Consider the following problem:
The length s(t) of the side of the base of a square prism is decreasing at a rate of 7
kilometers per minute and the height h(t) of the prism is increasing at a rate of 10
kilometers per minute. At a certain instant to, the base's side is 4 kilometers and the
height is 9 kilometers. What is the rate of change of the surface area A(t) of the
prism at that instant?
Match each expression with its given value.
Answers
The rate of change of the surface area A(t) of the prism is 136 kilometers per minute.
What does rate of change mean?
An indicator of how one quantity changes in proportion to another is called a rate of change. If x and y are the independent and dependent variables, respectively, then the rate of change is equal to y-to-x conversions. Positive or negative change rates are possible.
Surafce area of a prism is equal to
2(Area of base) + (perimeter of base)(height)
2b^2+4bh
[tex]S=2b^2+4bh[/tex]
[tex]\frac{ds}{dt}=4b\frac{db}{dt} + 4b\frac{db}{dt} + 4h\frac{db}{dt} \\[/tex]
It is given that db/dt= -7 and dh/dt -=10.
At a particular instant b= 4km, h=9 km.
Now we will substitute the values in this formula:
[tex]\frac{ds}{dt}=-4*4*7-4*4*7+ 4*9*10\\\frac{ds}{dt}=136[/tex]
The rate of change of the surface area A(t) of the prism is 136 kilometers per minute.
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Related Questions
Find the area of a regular hexagon with a side length of 10 cm
Answers
60 is my resultados of area
Answer
[tex]54 \sqrt{3} [/tex]
Step-by-step explanation:
Each interior angle is 120°for an hexagon.... Bisecting each will give an angle of 60° and thus dividing the hexagon into 6 equilateral triangles as the Bisecting lines meet at the centre of the hexagon. So find area of each equilateral triangle and multiply by 6
Area=
[tex] \frac{1}{2} b \times h \times 6 \\ = 3bh \\ = 3 \times 6 \times 3 \sqrt{3} [/tex]
[tex] = 54 \sqrt{3 } cm ^{2} [/tex]
answer fast and correct pls
Answers
Answer:
A
Step-by-step explanation:
A group of 30 people, 12 females and 18 males, are electing 5 representatives.
a. How many ways can the 5 representatives be chosen from the group?
b. How many ways can the 5 representatives be 2 males and 3 females?
c. What is the probability that the representatives end up being 2 males and 3 females if they are randomly selected? Enter your answer as a decimal rounded to the nearest thousandth. (3 decimal places).
Answers
Answer:
Total number = 30Number of females = 12Number of males = 18a) Combination of 5 out of 30:
30C5 = 30!/[5!*(30 - 5)!] = 142506b) Combination of 2 males:
18C2 = 18!/[2!*(18 - 2)!] = 153Combination of 3 females:
12C3 = 12!/[3!*(12 - 3)!] = 220The number of ways with 2 males and 3 females:
153*220 = 33660c) Required probability is:
P(2 males and 3 females) = 33660 / 142506 = 0.236I need help with this question ASAP please.
Answers
[tex]arc \ length = 2\pi r \frac{\theta}{360} = \\\\[/tex][tex]2 \pi *9 * \frac{135}{360} =21.205[/tex]
[tex]\frac{3\pi }{4} =\frac{3*180}{4}=135[/tex]
Is a student takes out a $750 loan at 4% interest, how much interest is paid back in 60 days
Answers
Answer:
754.93 in total with an increase of 4.93
Step-by-step explanation:
What is the lateral surface area, in square inches, of the figure formed by the net?
Answers
Answer:
71 in²
Step-by-step explanation:
surface area = (4×6)+(2×½×4×5)+(2×½×6×4.5)
= 24+20+27 = 71 in²
5 pizzas cost £35.00. How much do 3 pizzas cost?
Answers
Answer:£21.00
Step-by-step explanation:
One pizza: (£35/5) =£7
Three pizza's: (£7x3)=£21
Find the reference angle for 342°.
Answers
Answer:
18 degree
Step-by-step explanation:
Raj was getting a 5% commission, but now he's getting 6.5%. How much more money will he make on $24,000 of sales than on his old commission?
Answers
If Raj was getting a 5% commission, he would make 24000 * 5% = $<<240005.01=1200>>1200 on $24,000 of sales.
If he is now getting a 6.5% commission, he will make 24000 * 6.5% = $<<240006.5.01=1560>>1560 on $24,000 of sales.
Thus, Raj will make 1560 - 1200 = $<<1560-1200=360>>360 more on $24,000 of sales with his new commission rate of 6.5% than he did with his old commission rate of 5%.
Peter is building a ramp at his home. He wants to build it 11 inches high with aa 60 inch base. How long will the ramp be that Peter is building? Round to the 10ths if needed.
Answers
Explanation:
You have a right triangle with legs of 11 and 60. The hypotenuse is unknown.
Use the pythagorean theorem to find the hypotenuse.
[tex]a^2 + b^2 = c^2\\\\11^2 + 60^2 = c^2\\\\121 + 3600 = c^2\\\\3721 = c^2\\\\c^2 = 3721\\\\c = \sqrt{3721}\\\\c = 61\\\\[/tex]
The ramp is exactly 61 inches long.
A doctor gives 10 patients Drug A and 10 patients Drug B and records the differences. Is this an observation, survey, experiment, or simulation?
Answers
The given drug experiment is an example of observation.
What are the types of statistical studies worksheet?There are three major types of statistical studies :
observational studiessurveysexperiments.Given is that a doctor gives 10 patients Drug A and 10 patients Drug B and records the differences.
Giving 10 patients Drug A and 10 patients Drug B and then recording the differences is an example of observation.
Therefore, the given drug experiment is an example of observation.
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What is the equation of the line that passes through the point (6,-5) and has a
slope of 1/3?
Answers
Answer:
y = 1/3x - 7
Step-by-step explanation:
start with the point-slope form:
(y-y1) = m(x-x1)
substitute the values of (x,y) into the formula:
(y-(-5)) = 1/3(x-6)
y+5 = 1/3x - 2
now write in slope-intercept form:
y = 1/3x - 2 - 5
y = 1/3x - 7
I need help with this ASAP
Answers
Given:
Radius of the circle = 6 inches
Central angle = 75 degrees.
To find:
The length of subtended arc, i.e., x.
Solution:
The formula for arc length is:
[tex]s=2\pi r\times \dfrac{\theta}{360^\circ}[/tex]
Where, r is the radius and [tex]\theta [/tex] is the central angle.
Putting [tex]s=x, r=6, \pi=3.14, \theta =75^\circ[/tex] in the above formula, we get
[tex]x=2(3.14)(6)\times \dfrac{75^\circ}{360^\circ}[/tex]
[tex]x=2(3.14)(6)\times \dfrac{5}{24}[/tex]
[tex]x=7.85[/tex]
[tex]x\approx 7.9[/tex]
Therefore, the value of x is 7.9 inches.
Answer:Radius of the circle = 6 inchesCentral angle = 75 degrees.
Step-by-step explanation:
Let f(x) = x ^ 3 - x ^ 2 - 5x - 3 and g(x) = x + 3 3. Find (f/g)(x) . a .) x ^ 2 - 4x + 7R - 24
b .) x ^ 2 - 4x + 7
C.) x ^ 2 - 4x - 7R - 24
d.) x ^ 2 - 4x + 7x
Answers
Answer:
[tex](\frac{f}{g})(x) = \frac{\left(x+1\right)^2\left(x-3\right)}{x + 3}[/tex]
Step-by-step explanation:
The question is not properly formatted.
Given
[tex]f(x) = x^3 - x^2 - 5x - 3[/tex]
[tex]g(x) =x + 3[/tex]
Required
[tex](\frac{f}{g})(x)[/tex]
This is calculated as:
[tex](\frac{f}{g})(x) = \frac{f(x)}{g(x)}[/tex]
So, we have:
[tex](\frac{f}{g})(x) = \frac{x^3 - x^2 - 5x - 3}{x + 3}[/tex]
Factorize the numerator: using a calculator
[tex](\frac{f}{g})(x) = \frac{\left(x+1\right)^2\left(x-3\right)}{x + 3}[/tex]
Does the equation y = 5(2.3)* model exponential growth, exponential decay or neither?
Answers
Answer:
It models exponential growth
Step-by-step explanation:
Use the formula f(x)=a(1+r)^x where r is the growth rate, a is the principal value, and x is the length of time.
Since r would be equal to 2.3-1=1.3, this means a growth rate of 130%, which means the model models exponential growth since r>1.
help me pls i ghave the first bit odne
Answers
Answer:
1 = 24 degrees
2 = 156 degrees
Step-by-step explanation:
Solve the equation for x:
x - 15 +4x = 180
5x = 195
x = 39
so 1 = (39-15) = 24 degrees
so 2 = (4x39) = 156 degrees
Latoya's Coffee Shop makes a blend that is a mixture of coffee types A and B. In one bag of the blend, there are 6 kilograms of type A. Four bags of the blend are a total of 36 kilograms. How many kilograms of type B are there in one bag?
Answers
The Kilograms of type B that are in one bag of the Latoya's Coffee shop blend would be = 3kg
What is a mixture?A mixture is defined as the combination of two or more components which can or cannot be separated by ordinary methods.
The coffee blend of LaToya shop = Type A and B
A bag of the coffee blend = 6kg of Type A.
4 bags of coffee blend = 36kg
Therefore 4 bags of coffee blend contains = 6 see×4 = 24 kg of Type A
Type B in each bag = 36 - 24 = 12/4 = 3kg.
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Two numbers are in the ratio 5 : 7. If they differ by 18 then, find the numbers.
Answers
Answer:
45 and 63
Step-by-step explanation:
7x-5x=18
2x=18
2 2
x=9
7(9)=63
5(9)=45
15 x 109 is how many times greater than 5 x 103?
Enter the answer using scientific notation
Answers
The number of times 5×10³ greater than 15×10⁹ is 3×10⁶.
What is scientific notation?Scientific notation is a method for expressing a given quantity as a number having significant digits necessary for a specified degree of accuracy, multiplied by 10 to the appropriate power such as 1.56×10⁷.
Given that, 15×10⁹ and 5×10³.
Number of times 5×10³ greater than 15×10⁹ is
Now, 15×10⁹/5×10³
= 3×10⁶
Therefore, 3×10⁶ times 5×10³ greater than 15×10⁹.
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Sean bakes 18 dozen chocolate cupcakes and 13 dozen vanilla cupcakes. About how many cupcakes did Sean bake? EXPLAIN now!!!
Answers
Sean baked 372 cupcakes in total.
What is multiplication?Multiplication is a mathematical arithmetic operation. It is also a process of adding the same types of expression for some number of times.
Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.
Given:
Sean bakes 18 dozen chocolate cupcakes,
and 13 dozen vanilla cupcakes.
There are 12 cupcakes in one dozen.
To find the number of cupcakes:
Using multiplication operation,
18 x 12 = 216.
13 x 12 = 156.
The number of cupcakes = number of chocolate cupcakes + number of vanilla cupcakes.
The number of cupcakes = 216 + 156
The number of cupcakes = 372
Therefore, the number of cupcakes are 372.
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1. Convert the following improper fractions to mixed numbers; a. 55
2
b. 43 3
2. Convert the following mixed numbers to improper fractions; a. 72
5
b. 121 2
[1]
[1]
[1]
Answers
7½
7×2+1/2
14+1/2
15/2
212½
12×2+1/2
24+1/2
25/2
Find the surface area of the cylinder.
13 m
20 m
Answers
Answer:
2695.49 m
Step-by-step explanation:
A = 2πrh + 2πr2
2 · π · 13 · 20 + 2 · π · 132
2695.4865
whitch lines are perpendicular??
Answers
Answer:
A
Step-by-step explanation:
multiple lines meeting at 90 degrees. hope this helped
Jocelyn has a collection of 100 coins. How many coins represent 25% of her collection?
Answers
25 coins represent 25 percent of Jocelyn's collection.
What is the percentage?A percentage is a quantity or ratio that, in mathematics, represents a portion of one hundred. A dimensionless relationship between two numbers can be represented in a variety of ways, such as through ratios, fractions, and decimals. The symbol "%" is frequently written after the number to indicate percentages.
given, Jocelyn has a collection of 100 coins.
100% of her collection represents = 100 coins
1 % of her collection represents = 100/100 coins
1% of her collection represents = 1 coin
thus,
25% of her collection represents = 1*25 coins
25% of her collection represents = 25 coins
therefore, 25 percent of the collection of Jocelyn represents 25 coins.
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There is a 3 out of 20 chance that you can win a game. How many "wins" would you predict if you played the game 50 times? (NO LINKS OR FILE PLEASE, I WILL REPORT)
A 3
B 6
C 17
D 8
Answers
Answer:
D. 8
Step-by-step explanation:
set up a proportion
3/20 = x/50
to get from 20 to 50 you have to multiply by 2.5
so multiply the top number (3) by 2.5 to find x
this comes out to 7.5 which you then round up to 8
Answer:
D
Step-by-step explanation:
Please help with this math problem if You don’t give me a file link I will mark you brainlist!!
WXYZ is dilated by a scale factor of 3. The length of W'X'Y'Z' is ____
units, and the width is____
units.
Answers
Answer:
18, 12
Step-by-step explanation:
Assuming this is follow-up from the previous question you asked? If not, I apologize for misunderstanding.
Dilation factor by 3 is bigger than 1 = Expansion
Originally 6, 4
6*3 = 18
4*3 = 12
Answer:
18,12
Step-by-step explanation:
W (1, -2), X (7,-2), Y (7,-6), and Z (1, -6).
To dilate the shape, multiply it's coordinates by the scale factor.
W'(3,-6), X'(21,-6), Y'(21,-18), Z(3, -18)
The distance formula: [tex]d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}[/tex]
plug W'(3,-6) and X'(21,-6) in to get the length
[tex]\sqrt{(3-21)^2+(-6-(-6))^2}=\sqrt{(-18)^2 +0^2}=\sqrt{324} =18[/tex]
plug X(21,-6) and Y(21,-18) to get the width
[tex]\sqrt{(7-7)^2+(-2-(-6))^2}=\sqrt{0^2 +4^2}=\sqrt{16} =4[/tex]
[tex]\sqrt{(21-21)^2+(-6-(-18))^2}=\sqrt{0^2 +12^2}=\sqrt{144} =12[/tex]
Show your work please help
Answers
The error in the work lies in line 3 where the square root is calculated inaccurately.
What is square root of a number?The opposite of squaring an integer is finding its square root. The square root of a number can be found by looking for a number that, when squared, yields the original value.
The error is in line 3, line 4 and line 5.
The error in line 3 is inaccurate calculation of the value of square root of 4.
The error in line 4 is a mathematical calculation error.
The error in line 5 is a mathematical calculation error.
The correct answer in Line 3 is:
[tex]6 * 2 *\sqrt{5} -3\sqrt{5}[/tex]
The correct answer in Line 4 is:
[tex]12\sqrt{5} - 3\sqrt{5}[/tex]
The correct answer in Line 5 is:
[tex]9\sqrt{5}[/tex]
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Solve for p if L = 2 1/2 ft and W = 3 2/5 ft. P = 2L + 2W
Answers
Answer:
P = 59/5
Step-by-step explanation:
b) 6q + 4-q + 5 simplify
Answers
Answer:
5q + 9
Hope that helps! :)
-Aphrodite
Step-by-step explanation:
The prism below is made of cubes which measure 1/3 of an inch on one side what is the volume
Answers
Answer:
Volume of rectangular prism = 10/9 inch³
Step-by-step explanation:
Given:
Size of each cube = 1/3 inch
Find:
Volume of rectangular prism
Computation:
Length of rectangular prism = 2 x [1/3]
Length of rectangular prism = 2/3 inch
Width of rectangular prism = 3 x [1/3]
Width of rectangular prism = 3/3
Width of rectangular prism = 1 inch
Height of rectangular prism = 5 x [1/3]
Height of rectangular prism = 5/3 inch
Volume of rectangular prism = Length x Width X Height
Volume of rectangular prism = [2/3] x [1] x [5/3]
Volume of rectangular prism = 10/9 inch³