Kirstie is testing values that would make triangle klm a right triangle when ln is an altitude, and km = 16, as shown below. which lengths would make triangle klm a right triangle? 1) lm = 13 and kn = 6 2) lm = 12 and nm = 9 3) kl = 11 and kn = 7 4) ln = 8 and nm = 10
Answers
Answer: Option (2) is correct.
Step-by-step explanation:
Since we have given that
KLM is a right triangle, in which KM = 15, and ln is an altitude.
As we know that for right angled triangle, there are 3 conditions :
[tex]KL^2=KN.KM-----(1)\\\\ML^2=MN.KM-------(20\\\\LN^2=KN.MN------(3)[/tex]
So, According to the options ,
Put LM = 12, NM = 9,
[tex]\text{Using eq. (3), we have}\\\\LN^2=KM.MN\\\\12^2=9\TIMES 16\\\\144=144[/tex]
Since, it satisfies that KLM is a right triangle.
Hence, Option (2) is correct.
Using Pythagorean theorem, Option D: [tex]\( LM = 8 \)[/tex] and [tex]\( NM = 10 \)[/tex], satisfies [tex]\( KM^2 = LM^2 + NM^2 \)[/tex].
[tex]\( LM = 12 \) and \( NM = 9 \).[/tex]To determine which lengths would make triangle [tex]\(KLM\)[/tex] a right triangle when [tex]\(\overline{LN}\)[/tex] is an altitude and [tex]\(KM = 16\)[/tex], we can use the Pythagorean theorem to check each given set of values. We know that [tex]\(\overline{LN}\)[/tex] divides [tex]\(KLM\)[/tex] into two right triangles, [tex]\( \triangle KNL \)[/tex] and [tex]\(\triangle LNM\)[/tex].
We will check each given option to see if the Pythagorean theorem holds.
Option A: [tex]\( LM = 13 \)[/tex] and [tex]\( KN = 6 \)[/tex]
Here, [tex]\( LN \)[/tex] is the altitude. Let [tex]\( NM = x \)[/tex], then [tex]\( KM = KN + NM \)[/tex], so:
[tex]\[ x = 16 - 6 = 10 \][/tex]
For [tex]\( \triangle LNM \)[/tex]:
[tex]\[ LM^2 = LN^2 + NM^2 \][/tex]
[tex]\[ 13^2 = LN^2 + 10^2 \][/tex]
[tex]\[ 169 = LN^2 + 100 \][/tex]
[tex]\[ LN^2 = 69 \][/tex]
[tex]\[ LN = \sqrt{69} \approx 8.3 \][/tex]
For [tex]\( \triangle KNL \)[/tex]:
[tex]\[ KL^2 = KN^2 + LN^2 \][/tex]
[tex]\[ KL^2 = 6^2 + 69 \][/tex]
[tex]\[ KL^2 = 36 + 69 \][/tex]
[tex]\[ KL^2 = 105 \][/tex]
[tex]\[ KL \approx 10.2 \][/tex]
These calculations do not match the given [tex]\(KL\)[/tex] value.
Option B: [tex]\( LM = 12 \) and \( NM = 9 \)[/tex]
Here, [tex]\( LN \)[/tex] is the altitude. Let [tex]\( KN = x \)[/tex], then:
[tex]\[ x = 16 - 9 = 7 \][/tex]
For [tex]\( \triangle LNM \)[/tex]:
[tex]\[ LM^2 = LN^2 + NM^2 \][/tex]
[tex]\[ 12^2 = LN^2 + 9^2 \][/tex]
[tex]\[ 144 = LN^2 + 81 \][/tex]
[tex]\[ LN^2 = 63 \][/tex]
[tex]\[ LN = \sqrt{63} \approx 7.9 \][/tex]
For [tex]\( \triangle KNL \):[/tex]
[tex]\[ KL^2 = KN^2 + LN^2 \][/tex]
[tex]\[ KL^2 = 7^2 + 63 \][/tex]
[tex]\[ KL^2 = 49 + 63 \][/tex]
[tex]\[ KL^2 = 112 \][/tex]
[tex]\[ KL \approx 10.6 \][/tex]
These calculations do not match the given [tex]\(KL\)[/tex] value.
Option C: [tex]\( KL = 11 \)[/tex] and [tex]\( KN = 7 \)[/tex]
Here, [tex]\( LN \)[/tex] is the altitude. Let [tex]\( NM = x \)[/tex], then:
[tex]\[ x = 16 - 7 = 9 \][/tex]
For [tex]\( \triangle KNL \)[/tex]:
[tex]\[ KL^2 = KN^2 + LN^2 \][/tex]
[tex]\[ 11^2 = 7^2 + LN^2 \][/tex]
[tex]\[ 121 = 49 + LN^2 \][/tex]
[tex]\[ LN^2 = 72 \][/tex]
[tex]\[ LN = \sqrt{72} \approx 8.5 \][/tex]
For [tex]\( \triangle LNM \)[/tex]:
[tex]\[ LM^2 = LN^2 + NM^2 \][/tex]
[tex]\[ LM^2 = 72 + 9^2 \][/tex]
[tex]\[ LM^2 = 72 + 81 \][/tex]
[tex]\[ LM^2 = 153 \][/tex]
[tex]\[ LM \approx 12.4 \][/tex]
These calculations do not match the given [tex]\(LM\)[/tex] value.
Option D: [tex]\( LN = 8 \) and \( NM = 10 \)[/tex]
Here, [tex]\( LN \)[/tex] is the altitude. Let [tex]\( KN = x \)[/tex], then:
[tex]\[ x = 16 - 10 = 6 \][/tex]
For [tex]\( \triangle LNM \)[/tex]:
[tex]\[ LM^2 = LN^2 + NM^2 \][/tex]
[tex]\[ LM^2 = 8^2 + 10^2 \][/tex]
[tex]\[ LM^2 = 64 + 100 \][/tex]
[tex]\[ LM^2 = 164 \][/tex]
[tex]\[ LM \approx 12.8 \][/tex]
For [tex]\( \triangle KNL \)[/tex]:
[tex]\[ KL^2 = KN^2 + LN^2 \][/tex]
[tex]\[ KL^2 = 6^2 + 8^2 \][/tex]
[tex]\[ KL^2 = 36 + 64 \][/tex]
[tex]\[ KL^2 = 100 \][/tex]
[tex]\[ KL = 10 \][/tex]
These calculations match the given lengths.
Thus, the correct answer is:
D. [tex]\( L N = 8 \) and \( N M = 10 \)[/tex]
The correct question is given below:
Related Questions
Write the first five terms of a sequence. Don’t make your sequence too simple. Write both an explicit formula and a recursive formula for a general term in the sequence. Explain in detail how you found both formulas.
Answers
The first five terms of a complex sequence are 4, 7, 10, 16, and 28.
Let's consider a non-trivial sequence.
Let's say the first term of our sequence, a1, is 4.
From then on, the sequence increases by 3 times the previous term, but instead of simply multiplying by 3, we will multiply by 3 raised to the power of one less than the term's position in the sequence. However, we are given that the general expression for the nth term is 4 + 3 x 2(n-2), except for the first term which remains 4.
This gives us a starting point for both our formulas.
To find the first five terms of this sequence, we can manually calculate them using the explicit formula given:
a1 = 4 (by definition)a2 = 4 + 3 x 2(2-2) = 4 + 3 x 1 = 7a3 = 4 + 3 x 2(3-2) = 4 + 3 x 2 = 10a4 = 4 + 3 x 2(4-2) = 4 + 3 x 4 = 16a5 = 4 + 3 x2(5-2) = 4 + 3 x 8 = 28Therefore, the first five terms are 4, 7, 10, 16, and 28.
Explicit Formula:
The explicit formula for any term an in the sequence is:
an = 4 + 3 x 2(n-2) for n > 1, with a1 = 4.
Recursive Formula:
The recursive formula builds each term based on the preceding term. For n > 1, the recursive formula is an = an-1 + 3 imes 2(n-2), with a1 still equal to 4.
Cassie rolls a fair number cube with 6 faces labeled 1 through 6.She rolls the number cube 600 times. Which result is most likely
Answers
Answer:
All results are most likely.
Step-by-step explanation:
Each result 1-6 has an equal chance. The probability is the number of chances divided by the total number. The total number of options is 6 since it is a six sided cube. Each options is represented once so 1 out 6 is the likelihood.
1 out of 6 is 1/6 = 0.17 = 17%.
No matter how many times she has rolled it, it's the same likelihood.
Which reason best describes why you can divide any number by 100 by moving the decimal point two places to the left?
Dividing a number by 100 is the same as subtracting the number 100 times.
Dividing by 100 is the same as removing a zero.
Moving the decimal point makes the number smaller.
Moving the decimal point two places to the left makes the number 1/100 of its original value.
Answers
Answer:
Option D, Moving the decimal point two places to the left makes the number 1/100 of its original value.
Step-by-step explanation:
Step 1: Find the answer
I believe that it is the last choice because a number divide by 100 gives 1/100 of the value.
Example: Find 4 / 100
[tex]\frac{4}{100} = 0.04[/tex]
[tex]4*\frac{1}{100} = \frac{4}{100}=0.04[/tex]
Answer: Option D, Moving the decimal point two places to the left makes the number 1/100 of its original value.
I really need help ASAP
Answers
.. tan(a) = 78'/36'
.. a = arctan(78/36) ≈ 65.22°
You also know that
.. a = c = k = j
and that
.. a +c +e = 180°
.. e = g = 180° -2a = 49.55°
f = h = 180° -e = 130.45°
Of course the other corner angles are
.. b = d = i = l = 90° -a = 24.78°
_____
One bit of trigonometry and the rest is arithmetic.
what is the solution of the equation x^2-1=0
Answers
x^2 -1^2 = 0
(x + 1) (x - 1) = 0
x + 1 = 0 or x - 1 = 0
x = -1 or x = 1
Ans: -1 and 1
Solve it like this
x^2 - a^2 = (x + a)(x - a)
so for x^2 - 1 you get
(x + sqrt(1) ) (x - sqrt(1) = (x + 1)(x-1)
x^2 - 1 = (x + 1)(x - 1)
(x - 1)(x + 1) =0
x - 1 =0
x = 1
x + 1 = 0
x = - 1
The two answers are x = 1 and x = - 1
You might want to try these. If you post the answers, I'll tell you how you did. Just make comments
x^2 - 25 = 0
x^2 - 9 =0
x^2 - 36 = 0
x^2 - 49 = 0
What is the volume of a rectangular prism with a length of 81\2 centimeters, width of 9 1\3 centimeters, and a height of 12 2\5 centimeters?
Answers
We must use a certain formula to find the volume of a rectangular prism. The formula is:
V = l × w × h
Let's multiply the 3 dimensions together. Before we can do that, though, we must convert the mixed fractions to improper fractions.
8 1/2 = (8 × 2) + 1 / 2 = 17/2
9 1/3 = (9 × 3) + 1 / 3 = 28/3
12 2/5 = (12 × 5) + 2 / 5 = 62/5
17/2 × 28/3 = 476/6 (which can be simplified to 238/3)
238/3 × 62/5 = 14756/15
Final Answer:
The volume of the rectangular prism is 983 11/15 centimetres cubed, and 983.733 centimetres cubed (Repeating decimal) as a decimal.
A toy plush weighed 1/5 of a pound. a flimsy box can hold 3 pounds. how many toy plushes could the box hold?
Answers
total weight = 1/5 times the amount of toys
3 = 1/5 x
rewrite
3 = 1x /5
multiply both sides by 5
15 = 1x
15 = x
The flimsy box can hold 15 toy plushes.
Hope this helps
Give the coordinates of the points after a reflection over the line y=-4
A( 4,5) A' (_,_)
B(0,4) B' (_,_)
C(-2,1) C' (_,_)
use algebraic representation and please show your work !
Answers
.. (y +y')/2 = -4
.. y +y' = -8
.. y' = -8 -y
The x-coordinate remains unchanged.
A' = (4, -8-5) = (4, -13)
B' = (0, -8-4) = (0, -12)
C' = (-2, -8-1) = (-2, -9)
A) –2n + 9m – 17p
B) –2n – 9mn + 17np
C) –2n + 9mn – 17np
D) –18n + 81mn – 153np
Answers
All you do is simplify the equation by distributing and multiplying the 1/3n to each of the numbers.
Hope this helps!
_____________________________________________________
[tex] \frac{1}{3} [/tex] n (−6 + 27m − 51p) =
( [tex] \frac{1}{3} [/tex] n * −6 ) + ( [tex] \frac{1}{3} [/tex] n * 27m ) −
( [tex] \frac{1}{3} [/tex] n * 51p ) ;
= −2n + 9mn − 17np ; which is: Answer choice: [C]: " −2n + 9mn − 17np" .
__________________________________________________________
PLEASE HELP!
Which transformations will produce similar, but not congruent, figures?
A)Triangle MNO is reflected across the y-axis and then rotated 180° clockwise to form triangle M"N"O" .
B)Triangle MNO is reflected across the y-axis and then dilated by a scale factor of 1.8 to form triangle M"N"O" .
C) Triangle MNO is reflected across the x-axis and then translated 9 units down to form triangle M"N"O" .
D)Triangle MNO is reflected across the x-axis and then rotated 90° clockwise to form triangle M"N"O" .
Answers
A sporting goods store offers a 40% discount on all golf clubs. Rocco spent 20% of the money in his savings account on a golf putter. He paid $48 for the putter after the discount. How much money did Rocco have in his savings before buyin the putter?
Answers
Rocco originally had $240
Explanation:
Before we begin, note that the price of the putter is given AFTER the discount. This means that the value of the discount doesn't affect the solution.
Assume that the amount Rocco had originally is x
Now, we are given that:
price of putter = $48
Price of putter represents 20% of what Rocco had
This means that:
price of putter = 20% * amount Rocco had
48 = 20% * x
48 = 0.2x
x = 48 / 0.2
x = $240
This means that Rocco originally had $240
Hope this helps :)
what is the answer for Theo is building a garden against his house. He bought two pieces of wood that are each five feet long. He wants to create a triangular garden against his house using the two pieces of wood, without cutting them. His house will be the third side of the triangle. He also wants the perimeter of his garden to be a whole number.
Answers
2 solutions: perimeter=6+5+5=16 or 8+5+5=18.
Solve the inequality and then graph its solution: 7s + 12 > 46 - 10s
Answers
Add 10s to both sides:
17s + 12 > 46
Subtract 12 to both sides:
17s > 34
Divide 17 to both sides:
s > 2
The inequality graphed would have an open dot on 2 and the arrow would be going to the right.
Matias stacked his cubes to make this rectangular prism.
rectangular prism with grid lines
How many cubes did Matias use?
cubes
Answers
SEE ATTACHED IMAGE.
The problem can be modeled as a pair of matrices:
First matrix:
(4) * (4) = 16
Second matrix:
(16) * (5) = 80
Since the second matrix depends on the first, then the number of cubes is:
N = 80
Answer
80 cubes.
Answer:
The answer is 80
Cylinder A has a volume of 360 cm3. Cylinder B has a base and height identical to that of cylinder B, but leans to the right in such a way that its slant length is greater by 4 cm. What is the volume of cylinder B? V = 270 cm3 V = 360 cm3 V = 480 cm3 V = 600 cm3
Answers
This is because the volume of the cylinder is dependent on the base and the perpendicular height, therefore, the slanting of the cylinder wont change its volume
Step-by-step explanation:
ndkfkasdjfkjdasl;fkjalksdfjlasdjf
Give the values a, b, and c needed to write the equations standard form. 2/3(x-4)(x+5)=1
Answers
ax ^ 2 + bx + c
What we must do in this case is to rewrite the given equation.
We have then:
2/3 (x-4) (x + 5) = 1
(x-4) (x + 5) = 3/2
(x ^ 2 + 5x-4x-20) = 3/2
2x ^ 2 + 2x-40 = 3
2x ^ 2 + 2x-43 = 0
Thus, the values of a, b and c are:
a = 2
b = 2
c = -43
Answer:
a = 2
b = 2
c = -43
Answer:I agree
Step-by-step explanation:
Please help
Part 1.] Match these items.
1.) The positive integers
2.) An ordering of quantities
3.) 2, 4, 8, 16, . . ., 256
4.) 1, 3, 5, 7, . . .
5.) No first term is available
A.) An example of a finite sequence
B.) A sequence
C.) The reason the numbers . . . -4, -2, 0, 2, 4, . . . are not a sequence
D.) The natural numbers
E.) An example of an infinite sequence
Part 2.] Write the first five terms of the sequence. [tex] a_{n}= n^{2}+2[/tex]
A.] 3,6,11,18,27
B.] 3,6,9,12,15
C.] 2,3,6,11,18
Part 3.] Write the first five terms of the sequence. [tex] a_{n}= -1( \frac{1}{3})^{n-1}[/tex]
A.] -1,-3,-9,-27,-81
B.] -1,[tex] \frac{-1}{3},\frac{-1}{9},\frac{-1}{27},\frac{-1}{81} [/tex]
C.] -1,[tex] \frac{1}{3},\frac{-1}{9},\frac{1}{27},\frac{-1}{81} [/tex]
Part 4.] In two or more complete sentences, explain whether the sequence is finite or infinite. Describe the pattern in the sequence if it exists, and if possible find the sixth term. [tex]2a,2a^{2}b,2a^{3}b^{2},2a^{4}b^{3}...[/tex]
Answers
1) The positive integers -----------> D.) The natural numbers
2.) An ordering of quantities -----------> B.) A sequence
3.) 2, 4, 8, 16, . . ., 256 -----------> A.) An example of a finite sequence
4.) 1, 3, 5, 7, . . . -----------> E.) An example of an infinite sequence
5.) No first term is available -----------> C.) The reason the numbers . . . -4, -2, 0, 2, 4, . . . are not a sequence
Part 2
[tex]a_n=n^2+2\\ a_1=1+2=3\\ a_2=4+2=6\\ a_3=9+2=11\\ a_4=16+2=18\\ a_5=25+2=27 [/tex]
The answers is A.
Part 3
[tex]a_n=-1(\frac{1}{3})^{n-1} \\ a_1=-1(\frac{1}{3})^{1-1}=-1\\ a_2=-1(\frac{1}{3})^{2-1}=-\frac{1}{3}\\ a_3=-1(\frac{1}{3})^{3-1}=--\frac{1}{9}\\ a_4=-1(\frac{1}{3})^{4-1}=--\frac{1}{27}\\ a_5=-1(\frac{1}{3})^{5-1}=--\frac{1}{81}\\ [/tex]
The answers is B.
Part 4
The pattern in this sequence is:
[tex]a_n=2a^nb^{n-1}[/tex]
Let's list first six terms:
[tex]a_n=2a^nb^{n-1}\\ a_1=2a^1b^0=2a\\ a_2=2a^2b^1=2a^2b\\ a_3=2a^3b^2\\ a_4=2a^4b^3\\ a_5=2a^5b^4\\ a_6=2a^6b^5\\[/tex]
This is a infinite sequence. The patern is obvious and we could find any term within the sequence.
The questions involve matching concepts related to sequences, finding the first terms of given sequences, and analyzing an infinite sequence. The correct matches were 1-D, 2-B, 3-A, 4-E, 5-C. Options C and C were correct for Parts 2 and 3, while for Part 4, the sequence was infinite, with the sixth term as [tex]2a^{6}b^{5}[/tex].
Explanation:
For Part 1, the correct matching of the items would be as follows:
1 - D (The positive integers can also be referred to as natural numbers)2 - B (A sequence is simply an ordering of quantities)3 - A (2, 4, 8, 16, ... , 256 is a finite sequence because it ends at 256)4 - E (1, 3, 5, 7, ... is an infinite sequence because it goes on indefinitely)5 - C (The numbers -4, -2, 0, 2, 4, ... can't be a sequence because there is no first term)
For Part 2, Option C is correct. The first five terms of the sequence [tex]a_{n} = n^{2} + 2[/tex] are 3, 6, 11, 18, 27, as these are the results you obtain when you plug the first five positive integers into the formula.
For Part 3, Option C is correct. The first five terms of the sequence [tex]a_{n} = -1 * (1/3)^{n-1}[/tex] are -1, 1/3, -1/9, 1/27, -1/81. Notice the alternating signs due to the factor of -1.
For Part 4, the sequence [tex]2a,2a^{2}b,2a^{3}b^{2},2a^{4}b^{3}...[/tex] is infinite since there is no last term. The pattern involves progressively increasing the powers of a and b in each term. The sixth term would be [tex]2a^{6}b^{5}[/tex] following this pattern.
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Jimmy is trying to figure out how many pennies are in his bank. He asked his mother to help him figure out the total. He tells her to let the amount in the bank equal 21x^3+18x^2+9x and each penny equal 3x. Can you help them figure out how many pennies are in the bank?
Answers
The ratio of two supplementary angles is 6:3. what is the measure of the smaller angle?
Answers
simplify
2:1
That means that the bigger angle is two times bigger than the smaller one
supplementary angles equal up to 180
smaller angle + larger angle = 180
s + l = 180
we can create our second equation using two times the smaller = larger
2s = l
our two equations are:
2s = l
s + l = 180
now that we have the two equations, we can solve using substitution to isolate the variable.
s + l = 180
s + (2s) = 180
simplify.
3s = 180
s = 60
the smaller angle has a value of 60.
now, remember that the larger angle is two times the smaller.
60 x 2 = 120
smaller angle: 60
larger angle: 120
we know this is correct because we know the smaller is 1/2 or 1:2 or 2:4 times the bigger, and the two angles add up to be 180 (60 + 120)
Hope this helps :)
Which set of ordered pairs represent a function
Answers
Answer: second set
Step-by-step explanation:
plzz hellp :( i will mark you the brainlist if some on helps (A rectangular prism has a length of 1 1/4 yards, a width of 2 1/2 yards, and a height of 4 yards.
Enter the volume of the prism as a mixed number in simplest form in the box.
Answers
So the volume V of prism with length [tex]1 \frac{1}{4} [/tex] yards, width [tex]2 \frac{1}{2} [/tex] yards and height of 4 yards will be:
[tex]V=1 \frac{1}{4} * 2 \frac{1}{2} *4 \\ \\ V= \frac{5}{4}* \frac{5}{2}*4 \\ \\ V= \frac{25}{2} \\ \\ V=12 \frac{1}{2} [/tex]
Thus the volume of prism as a mixed number in simplest form will be [tex]12 \frac{1}{2} [/tex] cubic yards
I don't understand this question.
the instructions say: "In exercises 1-4,tell whether the ordered pair is a solution of the inequality."
Answers
5 - 4 > 2
1 > 2
(5, 4) is not a solution to this inequality
Which are reasonable solutions for this situation if x represents the number of hot dogs sold and y represents the number of bottles of water sold? Check all that apply.
(–1, 5)
(0, 6)
(2, 1)
(1, 1.5)
(1, 3)
(2, 2)
Answers
its actually c, and e
Step-by-step explanation:
what is the value of x?
Answers
Answer:
x = 5
Step-by-step explanation:
In this figure with two similar triangles, corresponding edges are proportional. The proportion can be written several ways. One of them is ...
(x+5)/(x+1) = (x)/(x-2)
Multiplying by the product of denominators gives ...
(x -2)(x +5) = (x +1)(x)
x^2 +3x -10 = x^2 +x . . . eliminate parentheses
2x = 10 . . . . . . . . . . . . . . add 10 -x -x^2
x = 5 . . . . . . . . . . . . . . . . divide by 2
Two armies face each other for battle. One army has 1220 soldiers and the other has 549 soldiers. Both armies are divided into smaller groups of equal size called platoons. Find the largest possible number of soldiers in a platoon if the platoon size is equal for the two armies.
Answers
The largest possible number of soldiers in a platoon is 61.
What is the greatest common factor?The GCF (Greatest Common Factor) of two or more numbers is the greatest number among all the common factors of the given numbers. The GCF of two natural numbers x and y is the largest possible number that divides both x and y without leaving any remainder.
Given that, two armies face each other for battle. One army has 1220 soldiers and the other has 549 soldiers.
Factors of 1220 and 549 are
1220 = 2×2×5×61
549 = 3×3×61
So, GCF is 61
Therefore, the largest possible number of soldiers in a platoon is 61.
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suppose that the amount of algae in a pond doubles every 4 hours. if the pond initially contains 90 pounds of algae, how much algae will be in the pound after 12 hours?
720 pounds
360 pounds
1,440 pounds
114 pounds
Answers
Here is your answer:
The proper answer to this question is option B "360 pounds".
Here is how:
All you need to do is multiply 4 by 90 pounds to get your answer....
4*90=360 pounds
Your answer is B.
If you need anymore help feel free to ask me!
Hope this helps!
The radius and height of a right cylinder are each multiplied by 2. what is that change in the total surface area of the cylinder
Answers
The total surface area is multiplied by 4.
When both the radius and height of a right cylinder are multiplied by 2, the change in the total surface area is 4 times the original surface area.
Explanation:
The total surface area of a right cylinder is given by the formula A = 2πrh + 2πr², where r is the radius and h is the height. When both the radius and height are multiplied by 2, we can calculate the change in the total surface area:
The new radius is 2r, so the new area of the bases is 4πr².The new height is 2h, so the new area of the lateral surface is 2π(2r)(2h) = 8πrh.Therefore, the total surface area of the new cylinder is A' = 4πr² + 8πrh = 4(πr² + 2πrh) = 4A.Learn more about Total surface area of a cylinder here:https://brainly.com/question/35459045
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PLEASE HELP
7.02
1. Determine whether the sequence converges or diverges. If it converges, give the limit.
60, 10, five divided by three , five divided by eighteen , ...
A) Converges; 72
B) Converges; 0
C) Diverges
D) Converges; -15540
2. Find an explicit rule for the nth term of the sequence.
1, 3, 9, 27, ...
A) an = 1 • 3n + 1
B) an = 3 • 1n - 1
C) an = 1 • 3n - 1
D) an = 1 • 3n
3. Find an explicit rule for the nth term of the sequence.
-5, -25, -125, -625, ...
A) an = -5 • 5n
B) an = 5 • -5n + 1
C) an = 5 • -5n
D) an = -5 • 5n - 1
4. Find an explicit rule for the nth term of a geometric sequence where the second and fifth terms are -6 and 162, respectively.
A) an = 2 • 3n - 1
B) an = 2 • (-3)n - 1
C) an = 2 • 3n
D) an = 2 • (-3)n + 1
5. A certain radioactive isotope has a half-life of 11 days. If one is to make a table showing the half-life decay of a sample of this isotope from 32 grams to 1 gram; list the time (in days, starting with t = 0) in the first column and the mass remaining (in grams) in the second column, which type of sequence is used in the first column and which type of sequence is used in the second column?
Answers
2. C
5.
TABLE
0 32
5 16
10 8
15 4
20 2
after 25 days ----> from 32g to 1g
first column: increments of +5; arithmetic sequence
second clmn: x5 ; geometric sequence
Answers:
1-A, 2-C, 3- D, 4- B.
LCD for 13/4x and 27/3x^2
Answers
In the least common denominator, LCD, we consider the terms that are in the denominator of the fractions; therefore in this case, our focus will be on:
[tex]4x,3x^{2}[/tex]
Now,
Let us find LCD of the above two terms:
[tex]4x[/tex] = 2*2*[tex]x[/tex]
[tex]3x^{2}[/tex] = 3*[tex]x^{2}[/tex]
Therefore, the LCD = 2*2*3*[tex]x^{2}[/tex] (always go for the highest level exponent for LCD)
Ans: LCD = 12[tex]x^{2}[/tex]
4.2(3.9r – 5.9s) + 7.9s – 9.53r
A.
16.88r + 6.85s
B.
10.82r + 31.15s
C.
10.82r – 31.15s
D.
6.85r – 16.88s
Answers
Answer:
D. 6.85r – 16.88s
Step-by-step explanation:
Use the distributive property to eliminate parentheses, then collect terms.
4.2(3.9r -5.9s) +7.9s -9.53r
= 16.38r -24.78s +7.9s -9.53r
= (16.38 -9.53)r +(-24.78 +7.9)s
= 6.85r -16.88s