Answer:
11.08 cm/s
Step-by-step explanation:
Here it is given that the edges of a cube are increasing at a rate of 6.4 cm/s . And we need to find out the rate at which the diagonals are increasing . If we assume each side of the cube to be x , then ;
[tex]\longrightarrow \dfrac{da}{dt}= 6.4 \ cm/s\dots (i) [/tex]
Now we can find diagonal as ,
[tex]\longrightarrow d = \sqrt{ length^2+breadth^2+height^2} [/tex]
Here l = b = h = a ; so ,
[tex]\longrightarrow d =\sqrt{ a^2+a^2+a^2} [/tex]
Simplify,
[tex]\longrightarrow d =\sqrt{3a^2} [/tex]
Take out a from square root,
[tex]\longrightarrow d =\sqrt3 a[/tex]
Now , we can find the rate of change of diagonal as ;
[tex]\longrightarrow r =\dfrac{d\sqrt3 a}{dt} [/tex]
Take out the constant,
[tex]\longrightarrow r = \sqrt3\dfrac{da}{dt} [/tex]
From equation (i),
[tex]\longrightarrow r = 1.732 \times 6.4 \ cm/s [/tex]
Multiply ,
[tex]\longrightarrow \underline{\underline{ rate_{of\ change \ of \ diagonals}= 11.08\ cm/s}}[/tex]
This is the required answer!
If the side length increases at a rate of 6.4 cm/s, then the diagonal increases at a rate of 11.1 cm/s
At what rate does the diagonal increase?
The diagonal of a cube of side length S is given by:
d = S*√3
In this case, we know that the side length increases at a rate of 6.4 cm/s, then we can write:
S = S₀ + 6.4cm/s*t
Where S₀ is the initial side length, replacing that on the diagonal formula we get:
d = (S₀ + 6.4cm/s*t)*√3
Now if we differentiate it with respect to the time t, we get:
d' = 6.4cm/s*√3 = 11.1 cm/s
So, if the side length increases at a rate of 6.4 cm/s, then the diagonal increases at a rate of 11.1 cm/s.
If you want to learn more about rates of change, you can read:
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Help me asap i don’t know how to do this please help me
BRAINLY I NEED HELP NOWWWWW
Answer:
9/9/108/126
Step-by-step explanation:
1/2bh is how you find the area of a triangle ! :)
This means that for both triangles, the area is 2 times the height, 9, then multiplied by one half. The area is 9 for both the left and right triangle.
The area of the rectangle is the product of the two lengths: 9 and 12, which is 108.
This means that the area of the entire trapezoid is 126. :D
A pencil has a length of 17 cm measured to the nearest centimetre.
(a) Write down the least possible length of the pencil.
(b) Write down the greatest possible length of the pencil.
Answer:
(a) 16.89
(b) 17.44
Step-by-step explanation:
investment after 20 years equals 130000. original investment was 50000. What was the interest rate?
Step-by-step explanation:
The formula states that
S. I=P*R*T/100
R=S. I*100/P*T
Simple Interest= Amount - principal
Simple Interest = 130000 - 50000
Simple Interest = 80000
R= 80000*100/50000*20
R= 800000/100000
R=8%
One day ill get the hang of it but for now i'm asking for help
Answer:
37.68
Step-by-step explanation:
circumference is diameter, which in this case is 12,times pi which I always simplify to 3. 14
12 times 3. 14 is approximately 37cm so that is why I have given this answer
brainliest?
Option B) is correct.
Here, we are given –
Diameter of circle is = 12 cm [tex]\star{\underline{\boxed{\sf{\pink{Diameter = 2 \times Radius }}}}}[/tex]Let's find it's radius first.
[tex]\qquad[/tex][tex] \sf \longrightarrow Radius = \dfrac{Diameter }{2} [/tex]
[tex]\qquad[/tex][tex] \sf \longrightarrow Radius = \dfrac{12 }{2}[/tex]
[tex]\qquad[/tex][tex] \sf \longrightarrow Radius = \cancel{\dfrac{12 }{2}}[/tex]
[tex]\qquad[/tex][tex] \bf \longrightarrow Radius = 6 \: cm[/tex]
We know that–
[tex]\qquad[/tex][tex] \pink{\bf \longrightarrow Circumference \: of \: circle = 2\pi r}[/tex]
[tex]\qquad\qquad\quad\underline{\sf{Substituting \ Values \ :}}[/tex]
⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━
[tex]\qquad[/tex][tex] \sf \longrightarrow Circumference_{(Circle)} = 2 \pi r[/tex]
[tex]\qquad[/tex][tex] \sf \longrightarrow Circumference_{(Circle)} = 2 \pi \times 6[/tex]
[tex]\qquad[/tex][tex] \sf \longrightarrow Circumference_{(Circle)} =2 \times 3.14\times 6[/tex]
[tex]\qquad[/tex][tex]\pink{ \bf \longrightarrow Circumference_{(Circle)} = 37.68 \: cm }\\[/tex]
Henceforth, circumference of the given circle will be 37.68 cm.when asked for a measurement of a thing why do we not give a negative value of a number?
Answer:
See below.
Step-by-step explanation:
A measurement could be a distance or a length, or a weight, or a volume. All those quantities are expressed as positive numbers.
For example, what is the distance from New York to Los Angeles?
Answer: 2,800 miles
What is the length of a book?
Answer: 8 inches
How much does John weigh?
Answer: 150 lb
All those numbers are positive.
There is one measurement that is often a negative number. That is a temperature.
Rita makes and sells necklaces. The materials to make each necklace cost $2. 75. Last week she made 8 necklaces and wants to make a total profit of $78. Using the equation 8 (x 2. 75) = 78, Rita determined that she needs to sell each necklace for $7 to make a total profit of $78. Which error did Rita make? Although she has the correct equation, she needs to sell each necklace for $12. 50. Although she has the correct solution, she should have used the equation 8 (x minus 2. 75) = 78. The equation should be 8 (x minus 2. 75) = 78, and she needs to sell each necklace for $12. 50. The equation should be StartFraction 1 over 8 EndFraction (x minus 2. 75) = 78, and she needs to sell each necklace for $75. 25.
Profit function gives the profit earned for given input. Thus, Rita has correct solution, that is, she needs to make 7 necklace to get $78 profit.
How to find the value of unknown variable in a linear equation?It might not be always possible. But for simple cases, we can try using addition or subtraction or such operations in linear equations if there is single variable with single equation.
For the given case, the profit $78 for x necklace manufactured is
[tex]8(x + 2.75) = 78[/tex]
(remember that many times, when using letters or symbols, we hide multiplication and write two things which are multiplied, close to each other. As in [tex]2 \times (x + 3) = 2(x + 3)[/tex])
Solving this equation, we get:
[tex]8(x + 2.75) = 78\\\\\text{Dividing by 8 on both the sides}\\\\(x + 2.75) = \dfrac{78}{8} = 9.75\\\\\text{Subtracting 2.75 from both the sides}\\\\x = 9.75 - 2.75 = 7[/tex]
Rita has correct solution, that is, she needs to make 7 necklace to get $78 profit.
Learn more about solving linear equations here:
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Answer:
C
Step-by-step explanation:
What is the end behavior of the graph of f(x) = – 0.5x2 – 3x – 4?
Help me please i need it
Step-by-step explanation:
what are you looking for
drop ur comment below
Need help ASAP !
Are the two triangles similar? Why or why not?
Answer:
(c) Similar by AA~
Step-by-step explanation:
The outside segments are marked parallel, so the angles formed where the transversals meet them are congruent. That is ∠CBD ≅ ∠EDB, and ∠CED ≅ ∠ECB. (The vertical angles where the lines cross are congruent, as well.)
So, the angles in one triangle are congruent to the angles in the other triangle. The triangles are similar by the AA~ postulate.
Let a # b = a 2– b 2 . What is the value of (3 # 2) – (4 # 3)?
Answer:
-6
Step-by-step explanation:
[tex](3 \times 2) - (4 \times 3) \\ (6) - (12) \\ 6 - 12 \\ = - 6[/tex]
1 + 1 express as fraction
Answer: 2 over 1
Step-by-step explanation:
1+1=2
However we want this as a fraction
Any whole number as a fraction is just over one
Therefore the final answer is 2 over 1
You’re welcome Kaeya!
Answer: it’s 2 over 1 mate
Step-by-step explanation: you’re welcome
A city has current population of 55,000, and it is growing at a rate of 2% each year. What is the approximate predicted population after 7
years?
OA. 8,178
B. 14,000
C. 63,178
D. 142,075
the question is in the picture
Answer:
[tex]5^2 = 25[/tex][tex]5^{-2}[/tex] = [tex]\frac{1}{25}[/tex][tex](-5)^{2} = 25[/tex] [tex]-5^{2} =-25[/tex]Solution:
We know the following rules:
Rule: If an exponent is negative, it will be in the fraction 1/nˣ.Rule: If an exponent is positive, it will be in whole number form and will multiply itself m times.Rule: if a number's exponent is 0, then the number is 1.Now, let's solve each problem.
5² = 5 x 5 = 255⁻² = 1²/5² = 1/25(-5)² = (-5) x (-5) = 25-5² = -(5²) = -(25) = -25Learn more about exponents: https://brainly.com/question/26553706
Write the equation of the line that passes through the points (3, 2) and
(-8,4). Put your answer in fully simplified point-slope form, unless it
is a vertical or horizontal line.
Answer:
y= -2/11x + 28/11[tex]\frac{-2}{11}x + \frac{28}{11}[/tex]I need help please help
Answer:
Show similarity between triangle WXZ and triangle VXY then write XY/XZ=VY/WZ
The reason is: The ratio of corresponding sides of similar triangle are equal.
how can i solve -8/x-11=-2?
Answer:
See below
Step-by-step explanation:
-8/x - 11 = -2
First add 11 to both sides
-8/x - 11 + 11 = -2 + 11 simplifies to -8/x = 9
Now multiply both side by x
( -8/x) X ( x ) = ( 9 ) X ( x ) which simplifies to -8 = 9x
Divide each side by 9
-8/9 = (9x)/9 which simplifies to -8/9 = x or x = - 8/9
Multiple Choice, A standard circus ring has a radius of 6.5 meters, Which of the following is the approximate circumference of the circus ring? A. 13 meters B. 20.4 meters C. 40.8 meters D. 132,7 meters
Answer:
C 40.8 meters
Step-by-step explanation:
circumference equals diameter, aka 2r, times 3.14, aka pi
have a good day friend :)
I need help please if anyone can help that would be great
Answer:
f = 2.75p
Step-by-step explanation:
You can see that the amount of flour for 6 cakes is double the amount for 3 cakes, so the amount of flour is proportional to the number of cakes. An equation for a proportional relationship will have the form ...
f = kp
We can find the value of k from any column in the table.
8.25 = k(3) . . . . using the values in the first column
8.25/3 = k = 2.75 . . . . . divide by 3
The equation is ...
f = 2.75p
_____
Additional comment
If the input doubles, but the output does not, then the relationship is not proportional. We ordinarily expect recipes to have proportional relationships.
pls help plsssss due in a few minsss
6. x=1 , y=2
7. x=-4 , y=5
8. Infinitely Many Solutions
4(2x + 3) ÷ 5y From the expression above, provide an example of each of the following: sum, term, product, factor, quotient, and coefficient. If any are not present, write "not present." (6 points)
Answer:
sum: 2x + 3 but you cant add not like terms
Term 2x + 3
Product 8x+12
factor 2,x ;5,y; 4,(2x+3)
quotient 4(2x+3) ÷ 5 = 12 ÷ 5y
coefficient = 2 and 5
Step-by-step explanation:
sum: 2x + 3 but you cant add not like terms
Term 2x + 3
Product 8x+12
factor 2,x ;5,y; 4,(2x+3)
quotient 4(2x+3) ÷ 5 = 12 ÷ 5y
coefficient = 2 and 5
the cost of a meal is split evenly between between alania and her two friends.they determine that each person owes $ 14.68. how much was the entire meal?
write the equation:
and solution :
What fraction of an hour is 52 minutes
Answer:
As a decimal, it's 0.867. As a fraction it is 867/1000
Step-by-step explanation:
hi please help!! i will mark as brainliest if i can
Answer:
3.1x + 2.2x - 2.4y - 1.4y + 1.9 - 3.4
Step-by-step explanation:
3.1 x - 2.4 y + 1.9 + 2.2x - 1.4y - 3.4
→ Collect all the like terms
3.1x + 2.2x - 2.4y - 1.4y + 1.9 - 3.4
The graph shows the number of game consoles sold in millions since 2009.
Game Console
9
(0, 25.5)
25
20
(1, 15.3)
Number of Game Consoles Sold
(millions)
15
10
(2, 9.18)
0
2 3 4 5 6 7
Number of Years Since 2009
Based on this information, which function best models the number of game consoles sold in
millions x years since 2009?
A 9(x) = 0.6(25.5)
09(x) = 25.5(0.6)
c g(x) - 6.12(25.5)
D 9(x) = 25.516 Y
The graph is an illustration of an exponential function
The equation of the graph is: [tex]y = 25.5 * 0.6^x[/tex]
How to determine the equation of the graphFrom the graph, we have the following ordered pairs
(x,y) = (0, 25.5), (1, 15.3) and (2, 9.18)
An exponential function is represented as:
[tex]y = ab^x[/tex]
When x = 0, we have:
[tex]25.5 = ab^0[/tex]
[tex]a = 25.5[/tex]
When x = 1, we have:
[tex]15.3 = ab^1[/tex]
[tex]15.3 = ab[/tex]
Substitute 25.5 for a
[tex]15.3 = 25.5b\\[/tex]
Solve for b
[tex]b = 0.6[/tex]
So, the exponential equation is:
[tex]y = 25.5 * 0.6^x[/tex]
Hence, the exponential equation of the graph is: [tex]y = 25.5 * 0.6^x[/tex]
Read more about exponential functions at:
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g(x) =25.5(0.6)ˣ function best models the number of game consoles sold in millions x years since 2009?
From the given graph we can observe three ordered pairs which are (0, 25.5), (1, 15.3) and (2, 9.18).
We have to find the function which best models the number of game consoles sold in millions x years since 2009.
This we can find by using exponential function.
y=abˣ
When x = 0, we have:
a=25.5
When x=1, then y should be 15.3
15.3=ab
Substitute 25.5 for a
15.3=25.5b
Divide both sides by 25.5:
b=0.6
So the function is g(x)=25.5(0.6)ˣ
To learn more on Functions click:
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Write AB with A(-9, 2) and B (-1,
6) in component form.
The written form of vector AB in component form is; (4,8)
Vectors in component formFrom the given points;
The magnitude of vector AB is given as;AB = √((-1-(-9))² + (6-2)²AB = √80 = 4√5From evaluation, the angle direction of AB is;
Hence, the x and y components of vector AB are;
AB(x) = 4√5 × (1/√5) = 4AB(y) = 4√5 × (2/√5) = 8.Read more on component of vectors;
https://brainly.com/question/2142917
A function is represented by the graph.
Complete the statement by selecting from the drop-down menu.
The y-intercept of the function y = 3x + 2 is
Choose...less than, greater than, or equal to
the y-intercept of the function represented in the graph.
points passing (0,2) (2,6)
HELP! Find the value for x.
Answer:
x=6
Step-by-step explanation:
6 +2 is 8
2(6) - 9 = 3
8 times 3 is 24
Mark Brainliest :)
The sum of the digits of an odd 2-digit number is 1.What is the number?
Answer:
-23
Step-by-step explanation:
Negative 2 plus positive 3 equals 1.
-2 + 3 = 1
I hope this helps you out :)
please help me i dont know how to solve
Answer:
31.7079632679 round it up and you get 32
Step-by-step explanation:
pi times 25 +16 because 8 times 2 is the area of the base
so basically the equation is
pi x 25 + 16=
pi x 25 is about 15.7079632679 if my calculations are correct
and then 15.7079632679 + 25 and we get 31.7079632679
Answer:
A=264 pi
? Is 264
Hope this helps!