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 surface area is 524.02 square kilometers per minutes.
what is surface area of square prism?The total space occupied by a three-dimensional square prism is called surface area.
What is the rate of change of surface area of the prism?
Given, the decreasing rate of the base side with respect to time, ds/dt = 7 km/min
the increasing rate of height with respect to time, dh/dt = 10 km/min
At a time, t, base side, s = 4 km
and height, h = 9 km
we need to determine the rate of change of surface area with respect to time, d A/dt
from the differentiation chain rule, d A/ dt = d A /dt × ds /ds
d A /dt = d A/ ds × ds /dt ... equation 1
we know that the surface area for prism, A = 2s² + 4sh
if we differentiate with respect to s then we find d A /ds
d/ds (A) = d/ ds (2s² + 4sh)
d A /ds = 4s + 4h +4s dh/ds ...... equation 2
now dh /ds = dh /ds × dt /dt [ using differentiation chain rule]
dh/ds = dh/ dt× dt/ds
d h/ ds = dh/dt × 1/ ds/dt
it stated earlier that dh/ dt = 10 and ds /dt = 7
dh / ds = 10/7
putting this value in equation 2, we get
d A /ds = 4s +4h + 4s ×10/7
as we know at time t, s= 4 and h = 9
d A /ds = 4 × 4 + 4 ×9 +4×4 ×10 /7
d A /ds = 74.86
putting the value d A /ds in equation 1, we get
d A /dt = d A /ds × ds/ dt
d A/ dt = 74.86 × 7
d A /dt = 524.02 km² / min
hence, the rate of change of surface area = 524.02 square kilometers per minutes
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Related Questions
Use the diagram to solve 3 ÷ 1/6
Answers
Answer:
A. 1/18
Step-by-step explanation:
PLEASE HELP
A fly makes a bee-line from one corner of Mrs. Tomasi's room
to the opposite corner. The room is 30x 32 feet and 9 feet tall.
What angle is the angle of elevation of the flight path if he flies
straight there?
Answers
The angle of elevation of the fly's flight path is approximately 57.74 degrees.
What is hypotenuse?In a right triangle, the hypotenuse is the side opposite the right angle. It is always the longest side of the triangle and is the side opposite to the 90 degrees angle. It is also the side that forms the "hypotenuse" of the right triangle.
What is Pythagorean theorem?The Pythagorean theorem is a fundamental result in Euclidean geometry that states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. It can be written as c^2 = a^2 + b^2, where a and b are the legs of the triangle and c is the hypotenuse. This theorem can be used to find the length of the hypotenuse of a right triangle when the lengths of the other two sides are known.
Let's call the angle we're trying to find "theta". The horizontal distance is 30 feet, the vertical distance is 32 feet and the height is 9 feet.
Using pythagorean theorem:
$c^2 = a^2 + b^2$
$c = \sqrt{30^2 + 32^2}$ = $\sqrt{900 + 1024}$ = $\sqrt{1924}$
Now we can use the tangent function:
$\tan(\theta) = \frac{opposite}{adjacent} = \frac{32}{30}$
Now we can find the angle, theta, by using the inverse tangent function:
$\theta = \tan^{-1}(\frac{32}{30})$
The angle of elevation of the fly's flight path is approximately 57.74 degrees.
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Rick claims that the equation
×2 + 5x + 9 = 0 has no solution. Jenny claims that there are two solutions. Explain how Rick could be correct, and explain how Jenny could be correct.
Answers
Answer: Both Rick and Jenny could be correct because we do not know what "x" is.
Step-by-step explanation:
The purpose of the variable "x" is to substitute it for an unknown number. Since we do not know what "x" is we can not solve the equation. We can only add like terms.
I hope this helps :)
Find the surface area of the sphere.
Formulas for Spheres
S.A. = 4
V = for S.A. = [?] cm2
Round to the nearest tenth.
PLEASE HELP !
links will be reported.
Answers
Answer:
201.1 cm ^2 ( in
acellus )
Step-by-step explanation:
The surface area the sphere is 64π cm².
SphereA sphere is a three-dimensional equivalent of a two-dimensional circle. A sphere is a collection of points in three-dimensional space that are all the same distance r from a particular point. hat given point is the center of the sphere, and r is the sphere's radius
Surface area: 4πr²
How to determine the surface area of the sphere?Given the radius of the sphere is 4 cm.
then apply the formula
surface area = 4π(4)²
= 4π(16)
= 64π cm²
Hence the surface area is 64π cm².
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156x2.2=?????Help fast
Answers
Answer:
343.2
Step-by-step explanation:
156 × 2.2
= (156 × 22)/10
= 3432/10
= 343.2
Find the mean, median, and mode for the data set below.
weights of books (oz): 10 9 9 14 13 11
Answers
Answer:
Mean: 11
Median: 10.5
Mode: 9
Brielle entered a contest at work that awards prizes to individuals who walk 10,000 steps a day. On the first day of the contest, Brielle checks her Fitbit at 12:00 PM and sees that she has already completed of the goal. How many steps has Brielle already walked at 12:00 PM? 3/8
Answers
Answer:
3750
I wish you luck in your assignments.
Write and solve the inequality that represents
is greater than or equal to the product of 2 and a number.
5
3
Answers
The following is the proper response to this problem's inequality. The relationship between negative one fifth and negative two thirds is higher than or equal when y is bigger than or equal to three tenths.
what is inequality ?In mathematics, an inequality is a link between two expressions or values that is not equal. Thus, inequality arises as a result of imbalance. An inequality in mathematics describes the connection between two values that are not equal. Many simple inequalities can be eliminated by modifying both sides until just the variables are left. However, a number of things lead to inequality: On both sides, divide or add negative values. Toggle between left and right.
Given
One fifth less is -1/5.
When a negative two thirds is added to a number, the result is -2/3x. Since the value is unknown, we refer to it as x.
The following is the sign for more than or equal inequality:
The inequality is therefore: -1/5 -2/3x.
So that it will be easier for us to isolate x:
2/3x ≥ 1/5
2x ≥ 3/5
x ≥ 3/10.
Since y is more than or equal to three tenths, the right answer for the inequality is: negative one fifth is greater than or equal to negative two thirds y.
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A cone with a radius of 6 cm has a volume of 1200 cm3. What is the height of the cone? (The volume of a cone is given by the formula V = 7er A) 8 cm B) 10 cm 12 cm D) 15 cm
Answers
Answer:
31.8 cmStep-by-step explanation:
Volume of a cone:
V = 1/3πr²hWe have:
V = 1200 cm³r = 6 cmh = ?Substitute values and solve for h:
1200 = 1/3*3.14*6²h1200 = 37.68hh = 1200/37.68h = 31.8 cm (rounded)None of the choices is correct
1 + 2 + 4 + 8..., n= 7
evaluate the geometric series
Answers
Answer:
The ratio is 2
Step-by-step explanation:
The last value should be 64.
1 * 2 = 2
2 * 2 = 4
4 * 2 = 8
8 * 2 = 16
16 * 2 = 32
32 * 2 = 64
A rope 15 inches long has been divided into the greatest possible number of pieces in such a way that each piece has a different length, and each of these lengths in inches is expressed by a whole number. How many cuts were made?
A.3
B.4
C.5
D.6
E.7
Answers
Answer:
Below
Step-by-step explanation:
1+2+3+4+5 =15 5 lengths will require 4 cuts
18.
M is the midpoint of WX and
YZ. Is YW = ZX? Why?
W
M
Answers
Reasoning:
Because point M is the midpoint of segments WX and YZ, segments YM≅ZM and WM≅XM by the definition of a midpoint. Furthermore, ∠YMW≅∠ZMX by the Vertical Angles Theorem. Because we have a pair of corresponding, congruent sides, a pair of the included corresponding,congruent angles, and another pair of corresponding, congruent sides, the Side-Angle-Side Congruence Postulate can be used. By SAS, △YMW≅△ZMX. By CPCTC, segments YW≅ZX.
r + (-4) = 7 solve for r
Answers
Answer:
11
Step-by-step explanation:
Add 4 to both sides to get rid of -4 or if you want think of it as moving -4 to the other side and turning it into positive if its negative and negative if its positive
r=11
Tyler is 30 years younger than Naeste 9years ago
Answers
Answer:
i dont understand this question but i think maybe 21
Step-by-step explanation:
30-9 =21
Answer:
21
Step-by-step explanation:
PLZ HELPPPPPPPP
When y=4x-6 find y if x=o
Answers
learning task 2: pls help
Answers
Answer:
96=2(2x+x)24=3x[tex] \frac{2}{3} x = 72[/tex]x+(x+1)=294(x+8)=54Please!! What is the slope of each line?
Are they the same or different?
Answers
Given:
The graph of two lines.
To find:
The slope of each line and check whether they are same or different.
Solution:
If a line passes through two points, then the slope of a line is:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
From the graph 1, it is clear that the line passes through the points (2,175) and (3,165). So, the slope of first line is:
[tex]m_1=\dfrac{175-165}{3-2}[/tex]
[tex]m_1=\dfrac{10}{1}[/tex]
[tex]m_1=10[/tex]
The slope of first line is 10.
From the graph 2, it is clear that the line passes through the points (1,175) and (2,165). So, the slope of first line is:
[tex]m_2=\dfrac{175-165}{2-1}[/tex]
[tex]m_2=\dfrac{10}{1}[/tex]
[tex]m_2=10[/tex]
The slope of second line is 10.
[tex]m_1=m_2[/tex]
Therefore, the slopes of both lines are same, i.e. 10.
There are 10 boys in Mr. Lee's class. If 40% of the class are boys, which is the total number of students in Mr. Lee's class?
Answers
Answer:
25
Step-by-step explanation:
2.5 =10%
2.5*4= 10
2.5*6=15
Answer:
25
Step-by-step explanation:
Using P=(%)w we can substitute the values. First, I will define the variables. P = part (is), % = percent, w = whole (of)
10 = (40%)w
The reason for this is because 10 is a PART and 40% is a PERCENT and we are solving for the unknown WHOLE. We now divide 10 by 0.40 because to convert a percent to a decimal you just move the point two places to the left:)
10 divided by 0.4 = 25. So, there is a total of 25 students in Mr. Lee's class. Now, we can check this by multiplying 25 and 0.4 to get 10! It is in fact correct.
PLEASE READ PRACTICE AND UNDERSTAND! DO NOT JUST TAKE THE ANSWER. KNOWLEDGE IS POWER :^)
Reasoning Freezer A has interior dimensions 21x21x4 it and sells for $349.99. Freezer B has
interior dimensions 2.5 1x2.5 ftx3 it and sells for $449.99. Which freezer is a better buy in terms
of dollars per cubic foot? Use pencil and paper. Show your work and explain your reasoning
Which freezer is the bemer buy?
Freezer A
Preezers
Answers
Answer:
A
Step-by-step explanation:
Write the coordinates of the vertices after a translation 2 units left and 5 units down. B(0,2). C(9-1) D(9,4) E(0,4)
Answers
Answer:
B'(-2, -3)
C'(7, -6)
D'(7, -1)
E'(-2, -1)
Step-by-step explanation:
When you move translate a coordinate horizontally, if it is to the left, you subtract the x value with how many units you move, and if its to the right, you add however many units you move to the x-value. and when you move vertically, if you move down, subtract the amount of units you moved from the y-value, and if you move up, add however many units you moved to the y-value.
A family made three trips to the grocery store in one month. What was the total amount of money spent on groceries for the month?
Answers
Answer:
Step-by-step explanation:
So, first they spend $100
The next week, they spend 20% less than $100, so they spent $80 that week.
The 3rd week, they spend 3/4 of $80, so they spend $60 that week.
Finally, we add the spent money from the 3 weeks (100 + 80 + 60) and get $240. I hope this helps!
Rewrite the following equation in slope-intercept form. 17x + y = –19
Answers
Answer: y = 17x - 19
Step-by-step explanation:
17x + y = -19
Subtract 17 on both sides
Y= -19 - 17x
Then put it in y= mx + b
Y= -17x - 19
Answer:
y = -17x -19
Step-by-step explanation:
Slope intercept form is
y = mx+b where m is the slope and b is the y intercept
17x+y = -19
Solve for y
y = -17x -19
-11 2/3 x (-4 1/5) =?
Solve.
Answers
Answer:
[tex]44 \frac{2}{15} [/tex]
Choose all the pairs of fractions that are equivalent.
Answers
B and E Thank you for asking I'm good at fractions!!
IMPORTANT
Answer the two questions below please. Will wants to buy a new TV for $900. What is the minimum payment that she must pay each month to avoid paying interest on her credit card?
Answers
TRUE OR FALSES
No irrational numbers are integers.
All whole numbers are irrational numbers.
Some whole numbers are not rational numbers.
Some rational numbers are not whole numbers.
Answers
9514 1404 393
Answer:
T, F, F, T
Step-by-step explanation:
No irrational numbers are integers.
All integers are rational numbers. By definition, an irrational number is not a rational number. So it must be true that an irrational cannot be an integer.All whole numbers are irrational numbers.
Every whole number can be expressed as the ratio of two integers, hence is not an irrational number. The offered statement is false.Some whole numbers are not rational numbers.
Every whole number is rational. The offered statement is false.Some rational numbers are not whole numbers.
A reduced ratio of two integers with some number other than 1 in the denominator will not be a whole number. For example, 9/8 is not a whole number. The offered statement is true.Help againnnnnnnnnnnnnnnnnnnnnnnnn
Answers
Answer:
10 inchesStep-by-step explanation:
Hypotenuse = h
h^2 = 8^2 + 6^2
h^2 = 64 + 36
h^2 = 100
h = √100
h = 10
Hope that helps! :)
-Aphrodite
y-5=-7/3(x-3) in standard form
Answers
Answer: The equation Y-5 = -7/3(X-3) in standard form is:
3Y - 15 = -7X + 21
Step-by-step explanation:
x divided by 6 is what
Answers
Answer:x/6
Step-by-step explanation:
Here the value of x is not given and hence the answer to the question is
x/6
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19,22,25,28 the 11nth term
Answers
Answer:
31 hecause the èattern is adding 3
Step-by-step explanation: