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
Find the probability that a randomly
selected point within the circle falls in the
red-shaded triangle.
12
12
P = [?]
Enter as a decimal rounded to the nearest hundredth.
Answers
Step-by-step explanation:
a probability is always the ratio of
desired cases / totally possible cases.
so, in this case it is the
area of the triangle / area of the circle.
as everything of the triangle is also a part of the circle.
and so, that fraction of the area of the whole circle that is the area of the triangle in refutation to the area of the whole circle is the probability that a random point inside the circle would be also inside the triangle.
the area of a right-angled triangle is
leg1 × leg2 / 2
in our case
12 × 12 / 2 = 72 units²
the area of a circle is
pi × r²
in our case that is
pi × 12² = 144pi units²
the requested probability is
P = 72 / 144pi = 1/2pi = 0.159154943... ≈ 0.16
Solve each equation for the angle in standard position, for 0° ≤ 0 < 360° (nearest tenth, if necessary).
a) tan 0 = 1 / √3
b) 2cos 0= √3
Answers
Answer:
Step-by-step explanation:
a) To solve the equation tan θ = 1/√3, we can find the angle whose tangent is 1/√3 by taking the inverse tangent (arctan) of 1/√3.
θ = arctan(1/√3)
θ ≈ 30.0°
Therefore, the angle in standard position that satisfies tan θ = 1/√3 is approximately 30.0°.
b) To solve the equation 2cos θ = √3, we can isolate the cosine term by dividing both sides of the equation by 2.
cos θ = √3 / 2
Now, we can find the angle whose cosine is √3/2 by taking the inverse cosine (arccos) of √3/2.
θ = arccos(√3/2)
θ ≈ 30.0°
Therefore, the angle in standard position that satisfies 2cos θ = √3 is approximately 30.0°.
Write and solve an inequality that represents the number of gigabytes of data . G . You can use to stay under your budget of $130
Answers
Answer:
Sure, here is the inequality that represents the number of gigabytes of data (G) you can use to stay under your budget of $130:
```
cost_per_gb * G <= budget
```
where:
* cost_per_gb is the cost of data per gigabyte, which is $10 in this case
* G is the number of gigabytes of data
* budget is your budget, which is $130 in this case
To solve this inequality, we can first subtract cost_per_gb from both sides of the inequality. This gives us:
```
G <= budget / cost_per_gb
```
We can then plug in the values for cost_per_gb and budget to get:
```
G <= 130 / 10
```
```
G <= 13
```
This means that you can use up to 13 gigabytes of data and still stay under your budget. If you use more than 13 gigabytes of data, you will exceed your budget.
Here is a table that shows the cost of data for different amounts of data:
```
| Amount of data (G) | Cost (\$) |
|---|---|
| 1 | 10 |
| 2 | 20 |
| 3 | 30 |
| ... | ... |
| 13 | 130 |
| 14 | 140 |
| ... | ... |
```
Step-by-step explanation:
find the critical numbers of the function.
f(x)=x^2(x-3)^2
Answers
First, we find the derivative of f(x) using the product rule:
f'(x) = 2x(x-3)^2 + x^2(2(x-3))
Simplifying, we get:
f'(x) = 2x(x-3)(2x-6+x) = 2x(x-3)(3x-6)
Setting f'(x) = 0, we get:
2x(x-3)(3x-6) = 0
This equation is zero when x = 0, x = 3, and x = 2.
Now we need to check if these values make the derivative undefined. None of these values make the derivative undefined.
Therefore, the critical numbers of the function f(x) = x^2(x-3)^2 are x = 0, x = 3, and x = 2.
peter is 24 years younger than his father. In 5 years time, his father will be 3 times as old as peter? a). how old is peter. b). how old will peter's father be in 25 year's time?
Answers
Step-by-step explanation:
Let Peter's present age be "p" and his father's age be "x"
So, p = x-24 ;
5 years from now,
Peter's age will be (x-24) + 5 = x-19
His father's age will be x+5.
It is given that 3(x-19)= x+5.
3x - 57 = x + 5 => 2x = 62.
On solving, his father's present age (x) is 31.
So Peter's present age is (p) is x - 24 = 31 - 24 = 7.
Now going in the reverse oder to check the answer.
Peter's present is 7.
5 years from now, it will be 12.
His father's age is 31.
5 years from now, his age will be 36 (which is 3x12).
Hence , the answer to the given problem is 7
Determine the equation of the midline of the following graph.
Answers
Answer:
y = -3
Step-by-step explanation:
The midline of a sinusoidal function is the horizontal center line about which the function oscillates periodically.
The midline is positioned halfway between the maximum (peaks) and minimum (troughs) values of the graph. It serves as a baseline that helps visualize the oscillations of the function.
To find the equation of the midline, we need to determine the average y-value between the maximum and minimum y-values.
In this case, the maximum y-value is -1, and the minimum y-value is -5. To find the equation of the midline, sum the maximum and minimum y-values, and divide by 2:
[tex]y=\dfrac{-1 + (-5)}{2} = \dfrac{-6}{2}=-3[/tex]
Therefore, the equation of the midline for the graphed sinusoidal function is y = -3.
Reduce this fraction to lowest terms 64/72
Answers
Answer: 8/9
Step-by-step explanation:
64/72 Divide both the top and bottom by 8
8/9
On days when the temperature was less than 58
Answers
These are general considerations, and specific experiences may vary depending on geographical location, cultural practices, and individual preferences.
On days when the temperature was less than 58 degrees, it indicates that the weather was relatively cool. This could imply various conditions and experiences depending on the context and location. In general, some possible scenarios on such days may include:
Cooler outdoor activities: People might engage in activities such as hiking, jogging, or outdoor sports that are more enjoyable in cooler temperatures.
Layered clothing: Individuals may choose to wear warmer clothing, including jackets, sweaters, or scarves, to stay comfortable in the cooler weather.
Indoor activities: Cooler temperatures may encourage people to spend more time indoors, engaging in activities such as reading, watching movies, or pursuing hobbies.
Increased energy consumption: Cold weather often leads to an increased need for heating systems, resulting in higher energy consumption to maintain indoor comfort.
Changes in vegetation: Cooler temperatures can affect plant growth and flowering patterns. Certain plants may thrive in cooler conditions, while others may enter a dormant phase.
Changes in animal behavior: Some animals may adapt to cooler temperatures by seeking shelter or adjusting their activities and migration patterns.
Possible health effects: Cooler temperatures may impact individuals with certain health conditions, such as respiratory issues or joint pain, requiring them to take appropriate measures to stay comfortable.
These are general considerations, and specific experiences may vary depending on geographical location, cultural practices, and individual preferences.
for such more question on temperature
https://brainly.com/question/14820864
#SPJ8
Help, please!
Brianna predicted that 16 puppies would be sold at the pet store on Saturday. However, only 9 were sold. What was Brianna's percent error?
Answers
Answer:
Percent error is calculated using the formula:
Percent Error = ( |Predicted Value - Actual Value| / Actual Value ) * 100%
Plugging in Brianna's prediction and the actual number of puppies sold:
Percent Error = ( |16 - 9| / 9 ) * 100%
The absolute value of (16 - 9) is 7, so the calculation becomes:
Percent Error = ( 7 / 9 ) * 100%
This is approximately 77.78%, which is Brianna's percent error in her prediction.
Indefinite Integral for the equation
Answers
The antiderivative of ∫[[tex]x^\frac{1}{11}[/tex] - 7sin(x)]dx is:
[tex](11/12)x^\frac{12}{11} - 7cos(x) + C[/tex]
What is the indefinite integral?The indefinite integral, denoted as ∫f(x)dx, represents the antiderivative of a function f(x). It involves finding a function whose derivative is equal to the given function f(x).
Let's evaluate the indefinite integral of [tex]\int [x^\frac{1}{11} - 7sin(x)]dx[/tex]
To find the antiderivative of [tex]x^\frac{1}{11}[/tex], we add 1 to the exponent and divide by the new exponent:
[tex]\int x^\frac{1}{11} dx = (11/12)x^\frac{12}{11} + C_1[/tex], where C₁ is the constant of integration.
∫7sin(x)dx:
To find the antiderivative of 7sin(x), we use the trigonometric identity that the antiderivative of sin(x) is -cos(x):
∫7sin(x)dx = -7cos(x) + C₂, where C₂ is another constant of integration.
Combining the two results, the indefinite integral of [tex]\int[x^\frac{1}{11} - 7sin(x)]dx[/tex] is:
[tex](11/12)x^\frac{12}{11} - 7cos(x) + C[/tex],
where C = C₁ + C₂ represents the constant of integration.
Learn more on antiderivative here;
https://brainly.com/question/22008756
#SPJ1
please help I'm losing braincells
Answers
Answer:h equals 12
Step-by-step explanation:
Which of the following could be the ratio between the lengths of the two legs
of a 30-60-90 triangle?
Check all that apply.
A. √2:2
B. √√3:√√3
C. √5:3
D. 1 √3
□ E. 1: √2
O F. 2:3
SUBMIT
Answers
Answer: E
Step-by-step explanation:
Cellular phone usage grew about 22% each year from 1995 (about 34 million) to 2003. Write a function to model cellular phone usage over that time period. What is the cellular usage in 2003?
Answers
Answer:
Given the information you provided, we can model cellular phone usage over time with an exponential growth model. An exponential growth model follows the equation:
`y = a * b^(x - h) + k`
where:
- `y` is the quantity you're interested in (cell phone usage),
- `a` is the initial quantity (34 million in 1995),
- `b` is the growth factor (1.22, representing 22% growth per year),
- `x` is the time (the year),
- `h` is the time at which the initial quantity `a` is given (1995), and
- `k` is the vertical shift of the graph (0 in this case, as we're assuming growth starts from the initial quantity).
So, our specific model becomes:
`y = 34 * 1.22^(x - 1995)`
To find the cellular usage in 2003, we plug 2003 in for x:
`y = 34 * 1.22^(2003 - 1995)`
Calculating this out will give us the cellular usage in 2003.
Let's calculate this:
`y = 34 * 1.22^(2003 - 1995)`
So,
`y = 34 * 1.22^8`
Calculating the above expression gives us:
`y ≈ 97.97` million.
So, the cellular phone usage in 2003, according to this model, is approximately 98 million.
Given the graphs of y = f(x) and y = g(x),
g(x) = f(x) +
expresses g(x) in terms of f(x)
Answers
The expression g(x) = f(x) + represents the relationship between the two functions expression for g(x) in terms of f(x).
To express the function g(x) in terms of f(x), we need to understand the relationship between the two functions.
The given expression g(x) = f(x) + indicates that the function g(x) is obtained by adding a certain value or expression to the function f(x). expression for g(x) in terms of f(x).
In general, if we have the function g(x) = f(x) + c, where c is a constant value, then g(x) can be expressed in terms of f(x) as:
g(x) = f(x) + c
In this case, g(x) is obtained by adding the constant value c to the corresponding values of f(x).
It's important to note that without additional information about the specific relationship between f(x) and g(x), such as a functional equation or given values, we cannot provide a more precise expression for g(x) in terms of f(x).
Therefore, the expression g(x) = f(x) + represents the relationship between the two functions expression for g(x) in terms of f(x).
for such more question on functions
https://brainly.com/question/16332322
#SPJ8
Answer: 3
Step-by-step explanation: just 3
Edge 2020
50 Points! Multiple choice geometry question. Photo attached. Thank you!
Answers
Reason:
The order of ABCD and EFGH is important. This is because the letters pair up based on their position.
D and H pair up because they're the last letters of ABCD and EFGH respectively. Similar polygons have congruent corresponding angles.
Take note of how the angles are marked to indicate which angles pair up.
D = H
4x = 100
x = 100/4
x = 25
Answer:
25 is the answer by matching the equial sides
Step-by-step explanation:
100°/4=X
25=X
52 divided by 7 = 6r3
A. Incorrect
OB. Correct
Answers
Answer:
incorrect
Step-by-step explanation:
as 7 * 6 = 42 and r is 10
so 6r3 is incorrect
and 7 * 7 = 49 and r is 3
so 7r3 is correct
A square prism has a base length of 5 m, and a square pyramid of the same height also has a base length of 5 m. Are the volumes the same? A. Yes, because the heights are the same, and the cross-sectional areas at every level parallel to the bases are also the same. B. Yes, because the figures are congruent. C. No, because only the bases have the same area, not every cross section at every level parallel to the bases. D. No, because the heights are not the same.
Answers
The statement that correctly answers the question "A square prism has a base length of 5 m, and a square pyramid of the same height also has a base length of 5 m. Are the volumes the same?" is "No, because only the bases have the same area, not every cross-section at every level parallel to the bases."
Explanation: A square prism is a three-dimensional shape that has two square bases that are parallel to each other, and every side is a rectangle. In contrast, a square pyramid is a three-dimensional figure that has a square base and triangular faces that meet at a point called an apex or vertex. The height of a square pyramid is the distance from the base to the apex.
Therefore, the volume of a square prism can be calculated by multiplying the area of the base by the height, whereas the volume of a square pyramid can be determined by multiplying the area of the base by one-third of the height.
Thus, even though the base length is 5 m in both cases, the cross-sectional areas at every level parallel to the bases in a square pyramid are not the same. This implies that the answer is No, because only the bases have the same area, not every cross-section at every level parallel to the bases.
For more questions on: square pyramid
https://brainly.com/question/30615121
#SPJ8
1. The initial odometer reading of a cab is 369 km. It travelled for 2 hours and the final odometer reading showed 469 km. Find the approximate average speed of the cab.
Answers
The approximate average speed of the cab is 50 km/h.
To find the approximate average speed of the cab, we can use the formula:
Average Speed = Total Distance / Total Time
Given that the initial odometer reading is 369 km and the final reading is 469 km, the total distance covered by the cab is:
Total Distance = Final Odometer Reading - Initial Odometer Reading
Total Distance = 469 km - 369 km
Total Distance = 100 Km.
The cab traveled for 2 hours, so the total time is:
Total Time = 2 hours
Now, we can substitute the values into the average speed formula:
Average Speed = Total Distance / Total Time
Average Speed = 100 km / 2 hours
Average Speed = 50 km/h
For similar question on average speed.
https://brainly.com/question/4931057
#SPJ8
a. Find the slope of x^3+y^3-65xy=0 at the points (4,16) and (16,4).
b. At what point other than the origin does the curve have a horizontal tangent line?
c. Find the coordinates of the point other than the origin where the curve has a vertical tangent line.
Answers
a. The slope of the curve at the point (4,16) is approximately 1.165, and at the point (16,4) is approximately -0.496.
b. The curve has a horizontal tangent line at the points(0,0) and (3,27).
c. The curve has a vertical tangent lineat the points (0,0) and (65/2, (65/2)³).
How is this so?a. To find the slope of the curve given by the equation x³ + y³ - 65xy = 0 at the points (4,16) and (16,4),we can differentiate the equation implicitly with respect to x and solve for dy/dx.
Differentiating the equation with respect to x, we have -
3x² + 3y²(dy/dx) - 65y - 65x(dy/dx) = 0
To find the slope at a specific point, substitute the x and y coordinates into the equation and solve for dy/dx.
For the point (4,16) -
3(4)² + 3(16)²(dy/dx) - 65(16) - 65(4)(dy/dx) = 0
48 + 768(dy/dx) - 1040 - 260(dy/dx) = 0
508(dy/dx) = 592
(dy/dx) = 592/508
(dy/dx) ≈ 1.165
For the point (16,4) -
3(16)² + 3(4)²(dy/dx) - 65(4) - 65(16)(dy/dx) = 0
768 + 48(dy/dx) - 260 - 1040(dy/dx) = 0
(-992)(dy/dx) = 492
(dy/dx) = 492/(-992)
(dy/dx) ≈ -0.496
Thus, the slope of the curve at the point (4,16) isapproximately 1.165, and at the point (16,4) is approximately -0.496.
b. To find the point where the curve has a horizontal tangent line, we need to find the x-coordinate(s)where dy/dx equals zero.
This means the slope is zero and the tangent line is horizontal.
From the derivative we obtained earlier -
3x² + 3y²(dy/dx) - 65y - 65x(dy/dx) = 0
Setting dy/dx equal to zero -
3x² - 65y = 0
Substituting y = x³/65 into the equation -
3x² - 65(x³/65) = 0
3x² - x³ = 0
Factoring out an x² -
x²(3 - x) = 0
This equation has two solutions - x = 0 and x = 3.
hence, the curve has a horizontal tangent line at the points(0,0) and (3,27).
c. To find the point where the curve has a vertical tangent line, we need to find the x-coordinate(s) where the derivative is undefinedor approaches infinity.
From the derivative -
3x² + 3y²(dy/dx) - 65y - 65x(dy/dx) = 0
To find the vertical tangent line, dy/dx should be undefined or infinite. This occurs when the denominator of dy/dx is zero.
Setting the denominator equal to zero: -
65x = 65y
x = y
Substituting this condition back into the original equation -
x³ + x³ - 65x² = 0
2x³ - 65x² = 0
x²(2x - 65) = 0
This equation has two solutions - x = 0 and x = 65/2.
Therefore, the curve has a vertical tangent line at the points (0,0)
and(65/2, (65/2)³).
Learn more about slope:
https://brainly.com/question/3493733
#SPJ1
Jaxon's mother spends more than 2 hours cleaning the house. The inequality x> 2 represents the situation. Which
graph represents the inequality?
Answers
Answer:A
Step-by-step explanation:the graph shows the values that are greater than 2
One more question thank you
Answers
Answer:
Step-by-step explanation:
n=30
r=12
Plug into formula
you get:
1.7 in²
Find the missing side. 27° y= ?] 11
Answers
Answer:
21.6
Step-by-step explanation:
Tan 27= 11
y
y×tan27=11
y=21.6
The answer is:
y = 21.6
Work/explanation:
We are asked to use SOH-CAH-TOA. But what does it mean?
SOH CAH TOASOH stands for Sine = Opposite ÷ Hypotenuse
CAH stands for Cosine = Adjacent ÷ Hypotenuse
TOA stands for Tangent = Opposite ÷ Adjacent
Since we do not have the hypotenuse, we will use the TOA ratio:
[tex]\sf{Tangent=\dfrac{Opposite}{Adjacent}}[/tex]
The opposite is 11, and the adjacent is y:
[tex]\sf{\tan27=\dfrac{11}{y}}[/tex]
Take the tangent of 27 & approximate it:
[tex]\sf{0.5095=11\div y}[/tex]
Multiply each side by y
[tex]\sf{0.5095y=11}[/tex]
Divide each side by 0.5095
[tex]\sf{y=21.6}[/tex]
Hence, y = 21.6Graph the function f(x)= 3+2 in x and its inverse from model 1.
Answers
The graph of the function and its inverse is added as an attachment
Sketching the graph of the function and its inverseFrom the question, we have the following parameters that can be used in our computation:
f(x) = 3 + 2ln(x)
Express as an equation
So, we have
y = 3 + 2ln(x)
Swap x and y in the above equation
x = 3 + 2ln(y)
Next, we have
2ln(y) = x - 3
Divide by 2
ln(y) = (x - 3)/2
Take the exponent of both sides
[tex]y = e^{\frac{x - 3}{2}}[/tex]
Next, we plot the graphs
The graph of the functions is added as an attachment
Read more about functions at
brainly.com/question/2456547
#SPJ1
50 Points! Multiple choice geometry question. Photo attached. Thank you!
Answers
The length of the segment AD found using the triangle proportionality theorem is the option (B)
(B) = 4 1/2
What is the triangle proportionality theorem?The triangle proportionality theorem states that if a line drawn parallel to a side of a triangle, intersecting the other two points at two distinct point, then it will divide the two sides intersected in the same ratio.
The arrow markings indicates that the segment DE and ACV are parallel, therefore, according to the triangle proportionality theorem, we get;
8/12 = 3/AD
AD/3 = 12/8
AD = 3 × (12/8) = 4.5
AD = 4 1/2
Learn more on the triangle proportionality theorem here: https://brainly.com/question/27887351
#SPJ1
consider the graph function below
Answers
The equation of the red graph is g(x) = f(x) - 5
How to calculate the equation of the red graphFrom the question, we have the following parameters that can be used in our computation:
The functions f(x) and g(x)
Where, we have
f(x) = -x
i.e.. the parent equation of the function
From the graph, we can see that
The function is shifted down by 5 units
This means that
g(x) = f(x) - 5
This means that the equation of the red graph is g(x) = f(x) - 5
Read more about transformation at
brainly.com/question/27224272
#SPJ1
What is the place value of the 6- digit in the number 205.876?
Answers
Answer:
thousandths place value
Step-by-step explanation:
Dylan's mom told him that she would replace each one of his dimes with a quarter. If he uses all of his coins, determine if Dylan would then have enough money to buy a game priced at $20.98 if he must also pay an 8% sales tax.
Answers
First, we need to know the initial value of Dylan's dimes and the number of dimes he has. Since the value of a dime is $0.10, we'll assume that each dime is worth $0.10.
Let's say Dylan initially has "x" dimes. Therefore, the initial value of his dimes would be 0.10x.
Now, since his mom replaces each dime with a quarter, the value of each quarter is $0.25. So, the value of his quarters would be 0.25x.
The total value of his coins after the replacement would be the sum of the initial value of dimes and the value of quarters, which is 0.10x + 0.25x = 0.35x.
Now, to determine if Dylan has enough money to buy the game priced at $20.98, we need to consider the 8% sales tax. To calculate the total amount including tax, we multiply the game price by (1 + tax rate):
Total amount including tax = $20.98 * (1 + 0.08) = $22.65.
Now, we can set up an inequality to check if Dylan has enough money:
0.35x ≥ $22.65.
Dividing both sides of the inequality by 0.35, we get:
x ≥ $22.65 / 0.35.
x ≥ $64.71.
Therefore, Dylan would need to have at least $64.71 worth of dimes (before replacement) in order to have enough money to buy the game after his mom replaces each dime with a quarter.
Note: If Dylan has fewer dimes, the total value of his coins would be lower, and he would not have enough money to buy the game.
2.
Harry pours 650 cubic centimeters of water into cylindrical glass with a diameter of 10
centimeters. He then pours the water from the first glass to another cylindrical glass with a
diameter of 8 cm. How much higher did the water reach in the second glass than in the first
glass? Round to the nearest tenth of a centimeter.
agures of the
Answers
Answer:
113.1 is the answer. I used the arbitory height of 4 so the volume of both are now 314.16 and 201.06
314.16-201.06=113.1
Express 250% as fraction
Answers
Answer:
[tex]\frac{2.5}{1}[/tex]
Step-by-step explanation:
To express it as a fraction, divide 250 by 100 first to get 2.5. Then put that over 1.
Hope this helps!
Jerry tries to find the measure of ABC His work is shown. Which statement describes Jerry's error? The picture shows a circle with a center O. Two chords, BA and BC are drawn from the same internal point, B. The angle of A is 135 degrees and C is 119 degrees.
Answers
Jerry's error is that he incorrectly assumes that the measure of angle ABC is equal to the sum of the measures of angles A and C. Hence Statement B is answer.
This is not true because angle ABC is an inscribed angle, which means its measure is half the measure of the intercepted arc.
In this case, the intercepted arc is AC. Since angle A measures 135 degrees and angle C measures 119 degrees, the sum of their measures is 254 degrees. However, angle ABC is not equal to 254 degrees.
To find the measure of angle ABC, we need to find the measure of arc AC. Since arcs A and C are equal in measure, we can find the measure of arc AC by subtracting angle A's measure (135 degrees) from the full circle measure (360 degrees).
Therefore, the measure of arc AC is 360 - 135 = 225 degrees. Since angle ABC is an inscribed angle, its measure is half the measure of arc AC, which is 225/2 = 112.5 degrees.
Hence Statement B is answer.
For more similar questions on inscribed angle
brainly.com/question/22962244
#SPJ8