(i) The smallest angular speeds that cause the toast to hit and then topple to be butter-side down 3.84 rad / s
(ii) The largest angular speeds that cause the toast to hit and then topple to be butter-side down 11.51 rad / 5
The distance from the counter to the floor, d = 82 cm = 0.82 m
Rotation is less than 1 rev.
The toast rotates at a constant angular speed as it falls, and the toast is falling with a constant acceleration (gravitational acceleration).
Using the kinematic equations of motion to calculate the time taken by the toast to hit the floor
[tex]$d & =v_i t+\frac{1}{2} g t^2 \\[/tex]
[tex]$d & =0+\frac{1}{2} g t^2 \\[/tex]
Therefore [tex]$t & =\sqrt{\frac{2 d}{g}}=\sqrt{\frac{2 \times 0. 82}{9.8}[/tex]
= 0.409 s
Where
[tex]$v_i$[/tex] is the initial speed of the toast, [tex]$v_i=0$[/tex] because the toast is falling from rest.
t the time that the toast takes to hit the floor.
g is the gravitational acceleration.
d is the distance between the counter and the floor.
Part (a)The toast is accidentally pushed over the edge of the counter with the butter side up, then the toast rotates as it falls. If the toast hits the ground and then topples to be butter-side down, it has to land on one of its edges. The smallest angle, in this case, is [tex]$\frac{1}{4}$[/tex] revolution and corresponds to the smallest angular speed
[tex]$\omega_{\min } & =\frac{\Delta \theta}{\Delta t} \\[/tex]
[tex]$\omega_{\min } & =\frac{0.25 \mathrm{rev}}{\Delta t}=\frac{0.25 \times 2 \pi}{\Delta t} \\[/tex]
Therefore [tex]$ \omega_{\min } & =\frac{0.5 \pi}{0.409}[/tex]
= 3.84 rad/s
Where
[tex]$\omega_{\min }$[/tex] is the minimum angular speed for the toast to land butter-side down. [tex]$\Delta \theta$[/tex] is the smallest angle for the toast to land butter-side down in radians.
[tex]$\omega_{\min }$[/tex] = 3.84 rad / s
Part b:
The toast is accidentally pushed over the edge of the counter with the butter side up, then the toast rotates as it falls. If the toast hits the ground and then topples to be butter-side down, it has to land on one of its edges. The largest angle, in this case, is [tex]$\frac{3}{4}$[/tex] revolution and corresponds to the largest angular speed
[tex]$\omega_{\max } & =\frac{\Delta \theta}{\Delta t} \\[/tex]
[tex]$\omega_{\max } & =\frac{0.75 \mathrm{rev}}{\Delta t}=\frac{0.75 \times 2 \pi}{\Delta t} \\[/tex]
Therefore [tex]$ \omega_{\max } & =\frac{1.5 \pi}{0.409}[/tex]
= 11.51 rad / s
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When a slice of buttered toast is accidentally pushed over the edge of a counter, it rotates as it falls. If the distance to the floor is 82 cm and for rotation less than 1 rev, what are the (i) smallest and (ii) largest angular speeds that cause the toast to hit and then topple to be butter-side down?
HELP FAST WILL GIVE BRAINLYEST AND 100 PTS
The correct answers are: a reflection across the x-axis and a translation 1, unit right, a rotation of 180° about the origin and a translation of 1 unit left.
How to check for congruence?To check for congruence, we need to verify that the two triangles have the same shape and size, which means that one triangle can be mapped onto the other using a sequence of transformations.
For the first sequence of transformations (a reflection across the x-axis and a translation 1 unit right), we can reflect triangle ABC across the x-axis, which will map (-6, 2) to (-6, -2), (-4, 6) to (-4, -6), and (-2, 2) to (-2, -2). We can then translate the reflected triangle 1 unit to the right, which will map (-6, -2) to (-5, -2), (-4, -6) to (-3, -6), and (-2, -2) to (-1, -2). This mapped triangle is triangle ADEF, and since it was obtained by a sequence of transformations, we can conclude that ABC is congruent to ADEF.
For the second sequence of transformations (a rotation of 180° about the origin and a translation of 1 unit left), we can rotate triangle ABC 180° about the origin, which will map (-6, 2) to (6, -2), (-4, 6) to (4, -6), and (-2, 2) to (2, -2). We can then translate the rotated triangle 1 unit to the left, which will map (6, -2) to (5, -2), (4, -6) to (3, -6), and (2, -2) to (1, -2). This mapped triangle is also ADEF, and since it was obtained by a sequence of transformations, we can conclude that ABC is congruent to ADEF.
Therefore, the correct answers are:
a reflection across the x-axis and a translation 1 unit right
a rotation of 180° about the origin and a translation of 1 unit left.
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Match each equation from the first set with an equivalent equation from the second set. Some of the answer choices are not used.
3x+6=4x+7
3(x+6)=4x+7
4x+3x=7-6
9x=4x+7
3x+18=4x+7
3x=4x+7
3x-1=4x
7x=1
Simplifying the equations will give 3x -1 = 4x, 3x + 18 = 4x + 7 and 7x = 1
Match each equation from the first set with an equivalent equation from the second setLets simplify each of the equations in order to match with the equivalent equation from the second set
3x+6=4x+7
Collecting like terms
3x +6 - 7 = 4x
3x -1 = 4x
The second equation
3(x+6)=4x+7
expanding the bracket
3x + 18 = 4x + 7
The third equation
4x+3x=7-6
simplifying the equation
7x = 1
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Which of the following could be the areas of
the three squares shown?
A. 40 ft², 55 ft², 95 ft²
B. 35 ft²2, 25 ft², 45 ft²
C. 10 ft2, 10 ft², 100 ft²
D. 40 ft2, 30 ft², 1200 ft²
The areas of the squares are calculated from the Pythagoras relation of right angled triangle and it is 40 ft², 55 ft², 95 ft²
What is a Triangle?A triangle is a plane figure or polygon with three sides and three angles.
A Triangle has three vertices and the sum of the interior angles add up to 180°
Let the Triangle be ΔABC , such that
∠A + ∠B + ∠C = 180°
The area of the triangle = ( 1/2 ) x Length x Base
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
if a² + b² = c² , it is a right triangle
if a² + b² < c² , it is an obtuse triangle
if a² + b² > c² , it is an acute triangle
Given data ,
Let the right angle triangle be represented as ΔABC
Now , the measure of side AB = √40 feet
The measure of side BC = √55 feet
The measure of side AC = √95 feet
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
Substituting the values in the equation , we get
AC² = AB² + BC²
( √95 )² = ( √40 )² + ( √55 )²
On simplifying the equation , we get
95 = 40 + 55
95 = 95
Therefore , the area of squares formed is 40 ft², 55 ft², 95 ft²
Hence , the triangle is having sides √40 feet , √55 feet and √95 feet
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To save for retirement, a student invests $70 each month in an ordinary annuity with 3% interest compounded monthly. Determine the accumulated amount in the student's annuity after 30 years.
The accumulated amount will be $_______?
(Round to the nearest cent as needed.)
The accumulated amount will be $133.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
A student invests $70 each month in an ordinary annuity with 3% interest compounded monthly.
We know that;
⇒ Simple interest = P × r × t
Where, P is principle amount , 'r' is rate and t is time.
Here, P = $70
r = 3%
n = 30 years
Substitute all the values, we get;
Hence, We get;
⇒ Interest = P × r × t
⇒ Interest = 70 × 0.03 × 30
⇒ Interest = $63
Hence, The accumulated amount will be ;
⇒ P + Interest
⇒ $70 + $63
⇒ $133
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The critical points of a rational inequality are –1, 3, and 4. Which set of points can be tested to find a complete solution to the inequality? x = 1 and x = 3.5 x = –1, x = 3, and x = 4 x = –2, x = 2, and x = 5 x = –3, x = 1, x = 3.5, and x = 5
The possible set of inequalities are;
x = -3,
x = -1,
x = 1,
x = 3,
x = 5.
What are inequalities?Inequalities are the comparison of mathematical expressions, whether one quantity is greater or smaller in comparison to another quantity.
We use these symbols to represent inequalities, '>' , '<', '≥', '≤'
The critical points of a rational inequality are the x-values at which the inequality changes direction (from "<" to ">" or vice versa). In this case, the critical points are -1, 3, and 4.
To find the complete solution to the inequality, we need to test points on either side of the critical points. For example, if we test a value less than -1, such as -2, and find that it satisfies the inequality, then all values less than -1 also satisfy the inequality. On the other hand, if a value less than -1 does not satisfy the inequality, then no values less than -1 satisfy the inequality.
Therefore, a complete solution to the inequality can be found by testing values around each critical point. A common set of points to test for this purpose is the critical points themselves, and values just less than and just greater than each critical point.
So, a possible set of points to test to find the complete solution to the inequality is:
x = -3,
x = -1,
x = 1,
x = 3,
x = 5.
These points bracket the critical values and allow us to determine which intervals of values satisfy the inequality.
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What is the correct sequence of steps for calculating 96 on a scientific calculator?
First press button 9, then press the button on which the (^) sign is mentioned. Then button press 6. Then the value you get is 531,441.
What is the value of the expression?At the point when the important parts and fundamental cycles of a mathematical technique are given qualities, the articulation's outcome is the consequence of the calculation it portrays.
The meaning of straightforwardness is simplifying something to accomplish or get a handle on while likewise making it somewhat less troublesome.
The expression is given below.
⇒ 9⁶
First press button 9, then press the button on which the (^) sign is mentioned. Then button press 6.
The value of the exponent numerical expression 9⁶ will be 531,441.
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The correct question is given below.
What is the correct sequence of steps for calculating 9⁶ on a scientific calculator?
Let A be an mxn matrix, and let u and v be vectors in Rn with the property that Au = 0 and Av 0. Explain why A(u + v) must be the zero vector. Then explain why A(cu + dv) -0 for each pair of scalars c and d.
Suppose that, Au=0 and Av=0. Then, we already have A(u+v)=Au+Av. Now, A(u + v) = Au + Av = 0 + 0 = 0.
Now, let c and d be scalars. Using both parts of Theorem 5, A(cu + dv) = A(cu) + A(dv) = cAu + dAv = c0 + d0 = 0.
A matrix, also known as matrices, is a rectangular array or table with numbers, symbols, or expressions that are arranged in rows and columns to represent a mathematical object or a property of that object. Matrix types are not all associated with linear algebra. In particular, this applies to incidence matrices and adjacency matrices in graph theory.
Unless otherwise stated, all matrices in this article, which focuses on matrices related to linear algebra, represent linear maps or can be viewed as such. The majority of mathematical and scientific disciplines use matrices, either directly or indirectly through the use of geometry and numerical analysis.
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The following table gives the frequencies of the nest size (number of eggs) of 153 Great Blue Heron nests
recorded on a recent survey in Indian River County. Use the data to construct a discrete probability
distribution.
The discrete probability distribution is given as follows:
P(X = 0) = 0.3268.P(X = 1) = 0.2353.P(X = 2) = 0.0392.P(X = 3) = 0.0065.P(X = 4) = 0.1438.P(X = 5) = 0.2484.How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes.
There are 153 nests, hence the distribution in this problem is constructed dividing each of the amounts by 153, as follows:
P(X = 0) = 50/153 = 0.3268.P(X = 1) = 36/153 = 0.2353.P(X = 2) = 6/153 = 0.0392.P(X = 3) = 1/153 = 0.0065.P(X = 4) = 22/153 = 0.1438.P(X = 5) = 38/153 = 0.2484.More can be learned about probability at https://brainly.com/question/24756209
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there are 36 boys and 45 girls in the track meet.the coach wants an equal number of boys and girls on each team.what is the greatest number of boys and girls the coach can have on one team.how many teams will he have
the coach can form 4 teams of 9 boys and 9 girls each, and there will be 9 players left over who cannot form a complete team.
What is greatest common divisor?The GCD (Greatest Common Divisor), also known as the HCF (Highest Common Factor), is the largest positive integer that divides two or more integers without leaving a remainder.
For example, the GCD of 12 and 18 is 6, because 6 is the largest positive integer that divides both 12 and 18 without leaving a remainder.
Given by the question.
To form teams with an equal number of boys and girls, we need to find the greatest common divisor (GCD) of 36 and 45.
The prime factorization of 36 is 2^2 x 3^2, and the prime factorization of 45 is 3^2 x 5.
The common factors are 3^2 = 9. Therefore, the GCD of 36 and 45 is 9.
This means that the coach can form teams of 9 boys and 9 girls each.
To find out how many teams he can form, we need to divide the total number of boys and girls by the number of players on each team:
Number of teams = Total amount of players / Number of players per team
Number of teams = (36 + 45) / 18
Number of teams = 81 / 18
Number of teams = 4 with a remainder of 9
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A 1.08 km diameter asteroid has a density of 3000 kg/m3 and impact the surface at 23.0 km/sec. Assuming a spherical asteroid, what is the kinetic energy (in joule) of the asteroid? Convert the answer to megatons of TNT, where 1 megaton is about 4e15 joule. For comparison, the most energetic weapon in the human arsenal is about 100 megatons.
The kinetic energy (in joule) of the asteroid is, 33 million
What is kinetic energy ?The kinetic energy is the energy associated with the particle having mass m and moving with the velocity v.
To find the kinetic energy of the asteroid, we need to use the formula:
KE = (1/2)mv²
where KE is the kinetic energy, m is the mass of the asteroid, and v is its velocity.
The mass of the asteroid can be calculated using its density and volume:
V = (4/3)πr³
where V is the volume of the asteroid, r is its radius, and π is the mathematical constant pi.
Since the asteroid is spherical, its radius is half its diameter, which is 0.54 km.
So,
V = (4/3)π(0.54 km)³
= 0.65 km³
The mass of the asteroid is then:
m = density × volume
= 3000 kg/m³ × 10⁹ m³/km³ × 0.65 km³
= 1.95 × 10¹² kg
Now we can calculate the kinetic energy:
KE = (1/2)mv²
= (1/2) × 1.95 × 10¹² kg × (23.0 km/sec)²
= 1.32 × 10²³ joule
To convert this to megatons of TNT, we divide by the energy of one megaton:
= 1.32 × 10³ joule / (4 × 10¹⁵ joule/megaton)
= 3.3 × 10⁷ megatons
Hence, the KE of asteroid is 33 million
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2. Assume a firm operating in a purely competitive market has a constant selling price of
GH 60, a fixed cost of GH¢450 and a variable cost of GH¢35 an item. Derive;
a)
b)
c)
The total revenue function.
The total cost function.
The profit function.
The total revenue function is 60x.
The total cost function is 35x + 450.
The profit function is 25x - 450.
How derive the total revenue function, the total cost function and thee profit function?Since we have a constant selling price of GH 60, a fixed cost of GH¢450 and a variable cost of GH¢35 an item.
Let x be the number of items
Total revenue function = constant selling price * x
Total revenue function = 60x
Total Cost Function = Variable cost + Fixed cost
Total Cost Function = 35x + 450
Profit function = Total revenue function - Cost function
Profit function = 60x - (35x + 450)
Profit function = 60x - 35x - 450
Profit function = 25x - 450
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Help with this question
According to the figure of the right triangle
a = b = 10How to find angle a and b in the right triangleWhen a right triangle has one of the angles as 45 degrees the angle must be 45 degrees two. Also, the sides are equal, hence we have that
a = b
Using trigonometry we solve for b as follows
cos 45 = b / 10√2
multiplying both sides by 10√2
10√2 * cos 45 = 10√2 * b / 10√2
10√2 * cos 45 = b
rearranging
b = 10√2 * cos 45
where cos 45 = 1/√2 = √2/2
b = 10√2 * 1/√2
b = 10
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Write down the first two terms (and the error term) in the Taylor series expansion of f(h) = ln(3 - 2h) around h = 0, The error term should involve a mysterious unknown constant xi. There's no way to determine xi from the information given here: in practice, if you were to evaluate your Taylor expansion at, say, h =, you would know that xi elementof (0, 4) and you could get bounds on the error by bounding the derivatives of f(h) on this interval.
The Taylor series expansion of f(h) = ln(3 - 2h) around h = 0 is given by:
f(h) = f(0) + f'(0)h + R(h)
where f(0) = ln(3), f'(0) = -2/3, and R(h) is the remainder term.
To find the remainder term, we need to take the higher-order derivatives of f(h) and evaluate them at h = 0. We have:
f''(h) = 4/(3(3 - 2h))^2, f'''(h) = -32/(3(3 - 2h))^3, and so on.
Evaluating these at h = 0, we get f''(0) = 4/9 and f'''(0) = -32/27.
Thus, the remainder term can be expressed as:
R(h) = (1/2)f''(xi)h^2 = (1/2)(4/9)(xi)^2h^2 = (2/9)(xi)^2h^2
where xi is some unknown constant between 0 and 4.
Therefore, the first two terms in the Taylor series expansion of f(h) are:
ln(3) - (2/3)h
and the remainder term involves the unknown constant xi, given by R(h) = (2/9)(xi)^2h^2.
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Question 3 Charlie has a total of $7 in quarters and nickels. He has twice as many nickels as quarters. In which system of equations does q represent the number of quarters he has and n represent the number of nickels?
Answers are linked below. I need help like fast
A system of equations where n is the number of nickels and q is the number of quarters he has is represented by (C) 25q + 5n = 7, n = 2q.
What are equations?The equals sign is a symbol used in mathematical formulas to denote the equality of two expressions.
An equation is a mathematical statement that contains the symbol "equal to" between two expressions with identical values. as in 3x + 5 = 15, for example.
There are many different types of equations, including linear, quadratic, cubic, and others.
Let's learn more about math equations in this tutorial.
So, we know that nickels are double quarters.
And nickels are represented by n and quarters are represented by q.
Then, we can write as:
n = 2q
Then, the equation that represents the situation will be:
25q + 5n = 7
Therefore, a system of equations where n is the number of nickels and q is the number of quarters he has is represented by (C) 25q + 5n = 7, n = 2q.
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YZ = 9, LM = 3, MN = 2, and the measure of angle Z = 100 degrees. What additional information is needed to prove the triangles are similar by SAS?
The additional piece of information needed to prove that ΔLKN ~ ΔKNM by the SAS similarity theorem is; MN/LK||MN.
What is SAS (Side-Angle-Side) similarity theorem?The SAS (Side-Angle-Side) similarity theorem states that if two triangles have two pairs of corresponding sides that are in proportion, and the included angles are congruent, then the triangles are similar.
In this case, we are given that ΔLKN and ΔKNM share the angle at vertex K, and we know that LN/MN and LK/KN are in proportion.
However, we need to establish that MN/LK||MN, that means MN is parallel to LK and forms a transversal with LN.
This information is necessary to establish that the included corresponding sides are congruent, which is required for the triangles to be similar.
Therefore, the additional piece of information needed to prove that ΔLKN ~ ΔKNM by the SAS similarity theorem.
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Name the line of reflection that maps each pre-image to its image.
Answer: X axis , Y axis , y=-2
Step-by-step explanation:
HELP!!!!!!!!!!!!!!!!
The value of x and y are 13 and 3 respectively and the measure of angle mqr is 51 degree.
What are Exterior angle ?
It is an measure of rotation between one extended side(we extend it virtually) of the polygon with its adjacent side which is not extended.
WE are given that in the diagram, Ks, LT, MU are parallel to each other.
Angle knj = (2x-5)°, Angle lpn = (2y + 15), Angle pqu = (3x+4y)°.
Sine, the corresponding angles are equal
(2x-5) = (2y+15)
2x - 2y = 15 + 5
2x - 2y = 20
x - y = 10
x = 10 + y
Now,
(3x+4y) = (2y+15)
3x + 4y - 2y = 15
3x + 2y = 15
3(10 + y) + 2y = 15
30 + 5y = 15
y = 3
x = 13
Angle mqr = (3x+4y) = 51 degree.
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Evaluate y (x ÷2) if x = 20 and y = 10
Answer:
100
Step-by-step explanation:
1.) Plug in the values of x and y into the equation
10(20/2)
2.) Divide 20 by 2
10(10)
3.) Multiply 10 by 10
100
A bag contains 7 green marbles, 2 white marbles, 5 orange marbles, 9 green marbles, and 7 red marbles. A marble will be drawn from the bag and replaced 180 times. What is a reasonable prediction for the number of times a white or red marble will be drawn? Answer A 15 B 54 C 57 D 63
A Reasonable prediction for the number of times a white or red marble will be drawn is 3/10 x 180 = 54. Thus, option b is correct
If a marble is drawn and not replaced, what is the probability of drawing an orange marble on the second draw?If a marble is drawn and not replaced, the probability of drawing an orange marble on the second draw depends on the color of the marble drawn on the first draw. If an orange marble was drawn on the first draw, then there will be one less orange marble in the bag, and the probability of drawing another orange marble on the second draw will be 4 out of the remaining 29 marbles. If a non-orange marble was drawn on the first draw, then there will be 5 orange marbles in the bag, and the probability of drawing an orange marble on the second draw will be 5 out of 29.
There are a total of 30 marbles in the bag.
The probability of drawing a white or red marble is
2/30 + 7/30
= 9/30
= 3/10.
Therefore, a reasonable prediction for the number of times a white or red marble will be drawn is 3/10 x 180 = 54. Answer B.
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11. A line through (3, 5) and (k, 12) is perpendicular to a line through (0, 7) and (2, 10). Find the value of k that makes the above statement true.
Answer:
k = 23/7
Step-by-step explanation:
To solve the problem, we can use the fact that the product of the slopes of two perpendicular lines is -1. We can start by finding the slope of the line passing through the points (3, 5) and (k, 12).
slope = (12 - 5) / (k - 3)
We can simplify this expression by multiplying both numerator and denominator by -1:
slope = (-7) / (3 - k)
Now, let's find the slope of the line passing through the points (0, 7) and (2, 10):
slope = (10 - 7) / (2 - 0) = 3 / 2
Since the two lines are perpendicular, we can set the product of their slopes equal to -1:
(-7) / (3 - k) * (3 / 2) = -1
Simplifying this equation, we get:
(7/2) * (3 - k) = 1
Multiplying both sides by 2/7, we get:
3 - k = 2/7
Subtracting 3 from both sides, we get:
-k = 2/7 - 3 = -21/7 - 2/7 = -23/7
Finally, dividing by -1, we get:
k = 23/7
Therefore, the value of k that makes the statement true is k = 23/7.
Answer:
Step-by-step explanation:
m1=y2-y1/x2-x1=12-5/k-3=7/k-3
m2=10-7/2-0=3/2
two lines with slopes m1 and m2 are perpendicular if m1×m2 = -1.
(7/k-3) *3/2=-1
3(7)=-2(k-3)
21=-2k+6
-2k=15
k=-15/2
What values of x
and y
satisfy the system {y=−2x+3
{y=5x−4?
If there is no solution, enter "no"; if there are infinitely many solutions, enter "inf."
The required solutions of the given system of equation are x = 1 and y = 1.
What is equation?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
According to question:To find the values of x and y that satisfy the system, we need to solve the equations simultaneously:
y = -2x + 3 ... (1)
y = 5x - 4 ... (2)
Setting the right-hand sides of (1) and (2) equal to each other, we get:
-2x + 3 = 5x - 4
Simplifying this equation, we get:
7x = 7
Dividing both sides by 7, we get:
x = 1
Substituting x = 1 into either equation (1) or (2), we get:
y = -2(1) + 3 = 1
Therefore, the only solution that satisfies both equations is x = 1 and y = 1.
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Mr. Sanchez made a apple pie. The circumstances of his pie was 28.26 inches.
? What was the diameter of the pie?
The diameter of the pie is approximately 9 inches
What is a diameter ?
Diameter can be defined as the double of the radius
To determine the diameter of the pie, we need to use the formula for the circumference of a circle:
C = 2πr
where C is the circumference, π (pi) is a mathematical constant approximately equal to 3.14, and r is the radius of the circle.
In this case, we are given that the circumference (circumstances) of the pie is 28.26 inches, so we can set up the equation:
28.26 = 2πr
To solve for the radius, we can divide both sides of the equation by 2π:
r = 28.26 / (2π)
r ≈ 4.5
So the radius of the pie is approximately 4.5 inches. To find the diameter, we just need to double the radius:
d = 2r
d ≈ 9
Therefore, the diameter of the pie is approximately 9 inches.
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Decide if each is a measurement of length, area, volume, or weight (or mass).
How many centimeters across a handprint
How many square inches of paper needed to wrap a box
How many gallons of water in a fish tank
How many pounds in a bag of potatoes
How many feet across a swimming pool
How many ounces in a bag of grapes
How many liters in a punch bowl
How many square feet of grass in a lawn
Answer:
Step-by-step explanation:
1. measurement of length
2. measurement of area
3. measurement of volume
4. measurement of weight
5. measurement of length
6. measurement of weight
7.measurement of volume
8. measurement of area
find the open intervals on which the function is increasing or decreasing. use a graphing utility to verify your results. (enter your answers using interval notation.) increasing incorrect: your answer is incorrect. decreasing
The function is decreasing on the interval (-∞, -2), has a local minimum at x = -2, is increasing on the interval (-2, 2), and is increasing on the interval (2, ∞). The function has a relative minimum at x = 3 (f(3) = -27) and no relative maximum.
Begin by finding the derivative of y.
y' = 3x^2 - 12
Find the critical numbers. (Enter your answers as a comma-separated list.)
To find the critical numbers, we need to solve y' = 0 for x:
3x^2 - 12 = 0
x^2 - 4 = 0
(x - 2)(x + 2) = 0
So the critical numbers are x = -2 and x = 2.
Test the intervals to determine the open intervals on which the function is increasing or decreasing. (Enter your answers using interval notation.)
To test the intervals, we can use a sign chart:
Interval (-∞, -2) (-2, 2) (2, ∞)
y' (-)(-) (-)(+) (+)(+)
y Decreasing Local Min Increasing
So the function is decreasing on the interval (-∞, -2), has a local minimum at x = -2, is increasing on the interval (-2, 2), and is increasing on the interval (2, ∞).
f(x) = x^4 - 4x^3
To find the relative extrema, we need to find the critical numbers and then evaluate the function at those points.
Find the derivative of f(x).
f'(x) = 4x^3 - 12x^2
Find the critical numbers by solving f'(x) = 0 for x.
4x^3 - 12x^2 = 0
4x^2(x - 3) = 0
x = 0 or x = 3
So the critical numbers are x = 0 and x = 3.
Evaluate the function at the critical numbers and the endpoints of the interval to find the relative extrema.
f(-∞) = ∞
f(0) = 0
f(3) = -27
f(∞) = ∞
So the function has a relative minimum at x = 3 (f(3) = -27) and no relative maximum.
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____The given question is incomplete, the complete question is given below:
Find the critical numbers and the open intervals on which the function is increasing or decreasing. Use a graphing utility to verity your results.
y = x^3 − 12x + 2
Step 1: Begin by finding the derivative of y.
y'=
Step 2: Find the critical numbers. (Enter your answers as a comma-separated list.)
x=
Step 3: Test the intervals to determine the open intervals on which the function is increasing or decreasing. (Enter your answers using interval notation.)
Increasing (___)
Decreasing (____)
2) Find all relative extrema of the function. (If an answer does not exist, enter DNE.)
f(x) = x4 − 4x3
relative max:(____)
relative min:(_____)
statistics is the science of average - elucidate this statement
Answer:
The average of all the data is calculated in statistics.
However, statistics is a field that goes beyond average and is not a complete science of it.
There are other additional statistical tools.
which explains how statistics is an extension of mathematics.
One and Seventy One Hundredths
wright the number for the decimal names..
When one and seventy one hundredth is written in decimal form, it would be 1. 71
How to write as decimal ?A single part of something that has been evenly divided into one hundred parts is referred to as a hundredth in mathematics. The tenths place is represented by the first digit following the decimal. The hundredths place is represented by the digit that follows the decimal.
This means that when given the number one and seventy One Hundredths in words, then the number, " one " would be written before the decimal and the 71 would be 0. 71 as a hundredth figure.
When put together, this becomes:
= 1 + 0. 71
= 1. 71
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2 rectangular pyramids are connected at their bases. The total height of the 2 figures if 10 units. The base edge lengths are 9 units and 1.5 units. The height of each pyramid is 5 units.
Which statements about the composite figure are true? Check all that apply.
The composite figure consists of two rectangular pyramids.
The composite figure can be broken down into rectangular prisms.
The volume of the composite figure is
1.5(9)(5) + 1.5(9)(5).
The total volume is 45 units3.
The total volume is 90 units3.
The composite figure consists of two rectangular pyramids, volume is 45 unit³.
What is rectangular pyramid?Pyramids are three-dimensional structures having triangle faces and have an encompassing polygon shape at its base. If the base of a pyramid is rectangular, then it is called a rectangular pyramid.
Given,
Total height of two rectangular pyramids = 10 units
height of each pyramid is 5 unit.
Base lengths are 9units and 1.5 units.
Both are connected at their bases.
Dimensions are same of both pyramids
Composite figure consists of two rectangular pyramids.
Volume of the composite figure
= 2(length × width × height)/3
= 2(9×1.5×5)/3
= 2(13.5×5)/3
= 2(67.5)/3
= 135/3
= 45 unit³
Hence, 45 unit³ is volume of composite figure, that consists of two rectangular pyramids.
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Answer:A D
Step-by-step explanation:
Dave Drinks a 12-ounce cup of coffee each morning on his way to work. This cup of coffee contains 136 mg of caffeine.
The caffeine in his system decreases about 40% every hour.
Function to calculate amount of coffee in Dave's system after x hours
= y = 135(0.6)ˣ
What is exponential expression?An exponential function is a Mathematical function in the form f (x) = aˣ, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0. The most commonly used exponential function base is the transcendental number e, which is approximately equal to.
Given,
Dave drinks 12-ounce cup of coffee each morning
One cup has 136 mg of caffeine
caffeine in his system decreases about 40% every hour
In x hours,
Amount of caffeine in his system
y = a(1 - 40/100)ˣ
or
y = 136(1-0.4)ˣ
y = 135(0.6)ˣ
Hence, y = 135(0.6)ˣ is the function to calculate amount of caffeine in system of Dave after x hours.
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F and H are sets of real numbers defined as follows.
Evaluate 5r + p if p = 3 and r = 4
Work Shown:
5r + p
5*4 + 3
20 + 3
23