partial fractions,
[tex] \frac{-1}{s} * \frac{1}{s-5} * \frac{1}{s-6} * \frac{1}{s-30} [/tex]
From the given transformation equation:
-1/s ⇔ -e^0t ⇔ 1
1/(s-5) ⇔ e^-(-5t) ⇔ e^5t
1/(s-6) ⇔ e^-(-6t) ⇔ e^6t
1/(s-30) ⇔ e^-(-30t) ⇔ e^30t
Therefore, the laplace equation is equal to 1*e^5t*e^6t*e^30t which is simplified into e^41t,
Which figure has the correct lines of symmetry drawn in?
Answers
If you were to fold the hexagon in half, it would be symmetrical when folded from vertex-to-vertex and when folded from the midpoint of a side to the opposite side.
This means that while the first and third images are valid lines of symmetry, they are incomplete because they're missing the second set of lines from side-to-side.
The second image also has valid lines of symmetry, but it doesn't have all of them.
Thus, the answer is the fourth image.
Pick the correct description of the line 5x + 3y=15
Answers
3y = -5x + 15
y = -5/3x + 5
slope is -5/3
y int (where ur line crosses the y axis) is (0,5)
x int (where ur line crosses the x axis) is (3,0)
ur line will be slanting downward because of ur negative slope
Answer:
The correct description is [tex]y=5-\frac{5x}{3}[/tex]
Step-by-step explanation:
In this case, firts we have to organize the equation in the normal way, where y is alone in one side, this is:
[tex]5x+3y=15\\3y=15-5x\\y=\frac{15}{3}-\frac{5x}{3} \\y=5-\frac{5x}{3}[/tex]
The correct description is [tex]y=5-\frac{5x}{3}[/tex]
Now we can see that the slope of the equation is [tex]-\frac{5}{3}[/tex]
The pressure,p, of a gas varies inversely with its volume,v. Pressure is measured in units of pa. Suppose that a particular amount of a gas is initially at a pressure of 104 pa at a volume of 108 L. If the volume is expanded to 432 L, what will the new pressure be
Answers
In this case, the gas have 108L volume in 104pa pressure and you asked how much the pressure if the gas made into 432L volume. Since the volume is bigger it should be clear that the pressure would be lower.
The equation of the new pressure would be : 104pa x (108L / 432L) = 104pa x 0.25= 26pa
Answer: 26pa
If you were to use the substitution method to solve the following system, choose the new equation after the expression equivalent to y from the second equation is substituted into the first equation.
2x – 7y = 4
3x + y = –17
Answers
Equation 2: [tex]3x+y=-17[/tex]
Rearranging equation 2 to make 'y' the subject
[tex]y = -17 - 3x[/tex] ⇒ Call this Equation 3
Substituting Equation 3 into Equation 1
[tex]2x-7(-17-3x)=4[/tex]
[tex]2x+119+21x=4[/tex]
[tex]23x+119=4[/tex]
[tex]23x=4-119[/tex]
[tex]23x=-115[/tex]
[tex]x=-5[/tex]
Then substitute x = -5 into either Equation 1 or Equation 2 to solve for 'y'
[tex]2x-7y=4[/tex]
[tex]2(-5)-7y=4[/tex]
[tex]-10-7y=4[/tex]
[tex]-7y=4+10[/tex]
[tex]-7y=14[/tex]
[tex]y=-2[/tex]
Note: the original question did not attach the option for the equation after substitution so you might want to follow the working out here carefully and match it with the options given.
Calculus AB
lim x-->4 sqrt(x+5)-3 / 4-x
The answer is apparently -1/6
How do you solve this
Answers
[tex] \lim_{x \to 4} \frac{\sqrt{x+5}-3}{4-x}[/tex]
that means as x approaches 4
if we sub 0 for x we get
0/0
and intermitent form
use l'hopital's rule
so
take the derivitive of the top and bottom seperatly
l'hopitals rule is something like
if [tex] \lim_{x \to n} \frac{f(x)}{g(x)}[/tex] results in 0/0 or -∞/∞ or∞/∞ then keep doing it until f(n)/g(n) gives a form that isn't intermitent
so
take derivitive of top and bottom
[tex]\dfrac{\frac{1}{2\sqrt{x+5}}}{-1}[/tex]
now, if we subsitute 4 for x we get
[tex]\dfrac{\frac{1}{2\sqrt{4+5}}}{-1}[/tex]=
[tex]\dfrac{\frac{1}{2\sqrt{9}}}{-1}[/tex]=
[tex]\dfrac{\frac{1}{2(3)}}{-1}[/tex]=
[tex]\dfrac{\frac{1}{6}}{-1}[/tex]=
[tex]\dfrac{1}{-6}=\dfrac{-1}{6}[/tex]
What is the difference of the polynomials?
(8r6s3 – 9r5s4 + 3r4s5) – (2r4s5 – 5r3s6 – 4r5s4)
Answers
8r^6s^3 - 9r^5s^4 + 3r^4s^5 - 2r^4s^5 + 5r^3s^6 + 4r^5s^4 =
8r^6s^3 -5r^5s^4 + r^4s^5 + 5r^3s^6 <==
Answer: The required difference is [tex]8r^6s^3-5r^5s^4+r^4s^5+5r^3s^6.[/tex]
Step-by-step explanation: We are given to find the difference of the polynomials as follows :
[tex]DP=(8r^6s^3-9r^5s^4+3r^4s^5)-(2r^4s^5-5r^3s^6-4r^5s^4)~~~~~~~~~~~~~~~~~~~(i)[/tex]
To find the given difference, we need to choose the terms with same poers of the unknown variables r and s and then subtract their coefficients.
The difference (i) is as follows :
[tex]DP\\\\=(8r^6s^3-9r^5s^4+3r^4s^5)-(2r^4s^5-5r^3s^6-4r^5s^4)\\\\=8r^6s^3-9r^5s^4+3r^4s^5-2r^4s^5+5r^3s^6+4r^5s^4\\\\=8r^6s^3+(4-9)r^5s^4+(3-2)r^4s^5+5r^3s^6\\\\=8r^6s^3-5r^5s^4+r^4s^5+5r^3s^6.[/tex]
Thus, the required difference is [tex]8r^6s^3-5r^5s^4+r^4s^5+5r^3s^6.[/tex]
The area of a rectangular patio is 5 5/8 square yards, and it's length is 1 1/2 yards. What is the patio's width in yards?
Answers
First, let's take a look at our question, and evaluate it.
"The area of a rectangular patio is 5 5/8 square yards, and it's length is 1 1/2 yards. What is the patio's width in yards?"
To clarify this problem, we are looking for the patio's width.
Let's first understand what the area of a rectangular shape is.
The formula for the area of a rectangle is "Length times Width", or "L • W".
So this is how the equation should look like:
A = L • W
We have our area, 5 5/8, and we have our length, 1 1/2.
To make things more simple, let's convert our fractions to decimals. Now, to convert our fractions to decimals, let's set our denominators (the numbers on the bottom of a fraction) equal to another fraction, with x as the numerator (the numbers on the top of a fraction) and 100 as the denominator.
So we have 1/2 and x/100. Divide 100 by 2 to find x (as 1/2 of anything is dividing by 2).
100 / 2 = 50, so 1 1/2 = 1.50 as a decimal.
Now, let's try 5/8.
1/8 = 0.125, so multiply 0.125 by 5.
0.125 • 5 = 0.625.
5 5/8 = 5.625 as a decimal.
So, now we have our equation:
A = L • W
Plug in our numbers.
5.625 = 1.50x
To isolate and solve for x, we need to divide both sides by 1.50, so let's do that.
5.625 / 1.50 = 3.75
1.50x / 1.50 = x
We are now left with:
x = 3.75
Your answer is:
The patio's width is 3.75 yards.
I hope this helps!
How to solve 7.86 x 4.6
Answers
Two garden plots are to have the same area. One is square and one is rectangular. The rectangular plot is 2 meters wide and 18 meters long. How long is one side of the of the square garden plot in meters?
Answers
area of rectangle = l x w
area of rectangle = 2*18 = 36 square meters
area of square = S^2, or s = square root(area)
sqrt(36) = 6
length of side of square = 6 meters
The side length of the square garden plot with the same area as a rectangular plot of dimensions 2 meters by 18 meters is 6 meters.
The student is asking about finding the length of a side of a square garden plot that has the same area as a rectangular garden plot measuring 2 meters wide by 18 meters long. To find the area of the rectangular plot, we multiply the length by the width: 2 meters imes 18 meters = 36 square meters.
Since the area of the square plot must equal the area of the rectangular plot, we can use the formula for the area of a square, A = s2, where s is the side length of the square. Therefore, to find the side length of the square plot, we take the square root of the area of the rectangular plot:
√(36 square meters) = 6 meters
So, the side length of the square garden plot is 6 meters.
Suppose that a particular artillery piece has a range r = 8320 yards . find its range in miles. use the facts that 1mile=5280ft and 3ft=1yard.
Answers
The range in miles is 4.72 mile
What do you mean by 1 mile?mile, any of various units of distance, such as the statute mile of 5,280 feet (1.609 km). It originated from the Roman mille passus, or “thousand paces,” which measured 5,000 Roman feet.
Given : range= 8320 yards
1 mile= 5280 feet
3 feet= 1 yard
Now,
8320yards X 3ft = 24,960
Now, divide that by 5,280ft in a mile
= 24960/5280
= 4.72 miles
Hence, range is 4.72 miles.
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Final answer:
To convert the artillery piece's range of 8320 yards to miles, you multiply by 3 to change yards to feet and then divide by 5280 to convert feet to miles, resulting in a range of approximately 4.727 miles.
Explanation:
To find the artillery piece's range in miles, starting with its range in yards, we need to use unit conversion factors. Knowing that 1 mile equals 5280 feet and 3 feet equals 1 yard, we can set up a conversion to calculate the distance in miles.
Steps to Convert Yards to Miles:
Convert the given distance from yards to feet by multiplying the number of yards by 3 (since there are 3 feet in a yard).Next, convert the distance from feet to miles by dividing the number of feet by 5280 (since there are 5280 feet in a mile).For an artillery range of 8320 yards:
8320 yards is equivalent to 8320 yards * 3 feet/yard = 24960 feetThen 24960 feet / 5280 feet/mile gives us the range in miles.When you divide 24960 by 5280, you get 4.727 miles (rounded to three decimal places).
Helpp! -- A piece of wire 5 inches long is to be cut in two pieces. One piece is x inches long and is to be bent into the shape of a square. The other piece is to be bent in the shape of a circle. Find an expression for the total area made up by the square and the circle as a function of x.
Answers
since, we know that for the circle, the perimeter is s+s+s+s or 4s, then 4s = x and so on.
now, for the circle, the perimeter is just the circumference, circumference of a circle is 2πr, thus 2πr = 5-x and so on.
anyway... so... the equation of the area made by those two in x-terms, is just their sum... so let's do that then
[tex]\bf \pi \left( \cfrac{5-x}{2\pi } \right)^2\quad +\quad \cfrac{x^2}{4^2}\\\\ -------------------------------\\\\ \pi\cdot \cfrac{(5-x)^2}{(2\pi )^2}+\cfrac{x^2}{4^2}\implies \cfrac{\pi (5-x)^2}{2^2\pi^2}+\cfrac{x^2}{4^2}\implies \cfrac{(5-x)^2}{4\pi}+\cfrac{x^2}{4^2} \\\\\\ \textit{let's use the LCD of }4^2\pi \textit{ to add them up} \\\\\\ \cfrac{4(5-x)^2+\pi x^2}{4^2\pi }\implies \cfrac{4(5-x)^2+\pi x^2}{16\pi }[/tex]
now, you can expand the squared binomial on the numerator, but there will not be any like-terms to simplify, so, it won't make much difference, so.... you can expand it or not.
The expression for the total area made up by the square and the circle as a function of x is f(x) = x^2/16 + (25 - 10x + x^2)/(4*Pi) square inches.
Explanation:To solve this problem, you need to know the formulas for the areas of a square (Area = side^2) and a circle (Area = pi * radius^2). If a piece of the wire with length x inches is to be bent into the shape of a square, then each side of the square will be x/4 inches long (since a square has 4 equal sides). Therefore, the area of the square = (x/4)^2 = x^2/16 sq.inches.
The remaining piece of the wire is 5-x inches long and is to be bent into the shape of a circle. The circumference of the circle is 5-x inches (since it uses the remaining wire), therefore the radius of the circle is (5-x)/(2*Pi) inches. Therefore, the area of the circle = Pi*((5-x)/(2*Pi))^2 = (25 - 10x + x^2)/(4*Pi) sq.inches.
The total area made up by the square and the circle is the sum of their areas, therefore the function representing the total area f(x) = x^2/16 + (25 - 10x + x^2)/(4*Pi) sq.inches.
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What is the value of of angle BAD:
30◦
5◦
15◦
20◦
Answers
Davis Construction is building a new housing development. They begin by mapping the development out on a coordinate grid. They place one of the two swimming pools at coordinate (-16, -25) and the other at (18, 23). If they want the club house to be exactly halfway between the two pools, find the coordinate point for the clubhouse
Answers
To solve this problem, we can use the following ratio formulas to find for the coordinates of the club house:
x = [m / (m + n)] (x2 – x1) + x1
y = [m / (m + n)] (y2 – y1) + y1
Where,
m and n are the ratios (0.5 and 0.5 each since the club house are to be located exactly halfway)
x1 and y1 are the x and y coordinates of the 1st pool (-16, -25)
x2 and y2 are the x and y coordinates of the 2nd pool (18, 23)
Substituting:
x = [0.5 / (0.5 + 0.5)] (18 - -16) + -16
x = 1
y = [0.5 / (0.5 + 0.5)] (23 - -25) + -25
y = -1
Therefore the club house should be located at coordinates (1, -1).
0.025 in scientific notation (step by step)
Answers
In this case, you must move the decimal to the right by 2 place values.
Then, write the number again, this time with the decimal placed after the first nonzero digit. In this case, write 2.5
In scientific notation, you have to multiply that number by 10^x
The x value is the number of place values you moved. In this case it is 2.
If you moved to the right, add a negative sign before it. If you moved the decimal to the left, keep it as a positive value.
Final answer: 2.5 x 10^-2
0.025 in scientific notation is 2.5 × 10⁻².
To express 0.025 in scientific notation, we need to convert the decimal form to a number multiplied by a power of 10.
Here's how you can do it step by step:
Start with the given decimal number: 0.025.
Identify the non-zero digit. In this case, it is 2.
Move the decimal point to the right until there is only one non-zero digit to the left of the decimal point. Count the number of places you moved the decimal point. In this case, we moved the decimal point two places to the right.
0.025 -> 2.5
Write the non-zero digit (2.5) as a decimal number.
Finally, express the power of 10 that represents the number of places you moved the decimal point. Since we moved the decimal point two places to the right, the power of 10 is -2.
Putting it all together, we have:
0.025 = 2.5 × 10⁻²
Therefore, 0.025 in scientific notation is 2.5 × 10⁻².
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If all of the diagonals are drawn from a vertex of a pentagon, how many triangles are formed?
Answers
A picture helps. There are 2 non-adjacent vertices, so two diagonals can be drawn, resulting in 3 triangles.
Drawing all diagonals from one vertex of a pentagon to the non-adjacent vertices creates three triangles within the pentagon.
When all the diagonals are drawn from one vertex of a pentagon, it divides the pentagon into several triangles.
A pentagon has five sides, and when selecting a single vertex, we can draw diagonals to the non-adjacent vertices. In this case, there are three non-adjacent vertices, which means we can draw three diagonals, thus creating three triangles inside the pentagon.
This is because each diagonal, combined with two sides of the pentagon, forms a triangle.
John predicts the basketball team will score 68 points. If the basketball team actually scores 49 points, what is John's percent error? Round your answer to the nearest tenth of a percent.
Answers
%error=100(68-49)/49
%error≈38.8%
Since this is positive, John's error overestimated the teams score by about 38.8%
What's the next value?
1 I 2 L 3 F 4
Answers
Brainliest answer plzzzz