Answer:
a three-quarter circle of radius 18 ft, quarter circles of radii 10 ft and 6 ft
Step-by-step explanation:
i took the test and i got this as the right answer
Answer:
A a three-quarter circle of radius 18 ft, quarter circles of radii 10 ft and 6 ft
Step-by-step explanation:
In order to calculate this, you have to remember that you have a tether that is 18 ft long, thetered to a point, this would make a circle with a radius of 18 ft, but as the center of the circle would be where the theter is knotted, the shed forbids to make a full circle, it rather creates a 3/4 circle, and the dog can acces the other points of the shed, with le length of the theter, that is 8 ft after the long side, and 12 feet after the short side, creating another quarter circle with a radius of 8 and 12 ft.
Stefan's family rented a rototiller to prepare an area in their backyard for spring planting. The rental company charged an initial fee of $43 with an additional fee per hour. If they paid $64 after renting the rototiller for 7 hours, what was the hourly fee?
Answer:
The hourly fee is $ 3.
Step-by-step explanation:
Given,
The initial fee = $ 43,
Let x be the additional hourly fee ( in dollars ),
Thus, the total additional fee for 7 hours = 7x dollars,
And, the total fee for 7 hours = Initial fee + Additional fee for 7 hours
= ( 43 + 7x ) dollars,
According to the question,
43 + 7x = 64
7x = 21 ( Subtracting 43 on both sides )
x = 3 ( Divide both sides by 7 )
Hence, the hourly fee is $ 3.
Answer:
7h+43=64
$3
Step-by-step explanation:
did it on edge
A rectangular ower garden is 5.3 yards wide and 9.4 yards long. A uniform path of
width 2 yards is laid around the garden. Find the area of the path.
Answer:
74.8 square yards
Step-by-step explanation:
The centerline of the path is a rectangle 5.3+2 = 7.3 yards wide and 9.4+2 = 11.4 yards long. The perimeter of that rectangle is 2(7.3+11.4) = 37.4 yards long. The area of the path is this length times the width of the path:
path area = (37.4 yd)(2 yd) = 74.8 yd²
The area of the path is 74.8 square yards.
First, we calculate the area of the garden:
[tex]\[ A_{\text{garden}} = \text{length} \times \text{width} = 9.4 \text{ yards} \times 5.3 \text{ yards} \][/tex]
[tex]\[ A_{\text{garden}} = 49.82 \text{ square yards} \][/tex]
Next, we need to find the area of the entire region including the path. The path adds an additional width of 2 yards on all sides of the garden.
The total length and width of the region including the path are:
[tex]\[ \text{Total length} = 9.4 \text{ yards} + 2 \times 2 \text{ yards} = 13.4 \text{ yards} \][/tex]
[tex]\[ \text{Total width} = 5.3 \text{ yards} + 2 \times 2 \text{ yards} = 9.3 \text{ yards} \][/tex]
Now we calculate the area of the entire region including the path:
[tex]\[ A_{\text{total}} = \text{Total length} \times \text{Total width} = 13.4 \text{ yards} \times 9.3 \text{ yards} \][/tex]
[tex]\[ A_{\text{total}} = 124.62 \text{ square yards} \][/tex]
Finally, we subtract the area of the garden from the total area to find the area of the path:
[tex]\[ A_{\text{path}} = A_{\text{total}} - A_{\text{garden}} \][/tex]
[tex]\[ A_{\text{path}} = 124.62 \text{ square yards} - 49.82 \text{ square yards} \][/tex]
[tex]\[ A_{\text{path}} = 74.8 \text{ square yards} \][/tex].
Trapezoid ABCD and WXYZ are congruent trapezoids. What is the value of x?
A. x = -5
B. x = 5
C. x = 15
D. x = -15
B. x=5
Step-by-step explanation:Two shapes are congruent if you can turn one into the other by moving, rotating or flipping. So if we rotate 180 degrees, say, trapezoid WXYZ and then moving it to the left, it will match trapezoid ABCD. If so, it will be true that:
[tex]\angle BAD=\angle XWZ \\ \\ \angle BAD=4x-7 \\ \\ \angle XWZ=2x+3 \\ \\ 4x-7=2x+3 \\ \\ Solving \ for \ x: \\ \\ 4x-2x=7+3 \\ \\ 2x=10 \\ \\ \boxed{x=5}[/tex]
Answer:
Answer is B x=5
Step-by-step explanation:
Hope this helps!!
Find one positive angle and one negative angle that are coterminal with the given angle. Explain.
10. 255°
12. -800°
Answer: 10) 615° & -105°
12) -440° & 280°
Step-by-step explanation:
Coterminal means it is in the exact same spot on the Unit Circle but one or more rotations clockwise or counterclockwise.
Since one rotation = 360°, add or subtract that from the given angle until you get a positive or negative number.
10) 255° + 360° = 615° (this is a POSITIVE coterminal angle to 255°)
255° - 360° = -105° (this is a Negative coterminal angle to 255°)
12) -800° + 360° = -440° (this is a Negative coterminal angle to -800°)
-440° + 360° = -80° (this is a Negative coterminal angle to -800°)
-80° + 360° = 280° (this is a POSITIVE coterminal angle to -800°)
Final answer:
Coterminal angles for 255° are 615° (positive) and -105° (negative) by adding or subtracting 360° respectively. For -800°, the coterminal angles are -80° (positive) and -1160° (negative).
Explanation:
To find a positive and a negative angle coterminal with the given angle of 255°, we can add or subtract multiples of 360° (the total degrees in a circle). For a positive coterminal angle, we can add 360° to 255°:
255° + 360° = 615°
For a negative coterminal angle, we subtract 360° from 255° until we get a negative result:
255° - 360° = -105°
Similarly, for -800°, to find a positive coterminal angle, we keep adding 360° until we get a positive result:
-800° + 360° = -440°
-440° + 360° = -80°
For a negative coterminal angle, we can subtract 360° from -800°:
-800° - 360° = -1160°
Two rigid transformations are used to map ABC to QRS. The first is a translation of vertex B to vertex R. What is the second transformation?
a reflection across the line containing AB
a rotation about point B
a reflection across the line containing CB
a rotation about point C
Answer:a reflection across the line containing AB
Step-by-step explanation:
The correct option is A).
Step-by-step explanation:
Given :
First Transformation is a translation of vertex B to vertex R.
AB = RQ (refer the given figure)
Solution :
The second transformation is obviously a reflection across the line containing AB because AB = RQ and there is translation of vertex B to vertex R therefore there is also a translation of vertex A to vertex Q and through observing the given diagram we can say that there is a reflection across the line containing AB.
Hence, the correct option is A).
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You are given the system of equations to solve by the elimination method, which is an INCORRECT step that will NOT produce a system with the same solution?
3x + 6y = 8
4x + 2y = 10
A) subtract 6 times the second equation from 2 times the first equation
B) add 3 times the first equation and −9 times the second equation
C) multiply the first equation by 1/3
and subtract the second equation
D) multiply 6y by 1/3 in the first equation and subtract the second equation
D is the correct answer.
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
If a home is valued at $250,000 and the property tax rate is 2 percent, how much will the owners pay in property taxes? $50 $500 $5,000 $50,000
Answer:
$5,000
Step-by-step explanation:
NOT 100% SURE BUT I THINK ITS LIKE THIS
2% = 0.02 tax in a decimal form
$250,000 price of home
0.02 x 250,000= 5,000
The amount that the owner pay in property taxes is: $5,000.
Owner property taxes:Using this formula
Property taxes amount=House value×Property tax rate
Where:
House value=$250,000
Property tax rate=2%
Let plug in the formula
Property taxes amount=$250,000×2%
Property taxes amount=$5,000
Inconclusion the amount that the owner pay in property taxes is $5,000.
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My car uses 8 gallons of gasoline to travel 340 miles. After a Mechanic worked on it. The car uses 7 gallons of gasoline to travel 350 miles. The cost of the gasoline was $4 each per gallon. How much less, to the nearest cent per mile after the mechanic worked on it
But in cost
(50×4)-(42.5×4)
Rs30
Please help!!! Show work if needed
Answer:
2h+2f=10.50
4h+3f=19.50
Step-by-step explanation:
2h+2f=10.50
4h+3f=19.50
• To solve a pair of equations using substitution, first solve one of the equations for one of the variables. Then substitute the result for that variable in the other equation.
{2h2f=10.5,4h3f=19.5}
• Choose one of the equations and solve it for h by isolating h on the left hand side of the equal sign.
2h+2f=10.5
• Subtract 2f from both sides of the equation.
2h=−2f+10.5
• Divide both sides by 2.
h=1/2 (−2f+10.5)
• Multiply 1/2 times −2f+10.5.
h=−f+21/4
• Substitute −f+21/4 for h in the other equation, 4h+3f=19.5.
4(−f+21/4)+3f=19.5
• Multiply 4 times −f+21/4.
−4f+21+3f=19.5
• Add −4f to 3f.
−f+21=19.5
• Subtract 21 from both sides of the equation.
−f=−1.5
• Divide both sides by −1.
f=1.5
• Substitute 1.5 for f in h=−f+21/4. Because the resulting equation contains only one variable, you can solve for h directly.
h=−1.5+21/4
• Add 21/4 to −1.5 by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.
h=15/4
a carpenter agrees to work under the condition that she is to be paid $55 every day she works and she must pay $66 every day she does not work. at the end of 30 days, she finds she has earned 77$. how many days did she work?
Answer:
17 days
Step-by-step explanation:
For each day she works, she earns +55 and each day she DOES NOT work she earns -66. Total 30 days.
Let number of days she works be x
thus, number of days she DOES NOT work is 30 - x
We can setup an equation as:
55(x) + -66(30-x) = 77
This means, she works x days for 55 each and 30 - x days getting -66 each, totalling 77.
We can solve for x to find number of days she worked. Work shown below:
[tex]55(x) + -66(30-x) = 77\\55x-66(30)+66x=77\\121x -1980 = 77\\121x = 77+1980\\121x = 2057\\x=\frac{2057}{121}\\x=17[/tex]
Thus, she worked 17 days
Find the maximum value of the function for the polygonal convex set determined by the given system of inequalities (Picture provided)
Answer:
- The maximum value is 86 occurs at (8 , 7)
Step-by-step explanation:
* Lets remember that a function with 2 variables can written
f(x , y) = ax + by + c
- We can find a maximum or minimum value that a function has for
the points in the polygonal convex set
- Solve the inequalities to find the vertex of the polygon
- Use f(x , y) = ax + by + c to find the maximum value
∵ 3x + 4y = 19 ⇒ (1)
∵ -3x + 7y = 25 ⇒ (2)
- Add (1) and (2)
∴ 11y = 44 ⇒ divide both sides by 11
∴ y = 4 ⇒ substitute this value in (1)
∴ 3x + 4(4) = 19
∴ 3x + 16 = 19 ⇒ subtract 16 from both sides
∴ 3x = 3 ⇒ ÷ 3
∴ x = 1
- One vertex is (1 , 4)
∵ 3x + 4y = 19 ⇒ (1)
∵ -6x + 3y = -27 ⇒ (2)
- Multiply (1) by 2
∴ 6x + 8y = 38 ⇒ (3)
- Add (2) and (3)
∴ 11y = 11 ⇒ ÷ 11
∴ y = 1 ⇒ substitute this value in (1)
∴ 3x + 4(1) = 19
∴ 3x + 4 = 19 ⇒ subtract 4 from both sides
∴ 3x = 15 ⇒ ÷ 3
∴ x = 5
- Another vertex is (5 , 1)
∵ -3x + 7y = 25 ⇒ (1)
∵ -6x + 3y = -27 ⇒ (2)
- Multiply (1) by -2
∴ -6x - 14y = -50 ⇒ (3)
- Add (2) and (3)
∴ -11y = -77 ⇒ ÷ -11
∴ y = 7 ⇒ substitute this value in (1)
∴ -3x + 7(7) = 25
∴ -3x + 49 = 25 ⇒ subtract 49 from both sides
∴ -3x = -24 ⇒ ÷ -3
∴ x = 8
- Another vertex is (8 , 7)
* Now lets substitute them in f(x , y) to find the maximum value
∵ f(x , y) = 2x + 10y
∴ f(1 , 4) = 2(1) + 10(4) = 2 + 40 = 42
∴ f(5 , 1) = 2(5) + 10(1) = 10 + 10 = 20
∴ f(8 , 7) = 2(8) + 10(7) = 16 + 70 = 86
- The maximum value is 86 occurs at (8 , 7)
Answer:
B (5, 1)
Step-by-step explanation:
Assignment 01.11 Estimating
Step 1- Read the passage Who was Leonardo da Vinci?
Who was Leonardo da Vinci?
Leonardo da Vinci trained as a painter during the Renaissance and became a true master of the craft. His amazing powers of observation and skill as an illustrator enabled him to notice and recreate the effects he saw in nature, and added a special liveliness to all of his portraits. Curious as well as observant, he constantly tried to explain what he saw, and described many experiments to test his ideas. Because he wrote down and sketched so many of his observations in his notebooks, we know that he was among the very first to take a scientific approach towards understanding how our world works and how we see it. He had a keen eye and quick mind that led him to make important scientific discoveries, yet he never published his ideas. He was a gentle vegetarian who loved animals and despised war, yet he worked as a military engineer to invent advanced and deadly weapons. He was one of the greatest painters of the Italian Renaissance, yet he left only a handful of completed paintings.
Step 2- In the paragraph above, estimate the number of words by using the following three methods, and answer the the four questions that follow. You must show all work. Even if you have the right answer you will not get full credit without work.
Method 1 - Count the number of words in one sentence
and then multiply that number by the number of sentences in the paragraph.
Method 2 - Count the number of words in one line
and then multiply that number by the number of lines in the paragraph.
Method 3 - Find the number of words in three lines
and then divide by three to find out the average number of words in these lines.
Then multiply this by the number of lines in the paragraph.
Question 1
What is estimate of the total number of words with method 1? What sentence did you use?
Question 2
What is estimate of the total number of words with method 2? What line did you use?
Question 3
What is estimate of the total number of words with method 3?
Question 4
Which estimation method is the closest to the actual number of words?
Answer:
Q1. 168 words from sixth sentence.
Q2. 171 words from line 3.
Q3. 177 words from the first three sentences.
Q4. Method 3.
Step-by-step explanation:
Question 1.
The paragraph has seven sentences.
I chose the sixth sentence ("gentle vegetarian"). It contains 24 words.
7 sentences × (24 words/1 sentence) = 168 words
Question 2.
The passage contains 19 lines.
I chose line 3 ("amazing powers"). It contains nine words.
19 lines × (9 words/1 line) = 171 words.
Question 3.
I chose the first three lines. They contain 28 words.
Words per line = 28 words/3 lines = 9.33 words per line
Total words = 19 lines × (9.33 words/1 line) = 177 words
Question 4
The passage contains 176 words. Method 3 comes closest to the actual number of words.
Help is much needed!!!!
Answer:
b = 6√3.
Step-by-step explanation:
Use trigonometry.
cos 30 = adjacent side / hypotenuse = b / 12
√3 / 2 = b / 12
2b = 12√3
b = 6√3 answer.
Use a special triangle on the unit circle to determine the value of tan π/6.
Answer:
D) √3/3
Step-by-step explanation:
The coordinates of the point at the angle π/6 are shown as (√3/2, 1/2). The tangent of the angle is the ratio of the y-coordinate to the x-coordinate:
tan(π/6) = (1/2)/((√3)/2) = 1/√3 = (√3)/3 . . . . matches choice D
A function is created to represent the amount of money you save or spend each day of the week. What restrictions would be made to the range?
A) The range would only include integers.
B) The range would only include positive integers.
C) The range would only include negative integers.
D) The range would include all real numbers.
The range would only include positive integers.
Answer B
Let A = {x | x < 5} and B = {x | x ≤ 7}. Find A B.
Answer:
A B = {x | x < 5}
Step-by-step explanation:
The domain of A B will be given by {x | x < 5}
The domain of A is given as {x | x < 5} while that of B is {x | x ≤ 7}. From this we can infer that the domain of A is a subset of B since A is contained in B. The domain of A B is simply the intersection of these two sets which is A.
Examine today’s stock listing for SFT Legal, shown below.
52 wk High
52 wk Low
Symbol
Div.
Close
Net Change
74.80
44.61
SFT
8.94
56.11
5.74
What was the price of SFT Legal yesterday?
Answer:
its D
Step-by-step explanation:
Answer:it would be c because the stock increased by 5.74 over yesterday’s price
Step-by-step explanation:
The Earth completely rotates on its axis once every 24 hours.
A) How long does it take for it to rotate 310 degrees?
B) How long does it take to rotate 5 radians?
C) The diameter of the Earth is approximately 7920 miles. How far will a point on the equator rotate in 2 hours?
Show all work. Give answers to the nearest hundredth. Include the units in your response.
Answer:
A)
62/3 = 20.67 hours
B)
60.00 hours
C)
2074.29 miles
Step-by-step explanation:
If we assume the earth is a perfect circle, then in a complete rotation the earth covers 360 degrees or 2π radians.
A)
In 24 hours the earth rotates through an angle of 360 degrees. We are required to determine the duration it takes to rotate through 310 degrees. Let x be the duration it takes the earth to rotate through 310 degrees, then the following proportions hold;
(24/360) = (x/310)
solving for x;
x = (24/360) * 310 = 62/3 = 20.67 hours
B)
In 24 hours the earth rotates through an angle of 2π radians. We are required to determine the duration it takes to rotate through 5π radians. Let x be the duration it takes the earth to rotate through 5π radians, then the following proportions hold;
(24/2π radians) = (x/5π radians)
Solving for x;
x = (24/2π radians)*5π radians = 60 hours
C)
If the diameter of the earth is 7920 miles, then in 24 hours a point on the equator will rotate through a distance equal to the circumference of the Earth. Using the formula for the circumference of a circle we have;
circumference = 2*π*R = π*D
= 7920π miles
Therefore, the speed of the earth is approximately;
(7920π miles)/(24 hours) = 330π miles/hr
The distance covered by a point in 2 hours will thus be;
330π * 2 = 660π miles = 2074.29 miles
Which of these constructions is impossible using only a compass and straightedge?
A. Doubling the square
B. Bisecting any angle
C. Doubling the cube
D. Trisecting a right angle
Answer:
C.
Step-by-step explanation:
The topic is on: 'impossible geometric construction"
The three areas of concern are : Trisecting an angle, squaring a circle and doubling a cube.
In double a cube the , when the edge in 1 unit will give the equation will give the equation x³=2 whose solution yields cube root of 2. This problem can not be solve because cube root of 2 is not an Euclidean number.
Answer:
C. Doubling the cube.
Step-by-step explanation:
Geometric construction is majorly a two dimensional drawing, excluding some form of projections (isometric and oblique drawing) which are three dimensional. Essential instruments to use in construction are; a pair of compass and straightedge (eg ruler).
From the options stated in the given question, doubling the cube is difficult to construct using the instruments given. A cube is a three dimensional shape that has all sides to be equal. It is a prism formed from a square, and it has six faces.
Verify the identity
Answer:
see below
Step-by-step explanation:
sin x 1
------------------- = -----------
sec^2 x - tan ^2 x csc x
Sec = 1/cos and tan = sin/cos
sin x 1
------------------- = -----------
1/ cos ^2 x -sin^2/cos ^2 x csc x
Factor the denominator
sin x 1
------------------- = -----------
(1-sin^2 x)/ cos ^2 x csc x
We know that 1 - sin^2 x = cos ^2
sin x 1
------------------- = -----------
(cos^2 x)/ cos ^2 x csc x
sin x 1
------------------- = -----------
1 csc x
Multiply the top and bottom of the left hand side by 1/ sin x
sin x * 1/ sin x 1
------------------- = -----------
1 * 1 sin x csc x
1 1
------------------- = -----------
1 sin x csc x
We know that 1/sin x = csc
1 1
--------- = -----------
csc (x) csc x
is this right? in the triangle below what ration is csc 0?
Answer:
[tex]\frac{13}{5}[/tex]
Step-by-step explanation:
we know that
[tex]csc(\theta)=\frac{1}{sin(\theta)}[/tex]
In this problem
[tex]sin(\theta)=\frac{1.5}{3.9}[/tex]
substitute
[tex]csc(\theta)=\frac{3.9}{1.5}[/tex]
Multiply by 10 both numerator and denominator
[tex]csc(\theta)=\frac{39}{15}[/tex]
Divide by 3 both numerator and denominator
[tex]csc(\theta)=\frac{13}{5}[/tex]
The dairy cows on Mr. Aaron's farm eat 9,315 pounds of grain in 3 months.How many pounds of grain will the cows eat in one month.
Answer:
3,105
Step-by-step explanation:
the answer is 3,105 because you simply take the total number that was eaten in 3 months and divide it by 3 since they only want to know what was eaten in 1 month
polynomials what is the product of
1/2x - 1/4 and 5x^2-2x+6
Answer:
[tex]\frac{5}{2}x^3-\frac{9}{4}x^2+\frac{7}{2}x-\frac{3}{2}[/tex]
Step-by-step explanation:
Given polynomials are [tex]\frac{1}{2}x-\frac{1}{4}[/tex] and [tex]5x^2-2x+6[/tex].
Now we need to find their product which can be done as follows:
[tex]\left(\frac{1}{2}x-\frac{1}{4}\right)\left(5x^2-2x+6\right)[/tex]
[tex]=5x^2\left(\frac{1}{2}x-\frac{1}{4}\right)-2x\left(\frac{1}{2}x-\frac{1}{4}\right)+6\left(\frac{1}{2}x-\frac{1}{4}\right)[/tex]
[tex]=\frac{5}{2}x^3-\frac{5}{4}x^2-x^2+\frac{1}{2}x+3x-\frac{3}{2}[/tex]
[tex]=\frac{5}{2}x^3-\frac{9}{4}x^2+\frac{7}{2}x-\frac{3}{2}[/tex]
Hence final answer is [tex]\frac{5}{2}x^3-\frac{9}{4}x^2+\frac{7}{2}x-\frac{3}{2}[/tex].
Find the domain of y=\sqrt{3x-8}
Answer:
Step-by-step explanation
∣
∣
∣
x
{x|x≥8/3}
La expresión algebraica que indica: «Si al cuadrado de la suma de dos números a y b le restamos la mitad de c y la diferencia resultante la multiplicamos por 5» es:
The sum of two number a and b is [tex]a+b[/tex]
Its square is [tex](a+b)^2[/tex]
Half of c is [tex]\frac{c}{2}[/tex]
And we have to subtract this from what we got before:
[tex](a+b)^2-\dfrac{c}{2}[/tex]
Finally, we multiply everything by 5:
[tex]5\left[(a+b)^2-\dfrac{c}{2}\right][/tex]
Queremos, a partir de una frase, escribir la correspondiente expresión algebraica.
Obtendremos:
[tex][(a + b)^2 - c/2]*5[/tex]
-----------------------------------
Lo que nos dan es:
"Si al cuadrado de la suma de dos números a y b le restamos la mitad de c y la diferencia resultante la multiplicamos por 5"
Veamos esto en partes, la primera dice:
"Si al cuadrado de la suma de dos números a y b..."
El cuadrado de la suma de dos números a y b se escribe como:
[tex](a + b)^2[/tex]
Ahora tenemos:
"Si al cuadrado de la suma de dos números a y b le restamos la mitad de c ..."
Ahora le restamos la mitad de c a lo que encontramos antes:
[tex](a + b)^2 - c/2[/tex]
Finalmente:
"Si al cuadrado de la suma de dos números a y b le restamos la mitad de c y la diferencia resultante la multiplicamos por 5"
Es decir, debemos multiplicar por 5 a la diferencia (la resta) de arriba:
[tex][(a + b)^2 - c/2]*5[/tex]
Está es la expresión que queriamos encontrar.
Si quieres aprender más, puedes leer:
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What is the quotient (x3 – 3x2 + 5x – 3) ÷ (x – 1)?
What is the quotient (x3 + 3x2 + 5x + 3) ÷ (x + 1)?
Answer:
x^2 -2x +3x^2 +2x +3Step-by-step explanation:
The quotient in each case can be found by any of several means, including synthetic division (possibly the easiest), polynomial long division, or graphing.
1. The graph shows you the quotient is (x-1)^2 +2 = x^2 -2x +3.
2. The graph shows you the quotient is (x+1)^2 +2 = x^2 +2x +3.
A machine is set up to cut metal strips of varying lengths and widths based on the time (t) in minutes. The change in length is given by the function `l(t) = t^2 - sqrt(t)`, and the change in width is given by `w(t) = t^2 - 2t^(1/2)`. Which function gives the change in area of the metal strips? A. `a(t) = t^4 + 2t` B. `a(t) = t^4 + 2t + 3t^(5/2)` C. `a(t) = t^4 - 3t^(5/2) + 2t` D. `a(t) = t^4 + 2t - 2t^(1/2) + sqrt(t)`
Answer:
The change of area A(t) = t^4 - 3t^(5/2) + 2t ⇒ answer C
Step-by-step explanation:
* Lets study the problem
- The metal strip is in a shape of rectangle
- The change in length l(t) = t² - √t
- The change is the width w(t) = t² - 2t^1/2
* We must find function gives the change of area
∵ The area of the rectangle = length × width
∴ The change of rate of area A(t) = l(t) × w(t)
- We can write the √t in exponential form t^1/2
∴ l(t) = t² - t^1/2
∵ w(t) = t² - 2t^1/2
∵ A = l × w
∴ A(t) = l(t) × w(t)
∴ [tex]A(t)=(t^{2}-t^{\frac{1}{2}})(t^{2}-2t^{\frac{1}{2}})[/tex]⇒use the foil method
∴ [tex]A(t)=(t^{2})(t^{2})+(t^{2})(-2t^{\frac{1}{2}})+(-t^{\frac{1}{2}})(t^{2})+(-t^{\frac{1}{2}})(-2t^{\frac{1}{2}})[/tex]
- If we multiply two same numbers have exponents, then we add
the power of them
∴ [tex]A(t)=(t^{2+2})-2t^{2+\frac{1}{2}}-t^{\frac{1}{2}+2}+2t^{\frac{1}{2}+\frac{1}{2}}[/tex]
∴ [tex]A(t)=t^{4}-2t^{\frac{5}{2}}-t^{\frac{5}{2}}+2t[/tex]
* Now lets add the like terms
∴ [tex]A(t)=t^{4}-3t^{\frac{5}{2}}+2t[/tex]
* The change of area A(t) = t^4 - 3t^(5/2) + 2t
Answer:
the answer is C
Step-by-step explanation:
Which solid does NOT have the net form? hexagonal prism hexagonal pyramid rectangular prism rectangular pyramid
Answer:
hexagonal pyramid
Step-by-step explanation:
Which conic section is represented by the equation shown below?
[tex]2x^2-9x+4y^2+8x=16[/tex]
A. Parabola
B. Ellipse
C. Circle
D. Hyperbola
Answer: Option B. Ellipse
[tex]\frac{(x-\frac{1}{4})^2}{\frac{129}{16}}+\frac{(y-0)^2}{\frac{129}{32}}=1[/tex]
Step-by-step explanation:
To know what type of conic section the function is
[tex]2x ^ 2-9x + 4y ^ 2 + 8x = 16[/tex] we must simplify it.
[tex]2x ^ 2-9x + 4y ^ 2 + 8x = 16\\\\2x^2 -x +4y^2 =16[/tex]
complete the square of the expression:
[tex]2x ^ 2 -x\\\\\\2(x^2 -\frac{1}{2}x)\\\\2(x^2-\frac{1}{2}x +\frac{1}{16})-2\frac{1}{16}\\\\2(x-\frac{1}{4})^2 -\frac{1}{8}[/tex]
So we have
[tex]2(x-\frac{1}{4})^2 -\frac{1}{8}+4y^2 =16\\\\2(x-\frac{1}{4})^2+4y^2 =\frac{129}{8}\\\\\frac{8}{129}[2(x-\frac{1}{4})^2] +\frac{8}{129}[4y^2] =1\\\\\frac{16(x-\frac{1}{4})^2}{129}+\frac{32(y-0)^2}{129}=1[/tex]
[tex]\frac{(x-\frac{1}{4})^2}{\frac{129}{16}}+\frac{(y-0)^2}{\frac{129}{32}}=1[/tex]
We know that the general equation of an ellipse has the form
[tex]\frac{(x-h)^2}{a^2} +\frac{(y-k)^2}{b^2}=1[/tex]
Then the equation
[tex]\frac{(x-\frac{1}{4})^2}{\frac{129}{16}}+\frac{(y-0)^2}{\frac{129}{32}}=1[/tex]
is an ellipse with center [tex](\frac{1}{4}, 0)[/tex]
[tex]a =\sqrt{\frac{129}{16}}[/tex] and [tex]b=\sqrt{\frac{129}{32}}[/tex]
Observe the attached image
A certain forest covers an area of 2600 km 2 suppose that each year this area decreases by 9% . What will the area be after 5 years ?
Answer:
Final answer is approx 1622.48 square kilometers.
Step-by-step explanation:
Given that a certain forest covers an area of 2600 km 2 suppose that each year this area decreases by 9% . Now we need to find about what will the area be after 5 years.
So we need to plug these values into decay formula which is given by:
[tex]A=P(1-r)^t[/tex]
Where P=2600
r= rate = 9%= 0.09
t=time = 5 years
Plug these values into above formula, we get:
[tex]A=2600(1-0.09)^5[/tex]
[tex]A=2600(0.91)^5[/tex]
[tex]A=2600(0.6240321451)[/tex]
[tex]A=1622.48357726[/tex]
Hence final answer is approx 1622.48 square kilometers.
Final answer:
Using the exponential decay formula, A = A_0 (1-r)^t, the forest area after 5 years with an annual decrease of 9% is approximately 1622.4 km².
Explanation:
To calculate the forest area after 5 years with an annual decrease of 9%, we can use the formula for exponential decay. The original area of the forest is 2600 km2.
Formula for exponential decay: A = A_0 (1-r)^t, where A is the area after time t, A_0 is the original area, r is the rate of decrease, and t is time in years.Convert the percentage to a decimal: r = 9% or r = 0.09.Substitute the values into the formula: A = 2600 (1-0.09)^5.Calculate: A ≈ 2600 (0.91)^5.Compute the final area: A ≈ 2600 * 0.624 ≈ 1622.4 km2.So, if the forest continues to decrease by 9% annually, the area will be approximately 1622.4 km2 after 5 years.