Answer:
Step-by-step explanation:
We can simplify the expression on the left-hand side using trigonometric identities:
tan(-A) = -tan(A) (since tan(-θ) = -tan(θ))
sin(180°+A) = -sin(A) (since sin(180°+θ) = -sin(θ))
sec(270°-A) = -cos(A) (since sec(270°-θ) = -cos(θ))
cos²(90°+A) = sin²A (since cos²(90°+θ) = sin²θ)
Substituting these values, we get:
-x.sin(A).cos(A).tan(A) = x.sin(-A) - sin²A.sin(A)
-x.sin(A).cos(A).tan(A) = -x.sin(A) - sin³A
Now, we can simplify this equation by moving all the terms to one side:
-x.sin(A).cos(A).tan(A) + x.sin(A) + sin³A = 0
Factoring out sin(A), we get:
sin(A) (-x.cos(A).tan(A) + x + sin²A) = 0
Since sin(A) ≠ 0, we can divide both sides by sin(A):
-x.cos(A).tan(A) + x + sin²A = 0
Multiplying both sides by cos(A), we get:
-x.sin(A) + x.cos²(A) + sin²A.cos(A) = 0
Using the identity cos²(θ) + sin²(θ) = 1, we can write this as:
-x.sin(A) + x(1 - sin²A) + sin²A.cos(A) = 0
Simplifying and rearranging, we get:
x = sin(A)/(cos(A) - sin²(A))
Therefore, the value of x is given by the expression sin(A)/(cos(A) - sin²(A)).
According to Cavalieri’s Principle, which pair of shapes would have equal volumes?
a)a cylinder and a sphere with the same radius
b)a cone and a cylinder with equal base areas and heights
c)a cylinder and a right rectangular prism with equal heights
d) a cone and a pyramid with equal base areas and heights
A cone and a cylinder with equal base areas and heights.
What is volume?
A volume is simply defined as the amount of space occupied by any three-dimensional solid. These solids can be a cube, a cuboid, a cone, a cylinder, or a sphere. Different shapes have different volumes.
b) a cone and a cylinder with equal base areas and heights. According to Cavalieri's principle, if two solid figures have the same height and the same cross-sectional area at every level, then they have the same volume. In this case, the cross-sectional area of a cone and a cylinder with equal base areas and heights will be the same at every level, so their volumes will also be the same.
Therefore, a cone and a cylinder with equal base areas and heights.
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A baseball has radius of 2 inches. What is the volume in cubic inches of the baseball?
I don’t understand how to do this problem. Can anyone help?
I need help asap!!
Only 4% on babies are born on their due data.
Answer:
14
Step-by-step explanation:
yes
i just need to know the answers to the picture
Answer:
6.
[tex]48\pi \: {ft}^{3} [/tex]
7.
[tex]81\pi \: {m}^{3} [/tex]
8.
[tex]112 \: {in}^{3} [/tex]
9.
[tex]14.52\pi \: {cm}^{3} [/tex]
10.
[tex]68.75\pi \: {yd}^{3} [/tex]
11.
[tex]32.269\pi \: {m}^{3} [/tex]
12. h ≈ 3,3 yd
13. h ≈ 5,5 m
14. V ≈ 77,0 in^3
15. V ≈ 69,1 in^3
16. V ≈ 8517,0 in^3
17. V ≈ 2628,1 cm^3
Step-by-step explanation:
6.
[tex]v = \pi {r}^{2} \times h[/tex]
[tex]v = \pi \times {4}^{2} \times 3 = 48\pi[/tex]
.
7.
[tex]v = {9}^{2} \times \pi \times 1 = 81\pi[/tex]
.
8.
[tex]v = {4}^{2} \times \pi \times 7 = 112\pi[/tex]
.
9.
[tex]v = ( {2.2})^{2} \times \pi \times 3 =14.52\pi[/tex]
.
10. r = 0,5 × d
r = 0,5 × 5 = 2,5 yd
[tex]v = ({2.5})^{2} \times \pi \times 11 = 68.75\pi[/tex]
.
11. r = 0,5 × 4,6 = 2,3 m
[tex]v = ({2.3})^{2} \times \pi \times 6.1 = 32.269\pi[/tex]
.
12. V = 41,5 yd^3
r = 2 yd
[tex]v = \pi \times {r}^{2} \times h[/tex]
[tex]41.5= \pi \times {2}^{2} \times h[/tex]
[tex]h = \frac{41.5}{4\pi} = \frac{83}{8\pi} ≈3.3[/tex]
.
13. d = 1,5 m
r = 0,5 × 1,5 = 0,75 m
V = 9,7 m^3
[tex]v = \pi {r}^{2} \times h[/tex]
[tex]9.7 = \pi \times ( {0.75})^{2} \times h[/tex]
[tex]h = \frac{9.7}{0.5625\pi} ≈5.5[/tex]
.
14. Given:
h = 8 in
d = 3,5 in
Find: V - ?
First, let's find the radius:
r = 0,5 × 3,5 = 1,75
[tex]v = \pi {r}^{2} \times h[/tex]
[tex]v = \pi \times( {1.75})^{2} \times 8 =24.5\pi≈77.0[/tex]
.
15 Given:
h = 5,5 in
d = 4 in
Find: V - ?
First, let's find the radius:
r = 0,5 × 4 = 2 in
[tex]v = \pi {r}^{2} \times h[/tex]
[tex]v = \pi \times {2}^{2} \times 5.5 = 22\pi≈69.1[/tex]
.
16. This figure contains 2 cilinders and one rectangular prism
First, let's find the volume of 2 cilinders (r = 0,5 × 25 = 12,5 in)
[tex]v(both \: cilinders) = (\pi \times ({12.5})^{2} \times 4 ) \times 2= 1250\pi[/tex]
[tex]v(prism) = 30 \times 17 \times 9 = 4590[/tex]
[tex]v(total) = 1250\pi + 4590≈8517.0[/tex]
.
17. This figure contains one rectangular prism and two semi-cilinders
First, let's find the volume of 2 semi-cilinders (it counts as one cilinder, since there's 2 identical halves, also r = 0,5 × 8 = 4):
[tex]v(cilinder) = \pi \times {4}^{2} \times 23 = 368\pi[/tex]
[tex]v(prism) = 23 \times 8 \times 8 = 1472[/tex]
[tex]v(total) = 368\pi + 1472≈2628.1[/tex]
how do i get the area
[tex]\textit{area of a segment of a circle}\\\\ A=\cfrac{r^2}{2}\left( \cfrac{\pi \theta }{180}-\sin(\theta ) \right) ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=14\\ \theta =90 \end{cases}\implies A=\cfrac{(14)^2}{2}\left( \cfrac{\pi (90) }{180}-\sin(90^o) \right) \\\\\\ A=\cfrac{196}{2}\left( \cfrac{\pi }{2}-1 \right)\implies A=49\pi - 98~~ \approx ~~ 55.94~cm^2[/tex]
Given a parallelogram ABCD, the measures of angle B = 3x + 36 and angle D = 6x - 6 : find m angle A
Answer: In a parallelogram, opposite angles are congruent. So we know that angle A is congruent to angle C. Let's call the measure of angle A "y".
Therefore, we have:
angle A = y
angle B = 3x + 36
angle C = y (because opposite angles in a parallelogram are congruent)
angle D = 6x - 6
The sum of the measures of the angles in a parallelogram is 360 degrees. So we can write an equation:
angle A + angle B + angle C + angle D = 360
Substituting in the values we know:
y + (3x + 36) + y + (6x - 6) = 360
Simplifying:
2y + 9x + 30 = 360
2y + 9x = 330
Now we have an equation with two variables. But we also know that angle A and angle C are congruent, so y = angle A = angle C. Substituting this into the equation above:
2(angle A) + 9x = 330
2(angle A) = 330 - 9x
angle A = (330 - 9x)/2
Therefore, the measure of angle A is (330 - 9x)/2.
Step-by-step explanation:
Boys ride a bike 25 playing Soccer 26 Girl's ride a bike 22 total based on her data the teach concludes that if a girl is chosen a random there is a 56 probability that She preters Soccer. What's the total number of Student's Survey
Answer:
429
Step-by-step explanation:
Astronomers measure large distances in light-years. One light-year is the distance that light can travel in one year, or approximately 5.88 × 1012 miles. Suppose a star is 9.8 × 101 light-years from Earth. In scientific notation, approximately how many miles is it? (1 point) 5.88 × 1013 miles 5.76 × 1014 miles 5.88 × 1012 miles 9.8 × 1012 miles
The correct answer is 5.88 × 1013 miles. This is because a light-year is the distance that light can travel in one year, or approximately 5.88 × 1012 miles.
What is a light year?A light year is a unit of distance used to measure astronomical distances. It is the distance that light travels in a vacuum in one year, which is equal to 9.46 trillion kilometres. This means that light travelling at a speed of 300,000 kilometres per second would take one year to travel nine trillion kilometres. T
To find the distance of a star from Earth, one must multiply the number of light-years by 5.88 × 1012. In this case, the star is 9.8 × 101 light-years away, meaning that it is 9.8 × 101 times 5.88 × 1012 miles, or 5.88 × 1013 miles, away from Earth.
Light-years are a unit of distance used by astronomers to measure the great distances between stars and galaxies. Light travels at a speed of approximately 186,000 miles per second, and one light-year is the distance that light can travel in one year. For example, a star that is 9.8 × 101 light-years away from Earth is approximately 5.88 × 1013 miles away from Earth. To convert the number of light-years to the number of miles, one must multiply the number of light-years by 5.88 × 1012.
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2. Prove the trig identity.
sin x ( 1 + cot^2x)
I have a calculus exam tomorrow and have no idea how to solve this equation, please provide a detailed explanation. I'm slow.
Answer:
We'll start with the left-hand side (LHS) of the identity, which is:
sin x (1 + cot^2 x)
We can rewrite cot^2 x as (cos x / sin x)^2, since cotangent is the reciprocal of tangent. Substituting this into the LHS, we get:
sin x (1 + (cos x / sin x)^2)
Now we can simplify the expression in the parentheses by using the identity:
tan^2 x + 1 = sec^2 x
Rearranging this identity, we get:
tan^2 x = sec^2 x - 1
Substituting this into our expression, we get:
sin x (1 + (cos x / sin x)^2) = sin x (1 + (cos^2 x / sin^2 x))
= sin x (sin^2 x / sin^2 x + cos^2 x / sin^2 x)
= sin x ((sin^2 x + cos^2 x) / sin^2 x)
= sin x (1 / sin^2 x)
= sin x / sin^2 x
= 1 / sin x
Now we'll simplify the right-hand side (RHS) of the identity, which is:
csc x
We know that csc x is the reciprocal of sin x, so we can rewrite the RHS as:
1 / sin x
This is the same as the expression we obtained for the LHS, so we have shown that:
sin x (1 + cot^2 x) = csc x
And this proves the identity!
Remember, when you're proving trigonometric identities, it's important to be familiar with the fundamental trigonometric identities and the basic algebraic rules of manipulating equations
good luck with your exam
Find a formula for the linear function depicted in the following graph.
f(x)=
The formula for the linear function in the graph is f(x) = -2x + 4.
What is graph?The graph is a data structure that is used to represent relationships between objects. It is composed of nodes (or vertices) that are connected by edges (or lines). Graphs can be used to represent many types of data, such as networks of people, roads, and even abstract concepts like language. Graphs are used in a variety of fields, such as computer science, mathematics, and sociology. They allow for efficient storage and retrieval of data, as well as efficient traversal of the data.
The graph shown below is a linear graph with a slope of -2 and a y-intercept of 4.
To find the formula for the linear function, we can use the slope-intercept form, which is y = mx + b. In this equation, m is the slope of the line and b is the y-intercept.
Therefore, the formula for the linear function in the graph is f(x) = -2x + 4.
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complete question:
Find a formula for the linear function depicted in the following graph.
f(x)=
3.
The graph below represents the decrease in the number of frogs in a lake over time.
360
340
320
300
280
260
240
220
200
180
160
140
120
100
80
60
40
20
2
3
1
Write a function to represent the number of frogs, f, in the lake after m months.
f(m) =
The required function is f(m) = -53.33m + 360, where f(m) represents the number of frogs in the lake after m months.
What is function ?
In mathematics, a function is a rule that assigns a unique output or "dependent variable" to each input or "independent variable" in a set. It is a relation between a set of inputs and a set of possible outputs, with the property that each input is related to exactly one output.
Based on the given graph, it appears that the number of frogs in the lake is decreasing linearly over time. We can use the slope-intercept form of a linear equation to represent this relationship:
y = mx + b
where y is the number of frogs, x is the time in months, m is the slope (or rate of decrease) of the line, and b is the initial number of frogs at time zero.
To find the slope of the line, we can use the two points (0, 360) and (3, 200) from the graph:
m = (change in y) / (change in x) = (200 - 360) / (3 - 0) = -53.33
So the slope of the line is -53.33, which means that the number of frogs is decreasing by an average of 53.33 per month.
To find the initial number of frogs, we can use the y-intercept of the line, which appears to be around 360 on the graph. So we have:
b = 360
Putting it all together, the function that represents the number of frogs in the lake after m months is:
f(m) = -53.33m + 360
Therefore, the required function is f(m) = -53.33m + 360, where f(m) represents the number of frogs in the lake after m months.
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From a 2-pound bag of flour, Marcella took 1/4 pound to bake bread. Which expession tells the weight of the flour left in the bag?
2-0.25
2-1.4
2-0.14
2-0.025
2.5-2
1. Find the m
2. Determine the length of side AB.
3. What are the sine and cosine ratios for angles A and B?
sin
cos
sin
cos
4. What do you notice about the sine of angle A and cosine angle B?
5. What do you notice about the cosine of angle A and the sine of angle B?
6. Add up angles A and B. What do they equal?
7. Given the information you obtained in numbers 1-5, determine the missing angles in A-D below.
a. sin40 degrees=cos___
b. cos27 degrees= sin___
c. sin90 degrees = cos___
d. cos65 degrees = sin___
The length of the side AB in the triangle is AB = 13.9 inches
What is Pythagoras Rule?You should be aware that the Pythagoras' Theorem states that the square of the hypotenuse is equal to the sum of the squares of the other two sides.
The given sides are
AC = 8.5 inches
BC = 11 inches
AB = x
Using the Pythagoras rule we have
x² = 11² + 8.5²
x² = 121 + 72.25
x² = 193.25
x = √193.25
x = 13.9 inches
Therefore AB = 13.9 inches
3 The sine and cosine ratios for angles A and B are
Sine A = opposite/Hypotenuse
Sin A = 11/13.9
Sine A = 0..7914
A = Sin⁻¹0.7914
The ratio cos B = Adjacent /Hypo
Cos B = 8.5/13.9
Cos B = 0.6115
B = Cos⁻¹0.6115
4 The relationship between sine of angle A and cosine angle B is that
Sin A + Cos B = 1 approximately
The sum of angles A and B. are 1
7 a sin40 = cos 50
b cos27 = sin63
c sin 90 = cos0
d cos 65 = sin 25
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what is personal budgeting and why is it important
Personal budgeting is the process of creating a plan for managing your income and expenses to achieve your financial goals. It involves creating a realistic and practical plan and it is important because it help on how you will spend your money each month.
What is Personal budgeting ?Personal budgeting is important for several reasons. First and foremost, it helps you take control of your finances by giving you a clear understanding of your income and expenses, allowing you to identify areas where you can cut back or save more. This can help you avoid overspending and falling into debt, and can also help you save money for future goals such as buying a home, paying for education, or investing for retirement.
Additionally, personal budgeting can help you develop healthy financial habits and increase your financial literacy. By tracking your spending and setting financial goals, you can become more mindful of your money and make more informed decisions about how to allocate your resources. Over time, this can help you build wealth and achieve greater financial stability and security.
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What is 7.1 (2.5) x (2.1
A company sells colored sand for use in art projects. They are trying to decide which of the two cylindrical packa
shown to use.
D
Package A Package B
8 inches
The bases of both packages are congruent to one another. Which statement correctly compares the volumes of
two packages and explains the comparison?
Option C, The two packages have the same volume because their bases are congruent and they have the same height.
What is Volume?
Volume is a measure of the amount of space occupied by a three-dimensional object. It is typically measured in cubic units, such as cubic meters or cubic centimeters.
The volume of cylinder A = πr²h
= 6πr²
The volume of cylinder B= πr²h
= 6πr²
As both the cylinder have same values, Option C, The two packages have the same volume because their bases are congruent and they have the same height.
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Prove that the value of 9^7+3^12 is divisible by 90
PLEASE HELP ASAP
Answer:
90(3^10) is divisible by 90.
Step-by-step explanation:
9^7+3^12=(3^2)^7+3^12
=(3^7)^2+3^12
=(3^14)+(3^12)
=(3^12)(3^2)+3^12
=(3^12)(3^2+1)
=(3^12)(4)
=90(3^10)
A cuboid box whose external measures are 70 cm×28 cm×35 cm. The base, side faces, and back faces are to be covered with colored paper. Find the area of the paper needed.
7,310 cm^2 is the area of the paper that needed to be covered with colored paper as per the given cuboid box dimensions.
The Given data is:
The total surface area of the given cuboid box can be calculated by the sum of the areas of all six faces.
The given dimensions of cuboid box = 70 cm×28 cm×35 cm
The Area of the Base of the cuboid box is:
70 × 35 = 2450 cm^2
The Area of each face of the cuboid box is:
28 × 35 = 980 cm^2
The Area of each back of the cuboid box is:
70 × 28 cm= 1960 cm^2
The total surface area =
2450 cm^2+ 2 × 980 cm^2+ 2 × 1960 cm^2 = 7,310 cm^2
Therefore, we can conclude that 7,310 cm^2 is the area of the paper that needed to be covered with colored paper.
If the vertex of an angle is on the _____ of a circle, then its measure is ______ to the intercepted arc
An angle whose vertex lies on a circle and whose sides intercept the circle (the sides contain chords of the circle) is called an inscribed angle. The measure of an inscribed angle is half the measure of the arc it intercepts
Triangle with the coordinates A (-5,-1), B (-4,4), C (-1,-1)
please help. will mark brainliest
The value y is 35, Since HIJK is an isosceles trapezoid so its diagonal are equal.
What is quadrilateral?A quadrilateral in geometry is a four-sided polygon with four edges and four corners. The name is derived from the Roman words quadri, a variation of four, and latus, which means "side".
Isosceles trapezoid, it is a convex quadrilateral with one set of opposite sides divided by a line of symmetry in Euclidean geometry.
HIJK is an isosceles trapezoid.
So, HJ =IK ( Diagonals are equal in isosceles trapezoid)
5y - 1 = 4y + 34
5y - 4y = 34 + 1
y = 35.
So, the value of y is 35.
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Find a formula for the linear function depicted in the following graph.
f(x)=
The linear functions of the graph is y = 2x + 5
How to determine the linear function of the graphThe complete question is added as attachment
From the question, we have the following parameters that can be used in our computation:
(0, 5) and (-2.5, 0)
From the question, we understand that the function is a linear function
A linear function is represented as
y = mx + c
Using the above as a guide, we have the following equations
0 * m + c = 5
-2.5 * m + c = 0
When evaluated, we have
c = 5
So, we have
-2.5 * m + 5 = 0
This gives
-2.5m = -5
Evaluate
m = 2
So, the equation is y = 2x + 5
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Quantitative Problem: You own a security that provides an annual dividend of $150 forever. The security’s annual return is 7%. What is the present value of this security? Round your answer to the nearest cent. $ 2142.86
The present value of the security is $2142.86, rounded to the nearest cent.
What is value?Value is a subjective concept that is based on personal beliefs, experiences, and backgrounds. It is the appreciation of something, whether tangible or intangible, that is based on a person's perception of its worth. Value is often used to describe the worth or importance of something or someone, and can be expressed in monetary terms or in terms of the usefulness of something. Ultimately, value is the measure of how much something is worth to an individual.
The present value of this security is $2142.86. This is determined by using the formula:
Present Value = Dividend / (1 + R)t
Where Dividend is the annual dividend of $150, R is the rate of return which is 7%, and T is the time in years which is 1.
Therefore, the present value of the security is:
150 / (1 + 0.07)¹ = $2142.86
Thus, the present value of the security is $2142.86, rounded to the nearest cent.
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I will mark you brainiest!
Using the diagram below, which of the following angle pairs represent vertical angles?
A) ∠KDJ ≅ ∠FBG
B) ∠LAC ≅ ∠GBC
C) ∠DCE ≅ ∠BCA
D) ∠DCE ≅ ∠BCE
The following angle pairs represent vertical angles (C) ∠DCE ≅ ∠BCA.
What is Vertically Oppοsite Angle?Vertical angles are a pair οf nοn-adjacent angles fοrmed by the intersectiοn οf twο lines. Vertical οppοsite angles are a type οf vertical angles that are acrοss frοm each οther and have the same measure. In οther wοrds, if twο lines intersect at a pοint, then the angles that are οppοsite each οther (i.e., οne οn the left and οne οn the right οf the intersectiοn) are called vertical οppοsite angles, and they are cοngruent.
Vertical angles are fοrmed by the intersectiοn οf twο lines. They are cοngruent, which means they have the same measure.
Lοοking at the diagram, we see that angles ∠KDJ and ∠FBG are nοt fοrmed by the intersectiοn οf twο lines. They are bοth interiοr angles οf the quadrilateral KDFB. Therefοre, they are nοt vertical angles.
∠LAC and ∠GBC are nοt fοrmed by the intersectiοn οf twο lines. They are bοth interiοr angles οf the quadrilateral KDFB. Therefοre, they are nοt vertical angles.
Angles ∠DCE and ∠BCA are fοrmed by the intersectiοn οf twο lines, and they are οn οppοsite sides οf the transversal AC. Therefοre, they are vertical angles, and chοice (C) is the cοrrect answer.
Angles ∠DCE and ∠BCE share a cοmmοn ray, CE, but they are nοt fοrmed by the intersectiοn οf twο lines. Therefοre, they are nοt vertical angles.
Sο the cοrrect answer is (C) ∠DCE ≅ ∠BCA.
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Lines I1 and I2 are parallel lines. Determine the measures of angle 1 through 12
Answer
1) 58 2) 57 3) 65 4) 65 5) 58 6) 57 7) 58 8) 122 9) 65 10) 115 11) 122 12) 58
Step-by-step explanation:
jen's total assets are $8,794. Her liabilities are $2,670 in credit card debt and $3,622 for a student loan. What is her net worth?
Answer:
2502
Step-by-step explanation:
8,794-2,670-3,622=
given the line 4x+5y-9=0 find the gradient , intercept y and intercept x and sketch line
According to given conditions, Gradient = -4/5, y-intercept = 9/5, x-intercept = 9/4.
What is co-ordinate geometry ?
Coordinate geometry is a branch of mathematics that deals with the study of geometric shapes using a coordinate system. In this system, points are identified by their positions in relation to two or more perpendicular lines called axes.
To find the gradient and intercepts of the line 4x+5y-9=0, we need to rearrange the equation into the slope-intercept form y=mx+b, where m is the slope and b is the y-intercept.
First, we can solve for y:
4x + 5y - 9 = 0
5y = -4x + 9
y = (-4/5)x + 9/5
Now we can see that the slope (m) of the line is -4/5 and the y-intercept (b) is 9/5. To find the x-intercept, we can set y=0 and solve for x:
(-4/5)x + 9/5 = 0
-4x + 9 = 0
x = 9/4
So the x-intercept is (9/4, 0).
To sketch the line, we can plot the y-intercept at (0, 9/5), the x-intercept at (9/4, 0), and draw a straight line passing through both points:
Therefore, according to given conditions, Gradient = -4/5, y-intercept = 9/5, x-intercept = 9/4.
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5.937÷10 to the 3rd=
Answer:
Step-by-step explanation:
(5.937/10)^3=0.20926719195
or
5.937/(10^3)=0.005937
Which number is a rational number?
√56
√ 63
√ 196
√240
Step-by-step explanation:
Out of the given options, only √196 is a rational number.
A rational number is a number that can be expressed as the ratio of two integers. In other words, it can be written in the form of p/q where p and q are integers and q is not equal to zero.
√56 cannot be simplified further and has no integer factors that can be canceled out to express it as a ratio of two integers. Therefore, it is an irrational number.
Similarly, √63 and √240 cannot be simplified further and do not have any integer factors that can be canceled out to express them as a ratio of two integers. Therefore, they are also irrational numbers.
On the other hand, √196 simplifies to 14 which is a ratio of two integers (14/1). Hence, it is a rational number.
In summary, only √196 is a rational number out of the given options.