Find the exact value of cos 105⁰.
a. √√√2-√6
4
b.
√2+√6
4
C.
4
d. √2+√6
4
Answers
Answer:
[tex]\dfrac{\sqrt{2}-\sqrt{6} }{4} }[/tex]
Step-by-step explanation:
Find the exact value of cos(105°).
The method I am about to show you will allow you to complete this problem without a calculator. Although, memorizing the trigonometric identities and the unit circle is required.
We have,
[tex]\cos(105\°)[/tex]
Using the angle sum identity for cosine.
[tex]\boxed{\left\begin{array}{ccc}\text{\underline{Angle Sum Identity for Cosine}}\\\\\cos(A+B)=\cos(A)\cos(B)-\sin(A)\sin(B)\end{array}\right}[/tex]
Split the given angle, in degrees, into two angles. Preferably two angles we can recognize on the unit circle.
[tex]105\textdegree=45\textdegree+60\textdegree\\\\\\\therefore \cos(105\textdegree)=\cos(45\textdegree+60\textdegree)[/tex]
Now applying the identity.
[tex]\cos(45\textdegree+60\textdegree)\\\\\\\Longrightarrow \cos(45\textdegree+60\textdegree)=\cos(45\textdegree)\cos(60\textdegree)-\sin(45\textdegree)\sin(60\textdegree)[/tex]
Now utilizing the unit circle.
[tex]\boxed{\left\begin{array}{ccc}\text{\underline{From the Unit Circle:}}\\\\\cos(45\textdegree)=\dfrac{\sqrt{2} }{2}\\\\\cos(60\textdegree)=\dfrac{1}{2}\\\\\sin(45\textdegree)=\dfrac{\sqrt{2} }{2}\\\\\sin(60\textdegree)=\dfrac{\sqrt{3} }{2} \end{array}\right}[/tex]
[tex]\cos(45\textdegree)\cos(60\textdegree)-\sin(45\textdegree)\sin(60\textdegree)\\\\\\\Longrightarrow \Big(\dfrac{\sqrt{2} }{2}\Big)\Big(\dfrac{1 }{2}\Big)-\Big(\dfrac{\sqrt{2} }{2}\Big)(\dfrac{\sqrt{3} }{2}\Big)[/tex]
Now simplifying...
[tex]\Big(\dfrac{\sqrt{2} }{2}\Big)\Big(\dfrac{1 }{2}\Big)-\Big(\dfrac{\sqrt{2} }{2}\Big)(\dfrac{\sqrt{3} }{2}\Big)\\\\\\\Longrightarrow \Big(\dfrac{\sqrt{2} }{4} \Big)-\Big(\dfrac{\sqrt{6} }{4} \Big)\\\\\\\therefore \cos(105\textdegree)= \boxed{\boxed{\frac{\sqrt{2}-\sqrt{6} }{4} }}[/tex]
Related Questions
Lashonda is on a game show. She will choose a box to see if she wins a prize. The odds in favor of Lashonda winning a prize are 9/2
. Find the probability of Lashonda winning a prize.
Answers
The probability of Lashonda winning a prize is 9/11.
To find the probability of Lashonda winning a prize, we can use the odds given. The odds in favor of Lashonda winning a prize are expressed as 9/2.
Odds are typically represented as a ratio of favorable outcomes to unfavorable outcomes.
In this case, the favorable outcomes are Lashonda winning a prize, and the unfavorable outcomes are Lashonda not winning a prize.
The odds in favor of Lashonda winning a prize can be written as 9:2, where 9 represents the favorable outcomes and 2 represents the unfavorable outcomes.
To calculate the probability, we add the favorable and unfavorable outcomes to get the total number of possible outcomes.
In this case, the total number of outcomes is 9 + 2 = 11.
The probability of Lashonda winning a prize can be calculated as the ratio of the favorable outcomes to the total number of outcomes:
Probability = Favorable outcomes / Total outcomes
Probability = 9 / 11.
Therefore, the probability of Lashonda winning a prize is 9/11.
In conclusion, based on the given odds in favor of Lashonda winning a prize being 9/2, the probability of Lashonda winning a prize is 9/11.
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The area of a triangular road sign is 70 square ft. If the base of the sign measures 14 ft, what is the height of the sign?
Answers
Answer:
height = 10 ft
Step-by-step explanation:
the area (A) of a triangle is calculated as
A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the height )
given A = 70 and b = 14 , then
[tex]\frac{1}{2}[/tex] × 14 × h = 70
7h = 70 ( divide both sides by 7 )
h = 10 ft
Sampling based upon equal probability is called
Select one:
a. Cluster Sampling
b. Probability sampling
c. Stratified random sampling
d. Simple random sampling
e. Systematic sampling
Note: Answer E is NOT the correct answer. Please find the correct answer. Any answer without justification will be rejected automatically.
Answers
Sampling based upon equal probability is called d. Simple random sampling. The correct answer is d. Simple random sampling.
Simple random sampling is a sampling technique where each individual in the population has an equal probability of being selected for the sample. It is based on the principle of equal probability, ensuring that every element has the same chance of being chosen. This method involves randomly selecting samples without any specific grouping or stratification.
Cluster sampling involves dividing the population into clusters or groups and randomly selecting entire clusters for inclusion in the sample. It does not guarantee equal probability for individual units within each cluster.
Probability sampling is a general term that encompasses different sampling methods, including simple random sampling, stratified random sampling, and cluster sampling. It refers to sampling techniques that rely on random selection and allow for the calculation of probabilities associated with sample estimates.
Stratified random sampling involves dividing the population into distinct strata based on certain characteristics and then selecting samples from each stratum in proportion to their representation in the population. It does not guarantee equal probability of selection for all individuals.
Systematic sampling involves selecting every kth individual from a population list after randomly selecting a starting point. It does not guarantee equal probability of selection for all individuals.
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Point B is on line segment AC. Given AC = 2x + 7, BC = x, and
AB= 5x9, determine the numerical length of AB.
Answers
Answer:
Step-by-step explanation:
To determine the length of AB, we need to find the value of x.
We are given that AC = 2x + 7, BC = x, and AB = 5x + 9.
Since B is on the line segment AC, the sum of lengths AB and BC should equal the length of AC. Therefore, we can set up the equation:
AB + BC = AC
Substituting the given values, we have:
(5x + 9) + x = 2x + 7
Simplifying the equation:
6x + 9 = 2x + 7
Bringing like terms to one side:
6x - 2x = 7 - 9
4x = -2
Dividing both sides by 4:
x = -2/4
Simplifying:
x = -1/2
Now that we have the value of x, we can substitute it back into the expression for AB to find its numerical length:
AB = 5x + 9 = 5(-1/2) + 9 = -5/2 + 9 = (18 - 5)/2 = 13/2 = 6.5
Therefore, the numerical length of AB is 6.5.
20 Points N Brainly Promised
Answers
The coterminal of 4π/3 angle measure are 10π/3 and -2π/3
How do you find angles that are coterminal with an angle measure of 4π/3?We add or subtract integer multiples of 2π.
So, 4π/3 + 2π = 10π/3 is one coterminal angle, and
4π/3 - 2π = -2π/3 is another coterminal angle.
To convert 125.67° to degree, minute, and second measure:
125.67° = 125° + 0.67°
Since there are 60 minutes in 1 degree, we can multiply 0.67 by 60 to get the minutes:
0.67° × 60 = 40.2'
Since there are 60 seconds in 1 minute, we can multiply 0.2 by 60 to get the seconds:
0.2' × 60 = 12"
So, 125.67° is equivalent to 125° 40.2' 12".
To find the degree measure equivalent to 10π/13 rounded to the nearest hundredth of a degree, we can divide 10π/13 by π and then multiply by 180° to convert from radians to degrees:
(10π/13) / π * 180° ≈ 138.46° (rounded to the nearest hundredth).
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a die has red, blue and one white face. when the die is rolled, a red result wins, a blue result, and a white result. what is the "expected return" for one roll of this die.
Answers
Given:
Red result wins: This occurs on one of the faces, so the probability is 1/3. The return is 1 (winning).
Blue result: This occurs on one of the faces, so the probability is also 1/3. The return is 0 (no win or loss).
White result: This occurs on the remaining face, so the probability is 1/3. The return is -1 (losing).
Let p(x) = a1x^2 + b1x +c1 and q(x) = a2x^2 + b2x + c2 be polynomials in P2. Define an inner product in P2 as follows {p,q} = 5a1a2 + 4b1b2 + 3c1c2.
Given p(x) =5x^2 + (-1)x + (-3) and q(x) = 2x^2 + (4)x +(-3). Evaluate the following expressions
1. p(x) - q(x) = 3x^2 - 5x
2. {p - q, p-q} = 145
3. llp-qll = sqrt({p-q,p-q}) = sqrt(145)
For part 1, I know the answer and how to get it.
For part 2, I know the answer but I'm not sure how to get to it
Answers
Answer:
Step-by-step explanation:
To evaluate the expression {p - q, p - q}, which represents the inner product of the polynomial (p - q) with itself, you can follow these steps:
Given p(x) = 5x^2 - x - 3 and q(x) = 2x^2 + 4x - 3.
Subtract q(x) from p(x) to get (p - q):
(p - q)(x) = (5x^2 - x - 3) - (2x^2 + 4x - 3)
= 5x^2 - x - 3 - 2x^2 - 4x + 3
= (5x^2 - 2x^2) + (-x - 4x) + (-3 + 3)
= 3x^2 - 5x
Now, calculate the inner product of (p - q) with itself using the given inner product formula:
{p - q, p - q} = 5(a1)(a2) + 4(b1)(b2) + 3(c1)(c2)
= 5(3)(3) + 4(-5)(-5) + 3(0)(0)
= 45 + 100 + 0
= 145
Therefore, the value of {p - q, p - q} is 145.
Given: FR = AN
Prove: FA = RN
(Picture involved)
Answers
The proof to show that FA = RN should be completed with the following step and reasons;
Step Reason_______
FR = AN Given
RA = RA Reflexive property of Equality
FR + RA = AN + RA Addition Property of Equality
FR + RA = FA Segment Addition Postulate
AN + RA = RN Segment Addition Postulate
FA = RN Transitive Property of Equality
What is the Segment Addition Postulate?In Geometry, the Segment Addition Postulate states that when there are two end points on a line segment (F) and (N), a third point (A) would lie on the line segment (RN), if and only if the magnitude of the distances between the end points satisfy the requirements of these equations;
FR + RA = FA.
AN + RA = RN.
This ultimately implies that, the Segment Addition Postulate is only applicable on a line segment that contains three collinear points.
By applying the Segment Addition Postulate to the given end points, we can logically deduce that line segment FA is equal to line segment RN based on the steps and reasons stated in the two-column proof shown above.
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find the ratio for cos
Answers
The value of cos E in the triangle is √2/2
What is trigonometric ratio?Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle. Trigonometric ratio is only applied in right triangles.
Some of the trigonometric functions are ;
sinθ = opp/hyp
cosθ = adj/hyp
tanθ = opp/adj
In the triangle taking reference from angle E, 5 is the opposite and 5 is the adjascent and 5√2 is the hypotenuse.
Therefore;
cos E = 5/5√2
cos E = 1/√2
rationalizing the value;
cos E = √2/2
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A gravel company charges a fee for a load of gravel Plus a charge for each mile from
the gravel pit to the final destination of the load. Let x represent the number of
miles to the destination and y
represent the total cost of the load. The charge to deliver a load 40 miles is $280
and the charge to deliver a load 56 miles is $292.
Find the slope.
1) 16
2) 7
3) 0.75
4) 21.3
5) 5.21
Answers
The slope of 0.75 corresponds to option 3. So, the correct answer is 3) 0.75.
To find the slope, we can use the formula for the slope of a line:
slope (m) = (change in y) / (change in x)
In this case, x represents the number of miles to the destination and y represents the total cost of the load.
Given that the charge to deliver a load 40 miles is $280 and the charge to deliver a load 56 miles is $292, we can set up two points on the line: (40, 280) and (56, 292).
Now let's calculate the change in y and change in x:
Change in y = 292 - 280 = 12
Change in x = 56 - 40 = 16
Plugging these values into the slope formula:
slope (m) = (change in y) / (change in x) = 12 / 16 = 0.75
Therefore, the slope of the line representing the relationship between the number of miles (x) and the total cost of the load (y) is 0.75.
Option 3 is correct.
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find the value x, round the lengths of segments to nearest tenth and the measure of angles to the nearest degree
Answers
Answer:
Step-by-step explanation:
39 !!!!!
please help ?
I'm not good at this type of stuff(worth 10 points)
Answers
1. the linear equation 5(x + 7) - 3(x - 4) = 7x + 2, x = 9
2. In linear equation 4(3x + 5) - 3 = 9x - 7, x = -8
3. the linear equation 1/3(5x - 9) = 2(1/3x + 6), x = 15
What is a linear equation?A linear equation is an equation in only on variable.
1. To solve the linear equation 5(x + 7) - 3(x - 4) = 7x + 2, we proceed as follows
5(x + 7) - 3(x - 4) = 7x + 2
Expanding the brackets, we have
5x + 35 - 3x + 12 = 7x + 2
Collecting like terms in the expression, we have
5x + 35 - 3x + 12 = 7x + 2
5x - 3x - 7x = 2 - 35 - 12
-5x = -45
x = -45/-5
x = 9
2. To solve linear equation 4(3x + 5) - 3 = 9x - 7, we proceed as follows
4(3x + 5) - 3 = 9x - 7
Expanding the brackets, we have
12x + 20 - 3 = 9x - 7
Collecting like terms in the expression, we have
12x - 9x = - 7 + 3 - 20
3x = -24
x = -24/3
x = -8
3. To solve the linear equation 1/3(5x - 9) = 2(1/3x + 6), we proceed as follows
1/3(5x - 9) = 2(1/3x + 6)
Expanding the brackets, we have
5x/3 - 3 = 2/3x + 12
Collecting like terms, we have
5x/3 - 2x/3 = 12 + 3
3x/3 = 15
x = 15
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need help with tshdjkdkdndndndndkd
Answers
The length of this line segment is: B. 2√13 units.
How to determine the distance between the coordinates for each points?In Mathematics and Geometry, the distance between two (2) end points that are on a coordinate plane can be calculated by using the following mathematical equation:
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Where:
x and y represent the data points (coordinates) on a cartesian coordinate.
By substituting the given end points into the distance formula, we have the following;
Distance = √[(4 + 2)² + (1 + 3)²]
Distance = √[(6)² + (4)²]
Distance = √[36 + 16]
Distance = √52
Distance = 2√13 units.
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14. The Elizabeth Tower is 320 feet tall. At what time or times during your ride on the London Eye are you at the same height as the top of the tower? Show your work. (4 points: 2 points for finding the correct time(s), 2 points for work shown)
t=time
320=-197cos(π/15(t))+246
Answers
The correct time(s) when you are at the same height as the top of the tower are approximately -1.57 hours, 1.57 hours, 4.71 hours, 7.85 hours, 11.00 hours, and so on.
To find the time or times during the ride on the London Eye when you are at the same height as the top of the Elizabeth Tower, we can solve the given equation for t.
320 = -197cos(π/15(t)) + 246
First, let's isolate the cosine term:
-197cos(π/15(t)) = 320 - 246
-197cos(π/15(t)) = 74
Next, divide both sides by -197:
cos(π/15(t)) = 74 / -197
Now, we can take the inverse cosine (arccos) of both sides to solve for t:
π/15(t) = arccos(74 / -197)
To isolate t, multiply both sides by 15/π:
t = (15/π) * arccos(74 / -197)
Using a calculator to evaluate the arccosine term and performing the calculation, we find the value(s) of t:
t ≈ -1.57, 1.57, 4.71, 7.85, 11.00, ...
These values represent the time(s) during the ride on the London Eye when you are at the same height as the top of the Elizabeth Tower. Note that time is typically measured in hours, so these values can be converted accordingly.
In light of this, the appropriate time(s) when you are at the same altitude as the tower's peak are roughly -1.57 hours, 1.57 hours, 4.71 hours, 7.85 hours, 11.00 hours, and so forth.
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Given ABCD, what is the measure of
145
A. 90°
B. 35°
C. 10°
D. 145°
E. 55°
F. 235°
Answers
Answer: D. 145°
Step-by-step explanation:
Since it is a parallelogram given by the symbol, then angle B is equal to angle D which is 145°.
Solve the missing element . use 3.14 for pi and Area = pi r2 ; C= pi D
Answers
We can solve for the missing elements as follows:
1. Radius - 10 inches
Diameter - 20
Circumference - 62.8
Area - 314
2. Radius - 6ft
Diameter - 12
Circumference - 37.68
Area - 113.04
3. Radius - 18
Diameter - 36 yards
Circumference - 113.04
Area - 1017.36
4. Radius 15
Diameter - 30 cm
Circumference 94.2
Area - 706.5
5. Radius - 5 mm
Diameter 10
Circumference 31.4
Area -78.5
6. Radius 20
Diameter - 40 inches
Circumference 125.6
Area -1256
How to solve for the valuesTo solve for the given values, we will use the formulas for area, circumference. Also, we can obtain the radius by dividing the diameter by 2 and the diameter is 2r. So we will solve for the values this way:
1. radius = 10 inches
diameter = 20
circumference = 2pie*r 2 *3.14*10 = 62.8
Area = 314
2. radius = 6ft
diameter = 12
circumference = 37.68
Area = 113.04
3. radius = 18
diameter = 36 yards
circumference = 113.04
Area = 1017.36
4. radius = 15
diameter = 30 cm
circumference = 94.2
Area = 706.5
5. radius = 5 mm
diameter = 10
circumference = 31.4
Area = 78.5
6. radius = 20 inches
diameter = 40 inches
circumference = 125.6
area = 1256
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JLK is similar to PQR find the value of X
Answers
Answer:
30
Step-by-step explanation:
22/33=20/x
cross multiply
22x=33x20
22x=660
x=660/22
x=30
A population of a particular yeast cell develops with a constant relative growth rate of 0.4465 per hour. The initial population consists of 3.3 million cells. Find the population size (in millions of cells) after 4 hours. (Round your answer to one decimal place.)
Answers
Starting with an initial population of 3.3 million yeast cells and a constant relative growth rate of 0.4465 per hour, the population size reaches approximately 5.892 million cells after 4 hours.
To calculate the population size after 4 hours, we can use the formula for exponential growth:
Population size = Initial population * [tex](1 + growth rate)^t^i^m^e[/tex]
Given that the initial population is 3.3 million cells and the relative growth rate is 0.4465 per hour, we can plug in these values into the formula:
Population size = 3.3 million *[tex](1 + 0.4465)^4[/tex]
Calculating the exponent first:
[tex](1 + 0.4465)^4 = 1.4465^4[/tex] ≈ 1.7879
Now, we can substitute this value back into the formula:
Population size = 3.3 million * 1.7879
Calculating the population size:
Population size = 5.892 million
Therefore, the population size after 4 hours is approximately 5.892 million cells.
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If sin 0=8/17, and tan0<0, what is cos(0)
Use exact values. No decimals.
(0 means theta)
Answers
Answer: -15/17
Step-by-step explanation:
sin ∅ = 8/17
If you drew a a line in the 2rd quadrant because tan ∅ <0, which means tan∅ is negative.
Tan∅= sin∅/cos∅
they told you sin∅ is positive which is related to your y.
but cos∅ needs to be negative which is related to x
This happens in the second quadrant x is negative and y is positive.
Now we know which way to draw our line. Label the opposite of the angle 8 and the hypotenuse 17 because sin∅ = 8/17
Use pythagorean to find adjacent.
17² = 8² + a²
225 = a²
a = 15
The adjacent is negative because the adjacent is on the x-axis in the negative direction.
cos ∅ = adj/hyp
cos∅ = -15/17
Answer: -15/17
Step-by-step explanation:
In the first quadrant, all sine, cosine and tan are all positive. In the second quadrant, only sine is positive. Third quadrant, only tangent is positive and fourth quadrant, only cosine is positive.
Therefore, when sine is positive and tan is negative, the angle can only be in quadrant 2. Then draw the triangle. Draw a triangle with the angle from the origin, with the opposite leg from the angle with value of 8 and the hypotenuse of value 17. Since cosine is what the question is asking for, and we know the data given forms an right triangle, the value of the other leg is 15. It is an 8-15-17 special triangle or use the Pythagorean Theorem.
Finally, taking the cosine of the angle from the origin gives -15/17 since it is in quadrant 2.
[tex] \frac{350}{120} [/tex]
me ayudan siiiiiiiiiiiiiii
Answers
The simplified fraction of 350/120 is 35/12
How to simplify the fractionfrom the question, we have the following parameters that can be used in our computation:
350/120
Divide the zeros
So, we have
350/120 = 35/12
Divide the fractions by 3
This is impossible
Hence, the simplified fraction is 35/12
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Find the net area of the following curve on the interval [0, 2].
(SHOW WORK)
f(x) = ex - e
Answers
The net area of the curve represented by f(x) = ex - e on the interval [0, 2] is e2 - 1.
To find the net area of the curve represented by the function f(x) = ex - e on the interval [0, 2], we need to calculate the definite integral of the function over that interval. The net area can be determined by taking the absolute value of the integral.
The integral of f(x) = ex - e with respect to x can be computed as follows:
∫[0, 2] (ex - e) dx
Using the power rule of integration, the antiderivative of ex is ex, and the antiderivative of e is ex. Thus, the integral becomes:
∫[0, 2] (ex - e) dx = ∫[0, 2] ex dx - ∫[0, 2] e dx
Integrating each term separately:
= [ex] evaluated from 0 to 2 - [ex] evaluated from 0 to 2
= (e2 - e0) - (e0 - e0)
= e2 - 1
The net area of the curve represented by f(x) = ex - e on the interval [0, 2] is e2 - 1.
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special right triangle
Answers
Question 23 of 41
What is the name of the Platonic solid shown below?
A. Octahedron
B. Dodecahedron
C. Hexahedron
D. Icosahedron
Answers
Answer:
That Platonic solid is a dodecahedron.
B is the correct answer.
45% of the Walton High School student body are male. 90% of Walton females love math, while only 60% of the males love math. What percentage of the student body loves math?
Answers
Approximately 76.5% of the student body at Walton High School loves math.
To determine the percentage of the student body that loves math, we need to consider the proportions of males and females in the Walton High School student body and their respective percentages of loving math.
Given that 45% of the student body are males, we can deduce that 55% are females (since the total percentage must add up to 100%). Now let's calculate the percentage of the student body that loves math:
For the females:
55% of the student body are females.
90% of the females love math.
So, the percentage of females who love math is 55% * 90% = 49.5% of the student body.
For the males:
45% of the student body are males.
60% of the males love math.
So, the percentage of males who love math is 45% * 60% = 27% of the student body.
To find the total percentage of the student body that loves math, we add the percentages of females who love math and males who love math:
49.5% + 27% = 76.5%
As a result, 76.5% of Walton High School's student body enjoys maths.
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expresa en litros 4m³
Answers
4 cubic meters is equal to 4000 liters. 4 m³ becomes 4000 liters.
To express 4 m³ in liters, we first need to understand the conversions between cubic meters (m³) and liters (L).
1 cubic meter (1 m³) is equal to 1000 liters (1000 L). This is because 1 meter is equal to 100 centimeters, and when cubed, we get 100 cm x 100 cm x 100 cm = 1,000,000 cm³. And since 1 liter is equal to 1,000 cubic centimeters (1 L = 1000 cm³), then 1 m³ is equal to 1,000,000 cm³ / 1000 cm³ = 1000 liters.
Now, we can use this information to convert 4 m³ to liters:
4 m³ * 1000 L/m³ = 4000 liters
Therefore, 4 cubic meters is equal to 4000 liters.
In short, to convert cubic meters to liters, we multiply the value in cubic meters by 1000 to get the equivalent in liters. In this case, 4 m³ becomes 4000 liters. It is important to remember that this conversion is valid for substances that have a density similar to water, since the relationship between cubic meters and liters can vary for different substances.
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Which of the rays or segments below is a chord of circle O?
A) ->
TC
B)—
SO
C)—>
TU
D)—
FC
Answers
The ray or segment that is a chord is (d) segment FC
How to determine the ray that is a chordFrom the question, we have the following parameters that can be used in our computation:
The circle
By definition, a chord is a straight line that joins points of the circle without passing through the center
The ray that has the above properties is ray FC
Hence, the segments that is a chord is (d) FC
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13. A cylinder is shown. Find the exact volume of a cone with the
same dimensions.
on filled to the very top, it holds 480 cub
Answers
The exact volume of a cone with the same dimensions is 9428.57 cubic inches
Find the exact volume of a cone with the same dimensions.From the question, we have the following parameters that can be used in our computation:
The cylinder
The volume of the cone with the same dimensions is calculated as
Volume = 1/3 * Volume of cylinder
So, we have
Volume = 1/3 * 22/7 * (30/2) * (30/2) * 40
Evaluate
Volume = 9428.57
Hence, the exact volume of a cone with the same dimensions is 9428.57 cubic inches
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The function V(r)=¹ can be used to find the volume of air inside a basketball given its radius. What does V(r)
represent?
the radius of the basketball when the volume is V
the volume of the basketball when the radius is r
the volume of the basketball when the radius is V
the radius of the basketball when the volume is r
OOO
Answers
Answer:
In the given equation, V(r) represents the volume of the air inside a basketball when the radius of the basketball is r.
Step-by-step explanation:
The function V(r) represents the volume of the basketball when the radius is r. So, the correct interpretation is that V(r) represents "the volume of the basketball when the radius is r."
Find the axis of symmetry of the parabola defined by the equation... 100 points
Answers
Answer:
y=2
Step-by-step explanation:
The equation of a parabola in the form [tex](y-k)^2=4p(x-h)[/tex] has an axis of symmetry of [tex]y=k[/tex]. Therefore, the axis of symmetry is [tex]y=2[/tex].
Answer:
y = 2
Step-by-step explanation:
The axis of symmetry of a parabola is a line that divides the parabolic curve into two symmetric halves. It is a line of symmetry that passes through the vertex of the parabola.
Given equation of the parabola:
[tex](y-2)^2=20(x+1)[/tex]
As the y-variable is squared, the given parabola is horizontal (sideways).
The standard form of a sideways parabola is:
[tex]\boxed{(y-k)^2=4p(x-h)}[/tex]
where:
Vertex = (h, k)Focus = (h+p, k)Directrix: x = (h - p)Axis of symmetry: y = kComparing the given equation with the standard equation, we can see that:
h = -1k = 24p = 20 ⇒ p = 5As the axis of symmetry is given by the formula y = k, the axis of symmetry of the given parabola is y = 2.
HURRY PLEASEEE
A cylinder has a volume of 400 feet. If the height of the cylinder is 25 feet, what is the radius of the cylinder? Use 3.14 for π and a round to the nearest hundredth. radius ≈ type your answer… ft
Answers
Answer:
the radius of the cylinder is approximately 2.26 feet.
Step-by-step explanation:
To find the radius of the cylinder, we can use the formula for the volume of a cylinder:
Volume = π * radius^2 * height
Given that the volume is 400 feet, the height is 25 feet, and using π ≈ 3.14, we can rearrange the formula to solve for the radius:
400 = 3.14 * radius^2 * 25
Divide both sides of the equation by (3.14 * 25):
400 / (3.14 * 25) = radius^2
Simplifying:
400 / 78.5 ≈ radius^2
5.09 ≈ radius^2
To find the radius, we take the square root of both sides:
√5.09 ≈ √(radius^2)
2.26 ≈ radius
Rounding to the nearest hundredth, the radius of the cylinder is approximately 2.26 feet.
Answer:
Step-by-step explanation:
Volume Formula for a cylinder is V=πr²h
Substitute the following: 400 = 3.14(r²)(25)
r=[tex]\sqrt{\frac{V}{\pi h} }[/tex]
r=[tex]\sqrt{\frac{400}{\pi 25} }[/tex]
r≈2.25676ft
