Answer:
1) dA/dt = -21 cm²/s and Area is decreasing
2)dP/dt = 0 and perimeter is constant
3) dD/dt = 21/13 cm/s and diagonal is increasing
Step-by-step explanation:
We are given that;
length l of a rectangle is decreasing at a rate of 3 cm/sec.
Thus, dl/dt = -3 cm/sec
Also, the width w is increasing at a rate of 3 cm/sec. Thus;
dw/dt = 3 cm/sec
When l=5 cm and w=12 cm;
A) Area is given by the formula;
A = lw
The rate at which area is increasing is;
dA/dt = l(dw/dt) + w(dl/dt)
Plugging in the relevant values;
dA/dt = 5(3) + 12(-3)
dA/dt = 15 - 36
dA/dt = -21 cm²/s
This is less than 0.thus, A is decreasing.
B) Formula for perimeter is;
P = 2l + 2w
rate of change of perimeter is;
dP/dt = 2(dw/dt) + 2(dl/dt)
Plugging in the relevant values, we have;
dP/dt = 2(-3) + 2(3)
dP/dt = 0
Thus,Perimeter is constant
C) the length of the diagonal of a rectangle is given by;
D = √(w² + l²)
Rate of change of diagonal is;
dD/dt = [2w(dw/dt) + 2l(dl/dt)]/(2√(w² + l²))
2 will cancel out in numerator and denominator to give;
dD/dt = [w(dw/dt) + l(dl/dt)]/(√(w² + l²))
Plugging in the relevant values gives;
dD/dt = [12(3) + 5(-3)]/(√(12² + 5²))
dD/dt = (36 - 15)/13
dD/dt = 21/13 cm/s
This is greater than 0.
Thus, diagonal is increasing.
can u pls help me with this question
Answer:
5
Step-by-step explanation:
Let me know if I am wrong
It was found that an unknown solid had a density of 20 g/cm3 and a volume of 30 cm3. Determine the mass of the solid.
Answer:
30
Step-by-step explanation:
The mass of the solid is 600 grams if the unknown solid had a density of 20 g/cm3 and a volume of 30 cm3
What is density?It is defined as the mass-to-volume ratio. The density indicates the object's density and is represented by the symbol. The density is measured in kilograms per cubic meter.
It is given that:
It was found that an unknown solid had a density of 20 g/cm3 and a volume of 30 cm3
As we know, from the definition of density:the mass-to-volume ratio
Density = mass/volume
mass = densityxvolume
mass =20x30
mass = 600 grams
Thus, the mass of the solid is 600 grams if the unknown solid had a density of 20 g/cm3 and a volume of 30 cm3
Learn more about the density here:
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Select ALL the terms that are like 5b2
.
Question 4 options:
12b2
5
5b
10b2
Answer:
12b2 10b2
Step-by-step explanation:
Please explain the relationship between a hypothesis and an experiment.
Answer:
A hypothesis is "is a suggested solution for an unexplained occurrence that does not fit into current accepted scientific theory. The basic idea of a hypothesis is that there is no pre-determined outcome.". And an experiment is "is defined as to try out something new or to test a theory. An example of experiment is when you try out a new hair style. An example of experiment is when you use test tubes and chemicals in a lab to complete a project and to try to better understand chemical reactions.".
Meg's Bakery sells the following items.
• one cinnamon roll for $2.50 or four for $10.00
• one pie for $12.50 or two pies for $22.00
• a dozen brownies for $9.00
A. Determine if there is a proportional relationship between cinnamon rolls and the cost of cinnamon rolls. If there is determine the unit rate.
Answer:
it is $2.50 multiplied by 4
Step-by-step explanation:
this is because for every 1 cinnamon roll it is $2.50 and if you multiply that by 4 you get $10, or how much it costs for 1 roll
write 5/6 - 7/9 in simplest form
9514 1404 393
Answer:
1/18
Step-by-step explanation:
18 is a suitable denominator for both fractions:
5/6 = 15/18
7/9 = 14/18
Then the difference is ...
5/6 -7/9 = 15/18 -14/18 = (15 -14)/18 = 1/18
Write an equation in slope intercept form with the slope as 1/3 and the point (-3,4)
Answer:
[tex]y = \frac{1}{3}x + 5[/tex]
Step-by-step explanation:
Slope (m) = 1/3
(-3 , 4)
y - y1 = m(x -x1)
y - 4 = (1/3) (x - [-3])
[tex]y - 4 = \frac{1}{3}(x + 3)\\\\y - 4 = \frac{1}{3}x + \frac{1}{3}*3\\\\y - 4 = \frac{1}{3}x + 1\\\\ y = \frac{1}{3}x + 1 + 4\\\\ y = \frac{1}{3}x + 5[/tex]
A .14kg baseball is dropped from rest. It has a momentum of .78kg x m/s just before it lands on the ground. For what amount of time was the ball in the air?
Answer
what r the options? a b c d?????
i wuld say it is 2.5
Step-by-step explanation:
Last month you spent $30 on clothing. This month you spent 150% of what you spent last month. Set up a proportion to model this situation. How much did you spend this month?
You spent $*blank* this month.
Answer:
$45
Step-by-step explanation:
x=1.5(30)
x=45
-19 + 4k - 15k - k -9
Answer:
Let's simplify step-by-step.
−19+4k−15k−k−9
=−19+4k+−15k+−k+−9
Combine Like Terms:
=−19+4k+−15k+−k+−9
=(4k+−15k+−k)+(−19+−9)
=−12k+−28
Answer:
=−12k−28
Step-by-step explanation:
9 correct : 15 questions = 45 correct: q questions
please help me
Answer: it should be 75
Step-by-step explanation:
9 times 5 is 45 so 15 times 5 should be 75
A proportional relationship between y and x When x5, ym
What is the constant of proportionality, K?
Enter your answer as a simplified or improper fraction in the box
k -
Answer:
-7/5
Step-by-step explanation:
Answer:
-7/5
Step-by-step explanation:
can someone help me on this
Answer:
1) Reflections just change the signs of the coordinates, so (1.5, -2) and (-1 and 1/2, 2) are reflections of each other. Also (1.75, -4) and (-1 and 3/4, 4)
2) From left to right: -1.75, -3/4, 1/4, 0.75, 1 and 1/2.
Remember that each 1/4 = 0.25, so this could help you work out fractions and decimals.
Answer:
First question answer: D Second Question answer: (lowest to highest) -1.75, -3/4, 1/4, 0.75, and 1 1/2
Step-by-step explanation:
8 times the difference between a number and 6 is equal to 4 times the number.
What is the number?
OA. 12
OB. 4
OC. 16
OD. 48
Answer:
it's either A (12) or B(4) but I think it's 12
Step-by-step explanation:
if we make it into an equation, we get
8(x-6)=4x
8x-48=4x
-48=-4x
-12=-x
x=12
the reason why it might be 4 as well is if we switch the order
8(6-x)=4x
48-8x=4x
48=12x
x=4
So both of those could be correct, but I'm thinking that because they said between a number and 6, then x goes first, so therefore, I think it is 12
x^3-y^3 how to solve?
Answer:
x^(3)-y^(3)
Step-by-step explanation:
Miguel ate 1/4 of a pizza in 1/2 of an hour. How much pizza will Miguel eat in one hour?
Answer:
he will eat 2/4 or 1/2 in 1 hour
Step-by-step explanation:
$43 shirt; 6% tax Please Help!!
Answer:
tax is 2.58
Step-by-step explanation:
Answer:
.06 times 43 is $2.53 in tax
Step-by-step explanation:
Find the Values of X and Y in the diagram. PLZ HELP
Answer: x is 47, y is 75
Step-by-step explanation:
How do I solve this?
Answer:
The answer is 7.5
Step-by-step explanation:
3x+18=9x−27
3x+18−9x=9x−27−9x
−6x+18=−27
−6x+18−18=−27−18
−6x=−45
−6x /−6 = −45 /−6
x = 15 /2 which is equal to 7.5 as a decimal.
PLS HELP WILL GIVE BRAINLIEST
How can parents that dont have a O blood type still have a O blood type baby???
Answer: While a child could have the same blood type as one of his/her parents, it doesn’t always happen that way.
Step-by-step explanation:
For example, parents with AB and O blood types can either have children with blood type A or blood type B. These two types are definitely different than parents’ blood types!
What is the answer for 2m + 3m + 8 + 6
Answer:
5m+14
Step-by-step explanation:
Find the slope given the following ordered pairs (6,11) and (8,19)
Answer:
4
Step-by-step explanation:
solved it
Answer:
m = 4
Step-by-step explanation:
m = (y2 - y1) / (x2-x1)
Given points (6,11) and (8,19) Let y2 = 19, y1 = 11, x2 = 8, and x1 = 6
Subbing in
m = (19-11)/(8-6) = 8/2 = 4
So, the slope is 4
find the surface area of the cereal box of 30x20x5
Answer:
1700 units squared
Step-by-step explanation:
Answer:
ITS 3000
Step-by-step explanation:
plz help me im struggling hard
Answer:
0.20 × 65 is what you would do for the second
Step-by-step explanation:
btw listen to yungblud
Note that the cost for the rent is a function of the amount of the miles you drove. Let's call that [tex]C(m)[/tex].
Also note that the amount you pay will linearly increase, in other words, the increase in cost will always be the same for each mile. This tells us that our function is indeed a line, a first order polynomial of the form [tex]C(m) = am+b[/tex]
What would happen if you were to rent a truck and not drive it at all? You would pay only the one-time fee.
Therefore, [tex]C(0)=55[/tex]
So, [tex]C(m) = am + 50[/tex]
The cost will increase by $0.20 for each mile, wich tells us that [tex]a=0.20[/tex]
Finally, our expression is [tex]\boxed{C(m) = 0.2m+55}[/tex]
If we want to know how much would you pay if you drove 65 miles, we want to know what [tex]C(65)[/tex] is.
By plugging [tex]m=65[/tex] in the expression, we get
[tex]C(65) =68[/tex]
So you would pay $68
Solve for g: 19 > 2(g + 7.9).
Answer: g < 1 3/5
Step-by-step explanation:
first, i removed the parentheses.
19 > 2g + 15.8
then, i moved the terms.
-2g > 15.8 - 19
the, i calculated that.
-2g > -3.2
finally, i divided both sides.
g < 1.6
the alternative form is g < 1 3/5
(basically, the second answer)
Ms. Hartt burns 300 calories when she runs for 1 hour. If Ms. Hartt runs 5 hours in a week how many calories would she burn?
HEEELPPPPP PPLS The second side of a triangle is 8 inches less than the first side. The third side is 14 inches more than the first side. The perimeter of the triangle is 78 inches. Find each side of the triangle.
Answer: ):
Step-by-step explanation:
Answer:
second side is 16
third side is 38
Step-by-step explanation:
x + (x - 8) + (x + 14) = 78
3x + 6 = 78
3x = 78 - 6
3 x = 72
x = 72/3
x = 24
24 + (24 - 8) + (24 + 14) = 78
24 + 16 + 38 = 78
what 0.05% in as a decimal and a mixed number in simplest form
deimal: 0.05% / 100 = 0.0005
mixed number: 5/10000
8-4x for x = 9
The expression equals I
Answer:
- 28
Step-by-step explanation:
Step 1:
8 - 4x Equation
Step 2:
8 - 4 ( 9 ) Input x value
Step 3:
8 - 36 Multiply
Answer:
- 28 Subtract
Hope This Helps :)
A proportional relationship is graphed on the coordinate plane. The line that represents the relationship passes through points (0,0) and (5,10). What is the unit rate of the proportional relationship?
Answer:
Step-by-step explanation:
HELLPPPP