Yes, arcsin and sin^-1 both represent the inverse sine function.
process of finding inital speed:
a) To find the ball's initial speed, we can use the range formula for projectile motion:
R = (v₀² * sin(2θ)) / g
where R is the range (10 m),
v₀ is the initial speed,
θ is the launch angle (45 degrees), and
g is the acceleration due to gravity (9.81 m/s²).
We can solve for v₀:
10 = (v₀² * sin(90)) / 9.81
10 = (v₀²) / 9.81
v₀² = 10 * 9.81
v₀ = sqrt(10 * 9.81)
The ball's initial speed is sqrt(10 * 9.81) m/s.
b) For the same initial speed, we can find the two firing angles that make the range 6 m:
6 = (v₀² * sin(2θ)) / 9.81
Now, we can use the initial speed found in part (a):
6 = (10 * 9.81 * sin(2θ)) / 9.81
0.6 = sin(2θ)
To find the two angles, we can use the arcsin function:
θ₁ = 1/2 * arcsin(0.6)
θ₂ = π - 1/2 * arcsin(0.6)
The two firing angles are 1/2 * arcsin(0.6) and π - 1/2 * arcsin(0.6).Yes, arcsin is the same as sin^(-1);
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Taylor would like to have a karaoke deejay at her graduation party. her three sisters volunteered to split the cost of hiring the deejay. they need to rent a tent for $45 and a microphone system for $60 and then pay the deejay $30 an hour for four hours. how much do each of the sisters owe?
write out all the work used to determine the answer to the question.
Each of the three sisters owes $75 to cover the cost of hiring the karaoke deejay for Taylor's graduation party.
To determine how much each sister owes, we need to first calculate the total cost of the party and then divide that cost by three, since there are three sisters splitting the cost.
1. Tent rental: $45
2. Microphone system: $60
3. Deejay cost: $30/hour × 4 hours = $120
Now, we'll add these costs together to find the total cost:
Total cost = $45 (tent) + $60 (microphone) + $120 (deejay) = $225
Finally, we'll divide the total cost by the number of sisters (3) to find out how much each sister owes:
Amount owed per sister = $225 (total cost) ÷ 3 (sisters) = $75
So, each sister owes $75 for the karaoke deejay at Taylor's graduation party.
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If x = yand y = z, which statement must be true?
O A. -x=-z
O B. z=x
O c. x=z
O D. -x=z
Answer:
The answer is C. x=z
Step-by-step explanation:
The correct answer is C. x=z.
Since x = y and y = z, then x = z. This is the transitive property of equality.
Here is a more detailed explanation:
The transitive property of equality states that if a = b and b = c, then a = c.
In this case, x = y and y = z. Therefore, x = z.
a circular pool has a radius of 32 cm find its area?
John was visiting four cities that form a rectangle on a coordinate grid at A(O.
4), B(4,1). C(3. 1) and D(-1. 2). If he visited all the cities in order and ended up
where he started. What is the distance he traveled? Round your answer to the
nearest tenth
If he visited all the cities in order A(O,4), B(4,1). C(3. 1) and D(-1. 2). then he traveled 12.3 units distance ( nearest tenth).
John visited four cities that form a rectangle on a coordinate grid at A(0, 4), B(4, 1), C(3, 1), and D(-1, 2). If he visited all the cities in order and ended up where he started, the distance he traveled can be found by calculating the perimeter of the rectangle.
Calculate the distance between consecutive points.
AB = √[(4-0)^2 + (1-4)^2] = √[16 + 9] = √25 = 5
BC = √[(3-4)^2 + (1-1)^2] = √[1 + 0] = √1 = 1
CD = √[(-1-3)^2 + (2-1)^2] = √[16 + 1] = √17 ≈ 4.1 (rounded to nearest tenth)
DA = √[(0-(-1))^2 + (4-2)^2] = √[1 + 4] = √5 ≈ 2.2 (rounded to nearest tenth)
Calculate the total distance traveled (perimeter of the rectangle).
Total Distance = AB + BC + CD + DA = 5 + 1 + 4.1 + 2.2 = 12.3
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Help pls working and explanation needed
A. angle CXD = 140 degrees
Angle XCD and Angle XDC are congruent since the triangle is isosceles. Remember that the sum of the interior angles of a triangle is 180 degrees.
20 + 20 + x = 180
x = 140
B. 18 sides
To find the number of sides of the polygon, we need to know the measure of one interior angle. One interior angle is angle BCD. We can easily find the measure of this angle because it is on a straight angle of which we are given part of (angle XCD).
Angle XCD + Angle BCD = 180
20 + BCD = 180
BCD = 160
Now that we know the measure of an interior angle, we can use the formula to find the measure of an interior angle and algebraically solve for the number of sides.
[ (n - 2) x 180 ] / n = 160
(n - 2) x 180 = 160n
180n - 360 = 160n
-360 = -20n
n = 18 sides
C. 2880 degrees
The formula for the sum of the interior angles of a regular polygon is (n - 2) x 180, where n is the number of sides.
(18 - 2) x 180
16 x 180
2880
D. 140 degrees
If angle XCD is 20 degrees, then angle BED is also 20 degrees. Angle BED and Angle BEF make up one of the interior angles of the regular polygon. We know that one interior angle is equal to 160 degrees.
Angle BED + Angle BEF = 160
20 + BEF = 160
BEF = 140
Hope this helps!
WHATS THE AREA PLEASE HELP DUE in 5 minutes
Answer:
The answer to your problem is, 201.06 or 201.1
Step-by-step explanation:
To find the area you use the formula:
A = π [tex]r^2[/tex]
R = Radius
A = Area
We know the radius of the circle is 8
So replace A = π [tex]r^2[/tex]
= π × 8 ≈ 201.06193
Or 201.06 or 201.1
Thus the answer to your problem is, 201.06 or 201.1
Sara collects beads in a jar she weighs the jar every week to see how many grams of beads she has. she as 2.5 grams if blue beads. 4.9 grams of pink beads, 7.1 grams of yellow beads and the rest are white beads
if sara weighs her jar this week and finds out that she has 1.8 grams of beads, how many grams of white beads does she have?
Therefore, Sara has 3.5 grams of white beads in her jar.
Based on the information provided, Sara has 2.5 grams of blue beads, 4.9 grams of pink beads, and 7.1 grams of yellow beads. If she weighs her jar this week and finds out she has a total of 18 grams of beads, we can determine the number of grams of white beads she has by following these steps:
Step 1: Add the weights of the blue, pink, and yellow beads together.
2.5 grams (blue) + 4.9 grams (pink) + 7.1 grams (yellow) = 14.5 grams
Step 2: Subtract the total weight of the blue, pink, and yellow beads from the total weight of the jar (18 grams).
18 grams (total weight) - 14.5 grams (blue, pink, and yellow beads) = 3.5 grams
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The main span of a suspension bridge is the roadway between the bridges towers. The main span of the Walt Whitman Bridge in Philadelphia is 2000 feet long. This is 600 feet longer than two-fifths of the length of the main span of the George Washington Bridge in New York City. Write an equation to represent the given problem and solve it to find the length of the main span of the George Washington Bridge
The length of the main span of the George Washington Bridge is 3500 feet.
Let x be the length of the main span of the George Washington Bridge.
We know that the main span of the Walt Whitman Bridge is 600 feet longer than two-fifths of the length of the main span of the George Washington Bridge, so we can write the equation:
2000 = (2/5)x + 600
To solve for x, we can start by isolating the term with x on one side of the equation:
(2/5)x = 2000 - 600
(2/5)x = 1400
Then, we can solve for x by multiplying both sides by the reciprocal of (2/5):
x = 1400 / (2/5)
x = 3500
Therefore, the length of the main span of the George Washington Bridge is 3500 feet.
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Please upload a picture of a piece of paper with the problem worked out, and draw the graph for extra points, there will be 6 of these, so go to my profile and find the rest, and do the same, for extra points.
The solution of the system of equations is given by the ordered pair (-4, 5).
How to graphically solve this system of equations?In order to graph the solution to the given system of equations on a coordinate plane, we would use an online graphing calculator to plot the given system of equations and then take note of the point of intersection;
x - y = -9 ......equation 1.
3x + 4y = 8 ......equation 2.
Based on the graph shown in the image attached above, we can logically deduce that the solution to this system of equations is the point of intersection of the lines on the graph representing each of them, which lies in Quadrant II, and it is given by the ordered pairs (-4, 5).
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Select all of the statements that are true
The [9.7] = -9.7 because the distance from -9.7 to 0 on the number line is 9.7 units.
Numbers with the same absolute value are opposites because they are the same distance from each other.
The [7.1] = 7.1 because the distance from 7.1 to 0 on the number line is 7.1 units.
The [-8.4] = 8.4 because the distance from -8.4 to 8.4 on the number line is 0 units.
Numbers with the same absolute value are opposites because they are the same distance from 0 on the number line.
The [-12.5] = 12.5 because the distance from 12.5 to 0 on the number line is -12.5 units.
The true statements are Numbers with same absolute value are opposites because they are same distance from each other and from 0 on the number line. The |7.1| = 7.1. So, correct options are B, C and E.
b) Numbers with the same absolute value are opposites because they are the same distance from each other. This is true because absolute value is the distance from a number to zero on the number line, and if two numbers have the same distance from zero, then they must be equidistant from zero and therefore, they are opposite in sign.
c) The |7.1| = 7.1 because the distance from 7.1 to 0 on the number line is 7.1 units. This is true because the absolute value of a number is always positive, and it represents the distance of that number from zero on the number line.
d) The |-8.4| = 8.4 because the distance from -8.4 to 8.4 on the number line is 0 units. This is false, as the distance between -8.4 and 8.4 on the number line is 16.8 units. The correct value of the absolute value of -8.4 is 8.4.
e) Numbers with the same absolute value are opposites because they are the same distance from 0 on the number line. This is true because 0 is the midpoint of the number line, and if two numbers have the same distance from 0, then they must be equidistant from zero and therefore, they are opposite in sign.
Therefore, the correct statements are b, c, and e.
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Solve this system and identify the solution.
Select one:
a.
(5,-2)
b.
infinite solutions
c.
no solutions
d.
(2,-5)
The correct statement regarding the solution to the system of equations is given as follows:
b. Infinite solutions.
How to solve the system of equations?The system of equations in the context of this problem is defined as follows:
3y - 6x = 24.8 + 2x = y.Replacing the second equation into the first, the value of x is obtained as follows:
3(8 + 2x) - 6x = 24
24 + 6x - 6x = 24
24 = 24.
24 = 24 is a statement that is always true, hence the system has an infinite number of solutions, and thus option B is the correct option for this problem.
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A man buys a car at a cost of r60 000 from cape town and transported it to durban at a cost price of by r4 500. at what price must he sell the car to make an overall profit of 25%
He must sell the car at R80,625 to make an overall profit of 25%
To find the selling price of the car that gives a 25% profit, we need to use the following steps:
Calculate the total cost of buying and transporting the car to Durban:
Total cost = Cost of car + Cost of transportation
Total cost = R60,000 + R4,500
Total cost = R64,500
Calculate the desired profit:
Profit = 25% of total cost
Profit = 0.25 x R64,500
Profit = R16,125
Calculate the total amount that the car needs to be sold for:
Total amount = Total cost + Profit
Total amount = R64,500 + R16,125
Total amount = R80,625
Therefore, the man needs to sell the car for R80,625 to make an overall profit of 25%.
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A tree’s cross sectional area is called its basal area and is measured in square inches. Tree growth can be measured by the growth of the tree’s basal area. The initial base area of tree observed by a biologist is 154 square inches and annual growth rate is 6%. What will be the basal area after 10 years of growth?
The basal area of the tree after 10 years of growth would be approximately 279.7 square inches.
Given the initial basal area of a tree, which is 154 square inches, and the annual growth rate, which is 6%. To find out what the basal area of the tree will be after 10 years of growth.
By using the formula for compound interest, which can be applied to the growth of the basal area over time. The formula is:
A = P(1 + r)ⁿ
where:
A is the final amount
P is the initial amount
r is the annual growth rate
n is the number of years
To find A, the final basal area of the tree after 10 years of growth. We know that P is 154 square inches, r is 6% or 0.06 and n is 10.
By applying these values in the formula, we get:
A = 154(1 + 0.06)¹⁰
A = 154(1.06)¹⁰
A = ≈ 279.7
Therefore, the basal area of the tree after 10 years of growth would be approximately 279.7 square inches.
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1. Use integration in cylindrical coordinates in order to compute the vol- ume of: U = {(x,y,z):05:36 - 12 - y}
The volume of the region U is 16π cubic units.
To find the volume of the region U, we can use cylindrical coordinates. In cylindrical coordinates, a point in space is represented by the coordinates (r, θ, z), where r is the distance from the z-axis, θ is the angle between the x-axis and the projection of the point onto the xy-plane, and z is the height above the xy-plane.
In this case, the region U is defined by 0 ≤ r ≤ 2, 0 ≤ θ ≤ 2π, and 0 ≤ z ≤ 12 - r sin(θ).
To find the volume of U, we can integrate over the cylindrical coordinates. The volume of U is given by the integral:
V = ∫∫∫_U dV
where dV = r dz dr dθ is the volume element in cylindrical coordinates.
Substituting in the limits of integration, we have:
V = ∫₀²π ∫₀² ∫₀^(12-rsinθ) r dz dr dθ
Integrating with respect to z, we get:
V = ∫₀²π ∫₀² r(12-rsinθ) dr dθ
Integrating with respect to r, we get:
V = ∫₀²π [(6r² - (1/3)r³sinθ)] from r=0 to r=2 dθ
Simplifying, we get:
V = ∫₀²π [(24 - 16/3 sinθ)] dθ
Integrating, we get:
V = [24θ + 16/3 cosθ] from θ=0 to θ=2π
Simplifying, we get:
V = 48π/3 = 16π
Therefore, the volume of the region U is 16π cubic units.
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Can someone help me ASAP please? It’s due tomorrow. Show work please!! I will give brainliest if it’s correct and has work.
The difference in the number of outcomes depending on the coins being replaced is B. 10 outcomes.
How to find the outcomes ?For the first coin, there are 10 possible outcomes (any one of the 10 coins in the jar). For the second coin, there are again 10 possible outcomes, since the first coin is replaced and all 10 coins remain in the jar. Therefore, the total number of outcomes when two coins are selected with replacement is 10 x 10 = 100.
The number of outcomes when two coins are selected without replacement can be calculated as follows:
For the first coin, there are 10 possible outcomes (any one of the 10 coins in the jar). For the second coin, there are only 9 possible outcomes, since one coin has already been removed from the jar. Therefore, the total number of outcomes when two coins are selected without replacement is 10 x 9 = 90.
Difference is:
= 100 - 90
= 10 outcomes
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Unit 7: Right Triangles & Trigonometry Homework 4: Trigonometry Ratios & Finding Missing Sides #13
The value of sides are KL=5.34, JK=16.434, JL=17.29 and ML=22.25.
∵ ΔJLM is a right triangle, as ∠MJL=90°
∴ tan(∠JML)= JL/JM [∵ tan∅=perpendicular/hypotenuse]
⇒ tan(51°)=JL/14
⇒ JL=14×tan(51°)
= 14×1.23
= 17.29
∴ JL=17.29
Again, ΔJKL is a right triangle, with ∠JKL=90°
∴ cos(∠JLK)=KL/JL [∵ cos∅=base/hypotenuse]
⇒cos(72°)= KL/17.29
⇒KL=17.29×cos(72°)
= 17.29×0.309
= 5.34
∴ KL=5.34
Hence, the value of KL is 5.34.
Also, tan(∠JLK)=KJ/KL
⇒tan(72°)=JK/5.34
⇒JK=5.34×tan(72°)
= 5.34×3.077
= 16.434
∴ JK=16.434
And, cos(∠JML)=JM/ML
⇒cos(51°)=14/ML
⇒ML=14/cos(51°)
=14/.629
=22.25
∴ ML=22.25
Hence, the value of sides are KL=5.34, JK=16.434, JL=17.29 and ML=22.25.
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If a 35 N block is resting on a steel table with a coefficient of
static friction Hs = 0,40, then what minimum force is required to
move the block.
The minimum force required to move a block of 35 N resting on a steel table with a coefficient of static friction of 0.40 is 14 N.
Friction refers to the force that resists the motion and thus the force acts in the opposite direction of the force applied.
There are the following types of friction:
1. Static Friction
2. Limiting Friction
3. Kinetic Friction
F = μN
where μ is the coefficient of friction
N is the Normal Force
When the object is resting on a table, Normal force is the weight.
N = 35 N
μ = 0.40
F = 0.4 * 35
= 14 N
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A business award is in the shape of a regular hexagonal pyramid. the height of the award is 95 millimeters and the base edge is 44 millimeters.
what is the surface area of the pyramid to the nearest square millimeter?
The surface area of the hexagonal pyramid is 75240 square millimeters to the nearest square millimeter.
The surface area of the hexagonal pyramid can be calculated by finding the sum of the areas of its faces. The hexagonal pyramid has a base with six equal sides of length 44 millimeters, and six identical triangular faces with a height of 95 millimeters.
Each triangular face is an isosceles triangle, with two sides of length 44 millimeters and a base of length equal to the perimeter of the hexagonal base, which is 6 times 44 millimeters, or 264 millimeters.
To calculate the area of each triangular face, we can use the formula for the area of an isosceles triangle, which is (base x height) / 2. Substituting the values we have, we get: Area of each triangular face = (264 x 95) / 2 = 12540 square millimeters
Since the hexagonal pyramid has six identical triangular faces, we can multiply the area of one triangular face by 6 to get the total surface area of the pyramid: Total surface area = 6 x 12540 = 75240 square millimeters.
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1) You want your savings account to have a total of $23,000 in it within 5 years. If you invest your money in an account that pays 6.8% interest compounded continuously, how much money must you have in your account now? 2) You buy a brand new Audi R8 for $148,700 before taxes. If the car depreciates at a rate of 8%, how much will it be worth in 5 years?
After 5 years with 8% depreciation, the Audi R8's value will be around $81,249.36.
To determine how much money you must have in your account now, you can use the formula A = Pe^(rt), where A is the final amount, P is the principal (the initial amount invested), e is the constant 2.71828, r is the annual interest rate expressed as a decimal, and t is the time in years. We will calculate using this formula.Plugging in the given values, we get:
A = $23,000
r = 0.068 (6.8% expressed as a decimal)
t = 5 years
So, $23,000 = P*e^(0.068*5)
Solving for P, we get:
P = $16,376.59
Therefore, you must have $16,376.59 in your account now to reach your goal of $23,000 in 5 years with 6.8% continuous compounding interest. To determine how much the Audi R8 will be worth in 5 years, you can use the formula A = P(1 - r)^t, where A is the final amount, P is the initial amount, r is the annual depreciation rate expressed as a decimal, and t is the time in years. Plugging in the given values, we get:
P = $148,700
r = 0.08 (8% expressed as a decimal)
t = 5 years
So, A = $148,700*(1 - 0.08)^5
Simplifying, we get:
A = $81,249.36
Therefore, the Audi R8 will be worth approximately $81,249.36 in 5 years with 8% depreciation.
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how do i find the inverse
Step-by-step explanation:
To solve for inverse, utilize the following steps.
Step 1: let f(x)=y so we get
[tex]y = \sqrt{x - 6} + 5[/tex]
Step 2: Swap y and x
[tex]x = \sqrt{y - 6} + 5[/tex]
Solve for y.
[tex]x - 5 = \sqrt{y - 6} [/tex]
[tex](x - 5) { }^{2} + 6 = y[/tex]
Step 4: Let y =f^-1(x)
[tex](x - 5) {}^{2} + 6 = f {}^{ - 1} (x)[/tex]
Answer: [tex]f^{-1}(x) =[/tex] x²-10x+19
Step-by-step explanation:
Let's replace f(x) for y for now.
[tex]y=\sqrt{x-6}+5[/tex]
To find inverse. make your y into x, and your x into y
[tex]x=\sqrt{y-6}+5[/tex] >Now you solve for y. subtract 5 from both sides
[tex]x-5=\sqrt{y-6}[/tex] >Square both sides to get rid of root
[tex](x-5)^{2} =(\sqrt{y-6})^{2}[/tex] >drop root and square (x-5)
(x-5)(x-5) = y-6 >FOIL
x²-5x-5x+25 = y-6 > combine like terms
x²-10x+25 = y-6 >add 6 to both sides
x²-10x+19=y > this is your inverse now put the y into inverse form
[tex]f^{-1}(x) =[/tex] x²-10x+19
The mass of the Rock of Gibraltar is 1. 78 ⋅ 1012 kilograms. The mass of the Antarctic iceberg is 4. 55 ⋅ 1013 kilograms. Approximately how many more kilograms is the mass of the Antarctic iceberg than the mass of the Rock of Gibraltar? Show your work and write your answer in scientific notation
The mass of the Antarctic iceberg is approximately 2.56 × 10¹more kilograms than the mass of the Rock of Gibraltar.
To find out, we can subtract the mass of the Rock of Gibraltar from the mass of the Antarctic iceberg:
4.55 × 10¹³ kg - 1.78 × 10¹² kg = 4.37 × 10¹³ kg
Therefore, the mass of the Antarctic iceberg is about 2.56 × 10¹ (or 25.6) times greater than the mass of the Rock of Gibraltar.
This is because the mass of the Antarctic iceberg is much larger than the mass of the Rock of Gibraltar, as it is a massive block of ice floating in the ocean while the Rock of Gibraltar is a solid rock formation on land.
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Please solve, I rate! :)
Given f(t, y) = – 22 – 4cy3 + 3y5, find 2. - f1(,y) fy(x, y) = = frz(, y) = fry(x, y) =
The critical points are (t, y) = (t, 0) and (t, -4c/5).
To find the partial derivatives, we need to differentiate f(t, y) with respect to each variable separately.
f1(t, y) = ∂f/∂t = 0 (since there is no t term in the function)
fy(t, y) = ∂f/∂y = -12cy^3 + 15y^4
fz(t, y) = ∂^2f/∂t∂z = 0 (since there is no z term in the function)
fy(t, y) = ∂^2f/∂y∂z = 0 (since there is no z term in the function)
So, 2. - f1(,y) fy(x, y) = = frz(, y) = fry(x, y) = 0 - 12cy^3 + 15y^4 = 0 (since f1(,y) and frz(, y) and fry(x, y) are all 0)
Therefore, -12cy^3 + 15y^4 = 0
Factor out y^3:
y^3(-12c + 15y) = 0
This gives us two solutions: y = 0 or -4c/5.
So, the critical points are (t, y) = (t, 0) and (t, -4c/5).
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a. What does the size of each section tell you about that portion of the data? Select all that apply.
A. The relative importance of the category
B. The difference between the minimum and maximum values within the category
c. The count of data points within the category
D. The relative frequency of data within the category
The size of each section in a graph tells in relation to the portion of the data :
c. The count of data points within the categoryD. The relative frequency of data within the categoryWhat does the size show?The magnitude of a graphic's segment indicates a specific attribute of the data being presented. In charts like pie charts or stacked bar graphs, each component's size denotes the relative frequency or proportion of data points in a particular category.
This implies that larger fragments reflect an increased number of data points for its associated categories whereas smaller ones represent categories with lesser data points.
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Instructors led an exercise class from a raised rectangular platform at the front of the room. The width of the platform is (x+4) meters long and the area of the rectangular platform is 3x^2+10x−8. Find the length of the platform
Length of the platform at the front of the room whose area is 3x² + 10x - 8 and width is (x+4) m is (3x - 2) m
Area of the rectangular platform = 3x² + 10x - 8
Width of the rectangular platform = x+4
Area = length × width
Length = area/width
Length = [tex]\frac{3x^{2} + 10x - 8}{x+4}[/tex]
By splitting the middle term we get
Length = [tex]\frac{3x^{2} + 12x -2x -8 }{x+4}[/tex]
By taking common we get
Length = [tex]\frac{3x(x+4) - 2(x+4)}{x+4}[/tex]
By taking x+4 common we get
Length = [tex]\frac{(3x-2)(x+4)}{x+4}[/tex]
Cutting the x+4 from denominator and numerator we get
Length = 3x-2
Length of the platform at the front of room is 3x-2
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Bet you can’t solve this
Answer: The answer is (A
Step-by-step explanation:
The answer isB because A is constant, C is irrelevant, and D is dependent.
Calculate d²y/dx² y= 0.5x‐⁰.² d²y/dx²=
To calculate d²y/dx², we first need to find the first derivative of y, which is dy/dx. For y = 0.5x^-0.2, we can use the power rule of differentiation, which states that the derivative of x^n is n*x^(n-1). Therefore,
dy/dx = -0.1x^-1.2
To find the second derivative, d²y/dx², we need to differentiate dy/dx again. Using the power rule again, we get:
d²y/dx² = 0.12x^-2.2
This is the second derivative of y with respect to x.
In calculus, a derivative is a measure of how a function changes as its input changes. The second derivative is a measure of how the rate of change of the function itself changes as its input changes. It tells us about the curvature of the function at any given point.
In this case, we have calculated the second derivative of y, which gives us information about the rate of change of the slope of the function. If the second derivative is positive, the function is concave up (curving upward), and if it is negative, the function is concave down (curving downward). If the second derivative is zero, the function has an inflection point (a point where the curvature changes direction).
Overall, the second derivative is a powerful tool in calculus that helps us understand the behavior of functions in more detail.
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PLEASE HELP! PHOTO ATTACHED
The total area of the figure is 215π square feet
Calculating the total area of the figureFrom the question, we have the following parameters that can be used in our computation:
Radius, r = 5 cm
Height, h = 14 cm
So, we have
A1 = πr²
A1 = π * 5² = 25π
A2 = 2πrh
A2 = 2 * π * 5 * 14 = 140π
A3 = 1/2(4πr²)
A3 = 1/2(4π * 5²) = 50π
So, we have
Total area = 25π + 140π + 50π
Evaluate
Total area = 215π
Hence, the total area is 215π
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x An investor puts $4,500 into a life insurance policy that pays 8.0% simple annual interest. If no additional investment is made into the policy, how much accumulated interest should the investor expect at the end of 8 years? HELP PLEASE
The amount of accumulated interest the investor can expect in 8 years is $2,880.
How to find the accumulated interest ?To calculate the accumulated interest on the life insurance policy, we can use the simple interest formula:
I = P x r x t
In this case, the principal amount invested is $4,500, the annual interest rate is 8.0% (or 0.08 as a decimal), and the time period is 8 years. Therefore:
I = 4,500 x 0.08 x 8
I = $2,880
Therefore, the investor can expect to earn $2,880 in accumulated interest at the end of 8 years.
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7. AFIG has vertices at F(2, 4), I(5, 4) and G(3, 2). Graph AFIG and AP'I'G' after a rotation of 90° clockwise about the origin.
Thus, the coordinates of ΔF'I'G' after a rotation of 90° clockwise about the origin. are - F'(4,-2), I'(4,-5) and G'(2,-3).
Explain about the rotation rules:A rotation is a turn made about a specific axis. Both clockwise and anticlockwise rotations are possible. Whereas the image is really the rotating image, the pre-image is the original item.
From the pre-image point, calculate the image. The listed pre-image point is (x , y). Change the x and y coordinates, then multiply this same previous y coordinate by -1 to get a 90 degree anticlockwise rotation. Use the guidelines mentioned below to calculate each rotation.
Clockwise :
90 degree rotation: (x , y) ----> (y , -x)180 degree rotation: (x , y) ----> (-x , -y)270 degree rotation: (x , y) ----> (-y , x)Given :
F(2, 4), I(5, 4) and G(3, 2)
After 90 degree rotation: (x , y) ----> (y , -x)
F'(4,-2), I'(4,-5) and G'(2,-3).
Thus, the coordinates of ΔF'I'G' after a rotation of 90° clockwise about the origin. are - F'(4,-2), I'(4,-5) and G'(2,-3).
Graphs for the both triangles are obtained.
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Correct question:
ΔFIG has vertices at F(2, 4), I(5, 4) and G(3, 2). Graph ΔFIG and ΔF'I'G' after a rotation of 90° clockwise about the origin.
Given PQR with angle P = 42°, angle R = 26°, and PQ = 19, solve the triangle. Round all answers to the nearest tenth.
Angle Q =__
QR =__
PR =__
The solutions to the triangle PQR are:
Angle Q ≈ 112°
Side QR ≈ 8.98
Side PR ≈ 13.71
To solve the triangle PQR, we can use the fact that the sum of the angles in a triangle is always 180°. So we can find angle Q by subtracting the measures of angles P and R from 180°:
angle Q = 180° - angle P - angle R
angle Q = 180° - 42° - 26°
angle Q = 112°
Now, we can use the law of sines to find the lengths of the sides QR and PR.
The law of sines states that in any triangle ABC, the following equation holds:
a/sin(A) = b/sin(B) = c/sin(C)
where a, b, and c are the side lengths of the triangle, and A, B, and C are the opposite angles, respectively.
Applying this formula to triangle PQR, we can write:
QR/sin(R) = PQ/sin(Q)
QR/sin(26°) = 19/sin(112°)
Solving for QR, we get:
QR = (19 × sin(26°))/sin(112°)
QR ≈ 8.98
Similarly, we can find PR by applying the law of sines to triangle PQR as follows:
PR/sin(P) = PQ/sin(Q)
PR/sin(42°) = 19/sin(112°)
Solving for PR, we get:
PR = (19 × sin(42°))/sin(112°)
PR ≈ 13.71
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