A cone has radius 9 and a height 12. A frustum of this cone has height 4.
What are the radii of the bases of the frustum?
What is the slant height of the frustum?
What is the lateral area of the frustum?
(If you waste an answer it will be removed so don't try and get "Free" points.)
Answers
Answer:
Part A)
The lower base has a radius of 9 units, and the upper base has a radius of 6 units.
Part B)
5 units.
Part C)
75π or about 235.62 square units.
Step-by-step explanation:
Please refer to the figure below.
The cone has a radius of 9 units and a total height of 12 units.
A frustum of the cone has a height of 4 units.
Part A)
The lower radius of the frustum will simply be 9 units.
For the upper radius, we will use the properties of similar triangles. We will compare the smaller upper triangle to the overall larger triangle. This yields:
[tex]\displaystyle \frac{12}{8}=\frac{9}{x}[/tex]
Solve for x. Simplify:
[tex]\displaystyle \frac{3}{2}=\frac{9}{x}[/tex]
Cross-multiply:
[tex]18=3x\Rightarrow x=6[/tex]
The upper base has a radius of 6 units.
Part B)
We can first find the total slant height of the entire cone. By using the Pythagorean Theorem, this yields that the total slant height is:
[tex]SH^2=12^2+9^2[/tex]
Simplify:
[tex]SH^2=225\Rightarrow SH=15\text{ units}[/tex]
Now, find the slant height of the upper cone:
[tex](SH_\text{cone})^2=8^2+6^2=100[/tex]
So:
[tex]SH_\text{cone}=10[/tex]
Then the slant height of the frustum will be the cone subtracted from the total. Thus:
[tex]SH_{\text{frustum}}=15-10=5\text{ units}[/tex]
Part C)
We can first find the lateral area of the entire cone. The lateral area is given by:
[tex]LA=\pi r\ell[/tex]
The lateral area of the entire cone will be:
[tex]LA=\pi (9)(15)=135\pi[/tex]
The lateral area of the upper cone will be:
[tex]LA_\text{cone}=\pi(6)(10)=60\pi[/tex]
Then the lateral area of the frustum is:
[tex]LA_\text{frustum}=135\pi-60\pi =75\pi\text{ units}^2\approx235.62\text{ units}^2[/tex]
Related Questions
Roberto has $200 in spending money. He wants to buy some video games that cost $25.50 each. Write and solve an inequality to find the number of
games, g, that Roberto can buy.
Inequality (use g as your variable):
Roberto can buy up to
video games.
Answers
Answer:
$200.00/$25.50 = g
Step-by-step explanation:
200.00 / 25.50 = 7 games
4. The graph of h(x) = x^2 was transformed to create the graph of k(x) = -4x^2? Which of these describes the transformation from the graph of h to the graph
of k? A.) A reflection over the x-axis and a vertical
stretch
B.) A reflection over the x-axis and a vertical
compression
C.) A reflection over the y-axis and a vertical
compression
D.) A reflection over the y-axis and a vertical stretch
Answers
Answer:
A. A reflection over the x-axis and a vertical stretch.
Step-by-step explanation:
Let [tex]h(x) = x^{2}[/tex], to obtain [tex]k(x) = -4\cdot x^{2}[/tex], we need to use the following two operations:
(i) Vertical stretch
[tex]g(x) = k\cdot f(x)[/tex], [tex]k\in \mathbb{R}^{+}[/tex]
(ii) Reflection over the x-axis
[tex]g(x) = -f(x)[/tex]
Let prove both transformations in [tex]h(x)[/tex]:
Step 1 - Vertical stretch ([tex]k = 4[/tex])
[tex]h'(x) = 4\cdot x^{2}[/tex]
Step 2 - Reflection over the x-axis
[tex]k(x) = -4\cdot x^{2}[/tex]
Hence, correct answer is A.
The Sanchez family had dinner at their favorite restaurant. A 9% sales tax was added to their bill. Amy paid the bill with a $10 gift certificate plus $30.60. How much did the family's dinner cost before tax? Round your answer to the nearest penny.
Answers
Answer:
The bill was $36.95 without tax.
The price before tax was the amount of $37.25 which is before a 9% sales tax was added to their bill.
What are Arithmetic operations?Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions. The operator that performs the arithmetic operation is called the arithmetic operator.
Their bill was charged a 9% sales tax.
Amy paid the bill with a $10 gift certificate plus $30.60
Use the equation P + rP =T,
where P is the price before tax, r is the sales tax rate, and T is the total price, including tax.
The price before tax (P) is unknown.
The total price(T) = 30.60 + 10 = 40.60
The sales tax rate (r) = 9% = 9/100 = 0.09
⇒ P + rP = T
Substitute the values in the above equation, and we get
⇒ P + (0.09)P = 40.60
⇒ P(1 + 0.09) = 40.60
⇒ P(1.09) = 40.60
⇒ P = 30.60/(1.09)
Apply the Division operation, and we get
⇒ P = 37.247706
Rounded to the nearest hundredth
⇒ P = 37.25
Therefore, the price before tax was the amount of $37.25.
Learn more about Arithmetic operations here:
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Noelle and Micah went to the bank to open new checking accounts. The equation C=0.2n+1.20 represents the monthly cost, C, in dollars, where n is the number of checks written by Noelle. In Micah's account, the monthly cost is proportional to the number of checks written. The monthly cost for Micah's account is $1.20 for writing 3 checks. How many checks must Noelle and Micah write, if any, so that the cost of the accounts is the same for one month? What is the cost, if any?
Answers
Answer:
C = $2.40
n = 6
Step-by-step explanation:
For Noelle,
Equation that represents the monthly cost 'C',
C = 0.2n + 1.20
Here, n = number of checks written in a month
For Micah,
Monthly cost for writing checks 'C' = $1.20
Number of checks 'n' = 3
Since, Cost of writing checks ∝ Number of checks written
C' ∝ n
C' = kn
k = [tex]\frac{C'}{n}[/tex]
Here, k = proportionality constant
For C' = 1.2 and n = 3
k = [tex]\frac{1.2}{3}[/tex]
k = 0.4
Equation will be,
C' = 0.4n
For any month C = C'
Therefore, 0.2n + 1.20 = 0.4n
0.4n - 0.2n = 1.20
0.2n = 1.20
n = 6
Number of checks written by Noelle and Micah = 6
For n = 6,
C = 0.2(6) + 1.20
C = $2.40
Cost of writing checks = $2.40
The graphs below have the same shape. What is the equation of the blue
graph?
5
f(x) = x
W
Na
g(x) = 2
g(x) = -
O A. g(x) = (x - 4)2 + 1
O B. g(x) = (x+4)2 - 1
O c. g(x) = (x - 4)2 - 1
O D. g(x) = (x+4)2 + 1
Answers
Answer:
If the attached graph is the one you mean, the answer is g(x) = (x-4)^2 + 1
The equation of the blue graph is,
⇒ g (x) = (x - 4)² + 1
Given that;
The given function is,
⇒ f (x) = x²
Since, It is given that both graph has same shape it means the equation of blue graph is in the form of;
⇒ g (x) = (x - h)² + k
Where, (h,k) is the vertex of the parabola.
Hence, From the given graph it is noticed that vertex of blue parabola is (4,1),
Therefore, the equation of parabola is,
⇒ g (x) = (x - 4)² + 1
Thus, The equation of the blue graph is,
⇒ g (x) = (x - 4)² + 1
Learn more about the function visit:
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Write an explicit formula for an, the nth term of the sequence 35, 38, 41, ...
Answers
Answer:
[tex]a_{n}[/tex] = 3n + 32
Step-by-step explanation:
There is a common difference d between consecutive terms, that is
d = 38 - 35 = 41 - 38 = 3
This indicates the sequence is arithmetic with n th term ( explicit formula )
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = 35 and d = 3 , then
[tex]a_{n}[/tex] = 35 + 3(n - 1) = 35 + 3n - 3 = 3n + 32
Becky used 8 gallons of gas driving to visit her friend. Her car used gas at the rate of 24 miles per gallon. How far did she drive?
Answers
Answer:
192
Step-by-step explanation:
8 x 24 = 192
39/8 as a decimal... I've forgotten how to turn fractions into decimals
Answers
Answer:
4.222222 or jus 4.2 with - over the 2 to indicate multiple 2's
Answer:
4.875
Step-by-step explanation:
Pretty simple, just divide the numerator by the denominator.
You are putting money into a bank account. You start with $100 and add $12 every month. The total amount of money in your account can be represented by the following equation. (where T is total amount and M is the number of months):
T = 100 + 12 M
If you have $208, how many months have passed?
Show the equation and how you got the answer.
Answers
Answer:
9 months
Step-by-step explanation:
Answer:
it will be 9 months like the first person said
Dilate Point B by a scale factor of 1/2
a (1.5,-4)
b (-1.5,1)
c (-1,-1.5)
d (-2,-2)
PLEASE HELP
Answers
Answer:
B
Step-by-step explanation:
Divide each coordinate by 2
3/2=1.5
2/2=1
Estimate 12% of 77?
Answers
Answer: 9.24
Step-by-step explanation:
12*77 = 924
= 9.24
The answer to the given question is estimating 12% (percent) of 77, we get the answer 9.24.
To calculate 12% of 77 precisely, we can use the following formula: percent / 100 × given number
= 12% of 77
= (12/100) × 77
= 9.24
Therefore, 12% of 77 is 9.24.A percentage is a way of expressing a number as a fraction of 100. The symbol "%" is used to is used to indicate a percentage. For example, if we say that something is 25%, we mean that it is 25 out of 100 or 0.25 as a decimal. Percentages are used in many different areas, such as finance, statistics, and science. They can be used to represent proportions, rates of change, or as a way to compare different quantities. One common use of percentages is to calculate percentage change or increase. This is done by finding the difference between two values and expressing it as a percentage of the original value.
To learn more about Percentages click here
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Help If don't know do not answer(if link will report)
Answers
Answer:
x = 14
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityAlgebra I
Terms/CoefficientsGeometry
Supplementary Angles: Angles that add up to 180°Step-by-step explanation:
Step 1: Define
We can see from the diagram that the 2 angles are supplementary
(6x - 10)° + (7x + 8)° = 180°
Step 2: Solve for x
Combine like terms: 13x - 2 = 180[Addition Property of Equality] Add 2 on both sides: 13x = 182[Division Property of Equality] Divide 13 on both sides: x = 14Find the area of the figure below
Answers
Answer:
4.5 x 14 = 63
Explanation:
The area of a parallelogram is the product of any base and the altitude to that base: A = bh.
Find the gradient of the line segment between the points (4,3) and (5,6
Answers
Answer:
3
Step-by-step explanation:
us the formula
y1 - y2 divided by x1 - x2
=gradient
6 - 3 divided by 5 - 4 = gradient
3 = gradient
hope this helps
please mark it brainliest
Write an equation in point-slope form of the line that passes through (-1, – 4) with slope -2.
Answers
Answer:
y+4=-2(x+1)
Step-by-step explanation:
y-y1=m(x-x1)
y-(-4)=-2(x-(-1))
y+4=-2(x+1)
In an isosceles triangle, one side is 6 more than 3 times a number and the congruent side is 10 less than
5 times the same number, what is that number?
a.2
b.8
c.16
d. none of above
Answers
I'm very confused on what the answer to this one is
Answers
Answer:
(-3,1.5) (0,3) (3'3)
Step-by-step explanation:
multiply all the coordinates by 1/2
PLZZZ HELP WHAT IS THE AREA OF THIS TRAPEZOID?!?!?!
Answers
Trigonometry can anyone help me out
Answers
Answer:
y = 11
x = 11 root 3
[tex]x = 11\sqrt{3} [/tex]
[tex]y = 11[/tex]
Step-by-step explanation:
Cos 60 =
[tex] \frac{y}{22} \\ 0.5 = \frac{y}{22} \\ 0.5 \times 22 = y \\ 11 = y[/tex]
[tex]for x \\ \sin(60) = \frac{x}{22} \\ \frac{ \sqrt{3} }{2} = \frac{x}{22} \\ \frac{ \sqrt{3} }{2} \times 22 = x \\ 11 \sqrt{3 } = x[/tex]
Answer:
y = 11
x = 11 root \3
Step-by-step explanation:
solve for t i need help
Answers
[tex]4(t+\frac{1}{4})=3[/tex] distribute by multiplying 4 into the parenthesis.
[tex]4t+1 = 3[/tex]
[tex]-1[/tex] [tex]-1[/tex] subtract 1 on both sides, solve for 3 - 1, which is 2.
__________
[tex]\frac{4t}{4} =\frac{2}{4}[/tex] divide 4 on both sides.
[tex]t = \frac{2}{4}[/tex] simplify 2/4.
[tex]t = \frac{1}{2}[/tex] final answer
hope this helps :)
Triangle ABC has side lengths 8 inches, 17 inches, and 15 inches. Sofia uses the following steps to conclude that triangle ABC is not a right triangle.
a2+b2=c282+172=15264+289=225353 ≠ 225
What mistake did Sofia make?
Sofia made a calculation error.
Sofia used the length of one of the legs as c when she should have used the length of the longest side as c.
Sofia does not know if triangle ABC is a right triangle, so she cannot use the Pythagorean Theorem or its converse.
Sofia’s conclusion is incorrect. When the sides of a triangle do not satisfy a2+b2=c2, you cannot conclude that the triangle is a right triangle.
Answers
Answer: Sofia used the length of one of the legs as c when she should have used the length of the longest side as c.
Step-by-step explanation: The leg is the smallest number and the hypothenuse is the biggest nunber.
Answer:
Sofia used the length of one of the legs as c when she should have used the length of the longest side as c.
Step-by-step explanation:
A and b are positive integers and a-b=2 ... Evaluate the following:
27^1/3 b / 9^1/2 a
There is an image attached of the problem
Answers
Answer:
Step-by-step explanation:
a-b=2
[tex]\frac{27^{\frac{1}{3} b} }{9^{\frac{1}{2}a } } \\=\frac{(3^{3}) ^{\frac{1}{3} b} }{(3^{2} )^{\frac{1}{2} a} } \\=\frac{3^b}{3^a} \\=3^{b-a} \\=3^{-(-b+a)} \\=3^{-2}\\=\frac{1}{3^2} \\=\frac{1}{9}[/tex]
whts the factored answer
Answers
Step-by-step explanation:
x^2-25=
[tex] {x}^{2} - 25 = (x - 5)(x + 5) [/tex]
In a parenting magazine, Mrs. Smith read an advertisement about all the different ways that bleach can be used to kill bacteria. The advertisement claimed that some forms of bacteria triple in amount after each hour. Consider the situation where one bacterium is found on Mrs. Smith's countertop at home.
Answers
Question:
(a) How many bacteria would be found in 24 hours
(b) How many bacteria would be found in 2 days
(c) How long for 1000 bacteria to be found
Answer:
(a) 282429536481 bacteria
(b) [tex]7.97*10^{22[/tex] bacteria
(c) 6 days
Step-by-step explanation:
The question illustrates an exponential function
[tex]y = ab^x[/tex]
Where
[tex]a = Initial\ Value = 1[/tex]
[tex]b=Rate = 3[/tex] --- i.e. triples
[tex]x = number\ of\ hours[/tex]
Solving (a): Bacteria in 24 hours
In this case:
[tex]x = 24[/tex]
Substitute [tex]x = 24[/tex], [tex]b = 3[/tex] and [tex]a = 1[/tex]
So:
[tex]y = ab^x[/tex]
[tex]y = 1 * 3^{24[/tex]
[tex]y = 1 * 282429536481[/tex]
[tex]y = 282429536481[/tex] bacteria
Solving (b): Bacteria in 2 days
[tex]2\ days =48\ hours[/tex]
So:
[tex]x = 48[/tex]
Substitute [tex]x = 48[/tex], [tex]b = 3[/tex] and [tex]a = 1[/tex]
So:
[tex]y = ab^x[/tex]
[tex]y = 1 * 3^{48[/tex]
[tex]y =7.97*10^{22[/tex] bacteria
Solving (c): How long for 1000 bacteria
In this case:
[tex]y = 1000[/tex]
Substitute [tex]y = 1000[/tex], [tex]b = 3[/tex] and [tex]a = 1[/tex]
So:
[tex]y = ab^x[/tex]
[tex]1000 = 1 *3^x[/tex]
[tex]1000 = 3^x[/tex]
Take Log of both sides
[tex]Log1000 = Log3^x[/tex]
This gives:
[tex]Log1000 = xLog3[/tex]
Make x the subject
[tex]x = \frac{Log1000}{Log3}[/tex]
[tex]x \approx 6[/tex]
Hence: It takes 6 days
A blackboard has an area of 28 ft2 and a perimeter of 22 ft. What are the dimensions of the board?
Answers
Answer:
4 ft by 7 ft.
Step-by-step explanation:
Even more trig ratios see attachment
Answers
Step-by-step explanation:
1. Use the Pythagorean theorem to solve for side KM:
16^2+KM^2=34^2256+KM^2=1156KM^2=900KM=302. Cosine is adjacent over hypotenuse, so cosine of M would be KM/34, or 30/34
3. Tangent is opposite over adjacent, so tangent of L will be KM/16, or 30/16
4. Sine is opposite over hypotenuse, so sine of M will be 16/34
5. KM=30, solved for in step 1.
hope this helps!!
help neither me or my friend know how to do this
Answers
Answer:
X [tex]\leq[/tex] -5
Step-by-step explanation:
Answer:
x ≥ -6
Step-by-step explanation:
Here you go, this might help you
https://courses.lumenlearning.com/collegealgebracoreq/chapter/temp-4-review/
A magician performing a magic act has asked for 2 volunteers from the audience to help with his routine. If there are
250 people in the audience, which of the following expressions represents the number of possible pairs of volunteers ?
.
Answers
Answer:
The answer is 125. If you were to pair 250 people in 2, that would be 250 divided by 2. And 250 divided by 2 is 125.
Step-by-step explanation:
please help, i will give 20 points
Answers
4. Overall, there are 45 students.
13 students achieved a mark over 65
[tex]\frac{13}{45} *100[/tex] = 29%
Therefore the answer is b. 29%
5. b is incorrect.
This is because retrievers account for 10% of the dogs, not 15%.
100%-(35% + 45% + 10%) = 10%
19. “40 of what number is 34” i need work
Answers
Answer:
85%
40% × ? = 34
? =
34 ÷ 40% =
34 ÷ (40 ÷ 100) =
(100 × 34) ÷ 40 =
3,400 ÷ 40 =
85