Answers
[tex]\text{L.H.S}\\\\=\cot^2 \dfrac{\pi}6 -2\cos^2 \dfrac{\pi}{3}-\dfrac 34 \sec^2 \dfrac{\pi}4-4\sec^2 \dfrac{\pi}6\\\\\\=\cot^2 30^\circ -2 \cos^2 60^\circ- \dfrac 34 \sec^2 45^{\circ} -4 \sec^2 30^{\circ}~~~~~~~;[\pi= 180^{\circ}]\\\\\\=\left(\sqrt 3 \right)^2 -2 \left( \dfrac 12 \right)^2 -\dfrac 34 \left(\sqrt 2 \right)^2 -4 \left(\dfrac 2{\sqrt 3} \right)^2\\\\\\=3-2 \cdot \dfrac 14 - \dfrac 34 \cdot 2 -4 \cdot \dfrac 43\\ \\\\=3-\dfrac 12-\dfrac 32 - \dfrac{16}3\\\\\\[/tex]
[tex]\\=\dfrac{9-16} 3 - \dfrac 42 \\\\\\=\dfrac{-7}{3}-2\\\\\\=\dfrac{-7-6}3\\\\\\=-\dfrac{13}3\\\\\\=-4\dfrac 13 \\\\\\=\text{R.H.S}\\\\\\\text{Proved.}[/tex]
Related Questions
This box plot shows information about the marks scored in a test.
Nobody gained exactly 30, 48 or 70 marks.
120 students gained less than 70 marks.
How many students gained more than 48 marks?
Answers
we need to multiply 0.75 (75%) by something to get 120. which is 160 (the total number of all students).
and since 48 is the median score, find 50% of 160 which is 80!
hope this helps :)
Given: The two functions below, f(x) and g(x). Find: How do the value of each functions outputs compare when x=0?
f(x)< g(x).
g(x)=f(x)
f(x)> g(x)
Answers
We will see that, when evaluated in x = 0, g(x) is larger than f(x).
How to compare the functions when x = 0?First, we can see that:
g(x) = x + 3
Then, evaluating it in x = 0 we get:
g(0) = 0 + 3 = 3
Now, if we go to the table that represents f(x), we can see that it has the point (0, -6).
Then we can get:
f(0) = -6
With that, we can conclude that: g(0) > f(0), so the correct option is the first one.
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Question content area top
Part 1
A cake has two layers. Each layer is a regular hexagonal prism. You cut and remove a slice that takes away one face of each prism as shown. What is the volume of the slice? What is the volume of the remaining cake? Use pencil and paper. Describe two ways to find the volume of the slice.
5 in.
3 in.
2.6 in.
4.3 in.
2 in.
3 in.
(The figure is not to scale.)
Question content area bottom
Part 1
The volume of the slice is
40 in..
(Round to the nearest whole number as needed.)
Part 2
The volume of the remaining cake is
enter your response here in..
Answers
The volume of the slice is 40 in³. The volume of the remaining cake would be 197.014 in³.
What is a regular hexagon?A regular hexagon can be defined as a closed shape consisting of six equal sides and six equal angles.
Here we have two regular hexagons
one top small hexagon cake with a side of length = 3 in, height = 3 in
One big hexagon cake, side of length = 4 in, Height = 4 in
A slice cut such that it removes a side segment is equivalent to an equilateral triangle with a side
length = length of hexagon side
The length of the side of the removed equilateral triangle side
Top small cake slice triangle side = 3 in.
Area of surface of small slice = 1/2 x b x h = 1/2 x 3 x 3 x sin 60
= 9√3/ 4
The volume of a small slice
= Area of surface small slice × Height of small cake
= 9√3/ 4 x 3
= 11. 69
Big cake slice triangle side = 4 in.
Area of the surface of big slice = 1/2 x 4 x 4 x sin 60
= 4√3
The volume of big slice = Area of the surface of big slice × Height of big slice
= 16√3
= 28
The total volume of slice = Volume of small slice + Volume of big slice
Total volume of slice = 12 in³ +28 in³ = 40 in³
For the small cake,
the remaining volume = 5 x 11.69 = 58.45
For the big cake
the remaining volume = 5 x 27.71 = 138.56
Total volume remaining cake
= 58.45 in³ + 138.56 in³ = 197.014 in³
a = Length of side
h = Height of hexagon
The volume of each slice is,
= a^2 x h x √3/4
For the small cake, we have
a = 3 in.
h = 3 in.
The volume of small slice = a^2 x h x √3/4
= 9 x 3 x √3/4
= 27√3/4
For the big cake, we have
a = 4 in.
h = 4 in.
Volume of big slice = a^2 x h x √3/4
= 16 √3
The total volume of slice = Volume of small slice + Volume of a big slice
Total volume of slice = 27√3/4 + 16 √3
The total volume of the slice = 39404 in³.
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What is the sphere's volume?
Answers
Answer:
[tex]972\pi~ \text{in}^3[/tex]
Step-by-step explanation:
[tex]\text{Volume of sphere} = \dfrac 43 \pi r^3 \\\\\\~~~~~~~~~~~~~~~~~~~~~~~~=\dfrac 43 \pi \left( \dfrac d{2} \right)^3\\\\\\~~~~~~~~~~~~~~~~~~~~~~~~=\dfrac 43 \pi \cdot \left(\dfrac{18}{2}\right)^3\\\\\\~~~~~~~~~~~~~~~~~~~~~~~~=\dfrac{4\pi}3 \cdot 9^3 \\\\\\~~~~~~~~~~~~~~~~~~~~~~~~=972\pi~ \text{in}^3[/tex]
esi ran around a rectangular swimming pool 31 times if the distance around the pool is 800m. find the total distance covered by esi km and m
Answers
Answer:
24,800m or 24.8km or 24km 800m
Step-by-step explanation:
Perimeter of Rectangle (Given) = 800m or (800/1000)km = 0.8km
Total Distance covered by esi = Perimeter of Rectangle x Number of round ran
= 800m or 0.8km x 31
= 24,800m or 24.8km or 24km 800m
Not sure how you want the answer in so I came up with all possible answers.
Answer:
24.8km
24800m
Step-by-step explanation:
800 x 31 = 24800
24800m
to convert 24800m into km, we divide 24800 by 1000
24800/1000 = 24.8
24.8 km
hope this helps:)
Daisy is making an abstract painting with two triangles. The dimensions of the painting are shown below:
Two triangles share the same height of 10 inches. One triangle has a base of 8 inches, and the other is 12 inches.
The total area of the two triangles is _____ square inches.
Answers
Answer:
The total area of the two triangles is 100 square inches.
Step-by-step explanation:
Solution:
Area of one triangle:
Height = 10 inches
Base = 8 inches
Area of triangle =
= 40 square inches
Area of another triangle:
Height = 10 inches
Base = 12 inches
Area of triangle =
= 60 square inches
Total area of the two triangles = 40 square inches + 60 square inches
= 100 square inches
The total area of the two triangles is 100 square inches.
hope that helped:)
In a random population, out of 500 people, 160 had blue eyes. In a group of 2500 people, how many would have blue eyes?
Answers
======================================================
Work Shown:
(160 with blue eyes)/(500 total) = (x with blue eyes)/(2500 total)
160/500 = x/2500
x = 2500*(160/500)
x = 800
------------
Another approach:
160/500 = 0.32 = 32% of the first group has blue eyes
Assuming this percentage is the same for any group, then,
32% of 2500 = 0.32*2500 = 800 people of the second group are estimated to have blue eyes, of the 2500 total.
The volume of a rectangular pyramid is 220 units^3
3
. If the length of the rectangular base measures 6 units and the width of the rectangular base measures 10 units, find the height of the pyramid.
Answers
Answer:
h = 11 units
Step-by-step explanation:
Volume of a Rectangular Pyramid = lwh/3
220 = 6*10*h/3
(220) * (3) = ((6)*(10)*(h) / 3) * 3
660 = (6) (10) (h)
Simplify both sides of the equation.
660 = 60h
h = 11 units
In the xy-plane, The line P is perpendicular to the graph of the equation 4x+3y=12. Which of the following is the slope of line P? A. -4 B.-3 C. 3/4 D.12
Answers
A slope is also known as the gradient of a line. The slope of line P is 3/4.
What is Slope?A slope also known as the gradient of a line is a number that helps to know both the direction and the steepness of the line.
As it is known that for two perpendicular lines the slope of the lines will be negative reciprocal of each other. The slope of line 4x+3y=12 can be written as,
y = 4 - (4/3)x
m₁ = -1/m₂
-(4/3) = -1/m₂
m₂ = 3/4
Hence, the slope of line P is 3/4.
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5. Find the equation of the line in slope-intercept form.
a. (1,-6) and (-7, 2)
Answers
Step-by-step explanation:
y=1x-(-6)
y=-7x-2
follow and label y and x inside the equation
make sure you draw a graph to help you find the intercept form.
Solve for x: 1 over 3 (2x − 8) = 4. (1 point)
Group of answer choices
2
6
10
10 over 3
Answers
Answer:
x=6
Step-by-step explanation:
[tex]2x - 8 = 4 \\ 2x = 4 + 8 \\ 2x = 12 \\ x = \frac{12}{2} \\ x = 6[/tex]
Kevin bought 6lbs of jelly beans. Antonio bought 66oz of jelly beans.
How many more did Kevin buy than Antonio?
Answers
Answer:
30 ounces (1 pound 14 ounces)
Please give brainliest!
Hope this helps:)
To find this, we first need to convert 6 lbs into ounces
lb = 16 ounce
6 lbs = 96 ounces!
96-66 = 30
Kevin bought 30 more ounces, or 1 pound and 14 ounces more jelly beans than antonio.
can you find a five digit number which has no zeros, and no digit is repeated, and where:
the first digit is a prime number
the second digit is the fith digit minus the first digit.
the third digit is twice the first digit
the forth digit is the third digit plus 3
the fith digit is the diffrence between the first digit and the fourth digit
Answers
Answer:
13,254
hope this helps :)
please crown me brainliest!
The following scatter plot represents the height of a basketball in seconds during a free throw shot.
Answers
please help i have no idea how to do this
Answers
Answer (Step-by-step explanation):
so X is horizontal and Y is vertical. (X,Y) because X comes first and Y comes last and all you need to do is make sure your points are correct and that the best of my ability, you can also try drawing lines to each pin point and you can estimate these (X,Y) because X=? and Y=? so good luck i hope that helps! (:
Piece wise functions
Answers
Answer:
f(-5) = -6
f(-2.6) = 2.4
f(2.1) = 9.41
Step-by-step explanation:
In the question, we are told to find f(-5), f(-2.6), and f(2.1). The numbers in the parentheses represent x.
First, let's look at f(-5). Which equation should we use because x is -5? We should use the first equation because -5 is less than -3. Plug into the equation and solve:
f(-5) = -6 (We didn't have to do much because anything less than -3 equals -6)
Now, let's look at f(-2.6). We should use the equation in the middle because -2.6 is between -3 and 0. Plug -2.6 in the equation and solve:
f(-2.6) = -2.6 + 5
f(-2.6) = 2.4
Lastly, let's look at f(2.1). We should use the third equation because x is greater than 0. Plug 2.1 in the equation and solve:
f(2.1) = [tex](2.1)^{2} +5[/tex]
f(2.1) = 4.41 + 5
f(2.1) = 9.41
Therefore, the final answers are:
f(-5) = -6
f(-2.6) = 2.4
f(2.1) = 9.41
Hope this helps!! If you have questions about my work, please let me know in the comments!
A cylinder has a radius of 12 m and a height of 9 m.
What is the exact volume of the cylinder?
108π m³
216π m³
972π m³
1296π m³
Answers
[tex]\textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=12\\ h=9 \end{cases}\implies V=\pi (12)^2(9)\implies V=1296\pi ~m^3[/tex]
4 people completed their work in one hours how will it take 3 peoples to finish it give your answer in minutes
Answers
60/4= 15
15 x 3 =45 minutes
Evaluate:
[tex]\bf{\sum^{32}_{n=1}\:(2n+8)[/tex]
Please help A.S.A.P., thank you guys!
Please show work as well.
[tex]\bigstar[/tex]
Answers
Explanation:
[tex]\boxed{\sf \sum _{n=1}^{32}\left(2n+8\right)}[/tex]
Formula Required:
[tex]\sf sum \ of \ arithmetic \ series = \dfrac{n}{2} (2a \ + \ (n-1) \ d)[/tex]
Identify the following's:
First Term (a) = (2(1) + 8) = 10Common Difference (d) = 2nd term - first term = (2(2) + 8) - (2(1) + 8) = 2Total Terms (n) = 32Insert variables:
[tex]\rightarrow \ \sf S_{32} = \dfrac{32}{2} (2(10) + (32-1) 2) \quad \xrightarrow{\text{Simplify} } \quad 1312[/tex]
what is the diameter of the cylinder
Answers
Given :-
Volume of cylinder = 245π cubic unitsHeight of cylinder = 5 unitsTo Find :-
Diameter of cylinder?Solution :-
Firstly lets calculate radius of cylinder by using formula of volume of cylinder, as we know that;
Volume of cylinder = πr²hPutting all values we get;
➸ 245π = π × r² × 5
By cutting 'π' with 'π' we get;
➸ 245 = r² × 5
➸ 245/5 = r²
➸ 49 = r²
➸ √(49) = r²
➸ √(7 × 7) = r²
➸ 7 = r
➸ r = 7 units
Hence, radius of cylinder is 7 units.Now lets calculate its diameter, as we know that;
Diameter = Radius × 2Putting all values we get;
➸ Diameter = 7 × 2
➸ Diameter = 14 units
Hence, diameter of cylinder is 14 units.What percent of the first 20 natural numbers are one-diget numbers
Answers
Answer:
9/20 or forty five percent (45%)
Why is y=-2x considered a function?
because there are values of y that correspond to more than one value of x.
because x is bigger than y.
because the value of y corresponds only to one value of x.
because y is bigger than x.
Answers
Yes
Step-by-step explanation:
its a direct-variation function
I WILL GIVE BRAINLIEST look at the right angled triangle abc
the square fits exactly inside the triangle
work out the sizes of angles x y and z
Answers
Answer:
(a) y = 25°
(b) x = 90°
(c) z = 25°
Step by step explanation:
Part A
z + 90° + 65° = 180°
z = 180° - 65° - 90°
z = 25°
Part B
x + 90° = 180°
x = 90°
Part C
x + 65° + y = 180°
90° + 65° + y = 180°
y = 25°
Additional:A straight line has total 180° angle. A square has 4 sides of each 90° angle. A triangle is build up of 180° interior angle.
what is the surface area of the triangular prism? 15ft 9ft 24ft 40ft 15ft PLEASE BE FAST ILL GIVE BRAINLIESTTT TODAYS MY LAST DAY AG SCHOOL TO AHH
Answers
Answer:
B. 2376 Square feet
--------------------------------------------------
Bart had 36 marbles. he gives all of his marbles to four friends. he gives each friend the same number of marbles. how many marbles does each friend have?
Answers
Answer:
9
Step-by-step explanation:
He had 36 Marbles and he gives all to his four friends. And all friends get the same number of marbles so we will have to do division which will be :
36{marbles} divide by 4{friends}=9 so each friend got 9 marbles.
Each friend will have 9 marbles
What is division?
Division is a method of distributing a group of things into equal parts. It is one of the four basic operations of arithmetic, which gives a fair result of sharing.
The division is an operation inverse of multiplication. If 3 groups of 4 make 12 in multiplication; 12 divided into 3 equal groups give 4 in each group in division.
Given that:
[tex]4x=36[/tex]
[tex]36[/tex] ÷ [tex]4[/tex] [tex]=9[/tex]
Therefore, each friend will have 9 marbles
KEYWORDS:
equaldivideshareremainderleft overLearn more about division here:
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Write/Indicate the corresponding measures of 300- 600-900 right triangle.
Answers
Which of the following best describes ZAOR?
R
142⁰
A
Answers
A major arc is an arc that is greater than 180 degrees.
A minor arc is an arc less than 180 degrees.
An acute angle is an angle less than 90 degrees.
What is the central angle?
A central angle is an angle created in the center of a circle with 2 sides being the radius.
Thus, we can see in the figure that we are talking about the angle so we can eliminate the major arc and minor arc.
Now, we clearly see that the angle is greater than 90 degrees so it cannot be an acute angle.
The correct answer is the central angle as it goes with the definition.
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Vassil rounded to the nearest half to estimate the product of Five-eighths and StartFraction 8 over 9 EndFraction. How do the estimated and actual products compare?
(Hint: use 18 for the denominator when comparing.)
The actual product is about StartFraction 1 over 18 EndFraction greater than the estimate.
The actual product is about StartFraction 1 over 18 EndFraction less than the estimate.
The actual product is about StartFraction 1 over 9 EndFraction greater than the estimate.
The actual product is about StartFraction 1 over 9 EndFraction less than the estimate.
Answers
The correct answer is option B which is the actual product is about StartFraction 1 over 18 EndFraction less than the estimate.
What are fractions?The fraction is defined as the division of the whole part into an equal number of parts. here we have the following information Vassil rounded to the nearest half to estimate the product of Five-eighths and StartFraction 8 over 9 EndFraction.
E = [tex]\dfrac{5}{8}\times \dfrac{8}{9}[/tex] = 0.55
Thus the product of the fraction estimated in the nearest half is,
0.5×1= 0.50
Therefore the correct answer is option B which is the actual product is about StartFraction 1 over 18 EndFraction less than the estimate.
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Answer: B
Step-by-step explanation: took test/quiz
f(a)=a^3-10a^2+28a-17 at a=6
Evaluate function using the
Remainder theorem
Show work
I give Brainliest. :)
Answers
Answer:
727
Step-by-step explanation:
6^3-106^2=216+360=576+168=744-17=727
Help please!
preform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use size for measurements of very large or very small quantities (e.g use kilometers per year for sea floor apeading.) intercept scientific notation that has been generated by technology
Answers
Scientific Notation is EASY.
Just move the decimal to the right if it is positive:
6.2 x 10¹ = 62
6.2 x 10² = 620
6.2 x 10³ = 6,200
6.2 x 10⁴ = 62,000
6.2 x 10⁵ = 620,000
6.2 x 10⁶ = 6,200,000
Move the decimal to the left if it is negative:
6.2 x 10⁻¹ .62
6.2 x 10⁻² = .062
6.2 x 10⁻³ = .0062
6.2 x 10⁻⁴ = .00062
6.2 x 10⁻⁵ = .000062
6.2 x 10⁻⁶ = .0000062
What about about 6.2 x 10⁰?
6.2 It wouldn't change location.
I hope this helps!