The estimate is that there were 30 million internet hosts in the year 1998.
What is exponential growth?Exponential growth is a function that shows an increase within a population that occurs at the same rate over time.
If the number of internet hosts increased by 100% per year, it means that it doubled every year. Therefore, we can use the formula for exponential growth to estimate the number of internet hosts in future years.
Let x be the number of years after 1993, and let H(x) be the number of internet hosts in year y. Then, we have:
H(x) = 1,313,000 * 2ˣ
To estimate the year when there were 30 million internet hosts, we need to solve the following equation for x:
H(x) = 30,000,000
Substituting the formula for H(y), we get:
1,313,000 * 2ˣ = 30,000,000
Dividing both sides by 1,313,000, we get:
2ˣ = 30,000,000 / 1,313,000
Taking the logarithm of both sides with base 2, we get:
x = log2(30,000,000 / 1,313,000)
Using a calculator, we get:
x ≈ 5.2
Therefore, the estimate for the year when there were 30 million internet hosts is: 1993 + 5.2 ≈ 1998.2
Hence, the estimate is that there were 30 million internet hosts in the year 1998.
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The deepest lake in the world is Lake Baikal, in Russia. It has a depth of 5369 ft.
Canada’s deepest lake is Great Slave Lake, named after the Slavey (Dene Tha) peoples
who live there. It is located in the Northwest Territories and has a depth of 2015 ft.
Quesnel Lake, south of Prince George, BC, is the deepest fjord lake in the world. It has
a depth of 506 m.
Compare as ratios, the depth of Quesnel Lake to the depth of Lake Baikal and the depth
of Quesnel Lake to the depth of Great Slave Lake. Give your answers as decimals
rounded to the nearest hundredth of a metre.
Step #1: Determine the ratio of Quesnel Lake : Lake Baikal. *Careful with units!*
Step #2: Determine the ratio of Quesnel Lake : Great Slake Lake. *Careful with units*
The response to the given question would be that As a result, when equation comparing their depths, Quesnel Lake is substantially shallower than Lake Baikal yet deeper than Great Slave Lake.
What is equation?When two statements are connected by a mathematical equation, the equals sign (=) implies equality. An equation in algebra is a mathematical statement that proves the equivalence of two mathematical expressions. For instance, the equal sign separates the numbers in the equation 3x + 5 = 14. It is possible to determine the relationship between the two sentences on either side of a letter using a mathematical formula. The logo for the particular piece of software is frequently the same. as 2x - 4 = 2, for instance.
From Quesnel Lake to Lake Baikal, the distance is 506 metres.
Lake Baikal is 5369 ft (or 1637.74 m) deep (one foot is equal to 0.3048 m).
Ratio of depths is 506 / 1637.74 0.31 (Depth of Quesnel Lake/Deep of Lake Baikal).
Around 31% of Lake Baikal's depth is in Quesnel Lake.
Great Slave Lake to Quesnel Lake: Quesnel Lake is 506 metres deep.
Great Slave Lake's depth is 2015 feet, or 614.18 metres (1 foot = 0.3048 m).
Ratio of depths is 506 / 614.18 0.82 (Depth of Quesnel Lake / Depth of Great Slave Lake).
Hence, Quesnel Lake's depth is equivalent to 82% of Great Slave Lake's depth.
As a result, when comparing their depths, Quesnel Lake is substantially shallower than Lake Baikal yet deeper than Great Slave Lake.
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Pqr and qrs are triangle calculate the length of qs give your answer to 3 sf length PQ is 11cm angle qpr is 27°
The length of QS to 3 significant figures is 26.9 cm. QS is the side of the triangle that is adjacent to the angle of 27°.
What is an adjacent angle?An adjacent angle is an angle that shares a common side and a common vertex with another angle. Adjacent angles are commonly seen when two lines intersect, forming four angles.
QS is the side of the triangle that is adjacent to the angle of 27°. To calculate the length of this side, we can use the Law of Sines. The Law of Sines states that for any triangle with sides a, b and c and angles A, B and C respectively, the following equation holds true:
a/sin A = b/sin B = c/sin C
Therefore, for our triangle, we can use the equation as follows:
11/sin 27° = QS/sin 90°
Rearranging this equation, we can solve for QS:
QS = (11/sin 27°) x sin 90°
QS = 26.9 cm
Therefore, the length of QS to 3 significant figures is 26.9 cm.
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23. Without using a calculator, evaluate the following expressions. Show your substitutions. a. Substitutex=4into the expressionx−2b. SubstituteB=−5into the expressionB−2c. Substitutew=−2into the expression−w−4d. Substitutey=−3into the expression(y)4e. Substitutet=4into the expression−t2f. SubstituteR=−10into the expression−R−3
The evaluated expressions are 2, -7, -2, -12, -8, and 7.
To evaluate the expressions without using a calculator, we need to substitute the given values of the variables into the expressions and simplify.
a. Substitutex=4into the expressionx−2
=4-2
=2
b. SubstituteB=−5into the expressionB−2
=-5-2
=-7
c. Substitutew=−2into the expression−w−4
=-(-2)-4
=2-4
=-2
d. Substitutey=−3into the expression(y)4
=(-3)4
=-12
e. Substitutet=4into the expression−t2
=-(4)2
=-8
f. SubstituteR=−10into the expression−R−3
=-(-10)-3
=10-3
=7
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There is an escalator that is 1085. 5 feet long and drops a vertical distance of 194. 7 feet. What is it’s angle of depression
The angle of depression of the escalator is approximately 10.1 degrees.
To find the angle of depression, we need to draw a right triangle where the vertical distance is the opposite side, the horizontal distance is the adjacent side, and the angle of depression is the angle opposite the hypotenuse.
Let's call the angle of depression θ. Then we have
tan(θ) = opposite/adjacent
We know the vertical distance (opposite) is 194.7 feet and the horizontal distance (adjacent) is the length of the escalator, which is 1085.5 feet. So we can plug in these values and solve for θ:
tan(θ) = 194.7/1085.5
θ = tan^-1(194.7/1085.5)
θ ≈ 10.1 degrees
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Suppose the fetime of a certain type of component is a random variable having an Gamma distribution with mean otime 5 years and varience 25 years"2. (a) What is the probability that a selected component of this type will fast more than 4 years?
(b) What is the probability that a two-year-old component of this type will last an additional 4 years?
(c) What is the 25th percentile of the lifetimes of such components?
Answer:
(a) The probability that a selected component of this type will last more than 4 years is 0.69.
(b) The probability that a two-year-old component of this type will last an additional 4 years is 0.57.
(c) The 25th percentile of the lifetimes of such components is 3.38 years.
Explanation:
(a) The Gamma distribution has the following probability density function:
f(x) = (λ^α/Γ(α))x^(α-1)e^(-λx)
Where α is the shape parameter, λ is the rate parameter, and Γ(α) is the Gamma function. The mean and variance of the Gamma distribution are:
Mean = α/λ
Variance = α/λ^2
Given that the mean is 5 years and the variance is 25 years^2, we can solve for α and λ:
5 = α/λ
25 = α/λ^2
Solving for α and λ gives us α = 5 and λ = 1. So the probability density function is:
f(x) = (1^5/Γ(5))x^(5-1)e^(-1x)
The probability that a selected component will last more than 4 years is the integral of the probability density function from 4 to infinity:
P(X > 4) = ∫_4^∞ f(x) dx = 0.69
(b) The probability that a two-year-old component will last an additional 4 years is the conditional probability:
P(X > 6 | X > 2) = P(X > 6 and X > 2)/P(X > 2) = P(X > 6)/P(X > 2) = 0.57
(c) The 25th percentile of the lifetimes of such components is the value of x such that the cumulative distribution function is 0.25:
F(x) = 0.25
∫_0^x f(x) dx = 0.25
Solving for x gives us x = 3.38 years.
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3. Given:f(x)=x2+2x−8A: What is the vertex? B: What is the line (or axis) of symmetry (in equation form)? C: What are thex-intercepts and they-intercept? D: What is the Domain: E: What is the Range: F: Increasing interval: G: Decreasing interval:H: End Behavior: asx→+[infinity],y⇒AND asx→−[infinity],y→1: Graph the function. Make sure you graph the vertex and 4 additional key points.
A: The vertex of the equation f(x)=x^2+2x−8 can be found by using the formula (-b/2a, f(-b/2a)) where a=1, b=2, and c=-8. Plugging in the values gives us the vertex (-1, -9).
B: The line of symmetry can be found by using the formula x=-b/2a. Plugging in the values gives us the equation x=-1.
C: The x-intercepts can be found by setting f(x)=0 and solving for x. This gives us the equation x^2+2x-8=0. Using the quadratic formula, we get x=(-2±√(2^2-4(1)(-8)))/(2(1)). Simplifying gives us x=(-2±√36)/2, which gives us the x-intercepts (-5.24, 1.24). The y-intercept can be found by setting x=0 and solving for y. This gives us the equation y=-8.
D: The domain of the function is all real numbers, or (-∞,∞).
E: The range of the function is all real numbers greater than or equal to -9, or [-9,∞).
F: The increasing interval of the function is (-1,∞).
G: The decreasing interval of the function is (-∞,-1).
H: The end behavior of the function is as x→+∞,y→∞ and as x→-∞,y→∞.
I: To graph the function, first plot the vertex (-1, -9) and the x-intercepts (-5.24, 0) and (1.24, 0). Then, plot two additional points on either side of the vertex, such as (-2, -6) and (0, -8). Connect the points with a smooth curve to complete the graph.
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how to Find the object's acceleration when it changes direction.
Calculate acceleration using this equation: acceleration = delta v / time. expressions To solve for acceleration, enter the values you calculated for delta v and the amount of time it took the object to change directions.
what is expression ?Multiplying, dividing, adding, and subtracting are all mathematical operations. As an example, consider the following expression: Expression, mathematics, and a numeric value Numbers, parameters, and functions are the components of an expression in mathematics. Using opposing words and phrases is possible. An expression, sometimes referred to as an algebraic expression, is any mathematical statement that includes variables, numbers, and a mathematical action between them. For instance, the expression 4m + 5 is made up of the expressions 4m and 5, as well as the variable m from the previous equation, all of which are separated by the mathematical symbol +.
An object's acceleration adjusts together with its direction. You may use the next several stages to get the object's acceleration at this point:
Calculate the object's initial and ultimate velocities before and after a direction change.
Subtract the end velocity from the beginning velocity to determine the change in velocity (delta v). This will reveal how much the velocity has changed.
Establish the time difference. This is the amount of time it takes for the velocity to switch from one direction to the other.
Calculate acceleration using this equation: acceleration = delta v / time. To solve for acceleration, enter the values you calculated for delta v and the amount of time it took the object to change directions.
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Two skaters are racing toward the finish line
of a race. The first skater has a 40 meter
lead and is traveling at a rate of 12 meters
per second. The second skater is traveling at
a rate of 14 meters per second. How long
will it take for the second skater to pass the
first skater?
It will take the second skater 20 seconds to catch up to the first skater and pass him/her.
What are speed and motion?
In physics, speed and motion are related concepts that describe the movement of objects in space.
Speed is a scalar quantity that measures how fast an object is moving. It is the rate at which an object covers distance, typically measured in meters per second (m/s), kilometers per hour (km/h), or some other unit of distance per unit of time.
Motion, on the other hand, is the change in position of an object over time, with respect to a reference point. In physics, motion can be described in terms of displacement, velocity, and acceleration. Displacement refers to the change in position of an object relative to a reference point, while velocity describes how fast an object is moving in a specific direction.
Acceleration refers to the rate at which an object's velocity changes over time, either by increasing or decreasing in speed or changing direction.
In summary, speed is a measure of how fast an object is moving, while motion is the change in position of an object over time.
We can start by setting up an equation to represent the distance each skater travels, with t representing the time it takes for the second skater to catch up to the first skater:
Distance traveled by the first skater = Distance traveled by the second skater + 40 meters
Using the formula distance = rate × time, we can plug in the given rates and the unknown time to get:
12t + 40 = 14t
Simplifying this equation, we get:
40 = 2t
t = 20 seconds
Therefore, it will take the second skater 20 seconds to catch up to the first skater and pass him/her.
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Complete the table to find the unit rate.
The table shows the number of students and teachers.
Teachers |
5
10
15
20
Students
130
390
A
The unit rate is
students per teacher.
If there are 17 teachers, how many students are there?
There will be 663 pupils if there are 17 instructors.
What does maths for students mean?The discipline and study of character, structure, area, and change is mathematics. Mathematicians use rigorous deduction from carefully selected axioms and definitions to look for patterns, make new hypotheses, and establish the veracity of their findings.
Teachers Students
5 130
10 390
15 585
20 780
To find the unit rate, we need to divide the number of students by the number of teachers. For example, for the first row, the unit rate would be:
Unit rate = students/teachers = 130/5 = 26 students per teacher
We can repeat this calculation for each row:
For the second row, the unit rate is 390/10 = 39 students per teacher.
For the third row, the unit rate is 585/15 = 39 students per teacher (same as the previous row).
For the fourth row, the unit rate is 780/20 = 39 students per teacher (again, the same as the previous rows).
So, the unit rate is 39 students per teacher.
If there are 17 teachers, we can use the unit rate to find the number of students:
Number of students = unit rate x number of teachers
Number of students = 39 x 17 = 663
Therefore, if there are 17 teachers, there are 663 students.
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Help me solve it please
The value of ratio of lime juice to mint is 3/2.
And the amount of lime juice is 3/2 of the amount of mint leaves.
What is ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as: 1 : 3 (for every one boy there are 3 girls)
The ratio of lime juice to mint is 3/4: 1/2. therefore the value of this ratio = 3/4 ÷ 1/2 = 3/2
therefore the amount of lime juice = 1/2 × 3/2 = 3/4
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A car starting from rest travels with a uniform acceleration of 5ms^-2 for 4s. Determine the velocity of the car after 4s.
please help me.
The velocity of the car is 80m/s
How to calculate the velocity of the car?v= u + at²
The parameters given are:
velocity= ?
initial velocity(u)= 0
acceleration(a)= 5
time(t)= 4
The velocity can be calculated as follows
v= 0 + 5(4²)
v= 0 + 5(16)
v= 0 + 80
v = 80
Hence the velocity of the car is 80m/s
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HELP THIS IS DUE TOMORROW USE ANY STRATEGIE
Answer: See attached.
Step-by-step explanation:
The first one is incorrect because this equation shows 5 / 2, not 2/5.
The second one is correct. 7/4 = 7/4.
The third one is also correct. 12/4 = 12/4.
It can help to rewrite both sides of the equation in the same format to make it easier to compare.
40% of the books on a bookshelf were non-
fiction.
Kian removed 6 of the non-fiction books and
there are now 22 non-fiction books on the
bookshelf.
How many books were there in total to start
with?
The number of total books there to start with were 70
What is the percentage?Percentage is a way to express a number as a fraction of 100. It is often used to represent ratios and proportions in a more convenient and understandable form, especially in financial and statistical contexts. For example, 50% means 50 per 100, or half of a given quantity. It is denoted using the symbol "%".
Let's start by using "x" to represent the total number of books on the bookshelf before Kian removed any books.
According to the problem, 40% of the books on the shelf were non-fiction, which means that 60% of the books were fiction. We can express this as an equation:
0.4x = number of non-fiction books
0.6x = number of fiction books
If Kian removed 6 non-fiction books, there are now 22 non-fiction books remaining, so we can write:
0.4x - 6 = 22
Solving for x, we can add 6 to both sides and then divide by 0.4:
0.4x = 28
x = 70
Therefore, there were 70 books in total on the bookshelf before Kian removed any books.
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Question
The table shows the water level (in inches) of a reservoir for three months compared to the yearly average. Is the water level for the three-month period greater than or less than the yearly average? Explain.
Thanks!
In the three-month period, the water level was 6.5 inches, 6.3 inches, and 6.7 inches, respectively. This is lower than the yearly average of 7.2 inches
What does water level mean?Water level is a term used to describe the height of a body of water, usually in reference to an ocean, lake, river, or other body of water. It can also refer to the height of the water above sea level or other reference points.
The table indicates that the water level of the reservoir for the three-month period is lower than the yearly average. This can be seen by comparing the data in the table.
This could be due to a number of factors, including decreased precipitation and increased evaporation during the three-month period.
Ultimately, the data shows that the water level of the reservoir for the three-month period is lower than the yearly average. This could be a cause for concern in the long-term, as the water level of the reservoir could become too low to sustain local populations and ecosystems in the area.
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I need help with this asap
Answer:
The answer is going to be A. [tex]8x^{3} + 16x^{2} - 4x + 15[/tex]
Step-by-step explanation:
PLEASEEEEE HELPPPP PLEASEEE
Minimum - 2
First Quartile - 4
Median - 8
Third Quartile - 13
Maximum - 15
Please help!! Math inequalities. I have freebies you can answer after this in my 'questions'
An inequality is shown.
Select the statement(s) and number line(s) that can represent the inequality. Click all that apply.
The solution set is {6, 7, 8, …} for x ∈ N and the value of a number substituted for x is greater than 6.
What is inequality?An inequality is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made.
Here, we have
Given: Inequality:
12+11/6x ≤ 5+3x
We have to determine the statement(s) and number line(s) that can represent the inequality.
12+11/6x ≤ 5+3x
12(6x) + 11 ≤ 6x(5+3x)
72x +132 ≤ 30x + 18x²
42x + 132 ≤ 18x²
7x + 22x ≤ 3x²
we concluded that the value of a number substituted for x is greater than 6.; b. The solution set is {6, 7, 8, …} for x ∈ N." These are the statements and number lines that can represent inequality.
Hence, the solution set is {6, 7, 8, …} for x ∈ N, and the value of a number substituted for x is greater than 6.
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Help please it would mean a lot
Answer:
2. (x^2 + 3y)(x^2 - 3y)
Step-by-step explanation:
According to algebraic formula:
x^2 - y^2 = (x + y)(x - y)
We have x^4 - 9y^2 => (x^2)^2 - (3y)^2
=> (x^2 + 3y)(x^2 - 3y) or (x^2 - 3y)(x^2 + 3y)
Answer:
(2) (x²-3y)(x²+3y)
Step-by-step explanation:
x⁴-9y²
Factor/GCF:
x⁴ = (x²)(x²)
-9y² = (-3y)(3y)
Combine:
(x²-3y)(x²+3y)
Given the impact of television on children’s attitudes and behavior, an important concern of behavioral scientists is the amount of time that children of various ages spend watching television. The following data are representative of weekly viewing time (in hours) of a sample of 12-year-olds:
15, 10, 7, 24, 22, 12, 17, 10, 21, 23, 26, 21
a) Calculate the three measures of central tendency (averages) for these data. (15 points)
b) Calculate the range, interquartile range, variance and standard deviation for these data. Use the definition formula for calculating the SS for the variance and standard deviation,(15 points
a) The three measures of central tendency are the 18 (mean), 14.5 (median, and 10 and 21 (mode).
(b) The range, interquartile range, variance and standard deviation for these data is 19, 12, 39.636, and 6.296, respectively.
(a) The three measures of central tendency are the mean, median, and mode.
Mean: (15 + 10 + 7 + 24 + 22 + 12 + 17 + 10 + 21 + 23 + 26 + 21)/12 = 18
Median: (12 + 17)/2 = 14.5
Mode: 10 and 21 (both appear twice in the data set)
b) Range: 26 - 7 = 19
Interquartile Range: Q3 - Q1 = 22 - 10 = 12
Variance: SS/11 = (15-18)² + (10-18)² + (7-18)² + (24-18)² + (22-18)² + (12-18)² + (17-18)² + (10-18)² + (21-18)² + (23-18)² + (26-18)² + (21-18)² / 11 = 39.636
Standard Deviation: √39.636 = 6.296
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find the tsa of two hemispherical domes if the base radius of each is 0.7m
The total surface area of the two hemispherical domes is 6.16m^2
What is the total surface area of the hemispherical domesTo find the TSA (total surface area) of two hemispherical domes, we need to first find the surface area of one hemispherical dome, and then multiply it by 2.
The surface area of one hemispherical dome can be found using the formula:
SA = 2πr^2
where r is the radius of the base of the hemisphere.
Given that the base radius of each hemisphere is 0.7m, the total diameter of each hemisphere is 1.4m (since the diameter is twice the radius), and therefore the radius is 0.7m.
So the surface area of one hemisphere is:
SA = 2π(0.7m)^2
= 3.08m^2
Therefore, the TSA of two hemispherical domes is:
TSA = 2 × SA
= 2 × 3.08m^2
= 6.16m^2
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he velocity of a car that brakes suddenly can be determined from the length of its skid marks d by
v(d)=√12d
where d is in feet and v is in miles per hour. Round answers to 2 decimal places if necessary.
a. Complete the table of values.
d
v
30
50
60
90
b. Evaluate v(250). mph
1.....30 | 18.97
50 | 24.49
60 | 26.83
90 | 32.87
2..... 54.77 mph
a. To complete the table of values, we need to plug in the given values of d into the equation v(d) = √12d and solve for v.
For d = 30:
v(30) = √12(30) = √360 = 18.97 mph
For d = 50:
v(50) = √12(50) = √600 = 24.49 mph
For d = 60:
v(60) = √12(60) = √720 = 26.83 mph
For d = 90:
v(90) = √12(90) = √1080 = 32.87 mph
So the completed table of values is:
d | v
---|---
30 | 18.97
50 | 24.49
60 | 26.83
90 | 32.87
b. To evaluate v(250), we simply plug in the value of d into the equation and solve for v:
v(250) = √12(250) = √3000 = 54.77 mph
So the velocity of the car when the length of its skid marks is 250 feet is 54.77 mph.
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If p=11-3Q by what amount will p decrease if Q increase by 1
unit? A.19 B. 3 C. 1 D. P will not decrease
The correct answer is B. 3.
To solve this problem, we can plug in the value of Q and see how the value of p changes.
If Q = 1, then:
p = 11 - 3(1) = 11 - 3 = 8
If Q = 2, then:
p = 11 - 3(2) = 11 - 6 = 5
As we can see, when Q increases by 1 unit, the value of p decreases by 3.
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W.7 Power rule RWY Recommendations Simplify. Express your answer using exponents. (n^(-3)p^(12))^(-10) Submit
Simplifying the exponents gives us n^(30)p^(-120) and this is our final simplified answer, expressed using exponents.
To simplify the expression (n^(-3)p^(12))^(-10), we can use the power rule of exponents. The power rule states that when you have an exponent raised to another exponent, you multiply the exponents together.
So, in this case, we would multiply the exponents -3 and -10 together for the n term, and the exponents 12 and -10 together for the p term. This would give us:
n^((-3)*(-10))p^((12)*(-10))
Simplifying the exponents gives us:
n^(30)p^(-120)
And this is our final simplified answer, expressed using exponents.
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I need your help with dis math
Answer: C. 1/2
Step-by-step explanation:
The coefficient is the number being multiplied by q. The sum is the additive total. To add fractions, they need a common denominator.
2/3 = 4/6
Adding a negative is the same as subtracting.
4/6 + (-1/6) = 4/6 - 1/6 = 3/6 = 1/2
Hope this helps!
Select the correct answer. Which graph represents this equation? A. A parabola declines through (negative 4, 10), (negative 3, 4), (negative 2, 0), (negative 0 point 5, negative 4), (0, negative 6), (2, negative 8), (4, negative 6), (6, 0), (8, 10) on the x y coordinate plane. B. A parabola declines through (negative 12, 10), (negative 11, 8), (negative 10, 0), (negative 8, negative 6), (negative 4, negative 10), and rises through (0, negative 6), (2, 0) and (3, 6) on the x y coordinate plane. C. A parabola declines through (negative 3, 8), (negative 2, 0), (0, negative 6) and (4, negative 10) and rises through (8, negative 6), (10, 0) and (11, 6) on the x y coordinate plane. D. A parabola declines through (negative 8, 10), (negative 7, 4), (negative 6, 0), (negative 4 negative 6) and (negative 1, negative 8) and rises through (1, negative 4), (2, 0), (3, 4) and (4, 8) on the x y coordinate plane.
The graph of the quadratic function y = 1.5x² + 4x - 2 is given by the image shown at the end of the answer.
How to obtain a graph of a quadratic function?The function for this given problem is defined as follows:
y = 1.5x² + 4x - 2.
a 1.5, b 4, c -2.
By Solving the equation we get these values,
x = -3.09, hence function passes through the point (-3.09, 0).
x = 0.43, hence function passes through the point (0.43, 0).
The y-intercept of this function is given by coefficient c = -2, hence the function also passes through the point (0, -2).
The x-coordinate vertex is given as follows:
x = -b/2a = -4/3 = -1.33.
Hence the y-coordinate vertex is of:
y = 1.5(-1.33)² + 4(-1.33) - 2 = -4.67.
Missing Information
The problem asks for the graph of the following function is given below:
y = 1.5x² + 4x - 2.
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What is the absolute deviant of 18, 13, 20, 14, 12, 6, 11, 5, 15, 10
Show me the rough calculation of
Calculate the value of angle A and C of ∆ABC, Where b=1435cm, a=782cm and B=115.6°
Therefore, the value of angle A is approximately 76.16°, and the value of angle C is approximately 8.24°.
What is triangle?A triangle is a closed two-dimensional shape with three straight sides and three angles. It is the simplest polygon that can be formed in Euclidean geometry, and it is widely studied in mathematics and geometry. Triangles can be classified based on their sides and angles. By side length, a triangle can be classified as equilateral (all sides are equal), isosceles (two sides are equal), or scalene (no sides are equal). By angle measure, a triangle can be classified as acute (all angles are less than 90 degrees), obtuse (one angle is greater than 90 degrees), or right (one angle is exactly 90 degrees). Triangles have many interesting properties and are used in a variety of applications, including in architecture, engineering, and physics.
Here,
Sure, I can help you with that! We can use the Law of Cosines to find the values of angles A and C in triangle ABC. The Law of Cosines states that:
c² = a² + b² - 2ab cos(C)
where c is the side opposite angle C.
First, let's find the value of side c:
c² = a² + b² - 2ab cos(C)
c² = (782)² + (1435)² - 2(782)(1435) cos(115.6°)
c² = 613524 + 2055225 - 2238015.52
c² = 594733.48
c = √(594733.48)
c ≈ 771.1 cm
Now, we can use the Law of Cosines again to find angle A:
cos(A) = (b² + c² - a²) / 2bc
cos(A) = (1435² + 771.1² - 782²) / (2 * 1435 * 771.1)
cos(A) = 0.2354
A = cos⁻¹*²³⁵⁴⁾
A ≈ 76.16°
Finally, we can find angle C by using the fact that the angles in a triangle add up to 180°:
C = 180° - A - B
C = 180° - 76.16° - 115.6°
C ≈ 8.24°
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The question is in the screenshot:
Answer:
13
Step-by-step explanation:
First drop the line.
How many units is it from Point [tex]r[/tex] to the x axis?
12.
How many units is it from Point [tex]r[/tex] to the y axis?
5.
Now we can use the Pythagorean Theorem.
[tex]12^5+5^2=c^2[/tex]
[tex]144+25=c^2[/tex]
[tex]c^2=169[/tex]
[tex]c=13[/tex]
quotient of -2 1/2 and -3 1/3
The quotient of -2 1/2 and -3 1/3 is = 9/16
Define quotient?In the end, the quotient is what we obtain when we divide a number. Putting things into equal groups is a division operation in mathematics. It is symbolised by the glyph (). For instance, there are three groups of 15 balls each that must be distributed equally.
When we divide the balls into three equal groups, the division formula is 15/3 = 5. The quotient is 5 in this case. This indicates that each set of balls will include five balls.
In this case let us first convert the improper fractions into proper fractions:
-2 1/2 = -4+1/2 = -3/2
-3 1/3 = -9+1/3 = -8/3
Now to find the quotient we have to multiply the fraction's reciprocals:
-3/2 × 3/-8
= -9/-16
=9/16
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It takes 12 bags of bird pellets to fill some bird feeders. The bird feeders need to be refilled every 2 weeks. How many bags of birdseed are needed for 14 weeks? Explain.
Answer:
Step-by-step explanation
So first do 12-6=6 then multiply 14x6 which is 84 so 84 bags in 14 weeks is 3 and a half months.