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]
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Answer:
(-3,1.5) (0,3) (3'3)
Step-by-step explanation:
multiply all the coordinates by 1/2
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Answer:
y = 11
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Step-by-step explanation:
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[tex] \frac{y}{22} \\ 0.5 = \frac{y}{22} \\ 0.5 \times 22 = y \\ 11 = y[/tex]
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Step-by-step explanation:
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
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stretch
B.) A reflection over the x-axis and a vertical
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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]
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[tex]h'(x) = 4\cdot x^{2}[/tex]
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Hence, correct answer is A.
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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
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
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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
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
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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:
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A blackboard has an area of 28 ft2 and a perimeter of 22 ft. What are the dimensions of the board?
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Answer:
4 ft by 7 ft.
Step-by-step explanation:
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Answer:
3
Step-by-step explanation:
us the formula
y1 - y2 divided by x1 - x2
=gradient
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please mark it brainliest
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]
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
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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.
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Their bill was charged a 9% sales tax.
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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.
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The graphs below have the same shape. What is the equation of the blue
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5
f(x) = x
W
Na
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Answers
Answer:
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Answer:
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Answers
Answer:
C = $2.40
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Step-by-step explanation:
For Noelle,
Equation that represents the monthly cost 'C',
C = 0.2n + 1.20
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Number of checks 'n' = 3
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C' ∝ n
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k = [tex]\frac{C'}{n}[/tex]
Here, k = proportionality constant
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k = [tex]\frac{1.2}{3}[/tex]
k = 0.4
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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
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Number of checks written by Noelle and Micah = 6
For n = 6,
C = 0.2(6) + 1.20
C = $2.40
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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
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:
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
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Step-by-step explanation:
x^2-25=
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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)
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/
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
Find 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.
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 = 1419. “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
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.
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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 :)
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