Answer:
True
Step-by-step explanation:
For $6 and 4 oranges the unit price per orange is $1.50, and with $15 for 10 oranges the unit price per orange is also $1.50.
You ingest 200 mg of medicine and your body removes 15% of it per hour. How long until there is only 40 mg left?
Answer:
The time after which only 40 mg of medicine left inside body is 9.8 hours
Step-by-step explanation:
Given as :
The initial quantity of medicine ingest in body = i=200 mg
The final quantity of medicine in body = f= 40 mg
The rate at which body remove medicine = r = 15%
Let The time taken to remove = t hours
According to question
The final quantity of medicine in body after t hours = The initial quantity of medicine ingest in body × [tex](1-\dfrac{\textrm rate}{100})^{\textrm time}[/tex]
I.e f = i × [tex](1-\dfrac{\textrm r}{100})^{\textrm t}[/tex]
Or, 40 mg = 200 mg × [tex](1-\dfrac{\textrm 15}{100})^{\textrm t}[/tex]
Or, [tex]\dfrac{40}{200}[/tex] = [tex](1-\dfrac{\textrm 15}{100})^{\textrm t}[/tex]
Or , 0.2 = [tex](\frac{100 - 15}{100})^{t}[/tex]
Or, [tex](\frac{85}{100})^{t}[/tex] = 0.2
Taking Log both side
So, [tex]Log_{10}[/tex] [tex](\frac{85}{100})^{t}[/tex] = [tex]Log_{10}[/tex]0.2
Or, t × [tex]Log_{10}[/tex]0.85 = [tex]Log_{10}[/tex]0.2
Or, t (-0.07) = - 0.69
∴ t = [tex]\dfrac{.69}{.07}[/tex]
I.e t = 9.8 hours
So, The time after which only 40 mg left inside body = t = 9.8 hours
Hence,The time after which only 40 mg of medicine left inside body is 9.8 hours .Answer
The length of each side of a square was decreased by 2 inches so the perimeter is now 49 inches. What was the original length of each side of the square
The Original length of each side of square was 14.25 inches.
Step-by-step explanation:
Perimeter of a square is given by:
Perimeter = 4 * side
Let x be the original length of each side of square
So
decreasing 2 inch will mean
[tex]x-2[/tex]
Perimeter of square after reducing 2 inches from each side
[tex]4(x-2) = 49\\4x-8 = 49\\4x = 49+8\\4x = 57\\\frac{4x}{4} = \frac{57}{4}\\x = 14.25[/tex]
So,
The Original length of each side of square was 14.25 inches.
Keywords: Perimeter, square
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Which number belongs in the whole numbers area of the diagram?
A) −15
B) 1.5
C) 12
D) 7/8
Answer:
the answer is C) 12
Step-by-step explanation:
rawr
Hi again, This is the last time I annoy you guys with this, but I really need help with my last question.
It would have a greater slope and perhaps start higher on the y axis.
Step-by-step explanation:
I assume you can choose your own numbers as long as they are higher than the current. This means the numbers on your y axis will change but not the numbers on your x axis because that determines the time. So let's change the y axis numbers from going by 20 and make them go by 25. You could technically keep the dots in the same place as long as you change the y axis numbers because you are still earning more money.
Find the measure of each numbered angle.
Answer:
m∠1 = 30°
m∠2 = 60°
Step-by-step explanation:
There are two 30-60-90 triangles. For each, the angles have to add up to 180°
Answer:
m∠1 = 30°
m∠2 = 60°
Step-by-step explanation:
Select the correct answer.
Solve the equation by completing the square.
0 = 4x2 - 64x + 192
OA. x= 4, 12
OB. x=-12, -4
x= -8,24
x = -24, 8
Answer:
Option A) x=4,12 is correct.
The solution of the given quadratic equation is x=4,12
Step-by-step explanation:
Given equation is in quadratic form
Given quadratic equation is
[tex]0=4x^2-64x+192[/tex]
Rewriting the above equation
[tex]4x^2-64x+192=0[/tex]
Now dividing the equation by 4 we get
[tex]\frac{1}{4}(4x^2-64x+192)=\frac{0}{4}[/tex]
[tex]x^2-16x+48=0[/tex]
For quadratic equation [tex]ax^2+bx+c=0[/tex]
solution [tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
where a and b are coefficients of [tex]x^2[/tex] and x respectively, c is a constant
Here a=1, b=-16, c=48
[tex]x=-\frac{(-16)\pm\sqrt{(-16)^2-4(1)(48)}}{2(1)}[/tex]
[tex]=\frac{16\pm\sqrt{16^2-192}}{2}[/tex]
[tex]=\frac{16\pm\sqrt{256-192}}{2}[/tex]
[tex]=\frac{16\pm\sqrt{64}}{2}[/tex]
[tex]x=\frac{16\pm 8}{2}[/tex]
Therefore
[tex]x=\frac{16+8}{2}[/tex] and [tex]x=\frac{16-8}{2}[/tex]
[tex]x=\frac{24}{2}[/tex] and [tex]x=\frac{8}{2}[/tex]
[tex]x=12[/tex] and [tex]x=4[/tex]
Therefore the solution of the given quadratic equation is x=4,12
Option A) x=4,12 is correct.
Is 3/9 a terminating decimal?
Answer:
NO, It is non terminating / recurring decimal
Step-by-step explanation:
3/9= 0.33333333......
remainder= 3
Which expressions are equivalent to 2r+(t+r)
Choose all answers that apply:
A: 2rt+4r
B: r+t
C: None of the above
Answer:
Option C -> None of the above.
Step-by-step explanation:
Given-
2 r + ( t + r )
⇒ 2 r + t + r
⇒ 2 r + r + t
⇒ 3 r + t
∵ 2 r + ( t + r ) = 3 r + t.
∴ The given expression is equivalent to Option C : None of the above.
Answer:
C. None of the above
Step-by-step explanation:
Anatomy The surface area of S of a human body in Square meters can be approximated by S=^hm/36 where h is height and m is mass in kilometers.A basketball player with a height of 2.1 meters has a surface area of about 2.7 meters^.What is the players mass ?
The basketball player's mass is approximately 46.2857 kilograms.
Explanation:To solve for the player's mass, we can rearrange the equation to isolate the mass variable. The equation can be rewritten as m = 36S/h.
Plugging in the given values, we get m = 36 * 2.7 / 2.1.
Solving this expression gives us a mass of approximately 46.2857 kilograms.
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There are twice as many boys as girls in Mr.Brown's first period Algebra class. the class is 24 students total. How many more boys than girls are in the class?
explanation needed.
HERE'S YOUR ANSWER:
Let number of girls be- x
and number of boys be- 2x(boys are 2 times NO. of girls)
therefore
x + 2x = 24
3x = 24
x = 24/3
x = 8
hence number of girls = 8
boys are 2 times more than girls = 16
HOPE IT HELPS...
Helpppppppppppppppppppp
Answer:
$200,000
Step-by-step explanation:
Base Salary = 40,000
Total Salary = 70,000
So, the rest, Allison earns from commissions. How much??
70,000 - 40,000 = 30,000
So, 15% of total sales is equal to 30,000
Let total sales be "t", so we can write an equation as:
15% * t = 30,000
15% in decimal is:
15/100 = 0.15
So, equation to solve is:
0.15t = 30,000
Finding t:
t = 30,000/0.15 = 200,000
Allison's total sales were $200,000
If you need one gallon of gas for 20miles how many gallon do you need for 364 miles?
Divide total miles by miles per gallon:
364 miles / 20 miles per gallon = 18.2 gallons
please help and add an explanation if you can <3
The value of [tex]x_2 = 1[/tex]
Solution:
Given that a approximate solution to the equation [tex]x^2 +6x - 2=0[/tex] can be calculated using the iterative formula shown below
[tex]x_{n+1} = \frac{2-(x_n)^3}{6}[/tex]
Also given that [tex]x_1 =2[/tex]
To find: value of [tex]x_2[/tex]
To find value of [tex]x_2[/tex] , substitute n = 1 in given iterative formula
[tex]x_{1+1} = \frac{2-(x_1)^3}{6}[/tex]
Solve the above expression by substituting [tex]x_1 = 2[/tex]
[tex]x_2 = \frac{2-(2)^3}{6}[/tex]
[tex]x_2 = \frac{2-8}{6}\\\\x_2 = \frac{-6}{6}\\\\x_2 = -1[/tex]
Thus value of [tex]x_2 = 1[/tex]
Sin Qua Corporation is a company listed on the stock exchange and issues corporate bonds. Which statement is most likely true?
Answer:
B. Investors will have to pay tax on the interest income received from the bonds.
Step-by-step explanation:
Investors will have to pay tax on the interest income received from the bonds because it is a taxable income.
The interest earned from a corporate bond is subject to taxation by both the federal and state governments.
Again, the maturity of the bond is determined at the time they are issued. Creditworthiness will only affect the bond price but not its maturity period.
Erin purchased 100 shares through her online broker. The price per share on the day of the purchase was $15.84. Erin’s broker charged her $0.025 per share as a brokerage fee. How much did Erin pay in brokerage fees? Erin spent $ in brokerage fees.
Answer:
$2.50
Step-by-step explanation:
The total fee is the fee per share multiplied by the number of shares:
$0.025 × 100 = $2.50 . . . . Erin's brokerage fee
Answer:
2.50
Step-by-step explanation:
One cars average speed is 10 mph faster than the other. The faster car arrives at Ocean City at 11 AM, a half hour before the slower car. What is the average speed of each car?
Answer:
slower 50mph faster 60mph
Step-by-step explanation:
Distance=s⋅t
Distance
=
(
+
10
)
⋅
(
−
0.5
)
Distance=(s+10)⋅(t−0.5)
Equate the distances:
⋅
=
(
+
10
)
⋅
(
−
0.5
)
s⋅t=(s+10)⋅(t−0.5)
Expand and simplify:
⋅
=
⋅
−
0.5
+
10
−
5
s⋅t=s⋅t−0.5s+10t−5
0
=
−
0.5
+
10
−
5
0=−0.5s+10t−5
Rearrange to find
t:
0.5
=
10
−
5
0.5s=10t−5
10
=
0.5
+
5
10t=0.5s+5
=
0.5
+
5
10
t=
10
0.5s+5
Substitute
t back into the distance equation:
⋅
0.5
+
5
10
=
(
+
10
)
⋅
(
0.5
+
5
10
−
0.5
)
s⋅
10
0.5s+5
=(s+10)⋅(
10
0.5s+5
−0.5)
Simplify and solve for
s:
After solving, you will find that the average speeds are approximately:
Slower car: 50 mph
Faster car: 60 mph
Eric explains that all circles are similar using the argument shown.
1. Let there be two circles, Circle A and circle B.
2. There exists a translation that can be performed on circle A such that it will have the same center as circle B.
4. Thus, there exists a sequence of transformations that can be performed on circle A in order to obtain circle B.
5. Therefore, circle A is similar to circle B.
6. Since circle A and circle B can be any circles, all circles are similar
Which statement could be step 3 of the argument?
Step 3 of the argument could be that the translation preserves the size of circle A.
Explanation:Step 3 of the argument could be: 3. The translation preserves the size of circle A.
Explanation: In step 2, it is stated that there exists a translation that can be performed on circle A so that it will have the same center as circle B.
In order for this translation to be possible, the size of circle A must be preserved. This means that the radius of this circle A remains the same even after the translation is applied.
Therefore, step 3 could be that the translation preserves the size of the given circle A.
What comes next?
131,517,?,123
Answer:
192
Step-by-step explanation:
Your sequence of numbers is
131 517 … 123
Space them as a two-digit sequence
13 15 17 19 21 23
Now, regroup then as a three-digit sequence
131 517 192 123
The missing number is 192.
You divide two numbers and the quotient is 2.5. What might the two numbers be? Show at least 5 solutions.
Answer:
5/2
Step-by-step explanation:
does 5x-3y=-7
10x-6y=-14 have one solution or one solution or infinity solutions
Answer:
Problem 1: 5x-3y=-7 has One Solution
Problem 2: 10x-6y=-14 has One Solution
Find all solutions to
\sqrt[3]{15x-1} + \sqrt[3]{13x+1} =4\sqrt[3]{x}
Enter all the separated, seperated by commas.
Plz help asap
Answer:
Solution is x= 0 , x = \frac{1}{14} , x = \frac{-1}{12}
Step-by-step explanation:
Given, equation is \sqrt[3]{15x-1} + \sqrt[3]{13x+1} = 4\sqrt[3]{x} →→→ (1)
Now, by cubing the equation on both sides, we get
( \sqrt[3]{15x-1} + \sqrt[3]{13x+1} )³ = (4\sqrt[3]{x})³
⇒ (15x-1) + (13x+1) + 3×\sqrt[3]{15x-1}× \sqrt[3]{13x+1} (\sqrt[3]{15x-1} + \sqrt[3]{13x+1}) = 64 x.
(since (a+b)³ = a³ + b³ + 3ab(a+b) ).
⇒ 28x + 3×\sqrt[3]{15x-1}× \sqrt[3]{13x+1} (\sqrt[3]{15x-1} + \sqrt[3]{13x+1}) = 64x.
(since from (1), \sqrt[3]{15x-1} + \sqrt[3]{13x+1} = 4\sqrt[3]{x} )
⇒ 12×\sqrt[3]{15x-1}× \sqrt[3]{13x+1} (\sqrt[3]{15x-1}×\sqrt[3]{x}= 36x.
⇒ 3x = [tex]\sqrt[3]{(15x-1)(13x+1)(x)}[/tex] .
Now, once again cubing on both sides, we get
(3x)³ = ([tex]\sqrt[3]{(15x-1)(13x+1)(x)}[/tex])³.
⇒ 27x³ = (15x-1)(13x+1)(x).
⇒ 27x³ = 195x³ + 2x² - x
⇒ 168x³ + 2x² - x = 0
⇒ x(168x² + 2x -1) = 0
⇒ by, solving the equation we get ,
x = 0 ; x = \frac{1}{14} ; x = \frac{-1}{12}
therefore, solution is x= 0 , x = \frac{1}{14} , x = \frac{-1}{12}
What is the inverse equation of the function, y= 3x - 6?
Answer:
y=1/3x+2
Step-by-step explanation:
y=3x-6
x=3y-6
3y=x+6
y=1/3x+6/3
y=1/3x+2
Oder from smallest to largest 652/900 0.012 7/10 32% 1/10 0.721 65%
Answer:
The given numbers from smallest to largest is
[tex]0.012, \frac{1}{10}, 32\%, 65\%, \frac{7}{10}, 0.721, 0.721, \frac{652}{900}[/tex]
Step-by-step explanation:
Given numbers are
[tex]\frac{652}{900}, 0.012,\frac{7}{10}, 32\%,\frac{1}{10}, 0.721, 65\%[/tex]
We have to arrange the given numbers from smallest to largest
That is to write in ascending order.
Rewritting the given numbers are
[tex]\frac{652}{900}, 0.012,\frac{7}{10}, \frac{32}{100},\frac{1}{10}, 0.721, \frac{65}{100}[/tex]
[tex]\frac{652}{900}, 0.012,0.7, 0.32, 0.1, 0.721, 0.65[/tex]
[tex]0.724, 0.012, 0.7, 0.32, 0.1, 0.721, 0.65[/tex]
Now arranging the above numbers from smallest to largest
[tex]0.012, 0.1, 0.32, 0.65, 0.7, 0.721, 0.724[/tex]
ie, 0.12, [tex]\frac{1}{10}, 32\%, 65\%, \frac{7}{10}, 0.721, 0.721, \frac{652}{900}[/tex]
The given numbers in ascending order is
[tex]0.012, \frac{1}{10}, 32\%, 65\%, \frac{7}{10}, 0.721, 0.721, \frac{652}{900}[/tex]
Phil wants to buy more than two sandwiches at the city fair. There are three sandwich stands, and each is offering a different deal.
Benny's Sandwiches
4 sandwiches for $2.00
ABC Sandwiches, Inc.
2 sandwiches for $1.50
Sandwich Hut
1 sandwich for $2.00 *Buy 1, get 1 Free*
Which sandwich stand has the best deal for sandwiches?
OA. ABC Sandwiches, Inc.
OB Sandwich Hut
C. Both Benny's Sandwiches and ABC Sandwiches, Inc.
D. Benny's Sandwiches
Reset
Submit
Answer:
Benny's:
2.00 / 4 = $0.50 per sandwich
ABC:
1.50 / 2 = $0.75 per sandwich
Sandwich Hut:
2.00 / 2 = $1.00 per sandwich
Benny's has the best deal
Answer:
The answer for this question would be $3.00 for sandwiches
Step-by-step explanation:
A developer was buying land. He bought 4 acres at $1,863 per acre. He then spilt the land he purchased into 9 lots. How much should he sell each lot for just to break even.
answer: 828$
Step-by-step explanation:
step 1
Find out the total cost of the land
Multiply the total area in acres by $1,863 per acre
step 2
we know that
To determine the selling price of each lot to reach break even, divide the total cost by the number of lots.
What is the answer?!?!?!
The equation D is the equation that best fits the data.
Why?
We can find the best option by substituting the easiest values into the given options.
Let's substitute f(0), f(1) and f(4) for each equation:
A.
[tex]f(0)=3.02(3.67)^{0}=3.02[/tex]
[tex]f(1)=3.02(3.67)^{1}=11.08[/tex]
[tex]f(4)=3.02(3.67)^{4}=547.86[/tex]
We can see that the values are too far from the given values, so the equation A is discarded.
B.
[tex]f(0)=2.27(2.09)^{0}=2.27[/tex]
[tex]f(1)=2.27(2.09)^{1}=4.74[/tex]
[tex]f(4)=2.27(2.09)^{1}=43.31[/tex]
We can see that the values are too far from the given values, so the equation B is discarded.
C.
[tex]f(0)=8.04(0.98)^{0}=8.04[/tex]
[tex]f(1)=8.04(0.98)^{1}=7.87[/tex]
[tex]f(4)=8.04(0.98)^{4}=7.41[/tex]
We can see that the values are too far from the given values, so the equation B is discarded.
D.
[tex]f(0)=6.61(1.55)^{0}=6.61[/tex]
[tex]f(1)=6.61(1.55)^{0}=10.26[/tex]
[tex]f(4)=6.61(1.55)^{0}=38.15[/tex]
We can see that the values are the closest values from the given values, so the equation D is the equation that best fits the data.
Have a nice day!
Which inequality has no solution?
6 (x + 2) greater-than x minus 3
3 + 4 x less-than-or-equal-to 2 (1 + 2x)
Negative 2 (x + 6) less-than x minus 20
x minus 9 less-than 3 (x minus 3)
Answer:
Second option: [tex]3 + 4 x\leq 2 (1 + 2x)[/tex]
Step-by-step explanation:
Let's solve for "x" from each inequality:
[tex]a.\ 6 (x + 2)>x-3\\\\6x+12>x-3\\\\6x-x>-3-12\\\\5x>-15\\\\x>\frac{-15}{5}\\\\x>-3[/tex]
[tex]b.\ 3 + 4 x\leq 2 (1 + 2x)\\\\3+4x\leq 2+4x\\\\3-2\leq 4x-4x\\\\1\leq 0\ (FALSE.\ IT\ HAS\ NO\ SOLUTION)[/tex]
[tex]c.\ -2 (x + 6)<x-20\\\\-2x-12<x-20\\\\-12+20<x+2x\\\\8<3x\\\\x>\frac{8}{3}[/tex]
[tex]d.\ x-9<3(x-3)\\\\x-9<3x-9\\\\x-3x<-9+9\\\\-2x<0\\\\x>0[/tex]
The inequality that has no solution is: 3 + 4x ≤ 2(1 + 2x).
The correct option is 2nd.
Given are inequalities, we need to check which of them has no solution.
Let's solve each inequality to determine if it has a solution:
1) 6(x + 2) > x - 3
First, distribute the 6:
6x + 12 > x - 3
Now, let's isolate the variable x on one side:
6x - x > -3 - 12
5x > -15
Finally, divide by 5 to solve for x:
x > -3
This inequality does have a solution, and x can take any value greater than -3.
2) 3 + 4x ≤ 2(1 + 2x)
First, distribute the 2 on the right side:
3 + 4x ≤ 2 + 4x
Now, subtract 4x from both sides:
3 ≤ 2
This is not true, and there is no value of x that satisfies this inequality.
So, this inequality has no solution.
3) -2(x + 6) < x - 20
First, distribute the -2:
-2x - 12 < x - 20
Now, let's isolate the variable x on one side:
-2x - x < -20 + 12
-3x < -8
Finally, divide by -3 to solve for x (note the sign change when dividing by a negative number):
x > 8/3 or x > 2.67
This inequality has a solution, and x can take any value greater than 2.67.
4) x - 9 < 3(x - 3)
First, distribute the 3 on the right side:
x - 9 < 3x - 9
Now, move the variables to one side:
x - 3x < 9 - 9
-2x < 0
Finally, divide by -2 to solve for x (note the sign change when dividing by a negative number):
x > 0
This inequality has a solution, and x can take any value greater than 0.
Hence, the inequality that has no solution is: 3 + 4x ≤ 2(1 + 2x).
The correct option is 2nd.
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Find the slope of the line of (4,3) (1,-4)
Answer: -7/-3.
Step-by-step explanation: In this problem we're asked to find the slope of the line that passes through the points (4,3) and (1,-4).
Using our slope formula, we take the second y minus the first y which in this case is -4 - 3 over our second x minus our first x which in this case is 1 - 4.
-4 - 3 is -7 and 1 - 4 is -3.
So the slope of this line is -7/-3.
Answer:
-7/-3
Step-by-step explanation:
Slope is represented as m
m = Rise/Run =( Y2 - Y1) / (X2 - X1)
m = (-4 -3) / (1 - 4)
m = -7 / -3
The negative sign (minus) will cancel out
Therefore,
m = 7 / 3
m = 2 whole number, 1/3
Consider a triangle ABC with AB = 2, BC = 5, and AC = 6. If the triangle is rotated around AB, what is the volume of the solid that is generated?
The volume of the solid generated by rotating triangle ABC around AB is 24π cubic units.
To find the volume of the solid generated by rotating triangle ABC around side AB, you can use the method of cylindrical shells. The volume of the solid generated by rotating a region bounded by a curve around an axis is given by the formula:
[tex]\[ V = \int_{a}^{b} 2\pi x \cdot h(x) \, dx \][/tex]
Where:
[tex]\( a \) and \( b \) are the limits of integration along the x-axis (in this case, from 0 to the length of side AB),[/tex]
[tex]\( h(x) \) is the height of the curve at the position x, and[/tex]
[tex]\( 2\pi x \) represents the circumference of the cylindrical shell with radius x and height \( h(x) \).[/tex]
In this case, triangle ABC is a right triangle, so rotating it around AB will generate a cone with height AB and base radius AC.
Given that AB = 2 and AC = 6, the radius of the base of the cone formed by rotating the triangle will be [tex]\( r = AC = 6 \)[/tex]. The height of the cone will be the same as the length of side AB, so [tex]\( h = AB = 2 \).[/tex]
Now, we can calculate the volume:
[tex]\[ V = \int_{0}^{2} 2\pi x \cdot 6 \, dx \][/tex]
[tex]\[ = 12\pi \int_{0}^{2} x \, dx \][/tex]
[tex]\[ = 12\pi \left[\frac{x^2}{2}\right]_{0}^{2} \][/tex]
[tex]\[ = 12\pi \left(\frac{2^2}{2} - \frac{0^2}{2}\right) \][/tex]
[tex]\[ = 12\pi \left(\frac{4}{2}\right) \][/tex]
[tex]\[ = 12\pi \cdot 2 \][/tex]
[tex]\[ = 24\pi \][/tex]
So, the volume of the solid generated by rotating triangle ABC around side AB is [tex]\( 24\pi \)[/tex] cubic units.
The solid formed by rotating triangle ABC around side AB is a cone. The volume of this cone is calculated using the formula V = (1/3)πr^2h where r is the radius of the base and h is the height, resulting in approximately 57.91 cubic units.
The question asks for the volume of the solid generated by rotating a triangle around one of its sides. In this case, rotating triangle ABC with AB = 2, BC = 5, and AC = 6 around side AB will generate a conical surface. Since side AB will be the axis of rotation, the other two sides will act as generating lines of the cone, where side AC becomes the slant height (l) and side BC becomes the base's radius (r).
To calculate the volume of the cone, we use the formula V = (1/3)\u03c0r^2h, where r is the radius of the base, and h is the height of the cone. Here the height (h) of the cone is not directly provided, but with the Pythagorean theorem, we can find it since we know the slant height and radius: h = \\/(l^2 - r^2) = \\/(6^2 - 5^2) = \\/(36 - 25) = \\/11. Finally, the volume can be calculated: V = (1/3)\\(3.1415)\(5)^2\\/11\approx 57.91 cubic units.
The theorem of Pappus is a useful approach to solving this problem, but it requires knowing the centroid's distance from the axis of rotation, which is not provided, so we are not using that method here.
dolphin is 30 feet below the surface of the water. She rises 23 feet, sinks 17 feet, and finally rises another 27 feet. If there are no other changes, the dolphin is
Answer:
Dolphin is 3 feet above the surface of the water.
Step-by-step explanation:
Dolphin is 30 feet below the surface of the water, then its position on the vertical number line is -30.
She rises 23 feet - add 23, sinks 17 feet - subtract 17, and finally rises another 27 feet - add 27.Thus,
[tex]-30+23-17+27\\ \\=(-30-17)+(23+27)\\ \\=-47+50\\ \\=3[/tex]
Dolphin is 3 feet above the surface of the water.
Final answer:
After a series of movements, the calculated final position of the dolphin is 3 feet above the surface of the water, which is a reasonable result for a dolphin.
Explanation:
The question involves calculating the final position of a dolphin relative to the water surface after a series of vertical movements (rising and sinking). Initially, the dolphin is 30 feet below the surface. Then, the following movements occur:
The dolphin rises 23 feet.
The dolphin sinks 17 feet.
The dolphin rises another 27 feet.
To find out where the dolphin is relative to the surface after these movements, we can sum the changes in position:
Initial position: -30 feet (below the surface is considered negative)
+ Rise 23 feet: -30 + 23 = -7 feet
+ Sink 17 feet: -7 - 17 = -24 feet
+ Rise 27 feet: -24 + 27 = +3 feet
After calculating these movements, the dolphin is 3 feet above the surface of the water. Dolphins are known to be able to jump several times their length out of the water, and considering they measure about 2 meters long, this result of the dolphin being 3 feet above the water is reasonable.