The vertical velocity of the string at the origin at time t would be zero, as the origin is a fixed point.
The origin is a fixed point, so it does not move. This means that the vertical velocity of the string at the origin at time t would be zero.
The origin of the string is a fixed point, meaning that it does not move. This implies that the vertical velocity of the string at the origin at time t would be zero, as the origin does not move or change its position. Since the origin is a fixed point, the vertical velocity of the string at the origin at time t would remain constant, and would be equal to zero. Thus, the vertical velocity of the string at the origin at time t would be zero.
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The volume of a cylinder is 90pie cm³. If the radius is 3 cm, what is the height
of the cylinder?
Answer:
The height of the cylinder is 10 cm.
Step-by-step explanation:
1. The volume of a cylinder is given by
-V = pi r^2 h where r is the radius and h is the height
- 90 pi = pi r^2 h
2. We know the radius is 3
-90 pi = pi (3)^2 h
-90 pi = 9 pi h
3. Divide each side by 9 pi
- 90 pi /9 pi = 9 pi h / 9pi
- 10 =h
The height of the cylinder is 10 cm.
The graph of a piecewise function is shown.
The graph shows a piecewise function in 3 pieces. The first piece is curved and increasing from the left through negative 3 comma negative 7 and ends at a closed point negative 2 comma negative 2. The second piece is linear with an open point at negative 2 comma negative 1 and another endpoint at 2 comma 1. The third piece is curved with an endpoint at 2 comma 1, and it goes through the point 3 comma 6 and continues to increase to the right.
What is the domain of the function?
(−∞,∞)
[−∞,∞]
(−∞,0)
(0,∞)
The domain of the piecewise function as described in the task content is; ( −∞ , ∞ ).
What is the domain of the described piecewise function?It follows from the task content that the domain of the piecewise function which is as described in the task content be determined.
The domain of a function is the set of all possible input values of that function.
For the first piece, since the curve increases from left ( -∞ ) through a point and ends at a closed point (-2, -2). Hence, the set of inputs for the first piece in interval notation is; ( -∞, -2 ].
Also, for the second piece which is linear with an open point at (-2, -1) and ends at an endpoint (2, 1). Hence, the domain of the second piece is; [-2, 2].
Finally, the third piece is curved with an endpoint at (2, 1) and continues to increase tonthe right. Hence, the domain of the third piece is; [2, ∞)
Ultimately, by combining all sets of input values as determined; ( -∞, -2 ], [-2, 2] and [2, ∞); the domain of the whole piecewise function is; (−∞,∞).
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How likely is the spinner to land a consonant rather than a vowel?
The likelihood of the spinner to land on a consonant rather than a vowel is C. Less likely.
How to find the likelihood ?The likelihood of the spinner landing on a consonant rather than a vowel can be found by the formula :
= Number of consonants / Number of outcomes on the spinner
= 4 / 9
= 0. 44
This likelihood is less than 50 % which is what would have made the likelihood equally likely. However, it is not much lower than 50 % so the likelihood would be less likely.
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simplify. (9x2- 8x-3) + (2x+8)
A. 11x + 10x +5
B. 9x2-6x+5
C. 9x2+10x-11
D. 11x2-6x-11
The result of simplifying the quadratic polynomial (9x2- 8x-3) + (2x+8) is 9x2 - 6x + 5.
what is polynomial ?In mathematics, the intersection point is the place on the y-axis where the slope of the line passes. a place where the y-axis crosses on a line or curve. Y = mx+c, where m stands for the slope and c for the y-intercept, is used as the equation for the straight line to show this. The slope (m) of the line and its y-intercept (b) are highlighted in the equation's intercept form. When an equation has the intercept form (y=mx+b), the slope is m and the y-intercept is b. Some equations can also be rewritten so that they appear to be slope intercepts. If y=x is rewritten as y=1x+0, for instance, the slope and y-intercept are both changed to 1.
given
(9x2- 8x-3) + (2x+8)
9x2 - 8x - 3 + 2x + 8
9x2 - 6x + 5
Thus, the result of simplifying (9x2- 8x-3) + (2x+8) is 9x2 - 6x + 5.
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Does 15 12/9 make a triangle?
Answer: No it doesnt
Step-by-step explanation:
12+9 = 21 which is greater than 15 meaning it cannot create a triangle
What 2 - 3
5319
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a rectangular piece of marble is cut such that the width is triple the length and the height is double the width. write a polynomial function v (x) in standard form for the volume of the piece of marble, where a is the length of the marble. v(x) =
A polynomial function v (x) in standard form for the volume of the piece of marble is v(x) = 18a^3.
What is volume?
Volume is a term used in mathematics to describe the volume of three-dimensional space occupied by an object or a closed surface. The measurement of volume is done in cubic units, like m^3, cm^3, in^3, etc. Volume is also referred to as capacity on occasion.
Given:
A rectangular piece of marble is cut such that the width is triple the length and the height is double the width.
We have to write a polynomial function v (x) in standard form for the volume of the piece of marble.
Let 'a' is the length of the marble.
⇒ Width of marble = 3a (width is triple the length)
⇒ Height of marble = 2(3a) = 6a (height is double the width)
⇒ Volume of marble = length x width x height
= a x 3a x 6a
Volume of marble = 18a^3
Hence, a polynomial function v (x) in standard form for the volume of the piece of marble is v(x) = 18a^3.
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Find RS and QR in rectangle PQRS
RS and QR are -8 and -5, respectively, in the rectangle P Q R S. Consequently, v is equal to 23.
What is the value of QR and RS ?here, QR is 3 v - 77, RS is 4 v - 97, and PS is v-23.As a result, PS = v - 23 ⇒ v = 23. As a result, v has a value of 23. So, RS = 4 × 23 - 97 = -5 is used to calculate its value.So, QR = 3 × 23 - 77 = -8 is used to determine its value. A All of the internal angles of a rectangle's four sides are equal to 90 degrees.
Every corner or vertex has a right angle where the two sides meet. It differs from a square in that the length of the opposing sides of the rectangle are equal. First, determine the width w using the area of rectangle formula, which is "w = A/l," to determine the length and width of a rectangle.
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May I have help on this please? thanks if you do!
Answer: 1. linear equation
2. non-linear equation
3. non-linear equation
4. non-linear equation
5. linear equation
Step-by-step explanation:
not sure
Jacob is roller skating. He can skate 3/10 of a mile in 1/2 of a minute. What is Jacobs unit rate in miles per minute? please answer this is 100% of my grade TwT
Answer:
[tex]\frac{3}{5}[/tex] miles per minute
Step-by-step explanation:
3/10 ÷ 1/2
3/10 x 2 = 6/10 = 3/5
I need help on quiz 4-1 classifying and solving for sides/ angles
Step-by-step explanation:
I don't know because you have it to far
Wanda sews small and large gloves. It takes her 45 minutes to sew a small pair of gloves and 120 minutes to sew a large pair of gloves. The costs of producing the gloves are $2 for a small pair and $4 for a large pair. Wanda has 16 hours available to sew gloves. The materials to make the gloves must cost at most $40. The system of linear inequalities represents this situation.
{45x+120y≤9602x+4y≤40
The point represents the number of small gloves is 16 and the number of large gloves is 2.
What is linear inequality?According to the mathematical definition of inequality, neither side is equal. When a relationship leads to a non-equal comparison between two expressions or numbers, it is known as an inequality in mathematics. The equal sign "=" in this statement can be replaced with any of the inequality symbols, such as greater than (>), less than (<), greater than or equal to (≥), less than or equal to (≤), or not equal to (≠).
Given Wanda sews small and large gloves,
time for small gloves = 45 minutes
time for large gloves = 120 minutes
total time = 16 hours = 960 minutes
let x be the number of small gloves and y be the number of large gloves,
inequality equation is 45x + 90y ≤ 960
and the cost of small gloves = $2
cost of large gloves = $4
total amount = $40
equation 2x + 4y ≤ 40
let us assume the system of inequality in form of a linear equation,
45x + 90y = 960
2x + 4y = 40
by solving the equations
the equation is written as
x = 20 - y
45(20 -y) + 90y = 960
y = 2
and x = 16
so the minimum values for x and y are 16 and 2 to maximize the profit Wanda should not decrease the production of small gloves from 16 and large gloves to 2.
Hence the point of maximization is (16, 2).
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the complete question is in image.
Is a scale factor of 1/3 an enlargement?
A scale factor of 1/3 is not an enlargement. A scale factor of less than 1 is considered a reduction and not an enlargement.
An enlargement is a transformation that increases the size of a figure, it is characterized by a scale factor greater than 1. A dilation with a scale factor greater than 1 will increase the size of a figure and thus is considered an enlargement.
A dilation with a scale factor of 1/3 will decrease the size of a figure, as each point on the figure will be moved one-third as far from the origin as it was before the dilation. This means that the dilated figure will be smaller than the original figure and will have a scale factor of 1/3.
It's important to note that if the scale factor is less than 1, the dilation will reduce the size of the figure and if the scale factor is greater than 1, the dilation will increase the size of the figure.
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Katrina runs 15 miles in 2 1/2 hours what is the average number of minutes it takes her to run 1 mile
Answer: 45 min
Step-by-step explanation:
Please help! Trig!!!!!!!l. Look at the image! And answer the question! Thank u!
Therefore , the solution to the given problem of trigonometry comes out to be Sin( θ) = Cos(90 - θ).
Describe trigonometry.Correlations between triangles' angles and sides are studied in the mathematics discipline known as trigonometry. Since every straight-sided form can be reduced to a collection of triangles, trig can be found throughout geometry. The relationships between trigonometric and other branches of mathematics, in particular calculus, either real or complex, integrals, square root, and integrals, are astonishingly complicated.
Here,
Below is a list of the trigonometric values that are missing:
Angle A = θ-90.
28° sin = 62° cos
Cos 33° equals Sin 57°.
Cos 31° equals Sin 59°.
Sin( θ) = Cos(90 - θ).
Therefore , the solution to the given problem of trigonometry comes out to be Sin( θ) = Cos(90 - θ).
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Two sides of a triangle each measure 8 inches.
Maria says the triangle must be isosceles. Is Maria correct? Explain.
A.
No; the third side could measure 9 inches or 7 inches, and the triangle would be scalene.
B.
Yes; an isosceles triangle has at least two sides that have equal measures.
C.
Yes; the third side could measure 9 inches, and the triangle would be equilateral.
D.
No; the third side of the triangle could be 8 inches, and the triangle would be acute.
Answer:
B.) An isosceles triangle has at least two sides with equal measures.
Step-by-step explanation:
There are two equal sides and two equal angles in an isosceles triangle. There should be at least 2 equal sides for an Isosceles triangle. This means, even an equilateral triangle is an Isosceles triangle. In this case, at least two equal sides are 8 inches each. This is why the correct answer is 'Yes; an isosceles triangle has at least two sides that have equal measures.'
find the sum of the measures of interior angles of the indicated convex polygon
(a) nonagon (b)dodecagon c) 23-gon ?
(a) The sum of the interior angles of the nonagon is 1260°.
(b) The sum of the interior angles of the dodecagon is 1800°.
(c) The sum of the interior angles of the 23-gon is 3780°.
What is a convex polygon?
A convex polygon is a closed figure with all of its interior angles less than 180° and all of its vertices pointing outward. The term convex refers to a shape with a curve or a projecting surface. To put it another way, all of the lines across the outline are straight and point outwards.
The formula for the sum of the interior angle is (n -2)180°.
The number of sides of the nonagon is 9.
Putting n = 9 in (n -2)180°, to find the sum of interior angle of nonagon:
The sum of the interior angle is (9 -2)180° = 1260°.
The number of sides of dodecagon is 12.
Putting n = 12 in (n -2)180°, to find the sum of interior angle of dodecagon:
The sum of the interior angle is (12 -2)180° = 1800°
Putting n = 23 in (n -2)180°, to find the sum of interior angle of 23-gon:
The sum of the interior angle is (23 -2)180° = 3780°.
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Write a function in terms of $t$ that represents the situation.
Sales of $10,000 increase by 65% each year.
A function in terms of t that represents the situation of sales that is of $10,000 and increase by 65% each year is t = 10,000(1.65)ⁿ.
What is function?An element of one non-empty set and an element of another non-empty set are said to have a special relationship when they are connected by a function in mathematics.
An assignment of an element from set Y to each element of set X, where set X is the domain and set Y is the codomain, is what is meant when a function is applied from a set X to a set Y.
We have given that f(t) is given by the Sales of $10,000 increase by 65% each year, i.e.
As sales of $10,000 increase by 65% each year.
The situation is represented by an exponential growth function.
The initial amount a = 10,000
The rate of growth r = 65% = 0.65
Therefore, the function will be:
t = a(1 + r)ⁿ
Where,
t represents the final amount.
a represents the initial amount
r represents the rate of growth
1+r represents the growth factor
n represents the time.
⇒ t = a(1 + r)ⁿ
⇒ t = 10,000(1 + 0.65)ⁿ
⇒ t = 10,000(1.65)ⁿ
Thus, a function in terms of t that represents the situation of sales that is of $10,000 and increase by 65% each year is t = 10,000(1.65)ⁿ.
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What is the additive inverse of 14 /- 15?
The additive inverse of 14 /- 15 is -14 /+ 15.
The antithesis of a number is the additive inverse. It is found by changing the sign of the number. To find the additive inverse of 14 /- 15, start by changing the sign of the number from a negative sign to a positive sign. The result is 14 /+ 15. This is the additive inverse of 14 /- 15. The additive inverse of any number is the same number, but with the opposite sign. For example, the additive inverse of -14 is 14, and the additive inverse of 14 is -14. The additive inverse of any number always adds up to zero when added together, which is why it is called the "additive inverse".
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How do the graphs of the functions f(x) = (3/2)x and g(x)
The function g(x) = (2/3)ˣ is the graph of the function f(x) = (3/2)ˣ reflected over y-axis.
What is function?A function is a process or a relation that associates each element 'a' of a non-empty set A , at least to a single element 'b' of another non-empty set B. A relation f from a set A (the domain of the function) to another set B (the co-domain of the function) is called a function in math.
f = {(a, b)| for all a ∈ A, b ∈ B}.
Given, the function
f(x) = (3/2)ˣ
g(x) = (2/3)ˣ
We have to compare the graphs of the functions f(x) and g(x).
Exponential function is of the form: y = abˣ
Where a is the initial value and b is the growth factor.
a) If b > 1, then the function is an exponential growth function.
b) If 0 < b < 1, then the function is an exponential decay function.
f(x) = y = (3/2)ˣ
The function is an exponential growth function.
The rule of reflection over y-axis:
(x, y) → (-x, y)
Applying the rule, we get,
(3/2)ˣ = (3/2)⁻ˣ
= (2/3)ˣ
= g(x)
Therefore, g(x) is graph of f(x) reflected over y-axis
Hence, graph of the function f(x) = (3/2)ˣ reflected over y-axis is function g(x) = (2/3)ˣ .
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how to graph y=-2/3x-5
-2x+3y=-15
By plotting the given points (0,-5) , (1,-17/3 ) for y=-2/3x-5 and the points for-2x+3y=-15 are (0,-5) , (1,-13/3) and (2,-11/3) we get the required graph.
What is linear equation ?
Linear equation can be defined as the equation in which highest degree is one.
Given Equation,
y=-2/3x-5 and -2x+3y=-15
So,
use the slope form is
y= mx+b , where m is slope and b is the y-intercept.
find the valued of m an b using the form y = mx+b
m = -2/3 and b=-5
The slope of line is the value of m and y-intercept the value of b
slope = -2/3
Any line can be graphed using two points. Select two x values, and plug them into the equation to find the corresponding 2y values.
create a table for x and y values.
x y
0 -5
1 -17/3
and soon
Similarly for -2x+3y=-15
x y
0 -5
1 -13/3
2 -11/3
and soon
And Hence plot the points in the graph.
Therefore, By plotting the given points (0,-5) , (1,-17/3 ) for y=-2/3x-5 and the points for-2x+3y=-15 are (0,-5) , (1,-13/3) and (2,-11/3) we get the required graph.
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Change 20.4 yards to inches.
Answer: 734.4 inch
Step-by-step explanation:
Answer:
734.4 is the correct answer
i need help hurryyy !!
Answer: 3
Step-by-step explanation: -4 1/3 divided by 2 1/5 = -1 32/33
Answer:
-1 32/33
Step-by-step explanation:
Negative divided by positive is negative.
We know the answeer will be negative.
Now ignore the signs, and just divide the mixed numerals.
1. Convert the mixed numerals to fractions.
2. Divide.
3. Convert quotient back to mixed numeral.
4. Make answer negative.
1. 4 1/3 ÷ 2 1/5 = 13/3 ÷ 11/5
2. = 13/3 × 5/11 = 65/33
3. = 33/33 + 32/33 = 1 32/33
4. Answer: -1 32/33
Which of the angles measures more than 90 but less than 180?
Answer:
Isosceles triangle
Step-by-step explanation:
Isosceles triangle has more than 90 but less than 180, which means Isosceles triangle is equal to 120.
Can someone please help me
Therefore , the solution of the given problem of triangle comes out to be x = 32.376 side of the hypotunse length.
What precisely is a triangle?Since a triangle has four or even more sections, it is a polygon. It has an easy geometric form. Triangle ABC refers to a square with angles A, B, & C. A singular plane and square are produced by Euclidean geometry whenever the sides are still not collinear. A triangle is a polygon if it has 3 components and three corners. Where a triangle's three sides come together are known as the corners. A triangle's angles add up to 180 degrees.
Here,
Given:
Triangle having :
=> Sin 78° = h /30
=> 0.9781 = h /30
=> h = 30 * 0.9781
=>h =29.343
and
For x :
=> Sin 65° = 29.343 /x
=> 0.9063 = 29.343 /x
=> x = 29.343 / 0.9063
=> x = 32.376
Therefore , the solution of the given problem of triangle comes out to be
x = 32.376 side of the hypotunse length.
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The Expression (t^6) (t^-14) is equivalent to t^n . What is the value of n
The equation (t6)(t-14) is identical to tn when n = 8. A mathematical expression is composed of numbers .
what is expressions ?You can multiply, divided, add, or take something away in mathematics. An expression is put together as follows: Expression, numeric value, and math operator A mathematical expression is composed of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) Contrasting phrases and emotions is possible. An algebraic expression is any mathematical statement that has elements, quantities, and an arithmetic operation. As an illustration, the phrase 4m + 5 consists of the terms 4m and 5, as well as the given equation's variable m, which are all split by the algebraic sign +.
given
(t^6) (t^-14) = t^n
= 6 -14 = n
n = 8
The equation (t6)(t-14) is identical to tn when n = 8.
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ABCD is a parallelogram. Find the length of AB. A. 20 B. 17 C. 7
what is the function rule for the line ?
The function rule for the line is,
f(x) = -2/3x -2.
The correct option is B.
What is a slope?In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.
If a line passes through two points (x₁ ,y₁) and (x₂, y₂) ,
then the equation of line is
y - y₁ = (y₂- y₁) / (x₂ - x₁) x (x - x₁)
To find the slope;
m = (y₂- y₁) / (x₂ - x₁)
From the diagram,
the function has y-intercept at -2 and x-intercept at -3.
To find the slope:
First, we interpreted two points (-3, 0) and (0, -2).
Then the slope,
m = (y₂- y₁) / (x₂ - x₁)
m = (-2, 0)/(0 + 3)
m = -2/3
Now, the equation is,
f(x) = -2x/3 - 2
Therefore, the equation is,
f(x) = -2x/3 - 2
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What is -2[6^2-(8-5)^3]
Answer:
Well yeah its -18
Step-by-step explanation:
You want to know how long the road marked x is and you know the lengths of the other two roads that form a right angle with the road, has the measurements to find the length marked x