Answer:
The equation x - y = 7 represents a linear equation with two variables, x and y. To find three ordered pairs (x, y) that satisfy this equation, we can arbitrarily choose values for one variable and solve for the other.
Ordered Pair 1:
Let's choose x = 0:
x - y = 7
0 - y = 7 (Substituting x = 0)
y = -7
So, the first ordered pair is (0, -7).
Ordered Pair 2:
Let's choose y = 0:
x - y = 7
x - 0 = 7 (Substituting y = 0)
x = 7
So, the second ordered pair is (7, 0).
Ordered Pair 3:
Let's choose x = 5:
x - y = 7
5 - y = 7 (Substituting x = 5)
y = -2
So, the third ordered pair is (5, -2).
Therefore, three ordered pairs (x, y) that satisfy the equation x - y = 7 are: (0, -7), (7, 0), and (5, -2).
Which equation is true?
An equation which is true include the following: A. 4 × n × n × n × n = 4n⁴.
What is an exponent?In Mathematics, an exponent is a mathematical operation that is typically used in conjunction with an algebraic expression in order to raise a quantity to the power of another.
This ultimately implies that, an exponent is represented by the following mathematical expression;
bⁿ
Where:
the variables b and n are numerical values (numbers) or an algebraic expression.n is referred to as a superscript or power.By applying the multiplication law of exponents for powers to each of the expressions, we have the following:
4 × n × n × n × n = 4n⁴
4 × n⁴ = 4n⁴
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Hannon Company makes swimsuits and sells these suits directly to retailers. Although
Hannon has a variety of suits, it does not make the All-Body suit used by highly skilled
swimmers. The market research department believes that a strong market exists for thistype of suit. The department indicates that the All-Body suit would sell for approximately $100. Given its experience, Hannon believes the All-Body suit would have the following manufacturing costs
Direct materials $ 25
Direct labor 30
Manufacturing overhead 45
Total costs $100
Instructions
(a) Assume that Hannon uses cost-plus pricing, setting the selling price 20% above its
costs. (1) What would be the price charged for the All-Body swimsuit? (2) Under what
circumstances might Hannon consider manufacturing the All-Body swimsuit given this approach?
(b) Assume that Hannon uses target costing. What is the price that Hannon would charge the retailer for the All-Body swimsuit?
(c) What is the highest acceptable manufacturing cost Hannon would be willing to incur to produce the All-Body swimsuit, if it desired a profit of $20 per unit? (Assume target costing.)
Hannon's maximum allowable production cost for the All-Body swimsuit is $80 if it wants to make a profit of $20 per unit.
Given data ,
a)
Using cost-plus pricing, the selling price is set 20% above the costs.
Selling price=Costs+(Costs x Markup)
Selling price=$100 + ($100x0.20)
Selling price=$100+$20
On simplifying the equation , we get
Selling price=$120
The price charged for the All-Body swimsuit would be$120.
Hannon might consider manufacturing the All-Body swimsuit under the cost-plus pricing approach if the market demand is strong enough to justify the selling price of $120 and if Hannon can efficiently produce and sell the swimsuit to generate profits.
(b)
Using target costing, the price charged by Hannon to the retailer is determined by subtracting the desired profit per unit from the target selling price.
Target selling price=$100 (given)
Desired profit per unit=$20 (given)
Price charged to retailer=Target selling price - Desired profit per unit
Price charged to retailer=$100-$20
On simplifying the equation , we get
Price charged to retailer=$80
The price that Hannon would charge the retailer for the All-Body swimsuit under target costing is$80.
(c)
To determine the highest acceptable manufacturing cost for the All-Body swimsuit under target costing, we subtract the desired profit per unit from the target selling price.
Target selling price=$100 (given)
Desired profit per unit=$20 (given)
Highest acceptable manufacturing cost=Target selling price-Desired profit per unit
Highest acceptable manufacturing cost=$100-$20
Highest acceptable manufacturing cost=$80
Hannon would be ready to spend up to $80 in manufacturing costs to develop the All-Body swimsuit if it wanted to make $20 each unit.
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For each polynomial function, (a) list all possible rational zeros, (b) use a graph to eliminate some of the possible zeros listed in part (a), (c) find all rational zer…
For each polynomial function, (a) list all possible rational zeros, (b) use a graph to eliminate some of the possible zeros listed in part (a), (c) find all rational zeros, and (d) factor P(x). P(X)=x^3-2x^2-13x-10
Answer:
(a) ±{1, 2, 5, 10}
(b) attached
(c) {-2, -1, 5}
(d) P(x) = (x +2)(x +1)(x -5)
Step-by-step explanation:
You want the possible and actual rational zeros for P(x) = x^3-2x^2-13x-10, and the factored form of the polynomial.
(a) Rational zerosThe rational root theorem tells you the possible rational zeros of a polynomial will be of the form ...
±(divisor of the constant)/(divisor of the leading coefficient)
The leading coefficient is 1, and the divisors of the constant are {1, 2, 5, 10}, so the possible rational zeros are ...
{±1, ±2, ±5, ±10}
(b, c) Actual zerosThe attached graph shows the actual zeros of P(x) to be {-2, -1, 5}.
(d) FactorsEach zero q corresponds to a factor (x -q). The factored form of the polynomial is ...
P(x) = (x +2)(x +1)(x -5)
"Ugh, handouts are so old-fashioned," Raina tells her classmate who is
preparing an informal talk. "Why not use flashier technology?" What is the
best response to Raina's comment?
The best response to Raina's comment will be that technology is good but handouts still serve the useful purpose of being a hard copy that speakers can use in case technology fails.
How to respond to RainaTo respond to Raina, the best thing to do will be to acknowledge the fact that technology is good but handouts are still important because, unlike technology that can trip off by some sudden technical faults, handouts can be depended upon.
So, while responding to Raina, we will not discard her point but will let her know that technology is good but handouts still have their benefits.
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A bicycle training wheel has a radius of 3 inches. The bicycle wheel has a radius of 10 inches. Approximately how much smaller, in square inches and rounded to the nearest hundredth, is the area of the training wheel than the area of the regular wheel?
The training wheel has an area approximately 286.34 square inches smaller than the regular wheel.
The area of a circle is given by the formula A = πr², where A is the area of the circle and r is the radius of the circle. Since we have the radii of both wheels, we can use this formula to find their respective areas.
The area of the training wheel is A₁ = π(3)² = 9π square inches.
The area of the regular wheel is A₂ = π(10)² = 100π square inches.
To find the difference in their areas, we can subtract A₁ from A₂:
A₂ - A₁ = 100π - 9π = 91π
So the difference in their areas is 91π square inches. To round to the nearest hundredth, we can use the approximation π ≈ 3.14:
91π ≈ 286.34 square inches
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50 Points! Multiple choice algebra question. Photo attached. Thank you!
the object will fall a distance of 1024 feet in 8 seconds. So the answer is (C) 1024 ft.
what is distance ?
Distance is a scalar quantity that refers to the total length traveled by an object or person, without considering the direction. It is a measure of the path length between two points, usually measured in units such as meters (m), feet (ft), or kilometers (km).
In the given question,
The formula t = √(d/16) relates the time t (in seconds) it takes an object to fall a distance d (in feet) to the acceleration due to gravity, which is approximately 32.2 feet per second squared.
To find how far the object will fall in 8 seconds, we can rearrange the formula to solve for d:
t = √(d/16)
t² = d/16 (Squaring both sides)
d = 16t² (Multiplying both sides by 16)
Substituting t = 8 into the formula, we get:
d = 16(8)² = 1024
Therefore, the object will fall a distance of 1024 feet in 8 seconds.
So the answer is (C) 1024 ft.
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Kamrie wants to paint her living room. The rectangular room measures 20 feet by 15 feet and has 10-foot ceilings. Along one of the long walls, there are three windows that each
measure 3 feet by 8 feet. Along one of the short walls, there are two windows that each measure 3 feet by 8 feet. Along the other long wall, there is a rectangular opening that measures
7 feet by 8 feet. The cans of paint Kamrie will purchase cover 415 square feet.
Part A: Determine the area of the walls. Show your work.
Part B: Determine the area of the doors, windows, and rectangular opening. Show your work.
Part C: Determine the area that Kamrie will paint and then determine how many cans of paint Kamrie needs to buy.
A) The area of the walls is 700 ft²
B) The area of the doors, windows, and rectangular opening is 226ft²
C) The area that Kamrie will paint is 474 ft², and she will need to purchase 2 cans of paint.
How did we arrive at the above?Part A:
The area of each of the short walls is
10 ft x 15 ft
= 150 sq ft.
So, the total area of the four walls is:
2(200 sq ft) + 2(150 sq ft)
= 700 sq ft
Part B:
The area of the three windows along the long wall is
3 ft x 8 ft
= 24 sq ft each, so their total area is
3(24 sq ft)
= 72 sq ft
The area of the two windows along the short wall is also
3 ft x 8 ft = 24 sq ft each,
so their total area is
2(24 sq ft)
= 48 sq ft
The area of the rectangular opening along the other long wall =
7 ft x 8 ft = 56 sq ft.
So, the total area of the doors, windows, and rectangular opening is
72 sq ft + 48 sq ft + 56 sq ft
= 176 sq ft
Part C:
To determine the area that Kamrie will paint, we need to subtract the area of the doors, windows, and rectangular opening from the total area of the walls
700 sq ft - 176 sq ft
= 524 sq ft
To determine how many cans of paint Kamrie needs to buy, we divide the area to be painted by the coverage per can
524 sq ft ÷ 415 sq ft/can
≈ 1.26 cans
So Kamrie needs to buy at least 2 cans of paint to cover the entire living room.
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I need help with this please
The ordered pair that represents the week before is given as follows:
A. (1,7).
How to define the ordered pair?The general format of an ordered pair is given as follows:
(x,y).
In which the coordinates are given as follows:
x is the x-coordinate.y is the y-coordinate.The meaning of each coordinate in this problem is given as follows:
x: chores.y: homework.For the current week, the ordered pair is given as follows:
(5,3).
For the previous week, the total number of hours was the same, that is, 5 + 3 = 8, however with x = 1 and y = 8 - 1 = 7, as only one hour was spent on chores.
Thus option A is correct.
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The ratio of apples to pears at a farm stand is 5:3. What is the percentage of the fruit to apples?
I’m in 4th period and it’s almost over with in 3 minutes please help!!
-3x-24 ≤-36
Answer:
-3x - 24 < -36
-3x < -12
x > 4
The value of y is directly proportional to x. If x = 25 when y = 110, what is the value of y when x = 40?
Answer:
176
Step-by-step explanation:
To do this question, we can simplify it even further.
If x=25 when y=110, it is in the ratio 25:110.
If we divide by five on both sides, the ratio becomes:
5:22.
Then, if we multiply by eight on both sides,
it becomes 40:22x8 which means y is equal to 176.
A force of 350 newtons stretches a spring 30 centimeters. How much work is done in stretching the spring from 10 centimeters to 40 centimeters?
The work done in stretching the spring from 10 cm to 40 cm is 10,837.5 J.
The work done in stretching a spring is given by the formula:
W = (1/2)k[tex]x^{2}[/tex]
where W is the work done, k is the spring constant, and x is the displacement of the spring from its original position.
To find the spring constant k, we can use the given information:
F = kx
where F is the force applied to the spring. Rearranging this equation, we get:
k = F/x
Substituting the given values, we get:
k = 350 N / 30 cm = 11.67 N/cm
Now, we can find the work done in stretching the spring from 10 cm to 40 cm:
W = (1/2)k([tex](x_{2})^{2} -(x_{1} )^{2}[/tex])
where [tex]x_{1}[/tex] is the initial displacement of the spring (10 cm) and [tex]x_{2}[/tex] is the final displacement (40 cm).
Substituting the values, we get:
W = (1/2) * 11.67 N/cm * ([tex](40 cm)^{2} - (10 cm)^{2}[/tex])
W = (1/2) * 11.67 N/cm * (1600 [tex]cm^{2}[/tex] - 100 [tex]cm^{2}[/tex])
W = (1/2) * 11.67 N/cm * 1500 [tex]cm^{2}[/tex]
W = 10,837.5 joules (J)
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Find the length of each arc. Round your answers to the nearest tenth.
285⁰
A) 20.2 in
C) 5.8 in
OA
OB
OC
OD
16 in
B) 100.5 in
D) 79.6 in
The length of the arc with a central angle of 285 degrees and radius 16 inches is 79.6 inches
Finding the length of the arcFrom the question, we have the following parameters that can be used in our computation:
central angle = 285 degrees
Radius = 16 inches
Using the above as a guide, we have the following:
Length of arc = central angle/360 * 2 * 3.14 * Radius
Substitute the known values in the above equation, so, we have the following representation
Length of arc = 285/360 * 2 * 3.14 * 16
Evaluate
Length of arc = 79.6
Hence, the length of the arc is 79.6 inches
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You missed an A in your art course by only 8 points. Your point total for the course was 415. How many points were possible in the course? (Assume that you needed 90% of the course total for an A.)
The total possible points in the course is approximately 470.
HOW CAN WE SOLVE AN EQUATION?Let's assume that the total possible points in the course is "x".
Since you needed 90% of the course total for an A, that means you needed to earn 90% of "x" to get an A. This is equivalent to 0.90x.
You missed an A by only 8 points, so your actual earned points must be 90% of "x" minus 8. This can be expressed as 0.90x - 8.
Given that your actual earned points for the course is 415, we can set up an equation:
0.90x - 8 = 415
Now, we can solve for "x" to determine the total possible points in the course:
0.90x = 415 + 8
0.90x = 423
x = 423 / 0.90
x ≈ 470
So, the total possible points in the course is approximately 470.
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Over what interval does f(x) = 2x
increase faster than g (X) =
¿x?
A. 1
B. x > 3
C.20
D. 1 > x > 21
If over what interval does f(x) = 2x increase faster than g (X): A. 1
What is over the interval?To determine over what interval f(x) = 2x increases faster than g(x) = x^2, we need to compare their derivatives. The derivative of f(x) is 2, which is a constant, and the derivative of g(x) is 2x. Therefore, f(x) increases at a constant rate of 2, while g(x) increases at a rate that depends on x.
To find the interval where f(x) increases faster than g(x), we need to find where the derivative of g(x) is less than 2. Setting 2x < 2 and solving for x, we get x < 1.
So, over the interval x < 1, f(x) = 2x increases faster than g(x) = x^2.
Therefore, the answer is A. 1.
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and area of the original figure to
of the reduced figure using the
3
6
Which statements are true about the comparison
between the two figures? Check all that apply.
The scale factor is 2.
The scale factor is
2
The perimeter of the model is the product of the
scale factor and the perimeter of the original
rectangle.
The area of the reduced figure is half the area of
the original figure.
The area of the reduced figure is
area of the original figure.
(94
times the
The scale factοr is οne-half. The perimeter οf the mοdel is the prοduct οf the scale factοr and the perimeter οf the οriginal rectangle. The area οf the reduced figure is (1/2)² = 1/4 times the area οf the οriginal figure
What is the scale factοr?The ratiο between cοmparable measurements οf an οbject and a representatiοn οf that οbject is knοwn as a scale factοr in mathematics.
Here,
We have tο cοmpare the perimeter and area οf the οriginal figure tο the perimeter and area οf the reduced figure using the scale factοr.
The ratiο οf the length οf the οriginal rectangle tο that οf the reduced rectangle is 6 tο 3 οr a factοr οf 1/2.
The ratiο οf the width οf the οriginal rectangle tο that οf the reduced rectangle is 2 tο 1, οr, again, a factοr οf 1/2. Sο, because this ratiο οf 1/2 is cοnstant, we knοw the tοtal scale factοr is 1/2, making B cοrrect.
16 ×(1/2) = 8, which means that the perimeter οf the scale-factοred, reduced rectangle is "the prοduct οf the scale factοr and the perimeter οf the οriginal rectangle". Sο, C is cοrrect.
Hence, The scale factοr is οne-half.
The perimeter οf the mοdel is the prοduct οf the scale factοr and the perimeter οf the οriginal rectangle.
The area οf the reduced figure is (1/2)² = 1/4 times the area οf the οriginal figure.
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*HELP!!* MULTIPLE CHOICE!!
Consider the graph of the function f(x)=log2 x, what are the features of function g if g(x)=-f(x)-1
The features of function g if g(x) = -f(x)-1 include the following:
B. domain of (0, ∞).
C. vertical asymptote of x = 0.
D. x-intercept at (1/2, 0).
What is a domain?In Mathematics and Geometry, a domain is the set of all real numbers for which a particular function is defined.
Additionally, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.
By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following key features:
Domain = (0, ∞)
Range = (-∞, ∞).
vertical asymptote, x = 0.
x-intercept = (1/2, 0).
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HELPP SOMEONE PLEASE
Answer:
8. mArc ED = 38°
9. mArc EA = 142°
10.mArc BDC = 308°
Step-by-step explanation:
The measure of an a central angle and it's intercepted arc are equal
So if the measure of the angle for the angle that intercepts Arc ED is 38° the arc is also 38°
Same thing with Arc EA, the central angle that intercepts it is 142° so the measure of Arc EA is 142°
Arc BDC is a major arc so it is greater than 180°. It goes around the circle from point B to point C and point D is one of the points on the arc.
We could find the value of the arc two ways. We could add all the angles the that make up the central angle it is intercept by or we could simply subtract the 52° that isn'tt a part of the arc and subtract that from 360°
360 - 52 = 308
So the central angle intercepting Arc BDC is 308° so the arc also has a measure of 308°.
The vertices of a triangle are A(0,0), B(3,8), and C(9,0). What is the area of this triangle?
As a result, the triangle formed by the vertices A(0,0), B(3,8), and C(9,0) has an area of 18 square units.
what is the triangle?A triangular is a three-sided, tri-geometric shape. It is a double figure that is frequently represented by the character "." A triangle's angles can never add up to more than 180 degrees. Triangles can be categorized into equilateral, elliptic, and scalene varieties according to the length of their sides and the dimensions of their angles. Three equal edges and three equal, 60-degree angles make up an equilateral triangle. Equal size ends and equal size angles make up an isosceles triangle. The sides and angles of a scalene triangle are not equal.
Given a triangle's vertices in the coordinate plane, we can apply the following formula to get its area:
A is equal to [tex]|(x1(y_2 -y_3) + x_2(y_3 -y_1) + x3(y_1 -y_2)) / 2|.[/tex]
where the triangle's vertices' coordinates are [tex](x_1, y_1), (x_2, y_2), and (x_3, y_3).[/tex]
We obtain: by substituting the coordinates of the specified vertices.
[tex]A = |(0(8 - 0) + 3(0 - 0) + 9(0 - 8)) / 2| = |-36| / 2 = 18[/tex]
As a result, the triangle formed by the vertices A(0,0), B(3,8), and C(9,0) has an area of 18 square units.
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A ship leaves a port with a bearing of S80°E and a speed of 15 knots. After 1 hour, the ship turns 90° towards the North with the same speed in 2 hours. What is the bearing to the ship from the port (due North)? How far is the ship from the port now?
The bearing of B from P is N24.65°E (or S24.65°W), and the ship is approximately 33.54 nautical miles from the port.
Since the ship travels at a constant speed, we can use the formula:
distance = speed × time
For the first hour, the ship travels at a bearing of S80°E, which is equivalent to a bearing of N10°E. Therefore, the ship travels 15 nautical miles in a direction N10°E. This gives us:
PA = distance = speed × time = 15 × 1 = 15 nautical miles
After the first hour, the ship turns 90° towards the North. This means that the ship is now heading due East. Therefore, for the next 2 hours, the ship travels 15 × 2 = 30 nautical miles in an easterly direction. This gives us:
AB = distance = speed × time = 15 × 2 = 30 nautical miles
Now, we can use the Pythagorean theorem to find the value of y:
y² = x² + (AB)²
y² = 15² + 30²
y² = 225 + 900
y² = 1125
y ≈ 33.54 nautical miles
To find the bearing of B from P, we can use trigonometry. The bearing is the angle between the line PA and due North. Let θ be this angle. Then we have:
tan(θ) = x / y
θ = tan^-1(x / y)
Using the values we have found, we get:
tan(θ) = 15 / 33.54
θ ≈ 24.65°
Therefore, the bearing of B from P is N24.65°E (or S24.65°W), and the ship is approximately 33.54 nautical miles from the port.
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Charles drew a plan for a rectangular piece of material that he will use for a blanket. Three of the vertices are (−2.2,−2.3), (−2.2,1.5), and (1.5,1.5). What are the coordinates of the fourth vertex?
The coordinates of the fourth vertex are (-2.2, 1.5).
Understanding how to estimate coordinatesTo find the coordinates of the fourth vertex, we can use the fact that opposite sides of a rectangle have equal length and are parallel to each other.
First, we can find the length of one of the sides of the rectangle. Let's take the side connecting the points (-2.2, -2.3) and (-2.2, 1.5):
length = |1.5 - (-2.3)| = 3.8
Since this is a rectangle, the length of the side opposite to this one must also be 3.8. We can find this side by taking the points (-2.2, 1.5) and (1.5, 1.5):
width = |1.5 - (-2.2)| = 3.7
Now we know the length and width of the rectangle, so we can find the coordinates of the fourth vertex. Let's call this point (x, y).
Since the fourth vertex is opposite to the point (-2.2, -2.3), the x-coordinate of the fourth vertex must be the same as the x-coordinate of (-2.2, -2.3):
x = -2.2
Similarly, since the fourth vertex is opposite to the point (1.5, 1.5), the y-coordinate of the fourth vertex must be the same as the y-coordinate of (1.5, 1.5):
y = 1.5
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Use a net to find the surface area of the prism.
A. 426 m2
B. 213 m2
C. 306 m2
D. 336 m2
The surface area of the prism is 426 m²
What is surface area of cuboid?A cuboid is a rectangular prism. And has all the properties related to a prism. The general formula for the surface area of a cuboid is ;
SA = 2B + ph
We can use net formula to find the surface area of a cuboid.
surface area of a cuboid is expressed as;
SA = 2( lb+lh +bh)
l = 12m , b = 5m and h = 9m
lb = 12×5 = 60m²
lh = 12 × 9 = 108m²
bh = 5×9 = 45m²
SA = 2(60+108+45)
= 2(213)
= 426 m²
therefore the surface area of the cuboid is 426m²
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Choose the ordered pair that is a solution for this equation.
3x = 8 - y
A. (3, 1)
B. (2, 2)
C. (8, 0)
Answer:
B. (2, 2)
Step-by-step explanation:
(x, y)
3x = 8 - y
a) 3(3) = 8 - 1
9 = 8 - 1
9 = 7 False
b) 3(2) = 8 - 2
6 = 6 True
c) 3(8) = 8 - 0
24 = 8 False
A particle moves in the xy plane so that at any time
,
x=3sint
and
.y=t-4cost+1
What is the vertical component of the particle's location when it's horizontal component is 2?
Responses
y = -1.05
y = -1.05
y = -2.25
y = -2.25
y = -1.25
y = -1.25
y = 0.73
The vertical component of the particle's location, when its horizontal component is 2, is:
y = -1.25
How to solveTo find the vertical component of the particle's location when its horizontal component is 2, we need to first find the value of t when x = 2.
Given the equation:
x = 3sin(t)
Substitute x with 2:
2 = 3sin(t)
Now, isolate t by dividing both sides by 3:
sin(t) = 2/3
Take the inverse sine (arcsin) of both sides:
t = arcsin(2/3)
Now, plug the value of t back into the y equation:
y = t - 4cos(t) + 1
y = arcsin(2/3) - 4cos(arcsin(2/3)) + 1
Using a calculator to find the approximate value of y, we get:
y ≈ -1.25
Therefore, the vertical component of the particle's location when its horizontal component is 2 is:
y = -1.25
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Can anybody please help me with this. Quick
For each answer just type
1.
2.
3.
1. n - 4 = 12
2. n - 13 = 20
3. n + 9 = 25
4. n + 5 = 75
5. x + 6 = 13
6. n - 6 = 5
For 1 n = 16
For 2 n = 33
For 3 n = 16
For 4 n = 70
For 5 x = 7
For 6 n = 11
Hope that helps, :).
An architect creates a blueprint using a scale of 1 inch = 3.5 ft. If the actual
length of a patio is 21 feet, how long will the patio's length appear in the
blueprint?
O 6 inches
O 7 inches
O 17.5 inches
O 73.5 inches
6 inches will be the length of the patio.
According to the scale, 1 inch on the plan corresponds to 3.5 feet in real life.
We must convert the patio's real length of 21 feet to inches using the scale in order to determine how long it would look on the blueprint:
3.5 feet to one inch
21 feet in x inches
If we cross-multiply, we obtain:
1 inch/3.5 feet * 21 feet
= x inches
= 6 inches.
As a result, the length of the patio will be indicated on the blueprint as 6 inches.
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Find the circumference of the circle. Round to the nearest tenth.
A. 148.4 m
B. 169.6 m
C. 84.8 m
D. 54.0 m
Answer:
C. 84.8 m
Step-by-step explanation:
Circumference of circle = D x 3.14
D = 27 m
Let's solve
27 x 3.14 = 84.78 m
So, the circumference of the circle is C. 84.8 m
Which of the following sets of numbers could represent the three sides of a triangle O (6,8,14} O {11, 14, 22} O {13, 20, 34) O {13, 20, 35}
The set of numbers that can represent the sides of a triangle are:
{11, 14, 22} and {13, 20, 35}.
How to Determine the Set of Numbers that Can Represent the Sides of a Triangle?We can determine which set of numbers would represent the sides of a triangle by applying the triangle inequality theorem.
This theorem states that the sum of any two sides of a triangle must be greater than the length of the third side to make it a triangle.
Applying the theorem, we have:
A. (6,8,14)
6 + 8 > 14 (not true, since 6 + 8 = 14 and not greater than 14)
6 + 14 > 8 (true)
8 + 14 > 6 (true)
Therefore, (6,8,14) cannot represent the sides of a triangle.
B. {11, 14, 22}
11 + 14 > 22 (not true, since 11 + 14 = 25 and not less than 22)
11 + 22 > 14 (true)
14 + 22 > 11 (true)
Therefore, {11, 14, 22} does not represent the sides of a triangle.
C. {13, 20, 34}
13 + 20 > 34 (not true, since 13 + 20 = 33 and not greater than 34)
13 + 34 > 20 (true)
20 + 34 > 13 (true)
Thus, {13, 20, 34} cannot represent the sides of a triangle.
D. {13, 20, 35}
13 + 20 > 35 (not true, since 13 + 20 = 33 and not less than 35)
13 + 35 > 20 (true)
20 + 35 > 13 (true)
This means, {13, 20, 35} can represent the sides of a triangle.
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Find the measure of the angle
The angle turns through 5/8 of the circle
The angle mesure of 5/8 of the circle is _°
Stacy invests $55,000 into an account at 2.3% interest compounded monthly. Find the total value of the investment after 4 years.
In the formula, A is the amount after interest, P is the principal, r is interest rate in decimals, n is the amount of times the interest is compounded per year, and t is the amount of years.