The speed v[t] is always a positive value, since it's the magnitude of the velocity vector.
The velocity of the motion at time t is given by V[t] = x'[t], which is the derivative of the position function x[t] with respect to time.
To compute v[t], you take the square root of the magnitude of V[t], which is given by:
v[t] = |V[t]| = sqrt(|x'[t]|) = sqrt(sqrt[t] * |V[t]|)
Here, the square root of t is taken as a weighting factor for the velocity, which means that the speed increases with time. The speed v[t] is always a positive value, since it's the magnitude of the velocity vector.
Note that this formula assumes that the motion x[t] is differentiable, which means that the velocity V[t] is well-defined and continuous. If x[t] is not differentiable, then the velocity V[t] may not exist, and this formula wouldn't apply.T
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2. If lime juice has a pH of 1.7, what is the concentration of hydrogen
ions (in mol/L) in lime juice, to the nearest hundredth? Use the
formula pH = -log[H +].
Answer:0.02 mol/L
Step-by-step explanation:
Given: pH = 1.7
Required: [H+]
Equation: pH = -log [H+]
Solution:
Take the antilog of both sides
[H+] = antilog(-pH)
Antilog(-pH) is equal to 10^-pH. Therefore
[H+] = 10^-pH
Solve for [H+]
[H+] = 10^-1.7
Answer: [H+] = 0.02 mol/L
Please help on the question below
Any help is appreciated, thank you:)
Answer:
Here is your answer...
Hope it helps
Why does the equation 5(3x-4)-6x=3(3x-4) have no solutions?
Bureause when you subtract from both sides of the equation and simplify you get 20-20
Berise when you add to both sides of the equation and simplify you get = -12
Because when you add to both sides of the equation and simplify you get 2020
Because when you add-to both sides of the equation and simple you get 20-12
Which is the cubic polynomial in standard form
with roots 3, -6, and 0?
Group of answer choices
x^2 - 3x - 18
x^3 - 3x^2 - 18x
x^2 + 3x - 18
x^3 + 3x^2 - 18x
Answer:
D
Step-by-step explanation:
Roots are the solution to a polynomial equation. So construct the factors of the polynomial. (x-3)(x+6)(x-0). Now multiply the factors and you will get option D.
a certain bridge is 4,024 feet long. approximately how many minutes does it take to cross this bridge at a constant speed of 20 miles per hour? (1 mile
At a continuous speed of 20 miles per hour, it takes 2 minutes to cross this bridge.
What is a unitary approach?The unitary method is used to calculate the value of a single unit and then multiply that value by itself in order obtain the desired value. Unitary refers to a single, unique, or solitary unit. As a result,
this method's objective is to establish values in terms of a single unit. If a car can drive 44 kilometer two litres of gas, for instance, the unitary approach can be used to calculate how many kilometers it can travel on one litre of gas. The value of a single unit is determined by the unitary technique, and also the value of the required quantity of units can then be calculated using this value.
given,
0.76 miles = (4024/5280) miles
Speed =20 miles per hour
Time: =(Distance / Speed) = (0.76/20)
= 0.038 ( in hours )
into minutes = 2 min
At a continuous speed of 20 miles per hour, it takes 2 minutes to cross this bridge
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Please Help me - You will get 60 points for the rapid reply- Use isosceles trapezoid ABCD to determine the following measurements-
Answer:
1) AD = 9 in
2) DE = 9.25 in
3) ∠EDC = 36°
4) ∠AEB = 108°
5) 11.5 in
Step-by-step explanation:
1) AD = BC = 9in
2) AC = BD (diagonals are equal)
⇒ BD = 14.25
⇒ BE + DE = 14.25
⇒ 5 + DE = 14.25
DE = 9.25
3) Since AB ║CD,
∠ABE = ∠EDC = 36°
4) ∠ABE = ∠BAE = 36°
Also ∠ABE + ∠BAE + ∠AEB = 180 (traingle ABE)
⇒ 36 + 36 + ∠AEB = 180
∠AEB = 108
5) midsegment = (AB + CD)/2
= (8 + 15)/2
11.5
the tampa bay skeptics performed an experiment to see whether an acclaimed psychic has extrasensory perception (esp). a crystal was placed, at random, inside 1 of 10 identical boxes lying side by side on a table. the experiment was repeated seven times, and x, the number of decisions, was recorded. (assume that the seven trials are independent.) a. if the psychic is guessing (i.e., if the psychic does not possess esp), what is the value of p, the probability of a correct decision on each trial? b. if the psychic is guessing, what is the expected number of correct decisions in seven trials? c. if the psychic is guessing, what is the probability of no correct decisions in seven trials? d. now suppose the psychic has esp and p
a. The probability of a correct decision on each trial is 0.1.
b. The expected number of correct decisions in seven trials is 0.7.
c. The probability of no correct decisions in seven trials is approximately 0.478.
d. The probability that the psychic guesses incorrectly in all seven trials is approximately 0.0078.
What is probability?
Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.
a. If the psychic is guessing (i.e., does not possess ESP), there are 10 boxes, and only one of them contains the crystal.
Therefore, the probability of a correct decision on each trial is -
p = 1/10 = 0.1
b. If the psychic is guessing, the expected number of correct decisions in seven trials can be found by multiplying the probability of a correct decision on each trial (0.1) by the number of trials (7) -
E(X) = np = 7 × 0.1 = 0.7
Therefore, the number of correct decisions is 0.7.
c. If the psychic is guessing, the probability of no correct decisions in seven trials can be found using the binomial distribution formula -
\(P(X=0) = (n\ choose\ x) \times p^x \times (1-p)^{(n-x)}\)
In this case, n = 7, x = 0, and p = 0.1.
Substituting these values into the formula, we get -
\(P(X=0) = (7\ choose\ 0) \times 0.1^0 \times 0.9^7 = 0.478\)
Therefore, the probability value is 0.478.
d. If the psychic has ESP and p = 0.5, the probability of guessing incorrectly on any trial is -
q = 1 - p
q = 1 - 0.5
q = 0.5
The probability of guessing incorrectly in all seven trials can be found using the binomial distribution formula -
\(P(X=7) = (n\ choose\ x) \times p^x \times q^{(n-x)}\)
In this case, n = 7, x = 7, p = 0.5, and q = 0.5.
Substituting these values into the equation, we get -
\(P(X=7) = (7\ choose\ 7) \times 0.5^7 \times 0.5^0 = 0.0078\)
Therefore, the probability value is 0.0078.
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The Tampa bay skeptics performed an experiment to see whether an acclaimed psychic has extrasensory perception (ESP). A crystal was placed, at random, inside 1 of 10 identical boxes lying side by side on a table. The experiment was repeated seven times, and x, the number of decisions, was recorded. (Assume that the seven trials are independent.)
a. If the psychic is guessing (i.e., if the psychic does not possess ESP), what is the value of p, the probability of a correct decision on each trial?
b. If the psychic is guessing, what is the expected number of correct decisions in seven trials?
c. If the psychic is guessing, what is the probability of no correct decisions in seven trials?
d. Now suppose the psychic has ESP and p=.5. What is the probability that the psychic guesses incorrectly in all seven trials.
Which measurement is equal to 6 kilograms?
Answer:
6000 metres is equal to 6 kilograms
Plz help asap 15 points + might get the brilliant
Answer:
Step 1-2
Step-by-step explanation:
The person doing this question, did not distribute the 6 properly.
They distributed the 6 to the x, but not to the 4.
When done properly, it should be:
6x+24=3x-2
Answer:
step 2
Step-by-step explanation:
4 times 6=24
6(x+4)=3x-2
6x+24=3x-2
3x+24=-2
3x=-26
Find the distance between the points (7,9) and (1, 1).
Write your answer as a whole number or a fully simplified radical expression. Do not round.
____ Units
The percent change from 45 to 90 is
A change from 45 to 90 represents a positive change (increase) of 100%
Use the formula found below on this webpage to find the percent change by replacing the given values:
Percent change = New - Old|Old| × 100%
Percent change = 90 - 45|45| × 100% =
4545 × 100 = 100% (increase)
Where: 45 is the old value and 90 is the new value. In this case we have a positive change (increase) of 100 percent because the new value is greater than the old value.
The diameter of a circular coffee can lid is 5 inches. Which measurement is closest to the area of the coffee can lid? A. 7.9in. B. 19.6in C. 31.4in D. 78.5in
Answer:
Step-by-step explanation:
what is the rule
4, -4, 4, -4 ...
Answer:
i think its 4
Step-by-step explanation:
because first is 4 then is -4 then 4 then -4 so it should be 4
Plz mark me the Brainliest
A softball player throws a ball into the air with an initial velocity of 32 feet per second. The ball is released at a height of 5 feet. The function h(t) = \(-16t^{2}\)+32t+5 models the height h (in feet) of the ball as a function of the time t (in seconds) after it is thrown. Use the equation to find the time that the ball is in the air if the player lets the ball drop
The time that the ball is in the air if the player lets the ball drop is 2.145 sec
What is a quadratic equation?
A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax²+ bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term.
-16t²+32t+5
by comparing this equation to the standard form of the quadratic equation we get
a=-16 b=32 c=5
the time (t) needed for the ball to reach its maximum height using the axis of symmetry formula (x = -b/2a) for a parabola:
the time at which the ball reaches the maximum height using the axis of symmetry formula is (x=-b/2a)
t = -32/2×-16
t=1sec
by putting h(t) to zero and determining the time (t) when the ball hits the ground:
-16t²+32t+5=0
-16(t²+2t+5/16)=0
t²-2t-5/16=0
(t)²-2×1×t+(1)²-5/16=1
(t-1)²=21/16
t-1=√21/√16
t=1+4.58/4
t=1+1.145
t=2.245sec
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FILL IN THE BLANK. "a _____ is a three-dimensional figure that encloses a region of space."
A solid is a three-dimensional figure that encloses a region of space.
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FILL IN THE BLANK. "a __solid___ is a three-dimensional figure that encloses a region of space."
A solid is a three-dimensional figure that encloses a region of space. It can be defined as a geometric shape that has length, width, and height and is made up of atoms, molecules, or ions.
Therefore, a solid can be classified as a polyhedron or a curved surface figure. Examples of solids include cubes, pyramids, spheres, cylinders, and cones.
A polyhedron is a three-dimensional figure that encloses a region of space.
A polyhedron is a solid shape formed by flat polygonal faces, straight edges, and vertices. These faces enclose a three-dimensional region of space, giving the polyhedron its distinct shape.
In summary, the term you are looking for is "polyhedron," which describes a 3D figure composed of flat polygonal faces enclosing a region of space.
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two cars leave the origin; one goes north at mph and the other goes south at mph. after how many hours will they be miles apart?
After 2.94 Hr. or approximately 3 Hr. both cars will be 250 miles apart.
We have,
The value of the speed of the car moving in the north direction =35 mph
The value of the speed of the car moving in the south direction=50 mph
From above, we can conclude that both are going in the opposite direction
So, the value of the net speed/ relative speed of both the car will be =35+50=85 mph
As we know,
The value of distance can be determined by using the relationship:
Distance = speed * time
So, for determining the value of time, we will put the value of total distance covered and the value of relative speed in the above expression.
Thus, we will get it as:
250=85*t
So, the value of the time taken = t=250/85=2.94 hours approx 3 hours
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The complete question should be like:
Two cars leave the origin; one goes north at 35mph and the other goes south at 50 mph. After how many hours will they be 250 miles apart?
The circumference of a circle is 60π cm. What is the area of the circle to the nearest whole number?
Answer:
2827 cm
Step-by-step explanation:
The formula for the circumference of a circle is 2*pi*radius, meaning that to find the radius you would need to divide the circumference by 2*pi. By doing this, you get that the radius is 30cm. Now, the formula for area of a circle is pi * radius^2. Plugging the radius in, you get 30^2 * pi, which is equal to 900pi cm. This is about 2827 cm when you use a calculator.
The cross-section of the prism below is an equilateral triangle.
a) What is the area of the shaded face?
b) How many rectangular faces does the prism have?
c) What is the total area of these rectangular faces?
7 cm Scroll down
8 cm
a.) The area of the shaded face would be =54cm²
b.) The number of rectangular faces that the prism has =3
c.) The total area of the rectangular faces would be=162cm².
How to calculate the area of the shaded face in the diagram above?To calculate the area of the shaded face, the formula that should be used = length×width.
where;
Length = 9cm
width = 6cm
Area = 9×6 = 54cm²
The total number of rectangular faces = 3
The total area of these rectangular face would be area of one rectangular face multiplied by 3.
That is;
54×3 = 162cm²
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A house has increased in value by 28% since it was purchase. if the current value is $416,000, what was the value when it what was purchased?
Answer: 300,000
Step-by-step explanation:
Help ASAP
Polygons QRST and Q′R′S′T′ are shown on the coordinate grid:
A 180-degree clockwise rotation about the origin followed by a translation 1 unit to the right.
A 180-degree clockwise rotation about the origin followed by a translation 1 unit to the left.
A translation 1 unit to the left followed by a 270-degree counterclockwise rotation about the origin.
A translation 1 unit to the right followed by a 270-degree counterclockwise rotation about the origin.
Answer:
A 180-degree clockwise rotation about the origin followed by a translation 1 unit to the left.
Answer:
A 180-degree clockwise rotation about the origin followed by a translation 1 unit to the left.
Step-by-step explanation:
how many cups of granulated sugar in a 5 pound bag
There are approximately 11.25 cups of granulated sugar in a 5 pound bag.
To determine the number of cups of granulated sugar in a 5 pound bag, we can use the conversion factor of 2.25 cups per pound.
First, we multiply the number of pounds (5) by the conversion factor:
5 pounds * 2.25 cups/pound = 11.25 cups
Therefore, there are approximately 11.25 cups of granulated sugar in a 5 pound bag.
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Please answer correctly !!!!!!! Will mark brainliest answer !!!!!!!!!!
Answer:
625
Step-by-step explanation:
The maximum is the y-coordinate of the vertex. The vertex is (25, 625) so the answer is 625.
One day a store sold 28 sweatshirts. White ones cost $9.95 and yellow ones cost $13.50. In all, $321.20 worth of sweatshirts were sold. How many of each color were sold?
Answer:
white sold = 16
yellow sold = 12
Step-by-step explanation:
w = # of white sold
y = # of yellow sold
w + y = 28 solve this for w
w = 28 - y
9.95w + 13.5y = 321.20 substitute w = 28-y into this expression and solve for y
9.95(28-y) + 13.5y = 321.20
278.60 - 9.95y + 13.50y = 321.20
278.60 + 3.55y = 321.20
3.55y = 321.20 - 278.60 = 42.60
y = 42.60/3.55 = 12 substitute this into w = 28 - y and solve for w
w = 28 - 12 = 16
A bed measures 40 inches by 75 inches.
What is the distance between opposite corners of the bed?
Therefore, the distance between opposite corners of the bed is 85 inches.
What is triangle?A triangle is a three-sided polygon that is formed by connecting three non-collinear points. It is a simple closed figure with three sides and three angles. Triangles are classified according to the relative lengths of their sides and the measure of their angles. There are several types of triangles, including equilateral triangles, isosceles triangles, scalene triangles, acute triangles, obtuse triangles, and right triangles.
Here,
The distance between opposite corners of a rectangle can be found using the Pythagorean theorem, which states that for a right triangle with legs of length a and b and hypotenuse of length c, c² = a² + b².
In this case, the length and width of the bed form the legs of a right triangle, and the distance between opposite corners is the length of the hypotenuse.
Using the Pythagorean theorem, we can find the length of the hypotenuse:
c² = 40² + 75²
c² = 1600 + 5625
c² = 7225
c = √(7225)
c = 85
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An online shopping club has 4,600 members when it charges $9 per month for membership. For each $1 monthly increase in membership fee, the club loses approximately 200 of its existing members. Write and simplify a function R to represent the monthly revenue received by the club when x represents the price increase.
Hint – Monthly Revenue = # of members • monthly fee
ℙ !!
Answer: R = (4600 - 200x) ( 9 + 1x)
Step-by-step explanation:
We have that
Revenue = Members * (Cost Per Member)
Where x represents the number of $1 increases
write a statement that creates a list called my_nums, containing the elements 5, 10, and 20.
A statement that creates a list is my_nums= [5,10,15]. This is also known as array.
What is an array?An array is a grouping of identically typed elements that are stored in adjacent memory locations and may each be separately referred to using an index to a special identifier. There is no need to declare five distinct variables when declaring an array of five integer values (each with its own identifier).
What are three types of arrays?The three types of arrays are index, multidimensional and associative array.
my_nums= [5,10,15] is an array that stores multiples of 5.
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A statement that creates a list is my_nums= [5,10,15]. This is also known as array.
What is an array?
An array is a data structure consisting of a collection of elements (values or variables), each identified by at least one array index or key. An array is a combination of a set of elements which are all of the same data type, organized in a particular way. Arrays are used to store multiple values in a single variable, structure data, and access data more efficiently. Arrays are generally used to represent data in a structured way, and they can be used to perform various mathematical operations and other calculations. Arrays are also useful for sorting and searching data in a predetermined order.
What are three types of array?
The three types of array are index, multidimensional and associative array.
my_nums= [5,10,15] is an array that stores multiples of 5.
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How do I solve this. Please explain your method.
Answer:
x > 90 > y
Step-by-step explanation:
You want to know the relationship of the central angles in a rectangle where the diagonals cross.
Angle relationsAssuming we can trust the figure (not always a good idea), we notice that x° is an obtuse angle and y° is an acute angle. (The angle opposite the longer side in this geometry will always be obtuse.)
This means ...
x° > 90°
90° > y°
The two angles form a linear pair, so their sum is 180°.
The correct description is ...
x > 90 > y
__
Additional comment
If the diagonals crossed at right angles, the rectangle would be a square.
Complete the table for the function y=3(1/9)^x
For the given function the values are when x = -2, y = 243, when x = -1, y = 27, when x = 0, y = 3, when x = 1, y = 1/3.
What is function?
A function in mathematics is a set of instructions that takes one or more inputs, usually numbers, and produces a distinct output value for each input value. The output value is determined by the input value, and each input has a unique output.
The given function is:
\(y = 3(1/9)^x\)
We need to find the y-values for the given x-values. Let's substitute each x-value into the function and simplify to find the corresponding y-value:
For x = -2:
y = \(3(1/9)^{(-2)\) // substitute x = -2 into the function
y = \(3(9^2)\) // simplify using exponent rules: \(1/9^{(-2)\) = \(9^2\)
y = 243 // simplify further: 3 * 81 = 243
So, when x = -2, y = 243.
For x = -1:
y = \(3(1/9)^{(-1)\) // substitute x = -1 into the function
y = 3(9) // simplify using exponent rules: \(1/9^{(-1)\) = 9
y = 27 // simplify further: 3 * 9 = 27
So, when x = -1, y = 27.
For x = 0:
y = \(3(1/9)^{(0)\) // substitute x = 0 into the function
y = 3(1) // simplify using exponent rules: \(a^0\) = 1 for any non-zero number a
y = 3 // simplify further: 3 * 1 = 3
So, when x = 0, y = 3.
For x = 1:
y = \(3(1/9)^{(1)\)// substitute x = 1 into the function
y = 3(1/9) // simplify using exponent rules: \(a^1\) = a for any number a
y = 1/3 // simplify further: 3 * (1/9) = 1/3
So, when x = 1, y = 1/3.
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let be the tangent plane to the graph of (,)=26−132−262 at the point (4,2,−286). let (,)=26−2−2. find the point on the graph of where the tangent plane is parallel to .
The point on the graph where the tangent plane is parallel is (52, 52, -5382).
What is the tangent plane?
The surface that contains all tangent lines of the curve at a point, $P$, that lies on the surface and passes through the point is represented by the tangent plane. We discovered earlier in our talks of derivatives and tangent lines that we can use tangent lines to mimic the behavior of a graph. We may employ tangent planes for a similar reason now that we're working with multivariable functions and three-dimensional coordinate systems.
Here, we have
Given: Let P be the tangent plane to the graph of g(x, y) = 26 – 13x² – 26y² at the point (4, 2, –286). Let f(x, y) = 26 – x² - y².
We have to find the point on the graph where the tangent plane is parallel.
Let P be the tangent plane to the graph z = g(x, y) = 26 – 13x² – 26y² at the point (4, 2, –286).
φ(x,y,z) = 13x² + 26y² + z - 26
Δφ = 26xi + 52yj + k
Δφ(4, 2, –286) = 104i + 104j + k
Then,
P: 104(x-4) + 104(y-2)+1(z+286) = 0
104x + 104y + z = 338...(1)
Now, Let
ψ(x,y,z) = x² + y² + z - 26
Δψ = 2xi + 2yj + k
Let (x₀,y₀,z₀) be the point of the graph z = f(x,y) = 26 – x² - y² where the tangent plane in the plane is parallel to equation (1).
Δψ (x₀,y₀,z₀) = (2x₀,2y₀,1)
= 2x₀/104 = 2y₀/104 = 1/1
x₀ = 52 = y₀
Now, z₀ = 26 – x₀² - y₀² = 26 – 52² - 52²= -5382
Hence, the point on the graph where the tangent plane is parallel is (52, 52, -5382).
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Valerie is considering various savings options. At Bank 1, she can invest $1,000 in a CD that earns compound interest at an annual rate of 2.4%. At Bank 2, she can invest $1,000 in a savings account that pays 2% simple interest upon withdrawal. How much more money would Valerie earn in 5 years with the CD at Bank 1 than with the savings account at Bank 2?
Answer:
100.00
Step-by-step explanation: