We are given a cylinder and a cone of same volume i.e
[tex] \longrightarrow[/tex] Volume of cone = Volume of cylinder
And also the diameter of the cylinder is given 4 inches
[tex] \longrightarrow[/tex] Radius = [tex]\sf \dfrac{Diameter}{2}[/tex]
[tex] \longrightarrow[/tex] Radius = [tex] \sf\dfrac{4}{2}[/tex]
[tex] \longrightarrow[/tex] Radius = 2 inches
The height of cylinder is 3 inches. And the diameter of the cone is 6 inches
[tex] \longrightarrow[/tex] Radius = [tex]\sf\dfrac{Diameter}{2} [/tex]
[tex] \longrightarrow[/tex] Radius = [tex] \sf\dfrac{6}{2}[/tex]
[tex] \longrightarrow[/tex] Radius = 3 inches
First, let us recall the Formulas of volume of cylinder and cone:
[tex] \quad\longrightarrow\quad \sf {Cone = \dfrac{1}{3}\pi r^2 h }[/tex]
[tex] \quad\longrightarrow\quad \sf {Cylinder = \pi r^2 h }[/tex]
Now, we know that the volume of cone is equal to the volume of cylinder
[tex] \implies\quad \sf{\dfrac{1}{3}\pi r^2 h = \pi r^2 h }[/tex]
On putting the values:
[tex] :\implies\quad \sf{\dfrac{1}{3}\pi \times 3^2 \times h = \pi \times 2^2 \times 3 }[/tex]
[tex] :\implies\quad \sf{\dfrac{1}{\cancel{3}}\times 3.14 \times\cancel{ 9 }\times h = 3.14 \times 4 \times 3 }[/tex]
[tex] :\implies\quad \sf{3.14 \times 3 \times h = 3.14 \times 12 }[/tex]
[tex]: \implies\quad \sf{ h = \dfrac{ \cancel{3.14} \times 12 }{ \cancel{3.14} \times 3} }[/tex]
[tex] :\implies\quad \sf{ h =\cancel{ \dfrac{12}{3}}}[/tex]
[tex] :\implies\quad \underline{\underline{\pmb{\sf{h = 4 inches }}} }[/tex]
ㅤㅤㅤㅤㅤ~Hence the height of the cone is 4 inches.
Writing Equations of Parallel Lines
y
5
What is the equation of the line parallel to the given line
with an x-intercept of 4?
y =
4
V
3
2
-5 4 3 2 1
2
5
-1
-2
-3
-5
Intro
Done
Answer:
y = 4x -16
Step-by-step explanation:
The equation of the parallel line can be written from the given x-intercept when we know its slope. The slope will be the same as that of the graphed line. It can be found using the slope formula with the marked points (-3, -3) and (-1, 5).
m = (y2 -y1)/(x2 -x1)
m = (5 -(-3))/(-1 -(-3)) = 8/2 = 4 . . . . . slope of the lines
The point-slope equation for the line with slope 4 through point (4, 0) will be ...
y -k = m(x -h) . . . . line with slope m through point (h, k)
y -0 = 4(x -4) . . . . line with slope 4 through the given x-intercept
y = 4x -16 . . . . . . expanded to slope-intercept form
32. Michelle invested $10,000 in an account that earns 8.5% interest that is compounded monthly. Write an exponential model for the balance of the account, then determine the amount of money in the account in 15 years. Answer: Equation:
Answer:
$25,626.53
Step-by-step explanation:
You are going to want to use the compound interest formula, which is shown below.
P = initial balance
r = interest rate (decimal)
n = number of times compounded annually
t = time
First, change 8.5% into a decimal:
8.5% -> -> 0.085
Now lets plug in the values into the equation
Lastly, subtract the total from the initial balance:
Michelle earned $25,626.53 in interest.
Can someone help me with these questions
Answer:
Step-by-step explanation:
When you take the n-th root of a number, you can rewrite the expression by taking it to the 1/n-th power. For example:
[tex]\sqrt[n]{x} =x^\frac{1}{n}[/tex]
For the first expression, we can use this proprtery to get:
[tex]\sqrt[5]{a^x} =(a^x)^\frac{1}{5}[/tex]
Using exponent rules, you can combine the exponents by simply multiplying them to get:
[tex]a^\frac{x}{5}[/tex]
Moving on to the second expression. It is now the square root, or equivalently a 1/2 power. If we break up the terms under the radical into powers of 2, we can cancel a lot of the terms:
[tex]\frac{\sqrt{81a^3b^1^0} }{\sqrt{3}a } =\frac{\sqrt{81a^2*a*b^1^0} }{\sqrt{3}a }[/tex]
The a^2 and b^10 can be taken out of the radical because they have perfect roots:
[tex]\frac{\sqrt{81a^2*a*b^1^0} }{\sqrt{3}a }=ab^5\frac{\sqrt{81a} }{\sqrt{3}a }[/tex]
The square root of 81 has a perfect root of 9. We have:
[tex]ab^5\frac{\sqrt{81a} }{\sqrt{3}a }=9ab^5\frac{\sqrt{a} }{\sqrt{3}a }[/tex]
You can divide 9 and the square root of 3 by breaking up 9 into a product:
[tex]\frac{(3*3)ab^5}{\sqrt{3} } \frac{\sqrt{a} }{a }=3\sqrt{3} ab^5\frac{\sqrt{a} }{a }[/tex]
Simply by cancelling the 'a' terms to get:
[tex]3\sqrt{3} ab^5\frac{\sqrt{a} }{a }={3\sqrt{3}}\sqrt{a}b^5=3b^5\sqrt{3a}[/tex]
Expand the following expressions by multiplying out the brackets
-4(4f+3)
Answer:
- 16f - 12
Step-by-step explanation:
- 4(4f + 3) ← multiply each term in the parenthesis by - 4
= - 16f - 12
Hello!
In order to simplify this expression, we should use the Distributive Property and distribute -4:
-4(4f+3)
-16f-12
Note:
[tex]\square[/tex] A negative times a negative is a positive.
Hope everything is clear.
Let me know if you have any questions!
#KeepOnLearning
solve for x and please roundddd
how many 1/4 foot cubes would fill the inside of a rectangular prism
Answer: 192 cubes.
Step-by-step explanation: Each cube with side lengths of 1/4 have a volume of (1/4)3 which means each cube’s volume is 0.015625 cubic units. To find how many cubes are needed to fill the prism, divide 3 cubic units by 0.015625 cubic units. Your answer will be 192 cubes.
Which one doesn’t belong? A B C D
Answer:
A
Step-by-step explanation:
because its not an angle
Answer:
i would say a
Step-by-step explanation:
because b c and d sort of have an angle to them but a is straight
Select all that apply.
Green pencils are priced at $1.28 for 4. Blue pencils are priced at $5.52 for 24. Which of the following statements are true?
The unit rate for blue pencils is $0.28
The unit rate for green pencils is $0.32
The green pencils are priced less per pencil
The blue pencils are priced less per pencil.
Correct Statements:
1) The unit rate for green pencils is $0.32
2) The blue pencils are priced less per pencil.
Step-by-step explanation:
UNIT RATE:Green pencils:
Given that,
4 green pencils = $1.28
Divide 4 to both sides
1 green pencil = $1.28 / 4
1 green pencil = $0.32
Blue pencils:
Given that,
24 blue pencils = $5.52
Divide 24 to both sides
1 blue pencil = $5.52 / 24
1 blue pencil = $0.23
Blue pencil is priced less per pencil when compared to green pencil.
[tex]\rule[225]{225}{2}[/tex]
A circular pizza that is 17 inches in diameter is cut into 6 equal slices. What is the area of one of the slices?
The area of one slice is in?
Answer:
51
Step-by-step explanation:
17x6=51
Eva is solving the equation 4(x+32)=8
She says, “I can subtract 32 from each side to get 4x=132 and then divide by 4 to get x=138."
Dakota says, “I think you made a mistake.”
Determine the correct value for x.
x=
Answer:
The correct answer is -30
Step-by-step explanation:
4(x+32)=8 basically you multiply 4 times the numbers that are in the parentesis which that will equals to 4x+128 because 4x1= 4x and 4x32 = 128. then you subtract 128 from 8 which equals to -120. you divide -120 by 4 which equals to -30.
What is 1 3/8 written as a decimal
Answer:
1.625
Step-by-step explanation:
What is the value of the expression below?
4. 8 x 108
-x (2. 2 x 10-6)
1. 2 x 104
Answer:
I'm not sure I understand the formatting. I don't know what the x is supposed to be for the middle term (-x(2.2x10^6)), so I dropped the x for the calculation. I also assumed all terms are to be added. If these assumptioons are correct, the answer is:
4.58012 x 10^8 or 4.6x10^8 (see below)
Step-by-step explanation:
(4.8x10^8) - (2.2x10^6) + 1.2x10^4
(4.8x10^8) - (0.022x10^8) + (0.00012x10^8)
4.8
-0.22
+0.00012
4.58012
4.58012 x 10^8
There are only 2 significant digits (2.8x10^8) so if this is an answer relating to a scientific measurement, it would need to rounded to simply 4.6x10^8.
The quotient of forty-three and a number m
Answer:
43/m
Step-by-step explanation:
Quotient refers to the resulting answer when a number is divided by a divisorIn this case, our number is 43 and divisor is mTherefore, the quotient is :43/mAnswer:
43/m
Step-by-step explanation:
We can consider the word phrase 'the quotient of' to be a division property.
We can also contemplate that the phrase 'a number m' represents a variable, m, of an unknown value.
Together, we link these two to create the expression;
43 ÷ m which can also be known as 43/m.
What is the slope for the graph shown? Leave he answer as a fraction and simplify if necessary
Answer:
Slope 1/3
Step-by-step explanation:
Hope this helps! Please let me know if you need more help or think my answer is incorrect. Brainliest would be MUCH appreciated. Have a wonderful day!
Answer:
slope = [tex]\frac{1}{3}[/tex]
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (3, - 1) and (x₂, y₂ ) = (9, 1) ← 2 points on the line
m = [tex]\frac{1-(-1)}{9-3}[/tex] = [tex]\frac{1+1}{6}[/tex] = [tex]\frac{2}{6}[/tex] = [tex]\frac{1}{3}[/tex]
Solve 34x−5<8. Round your answer to the nearest thousandth
Answer:
x < 0.382
Step-by-step explanation:
because we know that 34x is smaller than 13. therefore after division we can find out that x must be smaller than 0.382
Trigonometry, how would I find the area of this triangle?
Answer:
Step-by-step explanation:
Area of triangle = 1/2 * base * height
Use the side of length 5.6cm as base, the height will be a perpendicular line from the base to the tip of the triangle.
From the right-angle triangle formed by the height and the side of length 3.9cm,
sin(56°45') = height / 3.9
height = 3.9*sin(56°45')
Substituting back into the area equation:
Area = 1/2*5.6*3.9*sin(56°45')
= 9.0cm^2
= 9cm^2
Use sine rule for Area
[tex]\\ \rm\rightarrowtail Area=\dfrac{1}{2}absinC[/tex]
[tex]\\ \rm\rightarrowtail Area=\dfrac{1}{2}(3.9)(5.6)sin56°45'[/tex]
[tex]\\ \rm\rightarrowtail Area=10.92(0.836)[/tex]
[tex]\\ \rm\rightarrowtail Area=10.22cm^2[/tex]
grade 6 math 1. Mr. Carlos bought a T-shirt for ₱ 254.95. Round this off to the nearest peso.
Answer:
255
Step-by-step explanation:
254.95
.95 is closest to 255.
254.95...255.
Which agency is responsible for promoting the welfare and opportunities of wage earners? a. fda b. hud c. dol d. cpsc
Answer:
DOL, also known as the Department of Labor, is the agency responsible for promoting the welfare and opportunities of wage earners.
Their main goal is to fight for equal rights among workers and to make their wishes and needs at the workplace come true.
Answer:
c
Step-by-step explanation:
) Andy is walking her dog Sherman on a local trail and Sherman falls 100 feet down a ravine. Andy is overcome with emotion and needs your help to save her dog. (Don’t mess this up!) You can repel down and successfully rescue Sherman, but you must first calculate how much rope is needed.
(a) Fill in your height here rounded to the nearest foot: ___________________
(b) Choose a measure for angle A between 31° and 51° (whole numbers only): ____________
Based on the calculations, the height of this ravine is equal to 143.95 feet.
Given the following data:
Height of ravine = 100 feet.How to calculate the length of rope.First of all, we would assign a variable to the height of the ravine, which is 100 feet tall.
Let the height of ravine be h.
Note: We would choose 46° as a measure for angle A.
From the image attached, we would determine the length of the hypotenuse by using Cosine trigonometric:
[tex]Cos A=\frac{Adj}{Hyp} \\\\Cos 46=\frac{100}{h} \\\\0.6947=\frac{100}{h}\\\\h=\frac{100}{0.6947}[/tex]
h = 143.95 feet.
Read more on trigonometry functions here: https://brainly.com/question/4515552
From the coordinate 8,12 to 10 and 15 what was the scale factor
Answer:
Scale factor is 5/4
Step-by-step explanation:
To find scale factor make a fraction. New coordinates/old coordinates
Make the fractions and reduce.
10/8 and 15/12
5/4 and 5/4
The scale factor is 5/4
please help me with this math! thank you!
Answer:
Heads or Tails
Step-by-step explanation:
its right there super simple.
Find the volume of the prism.
Answer:
the volume is 210
Step-by-step explanation:
length x width x height
length=6
width=5
height=7
6 x 5 = 30
30 x 7 = 210
express 59/2^4×5^4 in decimal form.
answer asap. Ill mark brainliest
Answer:
~Male Y/n here~ I think this would be your question in decimal form,
2304.6875
(Hope this helps!)
The point (-1, 3) is the turning point of the graph with equation y = x2 + ax + b,
where a and b are integers.
Find the values of a and b.
Answer:
a = 2
b = 4
Step-by-step explanation:
Δy = 2x + a.................for turning point, Δy/Δx = 0.
Δx
0 = 2x + a
x = -a/2.........from ( -1, 3), x = -1...............so,
-1 = -a/2.................a = 2.
y = x^2 + ax + b.
y = 3 , a = 2.................substitute.
3 = (-1)^2 + 2(-1) + b
3 = 1 -2 + b
b = 4
Answer:
The turning point of a parabola is the vertex
Vertex form of a quadratic equation: [tex]\sf y=a(x-h)^2+k[/tex]
(where (h, k) is the vertex and a is the coefficient of the variable x²)
Given:
[tex]\sf y=x^2+ax+b[/tex]vertex = (-1, 3)Therefore, a = 1
Substituting a = 1 and the given vertex into the equation:
[tex]\sf \implies y=1(x-(-1))^2+3[/tex]
[tex]\sf \implies y=(x+1)^2+3[/tex]
[tex]\sf \implies y=x^2+2x+1+3[/tex]
[tex]\sf \implies y=x^2+2x+4[/tex]
Therefore, a = 2 and b = 4
What is the diameter of a hemisphere with the volume of 74466
[tex]\textit{volume of a hemisphere}\\\\ V=\cfrac{1}{2}\cdot \cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ V=74466 \end{cases}\implies 74466=\cfrac{1}{2}\cdot \cfrac{4\pi r^3}{3} \\\\\\ 74466=\cfrac{2\pi r^3}{3}\implies 223398=2\pi r^3\implies \cfrac{22398}{2\pi }=r^3\implies \cfrac{111699}{\pi }=r^3 \\\\\\ \sqrt[3]{\cfrac{111699}{\pi }}=r~\hfill \stackrel{\textit{diameter = 2r}}{2\sqrt[3]{\cfrac{111699}{\pi }}\implies \sqrt[3]{\cfrac{893592}{\pi }}}~~ \boxed{\approx~~65.77}[/tex]
What is the solution to this system of equations?
4x+y=6
x-2y=6
A (-2)
B (1,2)
C (1/2, 4)
D (-2,2)
What is the surface area of this right triangular prism? enter your answer in the box.
Answer:
Step-by-step explanation:
where is the prism???
i can't answer without seeing the question
please help.......................
Answer:
what are the options? the answer I got was a fraction 19/4
Given g(x)=5x-3g(x)=5x−3, find g(-4)g(−4).
g(x)=5x-3
g(x)=5x−3
g(\color{green}{-4})=5(\color{green}{-4})-3
g(−4)=5(−4)−3
Plug input into x
-20-3
−20−3
Multiply
-23
−23
Answer:
the answer is 529
Step-by-step explanation:
see the explanation photo
The price of a car has been reduced from $14,500 to $10,730. What is the percentage decrease of the price of the car?