Answer:
Step-by-step explanation:
1)
[tex]cot x sec^4 x = cotx + 2tanx + tan^3 x[/tex]
[tex]RHS =[/tex]
[tex]=\frac{cosx}{sinx} + 2 \frac{sinx }{cosx} + \frac{sin^3x }{cos^3x}\\\\[/tex]
[tex]= \frac{cosx(cos^3x) + 2sinx(sinx \ cos^2x ) + sin^3x(sinx)}{sinx \ cos^3x}\\\\[/tex] [tex][\ taking LCM \ ][/tex]
[tex]=\frac{cos^4x + 2sin^2xcos^2x +sin^4x }{sinx cos^3x}[/tex]
[tex]= \frac{(sin^2 x + cos^2x)^2 }{sin x \ cos^3 x}[/tex] [tex][ \ a^4 + 2a^2b^2 + b^4 = (a^2 + b^2 ) ^2 \ ][/tex]
[tex]= \frac{1}{sinx \ cos^3 x}\\\\= \frac{1 \times cosx}{sinx \times cos^3x \times cosx}[/tex] [tex][ \ multiplying\ and \ dividing \ by \ cosx \ ][/tex]
[tex]= \frac{cosx}{sinx} \times \frac{1}{cos^4x}\\\\=cot x \ sec^4 x[/tex]
[tex]= LHS[/tex]
2)
[tex]sin x \ ( tanx \ cosx - cotx \ cosx) = 1 - 2cos^2x[/tex]
[tex]LHS =[/tex]
[tex]=sinx( [ \frac{sinx}{cosx} \times cosx)] - [ \frac{cosx}{sinx}\times cosx] )\\\\= sinx (sinx - \frac{cos^2x}{sinx})\\\\=sin^2x - cos^2 x\\\\=(1 - cos^2x ) -cos^2 x[/tex] [tex][ \ sin^2x = 1 -cos^2 x \ ][/tex]
[tex]= 1 -cos^2x - cos^2 x \\\\= 1 - 2cos^2x \\\\=RHS[/tex]
3)
[tex]1 + sec^2x \ sin^2x = sec^2 x[/tex]
[tex]LHS =[/tex]
[tex]= 1 +sec^2x \sin^2x \\\\= 1 + (\frac{1}{cos^2x} \times sin^2x )\\\\= 1 + \frac{sin^2 x}{cos^2x}\\\\= 1 + tan^2x \\\\= sec^2 x\\\\=RHS[/tex]
4)
[tex]\frac{sinx}{1 -cosx} + \frac{sinx}{1+cosx} = 2 \ cosec x[/tex]
[tex]LHS =[/tex]
[tex]=\frac{sinx}{1 -cosx} + \frac{sinx}{1+cosx} \\\\= \frac{sinx(1 +cosx)}{(1-cosx)(1+cosx)} + \frac{sinx(1-cox)}{(1+cosx)(1-cosx)}\\\\= \frac{sinx +sinx\ cosx}{(1 - cos^2x)} + \frac{sinx - sinx \ cosx}{1 - cos^2x}\\\\=\frac{sinx + sinx \ cosx + sinx - sinx \ cosx}{1 - cos^2x}\\\\=\frac{2sinx}{sin^2x}\\\\=\frac{2}{sinx}\\\\=2 cosec\ x\\\\=RHS[/tex]
5)
[tex]- tan^2 + sec^2 x = 1\\\\[/tex]
[tex]sin^2 x + cos^2 x = 1\\\\\frac{sin^2x }{cos^2x} + \frac{cos^2x}{cos^x} = \frac{1}{cos^2x}\\\\tan^2x + 1 = sec^2x \\\\1 = sec^2 - tan^2x \\\\-tan^2x + sec^2 x = 1[/tex]
To test this series for convergence
∝
∑ (4^n+7)/7^n
n=1
You could use the limit comparison test, comparing it to the series
∝
∑ r^n
n=1
Where r=???
Completing the test, it shows the series:
r should be 4/7. You're comparing the given series to a geometric series that converges. By the limit comparison test, you have
[tex]\displaystyle\lim_{n\to\infty}\frac{\frac{4^n+7}{7^n}}{\frac{4^n}{7^n}}=\lim_{n\to\infty}\frac{4^n+7}{4^n}=\lim_{n\to\infty}\left(1+\frac7{4^n}\right)=1[/tex]
and since this limit is positive and finite, and the series you're comparing to is convergent, then the first series must also be convergent.
Without using mathematical table or calculator simplify 3 4/9 ÷(5 1/3 _ 2 3/4) + 5 9/10
Answer:
[tex]{ \tt{3 \frac{4}{9} \div (5 \frac{1}{3} - 2 \frac{3}{4}) + 5 \frac{9}{10} }} \\ \\ = { \tt{ \frac{31}{9} \div ( \frac{16}{3} - \frac{11}{4} ) + \frac{59}{10} }} \\ \\ = { \tt{ \frac{31}{9} \div ( \frac{31}{12} ) + \frac{59}{10} }} \\ \\ { \tt{ = \frac{4}{3} + \frac{59}{10} }} \\ \\ { \bf{ = \frac{217}{30} }} \\ \\ { \boxed{ \tt{answer : 7 \frac{7}{30} }}} \\ \\ { \underline{ \blue{ \tt{becker ⚜jnr}}}}[/tex]
Answer:
[tex]7 \frac{7}{30}[/tex]
Step-by-step explanation:
[tex]3 \frac{4}{9} \div ( 5\frac{1}{3} - 2 \frac{3}{4}) + 5 \frac{9}{10}\\\\\frac{31}{9} \div (\frac{16}{3} - \frac{11}{4} ) + \frac{59}{10} \\\\\\Solving \ using \ BODMAS\\\\First \ Solve \ expression \ inside \ Bracket \\\\\frac{31}{9} \div (\frac{(16 \times 4) - ( 11 \times 3)}{12}) + \frac{59}{10} \\\\\frac{31}{9} \div (\frac{64- 33)}{12}) + \frac{59}{10} \\\\\frac{31}{9} \div \frac{31}{12} + \frac{59}{10} \\\\\\ \\\\\\Next \ solve \ Dvision \\\\\frac{\frac{31}{9}}{\frac{31}{12}} + \frac{59}{10}\\\\[/tex]
[tex](\frac{31}{9}} \times {\frac{12}{31}) + \frac{59}{10}[/tex]
[tex]\frac{4}{3} + \frac{59}{10}\\\\ Now \ solve \ final \ expression \\\\\\\frac{(4 \times 10) + ( 59 \times 3)}{30}\\\\\frac{40 + 177}{30}\\\\\frac{217}{30}\\\\7 \frac{7}{30}[/tex]
The perimeter of a square garden is 12 km. Find its area.
Please help me with this math word problem
2 [19 marks]
state of the main dams supplying the Cape Metropolitan area with water
as
compared to the five previous years is reflected in the table below.
The capacity is given in million cubic meters (million m').
TABLE 2: Water level of dams supplying water in the Cape Metropolitan area.
BULK
DAN STORAGE
Current Previous
CAPACITY
%
week
week
2012
2013
2014
2015
2016
6 Aug
WEMNERSHOEK
58,644
79.1
99.9
99.9
71.1
69.1
60.8
STEENBRAS LOWER
33,517
100.2
100.6
100.1
90.6
64.1
63.4
STEENBRAS UPPER
31,767
99.6
102.4
100.3
100.6
99.6
100.7
VOELVLEI
164,095
73.6
94.8
99.9
49.5
57.6
55.3
THEEWATERSKLOOF
480,188
84
103.3
102.9
71.9
50.2
49.2
BERG RIVER
130,010
103.8
101.8
100.7
85
64.5
62.2
TOTAL STORED
899,221 770,625 908,922 912,967 641,009 512,850 501,397
% STORAGE
85.8
1012
101.6
71.4
57.1
55.8
2.1
What does the word capacity mean?
(2)
2.2
Determine the range of the capacity of these dams.
(3)
2.3
Determine the median capacity of these dams.
(3)
2.4
Which dam showed an increase in the water level from 2015 to
2016?
(2)
2.5
(3)
Calculate, to the nearest million m. the current amount of water in
the Berg River dam
Which dam's water level remained the most constant over this five year
period?
2.6
(2)
Answer:
berg river
Step-by-step explanation:
it has good environmental health
2. Graph on a coordinate plane or explain how to graph: x = 5
Answer:
x = 5 is a vertical line at x = 5
Solve for X.
12x − 39 ≤ 9 AND −4x + 3 < −6
Choose 1 answer:
A. x ≥ 4
B. 9/4 < x < 4
C. x > -9/4
D. There are no solutions.
E. All values of X are solutions.
Answer: D.There is no answer.
Step-by-step explanation:
58% of U.S. adults have very little confidence in newspapers. You randomly select 10 U.S. adults. Find the probability that the number of U.S. adults who have very little confidence in newspapers is (a) exactly five, (b) at least six, and (c) less than four.
a) P(5)=
(b) P(x≥6)=
(c) P(x<4)=
Answer:
.216165788
.582225057
.417774943
Step-by-step explanation:
We need to use a binomial distribution here
A.
10C5*.58⁵*(1-.58)⁵= .216165788
B.
I honestly think the fastest way to solve this is adding the probabiblity of exactly 6,7,8,9,10
which means we write
10C6*.58⁶*(1-.58)⁴+10C7*.58⁷*(1-.58)³+10C8*.58⁸*(1-.58)²+10C9*.58⁹*(1-.58)+10C10*.58¹⁰= .582225057
C.
To solve this just take the compliment of answer B
1-.582225057= .417774943
Which fraction is closest to 1/2?
A:1/6
B:3/8
C:3/4
D:-1/2
Explain how to do this and provide with an answer.
Answer:
V=480m^2
Step-by-step explanation:
Find the area of the figure round to the nearest tenth
Answer:
Area of given figure = 60.8 mm² (Approx.)
Step-by-step explanation:
Given:
Length of figure = 9.3 mm
Width of figure = 7.8 mm
Height of triangular cut = 3 mm
Find:
Area of given figure
Computation:
Area of given figure = [(Length)(Width)] - Area of triangle
Area of given figure = [(9.3)(7.8)] - [(1/2)(b)(h)]
Area of given figure = [(9.3)(7.8)] - [(1/2)(7.8)(3)]
Area of given figure = [(9.3)(7.8)] - [(1/2)(7.8)(3)]
Area of given figure = [72.54] - [(1/2)(7.8)(3)]
Area of given figure = [72.54] - [11.7]
Area of given figure = 60.8 mm² (Approx.)
Find the value of x
(it needs to be 20 characters so don’t mind the extra ness ………..)
How can you use problem-solving strategies in solving personal, professional, and mathematical problems? Explain in 5-7 sentences and I will mark you the brainliest.
Answer:
Step-by-step explanation:
Problem-solving strategies are created as ways of making a problem easier to understand and this leads to it being easier to solve. For example, one strategy is known as compartmentalizing. This involves splitting a problem into various smaller problems. It makes solving these smaller problems easier and less stressful, and once the smaller problems are solved the bigger one is automatically solved as well. Such a strategy can be applied to any problem in any category including math.
Class 5A can complete a project in 15 days while class 5B needs twice that amount of time. To complete this project before the summer festival, both class 5A and class 5B need to work together. Due to other tasks, class 5A has to leave for 3 days while class 5B has to leave for 6 days. Knowing that both classes do not leave at the same time, and they do work together on some days, what is the total number of days taken to complete this project?
Answer:
it takne 23 days to complete it I hope it is clear add all the no
If n is a positive integer, how many 5-tuples of integers from 1 through n can be formed in which the elements of the 5-tuple are written in increasing order but are not necessarily distinct
This question is incomplete, the complete question is;
If n is a positive integer, how many 5-tuples of integers from 1 through n can be formed in which the elements of the 5-tuple are written in increasing order but are not necessarily distinct.
In other words, how many 5-tuples of integers ( h, i , j , m ), are there with n ≥ h ≥ i ≥ j ≥ k ≥ m ≥ 1 ?
Answer:
the number of 5-tuples of integers from 1 through n that can be formed is [ n( n+1 ) ( n+2 ) ( n+3 ) ( n+4 ) ] / 120
Step-by-step explanation:
Given the data in the question;
Any quintuple ( h, i , j , m ), with n ≥ h ≥ i ≥ j ≥ k ≥ m ≥ 1
this can be represented as a string of ( n-1 ) vertical bars and 5 crosses.
So the positions of the crosses will indicate which 5 integers from 1 to n are indicated in the n-tuple'
Hence, the number of such quintuple is the same as the number of strings of ( n-1 ) vertical bars and 5 crosses such as;
[tex]\left[\begin{array}{ccccc}5&+&n&-&1\\&&5\\\end{array}\right] = \left[\begin{array}{ccc}n&+&4\\&5&\\\end{array}\right][/tex]
= [( n + 4 )! ] / [ 5!( n + 4 - 5 )! ]
= [( n + 4 )!] / [ 5!( n-1 )! ]
= [ n( n+1 ) ( n+2 ) ( n+3 ) ( n+4 ) ] / 120
Therefore, the number of 5-tuples of integers from 1 through n that can be formed is [ n( n+1 ) ( n+2 ) ( n+3 ) ( n+4 ) ] / 120
Erika wondered if there is a relationship between the amount of sugar (in grams) and the number of calories in movie theater candy.
She gathered the data from a sample of 12 types of candy and constructed the scatter plot shown below.
Find the approximate slope and y-intercept (0,b) of an estimated line of best fit.
Answer:
the slope is 8/7 and the y-intercept is 300
Step-by-step explanation:
The y-intercept is 300 because that is where the estimated line of bets fit (the red line) crosses the y-intercept.
What is the length of Line segment H A? 7 units 8 units 24 units 48 units
dogs alpha an 125789 SMS Skoda Eloisa 124579 harm Occam
Answer:
48
Step-by-step explanation:
correct on Edge 2021
Complete the remainder of the
table for the given function rule:
y = = + 7
X-8 -4 0 4
4 8
y| 5 [?] [] [] []
Answer:
x = -4, y = 6.
x = 0, y = 7.
x = 4, y = 8.
x = 8, y = 9.
Step-by-step explanation:
We are given the following rule:
[tex]y = \frac{x}{4} + 7[/tex]
To solve this question, we replace x by the asked values.
When x = -4
[tex]y = \frac{-4}{4} + 7 = -1 + 7 = 6[/tex]
So x = -4, y = 6.
When x = 0
[tex]y = \frac{0}{4} + 7 = 0 + 7 = 7[/tex]
So x = 0, y = 7.
When x = 4
[tex]y = \frac{4}{4} + 7 = 1 + 7 = 8[/tex]
So x = 4, y = 8.
When x = 8
[tex]y = \frac{8}{4} + 7 = 2 + 7 = 9[/tex]
So x = 8, y = 9.
Solve the inequality: 7x + 5 > 2. - 35 Show all work on the "Scratch pad".
1. A resident lot has the shape of a parallelogram. Its base measures 20 meters. The distance between the
parallel sides is 8 meters. What is the area of the lot?
Answer:
160 m²
Step-by-step explanation:
Given :
A parallelogram shaped lot :
Base of lot = 20 m
Distance between parallel sides, = height of lot = 8 m
The area of the lot can be obtained using the area formula of a parallelogram :
Area = base * height
Area = 20 m * 8 m
Area = 160 m²
The manager of a furniture factory finds that it costs $3000 to manufacture 80 chairs in one day and $4800 to produce 280 chairs in one day. (a) Express the cost C (in dollars) as a function of the number of chairs x produced, assuming that it is linear. C
9514 1404 393
Answer:
C = 9x +2280
Step-by-step explanation:
The 2-point form of the equation for a line can be a place to start.
y = (y2 -y1)/(x2 -x1)(x -x1) +y1
C = (4800 -3000)/(280 -80)(x -80) +3000 . . . . . use given values
C = 1800/200(x -80) +3000 . . . . simplify some
C = 9x -720 +3000 . . . . eliminate parentheses
C = 9x +2280
It took Fred 12 hours to travel over pack ice from one town to another town 360 miles away. During the return journey it took him 15 minutes
Step-by-step explanation:
what is your question please
One side of a triangle is 12 feet shorter than the second side. The third side is 2 feet shorter than the second side. The perimeter of a triangle is 55 feet. Find the length of each side.
Answer:
The three sides are 27 feet, 15 feet, 13 feet
Step-by-step explanation:
Let second side of a triangle be = a
Let one side be 12 feet shorter than the second side = (a - 12)
Let the third side be 2 feet shorter than the second side= (a - 12) - 2 =(a - 14)
Perimeter of triangle = Sum of length of all 3 sides
55 = a + (a - 12) + (a - 14)
55 = a + a + a - 12 - 14
55 = 3a - 26
55 + 26 = 3a
81 = 3a
a = 27
Length of one side, a - 12 = 27 - 12 = 15 feet
Length of second side, a = 27 feet
Length of third side, a - 14 = 27 - 14 = 13 feet
The answer is attached. I hope this helps answer your question!
Please help me! I will give you Brainlist if you get it right!
Answer:
B
Step-by-step explanation:
Find the area of the circle with r = 36/2 Area1 = π r²
divide Area1 by two since the upper part of the figure is a semi-circle
then finally add and area of the rectangle Area2 = (18)(36)
Total area = Area 1 + Area 2
Answer:
1156.7 cm^2
Step-by-step explanation:
for finding area of semi circle
diameter=36 cm
radius=diameter/2
=36/2
=18 cm
area of semi circle=πr^2/2
=3.14*(18)^2/2
=3.14*324/2
=1017.36/2
=508.68 cm^2
area of rectangle=length*breadth
=18 cm *36 cm
=648 cm^2
area of the figure=area of semi circle + area of rectangle
=508.68 + 648
=1156.68
=1156.7 cm^2
the graph of y= -2x + 11 is:
Answer:
D. a line that shows only one solution to the equation
Step-by-step explanation:
I hope this helps uwu.
The tread life on tires produced at one factory has a standard deviation of sigma equals 4 comma 000 miles. What is the standard deviation of the sampling distribution of the sample means given the sample size is 4
Answer:
[tex]\sigma_x = 2000[/tex]
Step-by-step explanation:
Given
[tex]\sigma = 4000[/tex]
[tex]n = 4[/tex]
Required
The sample standard deviation
The sample standard deviation cannot be calculated directly. However, we can use the value of standard error because standard error approximates to sample standard deviation.
So, we have:
[tex]\sigma_x = \frac{\sigma}{\sqrt n}[/tex]
[tex]\sigma_x = \frac{4000}{\sqrt 4}[/tex]
[tex]\sigma_x = \frac{4000}{2}[/tex]
[tex]\sigma_x = 2000[/tex]
Hence, the sample standard deviation is 2000
Twain's decision to end "The War Prayer" with the townspeople ignoring what
the stranger said is a good example of
A. irony
B. polyptoton
C. coincidence
D. parallelism
SUBMIT
Answer:
Irony
Explanation:
I just took the test
Alice and Bob took a test, which has ten questions. Given that Alice answered six questions correctly and Bob answered eight questions correctly, compute the probability that there exists at least one question on the test which is answered correctly by Alice but not by Bob.
Answer:
0.12
Step-by-step explanation:
Total number of questions in the book = 10
Number of questions answered correctly by Alice = 6
Number of questions answered correctly by Bob = 8
Probability of Alice answering a question correctly = 0.6
Probability of Alice answering a question incorrectly = 1- 0.6 = 0.4
Probability of Bob answering a question correctly = 0.8
Probability of Bob answering a question incorrectly = 1- 0.8 = 0.2
Probability that there exists at least one question on the test which is answered correctly by Alice but not by Bob = 0.6 *0.2 = 0.12
If A varies directly as the cube root of B and if A = 3 when B= 64, find the formula con- necting the variables.
Answer:
A = [tex]\frac{3}{4}[/tex] [tex]\sqrt[3]{B}[/tex]
Step-by-step explanation:
Given A varies directly as [tex]\sqrt[3]{B}[/tex] then the equation relating them is
A = k [tex]\sqrt[3]{B}[/tex] ← k is the constant of variation
To find k use the condition A = 3 when B = 64 , then
3 = k [tex]\sqrt[3]{64}[/tex] = 4k ( divide both sides by 4 )
[tex]\frac{3}{4}[/tex] = k
A = [tex]\frac{3}{4}[/tex] [tex]\sqrt[3]{B}[/tex] ← equation of variation
Jenny made her uncle a quilt. The width is 7ft and the length is 5 ft. What is the area of the quilt?
Answer:
35 ft^2
Step-by-step explanation:
A = wl
A = 7 * 5
A = 35