The speed of landing is 15.69 ft/sec.
What is differentiation ?"Differentiation, in mathematics, process of finding the derivative, or rate of change, of a function. In contrast to the abstract nature of the theory behind it, the practical technique of differentiation can be carried out by purely algebraic manipulations, using three basic derivatives, four rules of operation, and a knowledge of how to manipulate functions.
The three basic derivatives (D) are: (1) for algebraic functions, D(xn) = nxn − 1, in which n is any real number; (2) for trigonometric functions, D(sin x) = cos x and D(cos x) = −sin x; and (3) for exponential functions, D(ex) = ex."
Let the length of the rope = r
Height of the balloon = h
we are given dr/dt = 15ft/sec
at any time t we know:
[tex]r = 125 + 15*t[/tex]
By the Pythagoras theorem we know:
[tex]h^2 + 125^2 = r^2[/tex]
We have to find dh/dt at time t = 20 sec
[tex]d/dh(h^2 + 125^2) = d/dt(r^2)[/tex]
By chain rule:
[tex]d/dh(h^2 + 125^2)*dh/dt\\ = d/dr(r^2)*dr/dt\\2h*dh/dt = 2r* dr/dt\\h*dh/dt = r*dr/dt\\dh/dt = (r/h)*dr/dt[/tex]
[tex]= [(125 + 15*20)/(425^2 - 125^2)^1/2]*15[/tex]--------------------- at time t = 2
=15.69 ft/sec
Hence dh/dt = 15.69 ft/sec
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help pleseeeeeeeeeeeeeeeeeeeeeeee
Complete the information as requested:
1.- Indicated dose: 300 mg of Ceftriaxone ampoules IV every 6 hours for 10 days.
Available: 1.2 g of Ceftriaxone vial. Reconstitute with 5ml of Sterile Water
a) Dose volume … Calculations
b) Number of doses per day to comply with the indication.
c) Number of ampoules needed for the entire treatment
2.- The patient has indicated:
Indicated quantity: 250 mg Tobramycin ampoule every 12 hours
Available Tobramycin 100 mg /ml vial
a) Dose volume for administration according to indication.
b) Number of ampoules needed for one day of treatment.
c) Amount of Tobramycin received per day - mg
3.- A doctor indicates 0.5 g PO c6h x 5 days
The drug available is 125 mg / 5 mL
a) What is the amount of drug administered per dose? in ml
b) how many total doses for the 5 days are required
c) how many 100 ml bottles do I need to deliver
Question 6 of 10
Estimate the sum of the decimals below by rounding to the nearest whole
number. Enter your answer in the space provided.
6.833
3.594
+1.369
————
Answer here
Step-by-step explanation:
7
4
1
----
12
reality
6.833
3.594
1.369
----------
11.796
when a number x is added to it's square, the total is 12. find two possible values of x
Answer:
x=3 or x=−4Step-by-step explanation:
when a number x is added to it's square, the total is 12. find two possible values of x
x+x^2=12
x^2+x=12
x^2+x−12=12−12
x^2+x−12=0
(x−3)(x+4)=0
x−3=0 or x+4=0
x=3 or x=−4
x=3 or x=−4
Translate then Solve for the variable:
The sum of two times a number and 10 is five times the difference of a number and six.
Solve for the variable then type the answer after rounding your answer to the nearest hundredths
The linear equation will be 2x + 10 = 5(x - 6). Then the value of the variable x will be 23.33.
What is the linear system?A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.
Translate then Solve for the variable:
The sum of two times a number and 10 is five times the difference between a number and six.
Let the number be x.
Then the equation will be
2x + 10 = 5(x - 6)
Then the value of x will be
2x + 10 = 5x - 60
5x - 2x = 60 + 10
3x = 70
x = 23.33
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Calculate the volume of each diagrams.
The volume of the solid objects are 612π in³ and 1566πcm³
Volume of solid objectThe given objects are composite figures consisting of two shapes.
The volume of the blue figure is expressed as;
Volume = Volume of cylinder + volume of hemisphere
Volume = πr²h + 2/3πr³
Volume = πr²(h + 2/3r)
Volume = π(6)²(13+2/3(6))
Volume = 36π(13 + 4)
Volume = 612π in³
For the other object
Volume = Volume of cylinder + volume of cone
Volume = πr²h + 1/3πr²h
Volume = π(9)²(15) + 1/3π(9)²(13)
Volume= 81π (15+13/3)
Volume= 1566πcm³
Hence the volume of the solid objects are 612π in³ and 1566πcm³
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If kinaata goes for swimming lessons every 5 days while Wayo goes every 6 days. if both kinaata and Wayo had swimming lessons together at the pool today, after how many days will both meet again at the pool for lessons?
Step-by-step explanation:
we need the least or smallest common multiple for both numbers, 5 and 6.
this is very simple for the small numbers here, but in general we look at the prime factors of both numbers :
6 has the prime factors 2 and 3.
5 has only 5.
so, the LCM is 2×3×5 = 30.
they will meet again after 30 days.
FYI -
the LCM is for larger numbers a and b not automatically a×b. if both numbers share prime factors, the LCM can be smaller than a×b, as the LCM is using every overlapping prime factor only once.
hello fellow indians Question: Lawrence poured 27.328 L of water into a right rectangular prism- shaped tank. The base of the tank is 40 cm by 28 cm. When he finished pouring the water, the tank was ⅔ full. ( 1L=1,000 cm 3).
Answer: andres is 5 years old pls banned him he called e a mean word like the N word
Step-by-step explanation:
question attached please help
Answer:
h(0.1) = 4.97
Step-by-step explanation:
See attached working :)
Remember that h(0.1) is the same as saying find what the equation is equal to when x = 0.1
HELP ILL GIVE MONEY
Owners of a recreation area are filling a small pond with water. They are adding water at a rate of 27 liters per minute. There are 700 liters in the pond to start.
Let W represent the total amount of water in the pond (in liters), and let I represent the total number of minutes that water has been added. Write an equation
relating W to T. Then use this equation to find the total amount of water after 17 minutes.
Equation:__
Total amount of water after 17 minutes: __liters
Answer: Equation: 27t +700 = w
Total amount of water after 17 minutes: 1159 L
Step-by-step explanation:
Equation: 27t +700 = w
let t = minutes
let w = total amount of water in pond (liters)
Total amount of water after 17 minutes: 1159 L
t = 17
therefore
27(17) +700 = 1159
Answer:
425 l
Step-by-step explanation:
im really not sure with my answer, please tell which is the correct choice.
Answer:
the orange one
Step-by-step explanation:
(10 + 10) : (5-3) =
20 : 2 =
10
Which of the following produces an image that is not congruent to the pre-image?
A. translation
B. dilation
C. rotation
D. reflection
Answer:
Dilation
Step-by-step explanation:
it’s a dilation because the dilation changes how big the image is or what it looks like after the original image.
What is the volume of the following solid figure?
Answer: 450
Step-by-step explanation:
The volume is (1/2)(5)(12)(15)=450.
what is the answer to thiss
Hi Student!
This question is fairly simple because it gives us an equation and they also give us a value for the variable that is within the equation and they tell us evaluate the expression. So let's plug in the values and solve.
Plug in the values
[tex]m^2 + 5[/tex][tex](9)^2 + 5[/tex]Factor out the exponent
[tex](9*9) + 5[/tex][tex]81 + 5[/tex]Combine
[tex]86[/tex]Therefore, the final answer that we would get when substituting m with 9 in the given equation is that we get 86.
(Image: Start Fraction x over 4 End Fraction) + 2 = –2
If the linear equation with one variable is x / 4 + 2 = –2. Then the value of x will be negative 16.
What is simplification?Making anything easier to accomplish or comprehend, as well as making it less difficult, is the definition of simplification.
The equation is given below.
x / 4 + 2 = –2
Solving for x, we have
x / 4 + 2 = –2
x / 4 = – 2 – 2
x / 4 = – 4
x = – 4 × 4
x = – 16
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alex has a box of 250 nails. he uses 80 nails. then he loses 35 nails. how many nails does alex have left? what is the hidden question
A spinner is spun `40` times for a game.
This graph shows the fraction of games that are wins.
Based on the graph, what is the probability of a spin winning this game?
(i) In decimals: 0.65
(ii) In percentage: 65%
The graph shows that after the spinner is spun after 40 times. The Fraction of wins is 0.65 out of 1. Look at the very end of the graph to look at the conclusion for probability. Similar cases when, after the spinner is spun after 20 times, the probability is 0.65.
Answer:
0.65 or 65%
Step-by-step explanation:
Please show work and thank you
Answer: [tex]\sqrt{109} \text{ m }[/tex]
Step-by-step explanation:
If we let the length of the ladder be [tex]x[/tex], as shown in the diagram, this means that by the Pythagorean theorem, [tex]x=\sqrt{10^{2}+3^{2}}=\boxed{\sqrt{109}}[/tex] m.
The length of a rectangle is 3 inches more than the width. The area is 10 square inches. Find the dimensions
Answer:
Width = 2
Length = 5
Step-by-step explanation:
let A be the area of the rectangle
L be the length of the rectangle
w be the width of the rectangle
Formula: ‘area of a rectangle’
A = L × w
…………………………………………………
A = L × w
⇔ 10 = (w + 3) × w
⇔ 10 = w² + 3w
⇔ w² + 3w - 10 = 0
Solving the quadratic equation w² + 3w - 10 = 0 :
Δ = 3² - 4(1)(-10) = 9 - (-40) = 9 + 40 = 49
then √Δ = 7
[tex]\Longrightarrow w=\frac{-b+\sqrt{\Delta } }{2a} =\frac{-3+7}{2} =2[/tex]
[tex]or\ w=\frac{-b-\sqrt{\Delta } }{2a} =\frac{-3-7}{2} =-5[/tex]
-5 is not valid ,because w represents the width
which must be a positive number
Then w = 2
Conclusion:
Width = 2
Length = 2 + 3 = 5
Write the place value of the 1 in 742.513
Hi Student!
Looking at the problem statement, we are asked to find the place value of the 1 in the number 742.513. Let's go from right to left and name each of the place values. 7 is in the hundreds place, 4 is in the tens place, 2 is in the ones place, 5 is in the tenths place, 1 is in the hundredths place, 3 is in the thousandths place.
Therefore, our final answer for which place value the number 1 in 742.513 is, we come to the conclusion of the hundredths place.
can you please help me with this two questions
Answer:
2) d. 60°
3) a. AB
Step-by-step explanation:
Question 2
ΔABC and ΔCDA are congruent because:
they are both right trianglesthey share one side (AC)their hypotenuse are parallel (marked by the arrows)This means the corresponding side lengths and angles are equal.
Therefore,
∠CDA = ∠ABC
⇒ x = 60°
Question 3
The hypotenuse is the longest side of a right triangle - the side opposite the right angle (the right angle is shown as a small square).
Therefore, the hypotenuse of ΔABC is the line AB.
Correct to four significant figures (573.06*184.25)
105600
Step-by-step explanation:Significant figures are used in scientific fields to show precision.
Multiplication
When rounding to significant figures you need to first do the operation shown. So, before we round we need to multiply 573.06 * 184.25.
573.06 * 184.25 = 105586.305This is an important step whenever you are rounding to significant figures. If you preround, you will be left with the wrong answer.
Significant Figures
Now that we have the answer before rounding, we need to know how to determine significant figures. If there is a decimal point present, then start counting significant figures at the first non-zero digit from the left.
For example:
The number 539.760 has 6 significant figuresIf the decimal point is not present, then start counting significant figures from the first non-zero digit from the right.
For example:
The number 280020 has 5 significant figuresRounding
Finally, we can round our answer. Firstly, there are more than 4 digits before the decimal point. This means that our rounded answer will not have a decimal point, so when counting sig figs we will start from the right. Remember, even when rounding, a number should always have the same number of digits before the decimal point, even if they are not all significant.
Since we are rounding to 4 sig figs, we need to look at the 5th digit from the left, which is 8. This means we will round up.
So, write the first 4 digits of the number, but round the last one up. Then, write the remaining digits before the decimal point as 0.
105586.305 rounds to 105600SOMEONE HELP ASAP! PLEASE EXPLAIN IN DEPTH!
Find the area. You must show all work to receive credit. (10 points)
Figure ABCDEF is shown. A is located at negative 5, negative 8. B is located at 1, negative 8. C is located at 3, negative 5. D
The area of the figure is 51.4 unit²
The complete questionFigure ABCDEF is shown. A is located at 5, negative 8. B is located at 11, negative 8. C is located at 11, 0. D is located at 6
See attachment for the figure
The area of the figureThe figure can be divided into the following shapes:
Trapezoid 1: Opposite sides = (8 and 5) and height = 5Trapezoid 2: Opposite sides = (5 and 4.8) and height = 2Triangle: Base = 4.8 and height = 4The area of the trapezoid is:
Area = 0.5 * (Sum of opposite sides) * height
So, we have:
Trapezoid 1 = 0.5 * (8 + 5) * 5 = 32.5
Trapezoid 2 = 0.5 * (5 + 4.8) * 2 = 9.8
The area of the triangle is:
Area = 0.5 * Base * Height
This gives
Triangle = 0.5 * 4.8 * 4 = 9.6
Add the individual areas
Area = 32 + 9.8 + 9.6
Evaluate the sum
Area = 51.4
Hence, the area of the figure is 51.4 unit²
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Drag the tiles to the correct boxes to complete the pairs.
Match each radical equation with the corresponding value of x.
5√x^4=81
3√x^4= 625
3√x^5=32
4√x^3=64
The value of x for each radical equation is 243 , 125,8,256 respectively.
The correct question is attached as an image with the answer.
What is a Radical Equation ?
When in an equation the variable is under a radical it is called a Radical Equation.
It is given in the question that
which radical matches to the solution
[tex]\rm \sqrt[5]{x^4} = 81 \\\\\sqrt[3]{x^4} = 625\\\\\sqrt[3]{x^5} = 32\\\\ \sqrt[4]{x^3}=64[/tex]
[tex]\rm x^4 = 81^5\\x = 243[/tex]
[tex]\rm x^4 = 625^3\\x = 125\\[/tex]
[tex]x^5 = 32^3\\x = 8\\[/tex]
[tex]\rm x ^3 = 64^4\\x = 256[/tex]
Therefore for each radical the value of x is determined.
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Part 3 - Discussion/Explanation Question
In what ways can vertical, horizontal, and oblique asymptotes be identified? Use a mathematical example to
explain the ways.
Step-by-step explanation:
Vertical asymptote can be Identites if there is a factor only in the denominator. This means that the function will be infinitely discounted at that point.
For example,
[tex] \frac{1}{x - 5} [/tex]
Set the expression in the denominator equal to 0, because you can't divide by 0.
[tex]x - 5 = 0[/tex]
[tex]x = 5[/tex]
So the vertical asymptote is x=5.
Disclaimer if you see something like this
[tex] \frac{(x - 5)(x + 3)}{(x - 5)} [/tex]
x=5 won't be a vertical asymptote, it will be a hole because it in the numerator and denominator.
Horizontal:
If we have a function like this
[tex] \frac{1}{x} [/tex]
We can determine what happens to the y values as x gets bigger, as x gets bigger, we will get smaller answers for y values. The y values will get closer to 0 but never reach it.
Remember a constant can be represent by
[tex]a \times {x}^{0} [/tex]
For example,
[tex]1 = 1 \times {x}^{0} [/tex]
[tex]2 = 2 \times {x}^{0} [/tex]
And so on,
and
[tex]x = {x}^{1} [/tex]
So our equation is basically
[tex] \frac{1 \times {x}^{0} }{ {x}^{1} } [/tex]
Look at the degrees, since the numerator has a smaller degree than the denominator, the denominator will grow larger than the numerator as x gets larger, so since the larger number is the denominator, our y values will approach 0.
So anytime, the degree of the numerator < denominator, the horizontal asymptote is x=0.
Consider the function
[tex] \frac{3 {x}^{2} }{ {x}^{2} + 1} [/tex]
As x get larger, the only thing that will matter will be the leading coefficient of the leading degree term. So as x approach infinity and negative infinity, the horizontal asymptote will the numerator of the leading coefficient/ the leading coefficient of the denominator
So in this case,
[tex]x = \frac{3}{1} [/tex]
Finally, if the numerator has a greater degree than denominator, the value of horizontal asymptote will be larger and larger such there would be no horizontal asymptote instead of a oblique asymptote.
Lamar is considering two loans
Which loan will have the lowest total payback?
Answer:
Loan A will have the lowest total paycheck because the total of the principal than the same total for loan B
please answer will give brainly
Answer:
Step-by-step explanation:
The volume of a cube is given by the formula :
a³ (where a is the side length )
So now we have to cube these lengths :
Part A :
(3x²y)³ =
(3x²y)(3x²y)(3x²y) =
(9x^4y²)(3x²y) =
27x^6y³ (This is now fully simplified so our final answer for a)
Part B:
(5y²)³ =
(5y²)(5y²)(5y²) =
(25y^4)(5y²) =
125y^6 (This is now fully simplified so our final answer for b)
Hope this helped and have a good day
What does the expression n + 3 represent?
Answer:
Step-by-step explanation:
BASICALLY ANYTHING WITH 3
Given g(x)=^3√x+6, on what interval is the function negative?
A (-∞, -6)
B (-∞, 6)
C (-6, ∞)
D (6, ∞)
The interval which the function is negative is (-∞, -6)
How to determine the interval?The equation of the function is given as:
[tex]g(x) = \sqrt[3]{x + 6}[/tex]
When the function is negative.
It means that g(x) is less than 0
i.e. g(x) < 0
So, we have:
[tex]\sqrt[3]{x + 6} < 0[/tex]
Take the cube of both sides
x + 6 < 0
Subtract 6 from both sides
x < -6
The above represents a value from negative infinity to -6
i.e. (-∞, -6)
Hence, the interval which the function is negative is (-∞, -6)
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Can someone help me??
Answer:
9: 50
10: 90
11: 60
12: 25 and 115
13: 130 and 40
Thats all i can do, im sorry but i hope this helps ^^
Circle O has a radius of 5 centimeters and central angleAOB with a measure of 60°.
The arc length can be found using the formula, ∅ × r, which is: (5π)/3.
What is the Arc Length?Arc length = ∅ × r, where ∅ is the central angle in radians, and r is the radius of the circle.
Given the following:
∅ = 60° = 60° × π/180 (in radians)r = 5 cmLength of the arc = 60° × π/180 × 5 = (60 × π × 5)/180
Length of the arc = (300π)/180 = (5π)/3
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