answer please have no idea how to start or do it just please show the workings aswell.
Answers
The evaluation of P10–Focus 1 indicates that we get by using the equation for the volume of a cuboid and by calculus;
(a) [tex]L = 4\times x + 4\times 2\cdot x + 4\times \frac{81}{2\cdot x} =12\cdot x + \frac{162}{x^2}[/tex]
(b) [tex]L_{min}[/tex] = 54 cm
(c) L'' at x = 3, (where [tex]L_{min}[/tex] = 54 cm) is positive, therefore, x = 3 is a minimum point
P10-Focus2
The area = [tex]2\times x \times y+\frac{\pi\cdot x^2}{4} =4[/tex], therefore, [tex]y = \frac{16- \pi \cdot x^2}{8 \cdot x}[/tex]
The minimum point, which is an extremum point is a point where the derivative of the function is 0.
(a) The length of the cuboid = 2·x
The width of the cuboid = x
The volume of the cuboid = 81 cubic centimeters
The thickness of the cuboid is therefore;
Thickness = 81/(2·x × x) = 81/(2·x²)
The sum of the length of the twelve edges, L, is therefore;
[tex]L=x + x + x + x + x + 2\cdot x + 2 \cdot x + 2 \cdot x + 2\cdot x + \frac{81}{2 \cdot x^2} + \frac{81}{2 \cdot x^2} + \frac{81}{2 \cdot x^2} + \frac{81}{2 \cdot x^2}[/tex]
Therefore;
[tex]L=4\times x + 4\times 2\cdot x + 4\times \frac{81}{2 \cdot x^2} =12\cdot x + \frac{162}{x^2}[/tex]
The sum of the lengths of the twelve edges, L, is [tex]L = 12\cdot x + \frac{162}{x^2}[/tex]
(b) The minimum value of L can be found using calculus by finding the point at which dL/dx = 0 as follows;
[tex]\frac{dL}{dx} = 12 - \frac{324}{x^3} =0[/tex]
Therefore;
[tex]12-\frac{324}{x^3}=0[/tex]
[tex]12 = \frac{324}{x^3}[/tex]
x³ = 324 ÷ 12 = 27
x = ∛(27) = 3
x = 3
The minimum value of L can be obtained when x = 3 as follows;
[tex]L = 12\cdot x + \frac{162}{x^2}[/tex]
[tex]L_{min} = 12\times 3 + \frac{162}{3^2} = 54[/tex]
The [tex]L_{min}[/tex] = 54
The minimum value of L is 54 centimeters
(c) The value of the minimum value of L can be confirmed by further differentiation using the second derivative, L'' as follows;
At the x-value of a minimum point of a function, the value of the further derivative is larger than zero
The further derivative of the specified function is found as follows;
[tex]L'' = \frac{dL'}{dx} =\frac{972}{x^4}[/tex]
At the critical number, x = 3, from the first derivative, we get;
[tex]L'' = \frac{972}{3^4} = 12 > 0[/tex]
The value of the further derivative of the function at the point x = 3, is L'' = 12 > 0, therefore the point x = 3 is a relative minimum.
(b) The radius of the quarter circle = x
The area of the figure = 4 m²
The sum of the area of the composite figures are;
[tex]A = 2 \times x \times y + \frac{\pi \cdot x^2}{4} = 4[/tex]
Therefore;
[tex]y =\frac{\left(4 - \pi \cdot \frac{x^2}{4}\right)}{2\cdot x} = 16 - \frac{\pi \cdot x^2}{8\cdot x}[/tex]
Rearranging the right hand side expression as a fraction, we get;
[tex]y = \frac{16-\pi \cdot x^2}{8\cdot x}[/tex]
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Related Questions
HELP ASAP ITS URGENT!!!!!!!
ILL GIVE 50 POINTS
Answers
Answer: It's in the picture
Step-by-step explanation:
PLEASE HELP ASAP!!! THIS IS DO TN HELP WOULD BE VERY APPRECIATED<3
Answers
Answer:
1
Step-by-step explanation:
3(-0.5)+2(7+0.8)
13+1.1
-1.5+2(7+0.8)
13+1.1
-1.5+15.6
14.1
14.1
14.1
divide
1
hope that helps :)
Which product is represented by the model?
A. 0.05×0.04=0.002
B. 5×0.4=2
C. 0.5×0.4=0.2
D. 0.5×0.04=0.02
Answers
0.05×0.04=0.002 is the product represented by the model
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given:
5 column (hundred grid) = 5/100 = 0.05
4 row (hundred grid) = 4/100 = 0.04
We need to find Area equation
Computation:
Area equation = 0.05 x 0.04
0.05 x 0.04 = 0.002
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How many solutions does the following equation have?
-14(z-5) = -14z +70
Choose 1 answer:
A. No solutions
B. Exactly one solution
C. Infinitely many solutions
Answers
Answer: C. Infinitely many solutions
Step-by-step explanation: If the answer is <0, then there is no solution; if it is >1, then there is more than one solution; if = 0, then there are Infinitely many solutions
-14(z-5) = -14z +70 can be write as
-14z + 70 = -14z + 70
-14z = -14z
z= 0
Because the answer is 0 so there Infinitely many solutions
If you can, please give me a Brainliest; thank you!
Answer:
C. Infinite many solutions.
Step-by-step explanation:
Simplify the left side of the equation. Note the parenthesis. Distribute -14 to all terms within the parenthesis:
-14(z - 5) = -14z + 70
-14z + 70 = -14z + 70
C. Infinitely many solutions is your answer, as no matter what number you plug in for the variable z, the equation would still be true.
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Determine which set of side measurements could be used to form a right triangle.
A. 3, 11, 20
B. 5, 9, 17
C. 6, 7, 8
D. 6, 8, 10
Answers
Answer:
D. 6, 8, 10
Step-by-step explanation:
Apply the Pythagorean theorem equation to all set of number, and see which one works.
A.
3² + 11² ≠ 20²
9 + 121 ≠ 400
131 ≠ 400
B.
5² + 9² ≠ 17²
25 + 81 ≠ 289
106 ≠ 289
C.
6² + 7² ≠ 8²
36 + 49 ≠ 64
85 ≠ 64
D.
6² + 8² = 10²
36 + 64 = 100
100 = 100
What i the lope of the line that pae through the point (-7, -8)(−7,−8) and (-5, -6)(−5,−6)? Write your anwer in implet form
Answers
For the provided points (-7,-8) and (-5,-6) on the line, the slope is 1.
What is slope?The slope of a line is a measure of its steepness. Slope is calculated mathematically as "rise over run" (change in y divided by change in x). Determine the coordinates of two points along the line that you choose. Find the difference between these two points' y-coordinates (rise). Find the difference between these two points' x-coordinates (run). Divide the difference in x-coordinates (rise/run or slope) by the difference in y-coordinates.
Here,
Slope=(y2-y1)/(x2-x1)
=(-6-(-8))/(-5-(-7))
=2/2
=1
The slope of the line for given point (-7,-8) and (-5,-6) will be 1.
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Please help, need a diagram and correct calculations!!!
Answers
Buy the land !all angles will be greater than 30 °
How many piece of land he buy ?Trigonometry is the study of angles and the angular relationships between planar and three-dimensional shapes. The cosecant, cosine, cotangent, secant, sine, and tangent are among the trigonometric functions (also known as the circular functions) that make up trigonometry.
A branch of mathematics called trigonometry examines connections between triangles' sides and angles. Due to the fact that every straight-sided shape can be decomposed into a group of triangles, trigonometry can be found throughout all of geometry.
cos x = 500²+800²-900²/-2(800)(900)
x = [tex]cos^{-1}[/tex](+1200000/+1440000)
=336°
Buy the land !all angles will be greater than 30 °
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A shop has a sale of 1/3
off all items in stock.
If the original price of a dress is £42, what would be its sale price?
Answers
Answer:
£ 76
Step-by-step explanation:
Answer:
28
Step-by-step explanation:
Multiply 42 by 1/3 which is 14.
Then subtract 42-14 because your subtracting the discount from the original price which gives you 28.
If a firework is launched vertically upwards from a height of 20 feet above the ground. Its path is give by h(t)=-4t+16t+20, where h is the height of feet and t is the time in seconds.
can someone help me find the right answers for this with scratch work? i'm struggling quite a bit.
when is the firework at max height?
What was the highest point that the firework reached?
What is the starting point of the firework?
How high is the firework after 3 seconds?
When does the firework hit the ground?
Answers
The quadratic function defining the height of the firework in this problem after t seconds is given as follows:
h(t) = -4t² + 16t + 20.
From this definition, we can get the h-intercept giving the starting point of the firework, as follows:
h(0) = -4(0)² + 16(0) + 20 = 20 feet.
The height after 3 seconds is calculated with the numeric value as follows:
h(3) = -4(3)² + 16(3) + 20 = 32 feet.
The coefficients of the quadratic function are given as follows:
a = -4, b = 16, c = 20.
Due to the negative coefficient a, this is a concave down function, meaning that the vertex is a maximum point.
The t-coordinate of the vertex is given as follows:
tv = -b/2a = -16/2(-4) = -16/-8 = 2.
Then the maximum height of the firework is of:
h(2) = -4(2)² + 16(2) + 20 = 36 feet.
The firework hits the ground when h(t) = 0, hence, using a quadratic function calculator, the time is of:
5 seconds. (positive root).
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they are 40 people in 15 teenagers what percentage of the people on your guestlist are teenagers
Answers
Answer: 6
Step-by-step explanation:
40x0.15
6 are teens
If the area of square 3 is 80 cm2 and the area of square 2 is 100 cm2, what is the area of square 1?
Answers
Answer: 180cm^2
Step-by-step explanation:
The equation is a^2 + b^2 = c^2
a^2 = area of square 3 = 80cm^2
b^2 = area of square 2 = 100cm^2
c^2 = a^2 + b^2 = 80 + 100 = 180cm^2
So answer is 180cm^2
The line passes through
(14,-6) and has a slope = -2/7
Answers
The equation of the line passing through the given points and having slope -2/7 is obtained as y = -2/7m - 2.
How to write the equation of a straight line in slope-intercept form?A straight line can be written in the slope-intercept form as, y = mx + c.
In order to obtain the slope, the ratio of the difference of the coordinates are taken and c is the y-intercept which can be found by substituting x = 0 in the equation.
The given point and the slope for line are as (14,-6) and -2/7 respectively.
The general form of slope-intercept equation is as below,
y = mx + c
Substitute the value of x = 14, y = -6 and m = -2/7 to get,
-6 = -2/7 × 14 + c
⇒ c = -6 + 4 = -2
Thus, the equation can be written as follows,
y = mx + c
Substitute m = -2/7 and c = -2 to obtain,
y = -2/7x + (-2)
⇒ y = -2/7m - 2
Hence, the equation of the line is given as y = -2/7m - 2.
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PLEASE HELP!! WILL GIVE BRAINLIEST AND 25 POINTS!!
Find the value of x. Round your answer to the nearest degree.
A. 18°
B. 21°
C. 22°
Answers
Answer:
Sin(angle) = Opposite / hypotenuse
Sin(x) = 5/14
X = arcsin(5/14)
x = 20.9
X = 21 degrees.
the answer is da da b!
Step-by-step explanation:
Select all of the following that represent direct variation.
1. y = 5x
2. y = 2x + 1
3. 3 = xy
4. b = 1/2a
5. y= 2/x
6. m = 5n
Answers
The equations, y=5x, b = 1/2 a, m=5n are direct variations.
What is direct variation?A sort of proportionality known as "direct variation" occurs when one quantity directly changes in response to a change in another quantity. This suggests that if one quantity increases, the other quantity will also increase proportionately. Similar to the last example, if one quantity declines, the other amount also declines. The link between direct variation and the graph will be linear, resulting in a straight line.
We know that any equation, which can be expressed in the form of y=kx, can be called a direct variation.
y = 5x is in the form of y = kx, where k =5, hence this is a direct variation
y = 2x + 1 is not in the form of y = kx, hence this is not a direct variation
xy = 3 is not in the form of y = kx, hence this is not a direct variation
b = 1/2 a is in the form of y = kx, where k =1/2, hence this is a direct variation
y = 2/x is not in the form of y = kx, hence this is not a direct variation
m = 5n is in the form of y = kx, where k =5, hence this is a direct variation
Thus, y=5x, b = 1/2 a, m=5n are direct variation
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. The graph shows the amount of cleaning
product dispensed when using a spray
bottle. Determine if the linear
relationship is proportional. Find and
interpret the slope. Then find the unit
rate and compare it to the slope.
Answers
The required proportional relationship is given as y = 3/2x.
What is proportionality?proportionality is defined as between two or more sets of values, and how these values are related to each other in the sense are they directly proportional or inversely proportional to each other.
here,
From the graph,
It seems that the relationship given is a proportional relationship,
Now locate two points on the graph, as (0, 0) and (2, 3)
The equation of the line function is given as,
y - 0 = [3 / 2] (x - 0)
y = 3/2x
Thus, the required proportional relationship is given as y = 3/2x.
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Do males or females like basketball more? Show both raw numbers and percentages.
Answers
We can infer from the data set provided that more women than men are interested in basketball.
What is percentage?A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.
From table given in question
Number of males that like basketball = 21
Number of females that like basketball = 29
Percentage of males that like basketball = (21/50)*100 = 42%
Percentage of females that like basketball = (29/50)*100 = 58%
So, from above data we can conclude that females like basketball more than that of males.
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Given the area of a rectangle is A = x^(2) - 3x - 18, answer the following questions: What is the length of each side? What is the perimeter of the rectangle? Please answer I'm giving 30 points.
Answers
The dimensions of the rectangle in terms of x are (x-6) and (x+3).
What in mathematics is a quadratic equation?
x ax2 + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. a 0. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be simple or complicated.
Given that:
A = x^(2) - 3x - 18
By solving this equation we can get the values of length and breath of rectangle
A = x^(2) - 6x + 3x - 18
A = x(x-6)+3(x-6)
A = (x-6)(x+3)
Hence the area of rectangle is equal to L * W
Hence, the dimensions of the rectangle are (x-6) and (x+3).
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Use the following function rule to find f(–4).
f(x) =
–4 +
4
|x|
f(–4) =
Answers
By evaluating the function in x = -4, we will get:
f(-4) = 12
How to evaluate the function f(x)?Here we have the following function:
f(x) = -4 + 4*|x|
So we have an absolute value function.
We want to find f(-4), so we want to evaluate the function in x = -4, to do that, just replace the variable by that number.
We will get:
f(-4) = -4 + 4*|-4|
Remember that the absolute value of a negative number gives the opposite:
|-4| = 4
Then:
f(-4) = -4 + 4*|-4|
f(-4) = -4 + 4*4
f(-4) = -4 + 16 = 12
f(-4) = 12
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Please help
What inequality does the number line show?
Write your answer starting with
x (example: x < 3)
Answers
Answer:
x < 5
Step-by-step explanation:
the dot is empty so we don’t consider 5
The coloured arrow continues to the left so we use this symbol : < (minor)
x<5
The inequality for the number line show is x<5.
What is Inequality?Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
We can see that the inequality starts from 5 moves towards 2.
As, the starting of number line have open dot which shows we cannot include 5.
So, the inequality will have sign '<'.
Now, the inequality of the number line is
x < 5.
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Which of the following equations represent linear functions?
a.) y=x2
b.) y=3x+2
c.) y=6
d.)y=x−−√
Answers
Answer:
b.) y=3x+2
Step-by-step explanation: The linear equation is y= mx + b
m is the slope and b is the y-intercept
Answer b is the linear equation!
In the function g(x)=9-5x what is the value of g(3)
Answers
Answer:
g(3) = - 6
Step-by-step explanation:
g(3) = 9 - 5(3)
g(3) = 9 - 15
g(3) = - 6
Solve for x.
-12< -3x - 15 < 36
Enter your answer, as one inequality, in the box.
Answers
Step-by-step explanation:
-12 < -3x - 15 <= 36 | add 15 everywhere
3 < -3x <= 51 | divide by 3 everywhere
1 < -x <= 17 | multiply by -1 everywhere
-1 > x >= -17
or
-17 <= x < -1
remember that with every multiplication or division of a negative number the orientation of the inequality signs flip.
the same happens, of course, when we exchange the upper and lower limits from left to right and right to left, so that the smaller number is on the left, and the larger number on the right (yes, -1 is larger than -17).
Use f(x) = -4x+1, g(x) = x2 - 8x + 21, and h(x) = 19-3x|
Find h(8)-f(-7)
Answers
The function operation h(8) - f(-7) of the functions f(x) = -4x+1, and h(x) = 19-3x is -34.
What is the function operation h(8) - f(-7) in the given functions?A function is simply a relationship that maps one input to one output.
Given the data in the question;
f(x) = -4x + 1g(x) = x² - 8x + 21h(x) = 19 - 3xh(8) - f(-7) = ?First, solve for the output value of h(8) by replacing x with 8 and simplify.
h(x) = 19 - 3x
h(8) = 19 - 3(8)
h(8) = 19 - 24
h(8) = -5
Next, solve for the output value of f(-7) by replacing x with -7 and simplify.
f(x) = -4x + 1
f( -7 ) = -4( -7 ) + 1
f( -7 ) = 28 + 1
f( -7 ) = 29
Now, replace the function designators with the actual output values.
h(8) - f(-7) = -5 - ( 29 )
h(8) - f(-7) = -5 - 29
h(8) - f(-7) = -34
Therefore, the output of the function operation h(8) - f(-7) is -34.
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Last year, students planted 8 tomato plants and 16
garden. This year, the students planted
pepper plants in a school
15 tomato plants. They want to have the
same ratio of tomato plants to pepper plants as last year. Pepper plants cost
$4.33 each. What is the cost, in dollars, of the pepper plants for this year's garden?
Answers
Answer:
Step-by-step explanation:
From the ratio gotten, the total cost of the pepper will be $129.90.
How to solve a ratio
Since the students planted 8 tomato plants and 16 pepper plants in a school garden. The ratio will be:
= 8/16 = 1:2
This year, the students planted 15 tomato plants, the number of pepper will be:
= 15 × 2 = 30
Since pepper plants cost $4.33 each, the total cost will be:
= 30 × $4.33
= $129.90
pirya has picked 1 1/2 cups of raspberries, which is enough for 3/4 of a cake how many cups does she need for the whole cae
Answers
Pirya needs 1 1/2 cups of raspberries for 3/4 of a cake, so she needs 1 1/2 * (4/3) = 2 cups of raspberries for the whole cake.
What is fraction?A fraction is a numerical representation of a portion of a total. It consists of two integers, a numerator and a denominator, separated by a line or slash. The numerator reflects the number of equal portions of the whole that are being considered, while the denominator represents the total number of equal parts in the whole. For instance, the fraction "1/2" denotes one of two identical pieces, or half, of the whole. Mathematicians frequently utilize fractions to represent quantities, ratios, and proportions. They are also used in everyday life to signify amounts, such as one-half of a pizza or one-third of a cups of sugar.
How to solve?
she needs 1 1/2 * (4/3) = 2 cups of raspberries for the whole cake.
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Slope of (-8,-3) and (-8, -19)
Answers
Answer:
Undefined
Step-by-step explanation:
Knowledge Needed
Slope if is the constant change of the y-value when the x-value increases by 1 on a line.
Slope Formula: [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Question
Plug in your points.
[tex]\frac{-19--3}{-8--8}[/tex]
[tex]\frac{-16}{0}[/tex]
Any number divided by 0 is undefined.
The slope is undefined. This means the line is completely vertical.
what is the answer to this question?
Answers
Answer:
47.21
Step-by-step explanation:
a=47.4
b=0.19
a – b
47.4 – 0.19
=47.21
Contruct a polynomial function with the tated propertie. Reduce all fraction to lowet term. Third-degree, with zero of −3, −1, and 2, and pae through the point (0,-14)
Answers
On solving the provided the question, we got that - f(x) = 7/3[x - (2)] [x - (-1)] (x +3) is the equation which is formed.
What is equation?An equation can be defined in a variety of ways. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions.
Gives zeroes are -
-3, -1 and 2
and it passes through (0, -14)
Constructing a function from a product of factors containing the zeros, with an unknown coefficient
f(x) = a [x - (2)] [x - (-1)] (x +3)
with a ≠ 0.
f(x) = a(x -2)(x + 1)((x +3)
Use f(0) = -14 to find a.
-14 = a(-2)(1)(3) = -6a
a = 7/3
Now,
f(x) = 7/3[x - (2)] [x - (-1)] (x +3)
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$25 jeans; 16% markup
Answers
29$ 16% of 25 is 4, so add it, and theres the answer
Step-by-step explanation:
please help me with this
Answers
Measure of angle I greater than angle K and J. Therefore, option D is the correct answer.
Given that, in triangle IJK, JK=18, KI=11, and IJ=14.
What is the triangle inequality theorem?If one side of a triangle is longer than another side, then the angle opposite the longer side will be larger than the angle opposite the shorter side.
Here, JK is the longest side and KI is the shortest side
So, opposite to side JK, angle I is the biggest and opposite to the side KI angle J is the smallest
Here, the measure of IJ is greater than the side KI, then the angle K opposite to side IJ is greater than the angle J
Thus, m∠I>m∠K>m∠J
Measure of angle I greater than angle K and J. Therefore, option D is the correct answer.
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