a carpenter is making a brace for a chair to do so she intersects two pieces of wood to make two sets of vertical angles the obtuse angles formed are each 145 degrees what is the measurement of each acute angle formed?
Find the orbital period (in years) of an asteroid whose average distance from the sun is 5 au.
Final answer:
To find the orbital period of an asteroid at 5 AU, apply Kepler's Third Law, resulting in approximately 11.18 years.
Explanation:
The question asks to find the orbital period of an asteroid with an average distance of 5 astronomical units (AU) from the Sun. We can use Kepler's Third Law of Planetary Motion, which states that the square of the orbital period (T, in years) is proportional to the cube of the average distance from the Sun (a, in astronomical units) for any object orbiting the Sun, expressed as-
[tex]T^2 = a^3[/tex]
Applying the formula for the asteroid in question:
Identify the average distance from the Sun, which is given as 5 AU.Calculate the cube of this distance: 53 = 125.Find the square root to determine the orbital period: √125 ≈ 11.18 years.Therefore, the orbital period of the asteroid is approximately 11.18 years.
if a and b are acute angles such that sinA=4/5 and cosB=12/13, calculate, without using tables: sin(a-b)
Please help me with questions 5, 6, and 7
An amusement park ride rotates around a fixed axis such that the angular position of a point on the ride follows the equation: θ(t) = a + bt2 – ct3 where a = 0.3 rad, b = 0.85 rad/s2 and c = 0.035 rad/s3
At t = 2 seconds, the angular position of the point on the amusement park ride is approximately 3.42 radians.
We have,
The equation θ(t) = a + bt² - ct³ represents the angular position of a point on the amusement park ride as a function of time.
Given:
a = 0.3 rad
b = 0.85 rad/s²
c = 0.035 rad/s³
In this equation,
θ(t) represents the angular position of the point on the ride at time t.
The term a is the initial angular position when t = 0, which is 0.3 radians.
The term bt² represents the angular displacement due to the linearly increasing angular velocity.
The coefficient b determines the rate of change of the angular displacement over time.
The term -ct³ represents the angular displacement due to the cubic decrease in angular acceleration.
To find the angular position at a specific time t, substitute the given values of a, b, c, and the desired value of t into the equation
θ(t) = a + bt² - ct³.
For example, if we want to find the angular position at t = 2 seconds:
θ(2) = 0.3 + 0.85 * (2²) - 0.035 * (2³)
= 0.3 + 0.85 * 4 - 0.035 * 8
= 0.3 + 3.4 - 0.28
= 3.42 radians
Therefore,
At t = 2 seconds, the angular position of the point on the amusement park ride is approximately 3.42 radians.
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The angular position of a point on a ride is given by the equation θ(t) = a + bt² - ct³. Factors such as the moment of inertia can change the angular acceleration in the system. When a child is on the merry-go-round, the moment of inertia increases, leading to a decrease in angular acceleration.
Explanation:The angular position of a point on an amusement park ride can be described by the equation θ(t) = a + bt² - ct³. In this equation, angular position is represented by θ(t), 'a' represents the initial angular position (0.3 rad), 'b' represents the angular velocity (increase in angular position per unit time - 0.85 rad/s2) and 'c' is the rate of change in angular velocity or the angular acceleration (0.035 rad/s3).
The angular acceleration can change due to factors such as a change in the moment of inertia. For example, when a child is on a merry-go-round, the combined moment of inertia is greater, therefore reducing the angular acceleration. The moment of inertia depends on factors such as the mass and the location of that mass relative to the axis of rotation. The child can be approximated as a point mass at a distance of 1.25 m from the axis of rotation.
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Carson buys three pencils at $0.35 each, a box of crayons for $2.86, four notebooks at $1.99 each, and two pens at $1.09 each. Estimate the amount he spent on school supplies.
Answer with Step-by-step explanation:
Carson buys three pencils at $0.35 each.
Cost of 1 pencil=$0.35
So, Cost of 3 pencils=$1.05 (0.35×3=1.05)
Buys a box of crayons for $2.86.
four notebooks at $1.99 each.
Cost of 1 notebook=$1.99
So, Cost of 4 notebooks=$7.96 (1.99×4=7.96)
and two pens at $1.09 each.
Cost of 1 pen=$1.09
So, Cost of 2 pens=$2.18 (1.09×2=2.18)
We have to estimate the amount he spent on school supplies.
Total Amount spent=$(1.05+2.86+7.96+2.18)
= $14.05
Hence, Total amount spent by Carson on school supplies is:
$14.05
A 90% confidence interval for the mean percentage of airline reservations being canceled on the day of the flight is (1.1%, 3.4%). what is the point estimator of the mean percentage of reservations that are canceled on the day of the flight?
Lucy's employer pays 70% of the total cost of her family's health insurance plan, while Lucy pays the rest. If the total cost of the plan will increase from $450 per month to $650 per month, how much more will Lucy have to pay each month?
Lucy will have to pay $60 more each month.
What is the percentage?The quantity of anything is stated as though it were a fraction of a hundred. A quarter of 100 can be used to express the ratio. Per 100 is what the term percent signifies. The symbol ‘%’ is used to symbolize it.
Lucy's employer pays 70% of the total cost of her family's health insurance plan, while Lucy pays the rest. Then Lucy will be only 30%.
If the total cost of the plan will increase from $450 per month to $650 per month.
At $450, Lucy pays 30% of $450 = 0.3 x 450 = $135
At $650, Lucy pays 30% of $650 = 0.3 x 650 = $195
Then Lucy has to pay each month more will be
⇒ $195 - $135
⇒ $60
Lucy will have to pay $60 more each month.
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The line of best fit for a scatter plot is shown: A scatter plot and line of best fit are shown. Data points are located at 0 and 1, 2 and 1, 2 and 3, 4 and 3, 4 and 5, 6 and 3, 7 and 5, 9 and 4. A line of best fit passes through the y-axis at 1 and through the point 4 and 3. What is the equation of this line of best fit in slope-intercept form?
Answer:
y = (1/2)x +1
Step-by-step explanation:
Given the two points on the line are (0, 1) and (4, 3), the line's equation can be written using the two-point form:
y = (y2 -y1)/(x2 -x1)·(x -x1) +y1
y = (3-1)/(4-0)·(x -0) +1 . . . . use the given point values
y = (1/2)x +1
Answer:
y = (1/2)x +1
Step-by-step explanation:
Given the two points on the line are (0, 1) and (4, 3), the line's equation can be written using the two-point form:
y = (y2 -y1)/(x2 -x1)·(x -x1) +y1
y = (3-1)/(4-0)·(x -0) +1 . . . . use the given point values
y = (1/2)x +1
Step-by-step explanation:
Rewrite the equation in vertex form. y = x2 - 6x + 18
Find h(x, y) = g(f(x, y)). g(t) = t + ln(t), f(x, y) = 4 − xy 2 + x2y2 h(x, y) =
The function h(x, y) is given by the composition of the functions g(t) and f(x, y). With the given expressions for f and g, the function h(x, y) = g(f(x, y)) equals to (4 - xy^2 + x^2y^2) + ln(4 - xy^2 + x^2y^2).
Explanation:The question asks to find the function h(x, y) from the functions g(t) and f(x, y), where g(t) = t + ln(t), and f(x, y) = 4 − xy^2+ x^2y^2. To begin with, it is necessary to substitute f(x, y) in place of 't' in function g which is g(f(x, y)), since we have h(x, y) = g(f(x, y)).
Performing the substitution, we obtain:
h(x, y) = g(f(x, y)) = (4 - xy^2 + x^2y^2) + ln(4 - xy^2 + x^2y^2).
This is your final function h in terms of x and y.
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what is the answer to this solve for h 12h=180
The line graphed below has a slope of ____.
-3
-1/3
1/3
3
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Sketch the asymptote and graph the function y=8/(x+3)-2
Answer:
Please find the attached file.
Step-by-step explanation:
Given: [tex]y=\dfrac{8}{x+3}-2[/tex]
We need to draw the graph of function with asymptote.
For horizontal asymptote:-
[tex]x\rightarrow \infty[/tex]
[tex]y=\lim_{x\rightarrow \infty}(\dfrac{8}{x+3}-2)=-2[/tex]
HA: y=-2
For vertical asymptote:-
[tex]y\rightarrow \infty[/tex]
[tex]x+3=0[/tex]
VA: x=-3
For x-intercept, Put y=0
(1,0)
For y-intercept, Put x=0
(0,2/3)
Now we will plot on graph and draw the graph.
Please see the attachment for graph.
The radius of a globe is 7.5 inches. What is the volume of the globe? Use 3.14 for pi.
The radius of a globe is 7.5 inches. What is the volume of the globe? Use 3.14 for pi.
Volume of the globe=[tex] \frac{4}{3} \pi r^{3} [/tex]
Volume of the globe=[tex] \frac{4}{3}*3.14*7.5^{3} [/tex]
Volume=[tex] \frac{4}{3}*3.14*421.875 [/tex]
Volume=[tex] \frac{4}{3}*1324.6875 [/tex]
Volume=[tex] \frac{5928.75}{3} [/tex]
Volume=1766.25[tex] inches^{3} [/tex]
Volume of Globe=1766.25[tex] in^{3} [/tex]
Answer: 1766.25
Step-by-step explanation: tryust
Find the missing term of the following sequence. . . . –2, __, 456, . . .
The answer should be
228
What methods can be used to solve quadratic equations?
What would be the radius of A= 907.46 square feet
plz help! 7th grade advanced math!!!!! A car travels 1 /6 of the distance between two cities in 3/ 5 of an hour. At this rate, what fraction of the distance between the two cities can the car travel in 1 hour?
glenn races his motorcycle 30 times last season. he finished first 12 times, second 5 times and crashed in 9 races. what percent of the races did he crash? set up a proportion and solve.
A British company is sending you measurements for a table to build in your factory. The table top must be 50 cm × 75 cm. Your machine calibrates in inches. Find the size of the table in inches. (1 cm = .39 in) A. 89 in × 114 in B. 11 in × 36 in C. 19.5 in × 29.25 in D. 128.2 in × 192.3 in
Answer: C. 19.5 in × 29.25 in
Step-by-step explanation: (50 x .39) x (75 x .39)
About 50.4 billion pieces of unopened junk mail ends up in landfills each year. This is about 48% of all the junk mail that is sent annually. How many pieces of junk mail are sent annually?
Write an equation for the parabola whose vertex is at (4, 9) and which passes through (5, 24).
define a variable and write each phrase as an algebraic expression
2 less than one-third of the points that the Panthers scored
Which of the following shows the graph of y = 4x + 3?
The graph of [tex]y=4x+3[/tex] is a line with a slope of 4, meaning for every unit moved to the right on the x-axis, you move up four units on the y-axis. The y-intercept is 3, so the line intersects the y-axis at the point (0,3). We plot these points and draw the line through them for the complete graph.
Explanation:The question asks, which of the following shows the graph of [tex]y = 4x + 3?[/tex]This is a linear equation in the format of y=mx+b, where 'm' is the slope of the line and 'b' is the y-intercept. In this case, 'm' is 4, so for every step you move to the right on the x-axis, you move four steps up on the y-axis. 'b' is 3, so the line intersects the y-axis at the point (0,3). To graph this equation, start at the point (0,3) and for every 1 unit you move to the right, move up by 4 units. Repeat this process with other values of x to find corresponding values of y. Points are then plotted on the graph and a line is drawn through them showing the relationship between x and y.
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Let x and y be independent each uniformly distributed on {1,2,...,n} find p(x < y )
A carpenter is assigned the job of expanding a rectangular deck where the length is four times the width. The width of the deck is to be expanded by 3 feet and the length is to be expanded by the new width. If the area of the new rectangular deck is 124 ft larger than the area of the original deck,find the dimensions of the original deck
Billy drops a water balloon from the roof of his house since the balloon begin with an original velocity of zero how far above ground was the balloon dropping if it took 2.5 seconds to hit the ground
What is the truth value for the following conditional statement? If the snow is white, then the grass is red.
Final answer:
The truth value of the conditional statement 'If the snow is white, then the grass is red' cannot be determined to be true or false without context, as it is a statement that requires evaluation of its antecedent and consequent. In logic, a conditional statement is true unless the antecedent is true and the consequent is false.
Explanation:
The truth value for the conditional statement "If the snow is white, then the grass is red," cannot be evaluated as true or false based solely on the content of the statement. In logic, a conditional statement is considered to be true unless a situation occurs where the first part (the antecedent) is true and the second part (the consequent) is false.
Here, the statement "the snow is white" is true, but the statement "the grass is red" can be false, as grass is typically green. This illustrates an important logical principle where the truthfulness of a conditional does not require that the consequent actually follows from the antecedent. To evaluate the truth of a conditional statement, it would be more appropriate to look for a counterexample that disproves it or involves a scenario where the antecedent is true and the consequent is false.