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Step-by-step explanation:
L = 6t+5
H = √t
A = L*H
= (6t+5) *√t = 6t√t + 5√t
A'(t) = 6t * 1/2*√t + √t * 6 + 5/2*√t
= 6t/2√t + 6√t + 5/2√t
Expression for the rate of change of the area with respect to time will be,
A' = [tex]9t^{\frac{1}{2}}+\frac{5}{2}t^{-\frac{1}{2}}[/tex] cm per second
It's given in the question,
Length of a rectangle is given by the expression(6t + 5) cm
Width or height of the rectangle is given by the expression,[tex]\sqrt{t}[/tex] cm
Area of the rectangle is given by,
Area = Length × Height
A = (6t + 5)(√t)
A = [tex]6t^{\frac{3}{2}}+5t^\frac{1}{2}[/tex]
Now find the derivative of area (A) with respect to time (t).
[tex]\frac{dA}{dt}=\frac{d}{dt}(6t^{\frac{3}{2}}+5t^\frac{1}{2})[/tex]
A' = [tex](6\times \frac{3}{2})t^\frac{1}{2}+\frac{5}{2} t^{-\frac{1}{2}}[/tex]
A' = [tex]9t^{\frac{1}{2}}+\frac{5}{2}t^{-\frac{1}{2}}[/tex]
Therefore, expression for the rate of change of the area will be,
A' = [tex]9t^{\frac{1}{2}}+\frac{5}{2}t^{-\frac{1}{2}}[/tex]
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can someone help me solve this system. thanks
2y = 6
3(x + y) = 12
Answer
y=3 x=1
Step-by-step explanation:
3(x+3)=12
3x+9=12
subtract 9 from both sides to get...
3x=3
divide 3 from both sides to get...
x=1
Step-by-step explanation:
this is very easy
2y=6
y=2/6=3
so ,
3(x+y)=12
3x+3y=12
3x+3+3=12
3x+9=12
3x=12-9
3x=3
x=3/3
x=1
A restaurant charged Ms. Smith $120 for dinner,
while at dinner she met with a friend and they had a
great conversation about the 25 animals at the zoo.
When dinner was over she left a 15% tip. How much
was the tip amount?
Look at the picture to see question plz help quickly and step by step
Answer: 16.6
Step-by-step explanation:
What is the range of the function in this table x 1 2 3 4 Y 2 4 3 2
Answer:
(2, 4, 3)
Step-by-step explanation:
Range = Y
How do you write 8.43 × 10^-4 in standard form?
Answer:
0.000843
Step-by-step explanation:
simplify the expression:
8.43 × 0.0001
now simplify:
0.000843
If you find my answer helpful
Pls consider marking my answer as Brainliest! It would mean a lot!
Name the subset(s) of real numbers to which the number belongs.
−1.57
A. integer only
B. rational only
C. irrational and rational
D. rational and integer
what is the answer to 6y * 88 = 88 * 6y
Answer:
0 or No solutions
Step-by-step explanation:
hope this helps!
can someone PLEASE help me on this PLEASE.
The given table of values represents a linear equation. What is the slope?
Answer:
2
Step-by-step explanation:
slope=∆y/∆x
slope=(9-7)÷(3-2)
slope= 2.
Given m||n, find the value of x.
Answer:
27 degrees
Step-by-step explanation:
the 27 degrees
Answer:
27°
Step-by-step explanation:
X and 27° are both alternate interior angles (on opposite sides of the transversal, between the two parallel lines), which makes them congruent! So they are both 27°.
1+2x6+7= -13
where do i have to put the parenthesis so its correct
Answer:
you have to but it back 2 times
Step-by-step explanation:
ir is because it should be back 2 rimes
Ethan builds two different kinds of chairs, rockers and swivels. It takes him 3 hours to build a rocker and requires 2 oz of stain. It takes him 2 hours to build a swivel chair and requires 8 oz of stain. Ethan has 56 oz of stain available and he can only work up to 24 hours. He makes $12 profit on each rocker and $10 profit on each swivel chair. 1. Since there cannot be negative chairs, create two constraints to represent this. 2.Create a constraint for the hours it takes to build the chairs. 3. Create a constraint for the stain it takes for the chairs. PLEASE HELP
Answer:
(1) [tex]x\geq 0\; \text {and}\;y\geq 0[/tex]
(2) [tex]3x + 2y\leq[/tex] 24
(3) [tex]x+4y\leq 28[/tex]
Step-by-step explanation:
Let x and y be the numbers of rockers and swivels made by Ethan.
(1) Since the number of chairs can't be negative. So,
x\geq0 and y\geq 0 are the two constraints.
(2) He can work a maximum of 24 hours.
The time required to make 1 rocker chair and 1 swivels chair are 3 hr and 2 hr respectively.
So, the time required to make x rocker chair = 3x hr
and the time required to make y swivel chair = 2y hr.
The total time required is 3x + 2y hr which can't be more than the available time, 24 hr.
So, the required constraint is
[tex]3x + 2y\leq 24[/tex]
(3) Similarly,
As 1 rocker chair requires 2 oz strain and 1 swivel chair required 8 ox strain.
So, to make x rocker chair 2x oz required and make y swivel chair 8y oz required which can't be more than the available oz, 56.
So, the required constraint is
[tex]2x + 8y\leq 56[/tex]
[tex]\Rightarrow x+4y\leq 28.[/tex]
You work in a grocery store warehouse recording shipments. A driver delivers 25 crates of strawberries for distribution. A store calls needing seven crates of strawberries. After you fill this order, how many crates of strawberries are available for other stores?
Answer:
18 crates
Step-by-step explanation:
Data provided in the question
The Number of strawberries for distribution delivered is 25 crated
Now he seven crates is required
So the remaining crates left is
= 25 - 7
= 18 crates
hence, after filling the order the number of order crates of strawberries is 18 crates and the same is to be considered
do you guys know this by any chance
Answer:
[tex]10^{17}[/tex]
Step-by-step explanation:
Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the
10
10
. If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.
which is the best estimate of -14 1/9 × -2 9/10
Answer: 42
Step-by-step explanation:
-14 1/9 would round to -14
-2 9/10 would round to -3
-14 x -3= 42
A scale drawing of a rectangular park is 5 inches wide and 7 inches long. The actual park is 280 yards long. What is the area?
Answer:
315
Step-by-step explanation:
5 x 7 = 35
280 + 35 = 315
There sth answer
Answer:7 inches → 280 yards
1 inch → 280 ÷ 7 = 40 yards
5 inches → 40 x 5 = 200 yards
Area = 280 x 200 = 56 000 yards
hope this help btw i am 12
Step-by-step explanation:
Find the distance between V (4.4) and X (5.8). Round to the nearest tenth, if necessary. about units
Answer:
V= 5 X=6
Step-by-step explanation:
Which one?
A. B. C. or D?
Answer:
I think that the answer is D
Step-by-step explanation:
help me plzzzzzzzzzzz
can somebody help me pleaseee ?? it’s due soon & im stuck .
Answer:
a. lenqth=32 , width=2
b. m∠p=100 m∠Q=50 m∠R=30
c. XY=20 YZ=12
d.m∠1=90 m∠2=90
Step-by-step explanation:
a. the area of a rectangle is length×width so to find the possible sizes for L and W we need to list the factors (multiplication of two numbers to get 64) of 64, which are,
1 AND 64 (this answer is suitable but it's better to choose another
one if available for more accuracy)
2 AND 32 (this is a good answer to use)
4 AND 16 (this one already used in the question)
8 AND 8 (this answer will be wrong as the sizes need to be different because it's a rectangle but it will be good for square)
SO we will choose 2 AND 32 for the answer and we can put them in any order we want.
b. first of all acute angles are angles measured less than 90 degrees. so to have at least one angle not acute we use measures up to 90 degrees.
I will put one answer as 100 degrees (note you can use any number above 90 to not be an acute angle) and the other answers will be two numbers add up to be 80 degrees (and again you can choose any numbers for that).
c. the two answers should add up to be 32 so for this counterexample we can choose any two numbers to have the sum of 32 (remember that 16+16 already chosen in the question.
d. two supplementary angles are two angles add up to be 180 degrees so for this question we need to find two angles sum to 180 and not obtuse (that mean 90 degrees or less) and the only answer can appear is 90+90=180.
22+54=y+16 whats the answer
Answer:
y=60 or 60=y
Step-by-step explanation:
22+54= 76
76=y+16
60=y or the other way around
A 20 gallon tank is full. How many gallons are in the tank?
Answer:
20???
Step-by-step explanation:
What is the solution to 8x - 3(2x - 4) = 3x - 18?
Answer:
X=30
Step-by-step explanation:
The answer is X=30
HELP PLEASE HS GEOMETRY 50 POINTS!!!!!
Answer: 1,6,3,8
Step-by-step explanation: that one, and its opposite and the other one is the same
Answer:
1, 3, and 8
Step-by-step explanation:
You should know this because, 88 degrees and 2 are in a straight line which there means that 2 would be 92 degrees. So every length would be slightly shorter or longer than the other. As you can observe 1, 3, and 8 other than 6 are all the ones that are slightly shorter than their counterpart 2, 4, 5, and 7. Which means that 1, 3, and 8 all equal 88 degrees just like 6.
i need help answering the questions using distributive property. i already know the answers 3. will give brainliest.
Answer:
Hello
Step-by-step explanation:
by what i understood the awnser should be c
¡¡ANSWER MY QUESTION FIRST¡¡
Can you help me with these questions, please?
Answer:
∠5 = 70°
∠8 = 130°
Step-by-step explanation:
Since ∠5 and ∠1 are equal they will both equal 70°
Since ∠6 and ∠8 are also equal they will both equal 130°
Hope this helps
Plz mark brainliest
Write each equation/inequality in slope-intercept form.
y- 5 = 1/3 (x-6)
Answer:
Your answer is: y = 1/3x + 3
Use the formula y = mx + b
Step-by-step explanation:
Hope this helped : )
X^2+ 17x+91=0
Help please!!
Answer:
x^2+17x+91=0
a = 1; b = 17; c = +91;
Δ = b2-4ac
Δ = 172-4·1·91
Δ = -75
Delta is less than zero, so there is no solution for the equation
Step-by-step explanation:
If f(x) = -2 cos x, findf(-300 º). Do not use a calculator.
Answer:
- 1
Step-by-step explanation:
Using the trigonometric identity
cos(- x) = cosx and exact value cos60° = [tex]\frac{1}{2}[/tex]
Given
f(x) = - 2cosx , then
f(- 300° )
= - 2cos(- 300)°
= - 2cos(300)°
= - 2cos(360 - 300)°
= - 2cos60°
= - 2 × [tex]\frac{1}{2}[/tex]
= - 1
What is the constant RATIO (how do you you multiply ) of the exponential curve that passes through the points (0, 3) and (5, 96) ?
Answer:
The answer is 1.788
Step-by-step explanation:
An aircraft factory manufactures airplane engines. The unit cost (the cost in dollars to make each airplane engine) depends on the number of engines made. If engines are made, then the unit cost is given by the function . What is the minimum unit cost?C(x)=x^2-520x+73458
Answer:
Minimum unit cost = 5,858
Step-by-step explanation:
Given the function : C(x)=x^2−520x+73458
To find the minimum unit cost :
Take the derivative of C(x) with respect to x
dC/dx = 2x - 520
Set = 0
2x - 520
2x = 520
x = 260
To minimize unit cost, 260 engines must be produced
Hence, minimum unit cost will be :
C(x)=x^2−520x+73458
Put x = 260
C(260) = 260^2−520(260) + 73458
= 5,858