Using implicit differentiation, it is found that the rate of change is of the width is of -3 feet/min.
What is the area of a rectangle?The area of a rectangle of length l and height h is given by:
[tex]A = lh[/tex]
Applying implicit differentiation, the rate of change is given by:
[tex]\frac{dA}{dt} = l\frac{dh}{dt} + h\frac{dl}{dt}[/tex]
In this problem, we have that:
The area is constant, hence [tex]\frac{dA}{dt} = 0[/tex].Area of 2 square feet, height of 2 feet, hence [tex]h = 2, lh = 2 \rightarrow l = 1[/tex].The height is changing at a rate of 6 feet/minute, hence [tex]\frac{dh}{dt} = 6[/tex].Then:
[tex]\frac{dA}{dt} = l\frac{dh}{dt} + h\frac{dl}{dt}[/tex]
[tex]0 = 6 + 2\frac{dl}{dt}[/tex]
[tex]2\frac{dl}{dt} = -6[/tex]
[tex]\frac{dl}{dt} = -3[/tex]
The rate of change is of the width is of -3 feet/min.
To learn more about implicit differentiation, you can take a look at https://brainly.com/question/25608353
someone plzz help me i don't know if its right I'm lost out of time
Answer:
12. 30
13. 3
Step-by-step explanation:
PLZ HELP AND IF U TAKE MY POINTS I WILL REPORT U AN WHO EVER HELPS I WIL GIVE BRAINIEST
Answer:
the second one I can't give a explanation cause my wrist is broken so it's harder to type hope this helps
Help plz!
The Corresponding Angles Conjecture states that if two
parallel lines are cut by a transversal, the corresponding
angles are congruent. The picture below shows this
relationship
Answer:
B
Step-by-step explanation:
Corresponding angles form a sideways U when you connect the angles.
b is the only one that does that.
1 and 4 are consecutive angles.
1 and 3 are vertical angles
4 and 3 are linear pair angles.
find the surface area of the triangular prism
Answer:
608 ft²
Step-by-step explanation:
1) Find the area of the bases
[tex]A=\frac{1}{2} bh[/tex] where b is the base length and h is the height
Plug in b and h
[tex]A=\frac{1}{2} (12)(8)\\A=48[/tex]
Multiply the answer by 2 (because there are 2 bases)
A=96
Therefore, the area of the two bases is 96 ft².
2) Find the area of the two sides facing up
[tex]A=lw[/tex] where l is the length and w is the width
Plug in l and w
[tex]A=10*16\\A=160[/tex]
Multiply the answer by 2 (because there are 2 sides)
A=320
Therefore, the area of these two sides is 320 ft².
3) Find the area of the bottom side
[tex]A=lw[/tex] where l is the length and w is the width
Plug in l and w
[tex]A=12*16\\A=192[/tex]
Therefore, the area of this side is 192 ft².
4) Add all the areas together
96 ft² + 320 ft² + 192 ft²
= 608 ft²
Therefore, the surface area of the triangular prism is 608 ft².
I hope this helps!
Answer:
608
Step-by-step explanation:
first off you have to find the area of the base
the base is 16 by 12 feet.
so you multiply them and you get
16*12=192 you will have to come back later for this number
next, you find the two outsides of the triangular prism.
they are 10 by 16
10*16=160 and there are two of them so you double it and get 320
now save the 320 too with the 192
now we are going to find the triangles
the formula for an area of a triangle is A=1/2h*w
so we plug in the height which is 8 and the width which is 12
A=1/2(8)*(12)
Simplify
A=48 once again there are two of them so we double it to make it 96
now take all your saved numbers and add them all up
96+320+192
this should give you an answer of 608
hope this helps! have a nice day:)
Lydia is an architect. She has to design a courtyard garden inside a new hotel. On her blueprint, which is 1/20 the size of the actual garden, the width of the garden is 36 inches. What is the width of the actual garden?
Answer:
720 inches
Step-by-step explanation:
On her blueprint, which is 1/20 the size of the actual garden
the width of the garden is 36 inches.
What is the width of the actual garden?
Let width of the actual garden = x
1/20 of x = 36
1/20 * x = 36
x = 36 ÷ 1/20
x = 36 * 20/1
x = 720
x = 720 inches
The width of the actual garden = 720 inches
The area of a rectangle is 48x®y7
square yards. If the length of the
rectangle is 6x2y4 yards, which
expression represents the width of the
rectangle in yards?
A. 42x4y3
B. 42x6y3
C. 8x4y3
D. 8x6y3
Answer:
D
Step-by-step explanation:
Remember, area equals width x height so you can set up this equation.
[tex]48x^8y^7=6x^2y^4 * w[/tex]
Solving for w,
[tex]\frac{48x^8y^7}{6x^2y^4} =w[/tex]
Simplifying,
[tex]8x^6y^3[/tex]
Thus, D is the answer
Which of these is the best approximation of
5
to the nearest hundredth?
OA) 0.17
OB) 0.75
OC) 0.83
OD) 1.20
Answer:
oc)0.83
Step-by-step explanation:
have a good day!!!
(Help pls) When ayden mom drives to the gas station is the level in her gas tank increasing,decreasing,constant.
Answer:
Decreasing
Step-by-step explanation:
It is decreasing because it is being used.
Have a good day!!
Wich graph matches the equition x=5
Answer:
option 1
Step-by-step explanation:
do i need to?
Find f(5) for f(x)=1/4 (2)^x
f(5) = 1/4(2)^5
f(5) = 1/4 (32)
f(5) = 8
answer
A. 8
Which of the following units are units of volume? Select all that apply.
Answer:
we have these we ml and l
Step-by-step explanation:
Here, we want to select the units of volume ;
1. mg
This is a measure of mass and in fact it is called milligrams
2. mm
This is called millimeters and in fact is a measure of distance
3. cm
This is centimeters and it is a measure of distance too
4. ml
Milliliters, this is a measure of volume
5. m
meters;
this is a measure of distance
6. g
grammes
This is a measure of mass
7. l
This is liters
It is actually a measure of volume
8. km
this is kilometers, it is a measure of distance
what is the product of 3/7 and 3/8?
Answer:
9/56
Step-by-step explanation:
..................
WHat is the answer to number 2
Answer:
My best guess C im pretty sure.
Add: 2 2/3 + 3 1/12 PLEASE HURRY IM TIMED AND I WILL BE GROUNDED IF I FAIL BECAUSE I FAILED LAST TIME SO PLEASE HURRY AND HELP MEEEEE
Answer: 23/4 is you answer!!
Step-by-step explanation:
Answer: 5 3/4
Step-by-step explanation: I put them in the same denominator to add them
In a exam 90% students passed.if 15 students failed,find the number of students appeared in the examination?
Answer:
150
Step-by-step explanation:
10%=15
100%=150
15 x 10=150
to check find 90% of 150 which is 135
150-135=15
A Y U D E N P O R F A :(
Answer:
x=2
Step-by-step explanation:
Primero, necesitamos calcular <<a>>
Sabemos que AD=BC y AB=CD porque lados opuestos congruentes
Entonces, vamos a calcular <<a>>.
Usamos AD y BC
2a-1=4a-15
suma 15 a ambos lados
2a+14=4
añada 2 en ambos lados
14=2a
divida
7=a
Ahora, usamos esta información para calcular <<x>>
Usamos CD=AB
2a-8=4x-2
pero sabemos que <<a>> es 7
entonces:
14-8=4x-2
6=4x-2
8=4x
2=x
<<x>> es 2
(¡lo siento mi español no es perfecto!
SnackTime Foods produced 24,200,000 grams of popcorn last year, which was placed in 11-
gram bags. How many bags did the company fill?
bags
Hurry and plsssss
Answer:
2,200,000 :) give brainliest
Step-by-step explanation:
Will mark brainliest and give thirteen points explanation
Answer:
geyser =groundwater
glacier = freshwater
lake=freshwater
ocean=salt water
Step-by-step explanation:
i don’t understand how to do this and i need help!!
Answer:
x = 26
Step-by-step explanation:
6x + 6x + (x-2) + (x-2) = 360
14x - 4 = 360
14x = 364
x = 26
6(26) = 156
(26 - 2) = 24
answer the question please
Answer:
sin cos
Step-by-step explanation:
Answer:
hi my dear this is something which i use to remember if to use sin cos or tan u can try it i hope u get the answers
how 2 do?
(n)(n+7)(n+8)
Answer:
[tex]n^{3} + 15n^{2} + 56n[/tex]
Step-by-step explanation:
First FOIL (n + 7)(n + 8) and then distribute n
(n + 7)(n + 8) = [tex]n^{2} +15n + 56[/tex]
n ([tex]n^{2} +15n + 56[/tex])
= [tex]n^{3} + 15n^{2} + 56n[/tex]
Camden is deciding between two parking garages. Garage A charges an initial fee of
$12 to park plus $4 per hour. Garage B charges an initial fee of $8 to park plus $5 per
hour. Let A represent the amount Garage A would charge if Camden parks for t
hours, and let B represent the amount Garage B would charge if Camden parks for t
hours. Write an equation for each situation, in terms of t, and determine the hours
parked, t, that would make the cost of each garage the same.
Answer:
4 hours
Step-by-step explanation:
A = 12 + 4t
B = 8 + 5t
12 + 4t = 8 + 5t
t = 4
The cost of each garage would be the same when Camden parked the car for 4 hours
If a =3, b = 2 and c = 5, solve the following algebraic expressions: (3 marks)
a) 3c + 5 - b
b) b(4 - 2) + c
c) 4a - (2c)
Answer:
A) 18
B)9
C)-2
Step-by-step explanation:
Replace the a,b or c with the give number. So let’s say it’s says 2 + a. It would be 2+3.
The cost of the circular carpet, $C, varies as the square of the radius,
r metres. If C = 200 when r= 2
Find the cost of the circular carpet when r= 3
Answer:
$450
Step-by-step explanation:
C = k[tex]r^{2}[/tex]
200 = k([tex]2^{2}[/tex]) = 4k
k = 50
C = 50[tex]r^{2}[/tex] = 50([tex]3^{2}[/tex]) = 50(9) = $450
In ΔPQR, the measure of ∠R=90°, the measure of ∠P=53°, and QR = 17 feet. Find the length of PQ to the nearest tenth of a foot.
Answer:
21.2863≈21.3 feet
Step-by-step explanation:
Answer:
21.3
Step-by-step explanation:
Help! I'll give brainlyest!!!!!! FAST!!!!
What is X equal to in this problem?
Answer: X=80
Step-by-step explanation:
Know that all angles COMBINED in a triangle is 180, so we can use the two angles to setup the equation for the last one, since the total angle must be 180 then x added to those angles must add up to 180.so we get the equation x+59+41=180.x+100=180, subtract 100 from both sides to isolate x.x=80.please help! this is a huge chunk of my grade!!
Answer:
r=8Step-by-step explanation:
3r+4+8r-2 = 90
11r +2 = 90
11r= 88
r= 8simplify pls with steps 2⁵ x 3⁴ x 5 / 3 x 16
how do i solve 6y = 3
Answer:
y=1/2
Step-by-step explanation: