Answers
Answer:
(B) 3
Step-by-step explanation:
Qualitative answer. As x grows larger and larger, the contribute of lower degree terms (and constants) becomes irrelevant, and you rewrite everything picking the highest term for both numerator and denominator
[tex]\lim\limits_{x \to \infty} \frac{\sqrt{9x^4}}{x^2} $\lim\limits_{x \to \infty} \frac{3x^2}{x^2}=3[/tex]
Analitically.
Collect [tex]9x^4[/tex] in the numerator under the square root, [tex]x^2[/tex] in the denominator.
[tex]\lim\limits_{x \to \infty} \frac{\sqrt{9x^4(1+\frac{1}{9x^4})}}{x^2(1-\frac{3}{x}+\frac{5}{x^2})} = \lim\limits_{x \to \infty}\frac{3x^2\sqrt{(1+\frac{1}{9x^4})}}{{x^2(1-\frac{3}{x}+\frac{5}{x^2})}} = 3[/tex]
At this point the way you deal with it is the usual. Anything inside the bracket goes to 0 besides the lead coefficients (1 in both cases) and you're left with 3.
Related Questions
The rod is made of A-36 steel and has a diameter of 0.22 in . If the rod is 4 ft long when the springs are compressed 0.7 in . and the temperature of the rod is T= 30 ∘F , determine the force in the rod when its temperature is T= 150 ∘F .
Answers
The force in the rod when the temperature is 150 °F is 718.72 pounds-force.
How to determine the resulting the resulting force due to mechanical and thermal deformationLet suppose that rod experiments a quasi-static deformation and that both springs have a linear behavior, that is, force ([tex]F[/tex]), in pounds-force, is directly proportional to deformation. Then, the elongation of the rod due to temperature increase creates a spring deformation additional to that associated with mechanical contact.
Given simmetry considerations, we derive an expression for the spring force ([tex]F[/tex]), in pounds-force, as a sum of mechanical and thermal effects by principle of superposition:
[tex]F = k\cdot (\Delta x + 0.5\cdot \Delta l)[/tex] (1)
Where:
[tex]k[/tex] - Spring constant, in pounds-force per inch.[tex]\Delta x[/tex] - Spring deformation, in inches.[tex]\Delta l[/tex] - Rod elongation, in inches.The rod elongation is described by the following thermal dilatation formula:
[tex]\Delta l = \alpha \cdot L_{o}\cdot (T_{f}-T_{o})[/tex] (2)
Where:
[tex]\alpha[/tex] - Coefficient of linear expansion, in [tex]\frac{1}{^{\circ}F}[/tex].[tex]L_{o}[/tex] - Initial length of the rod, in inches. [tex]T_{o}[/tex] - Initial temperature, in degrees Fahrenheit.[tex]T_{f}[/tex] - Final temperature, in degrees Fahrenheit.If we know [tex]k = 1000\,\frac{lb}{in}[/tex], [tex]\Delta x = 0.7\,in[/tex], [tex]\alpha = 6.5\times 10^{-6}\,\frac{1}{^{\circ}F}[/tex], [tex]L_{o} = 48\,in[/tex], [tex]T_{o} = 30\,^{\circ}F[/tex] and [tex]T_{f} = 150\,^{\circ}F[/tex], then the force in the rod at final temperature is:
[tex]F = \left(1000\,\frac{lb}{in} \right)\cdot \left[0.7\,in + 0.5\cdot\left(6.5\times 10^{-6}\,\frac{1}{^{\circ}F} \right)\cdot (48\,in)\cdot (150\,^{\circ}F-30\,^{\circ}F)\right][/tex]
[tex]F = 718.72\,lbf[/tex]
The force in the rod when the temperature is 150 °F is 718.72 pounds-force. [tex]\blacksquare[/tex]
To learn more on deformations, we kindly invite to check this verified question: https://brainly.com/question/13774755
could you pls help me i have the question in the picture ok
Answers
Step-by-step explanation:
the answer is 44 you have to multiply 3 and 11 and you'll get 8 then calculate 33-8 and then subtract and then you get 25 so you put 44
Have a good day !!!
find the rate of change from the equation x=1 will mark brainiest
Answers
Answer:
undefined
Step-by-step explanation:
when graphed, x=1 goes up and down which makes it's slope undefined
Answer:
∞(infinity)
Step-by-step explanation:
rate of change for the equation x = 1
use the formula: y = mx + b
where:
y = how far up the line goes
m = slope
x = how far along
b = Y-intercept
the equation is a vertical line,
so the slope = ∞ (infinity)
71.6 less then or greater then 71.63
Answers
Answer:
less
Step-by-step explanation: 71.6 can also be seen as 71.60 therefore 71.63 is greater
Answer:
Less than.
Think of .6 as the tenths place to tens place.
.63 is 6 tenths and 3 hundredths, so 63.
Now ask yourself, "Is 63 greater than 60?"
And your answer is yes.
find f(343) & f(-64) .
Answers
f(343) = ?
[tex] \sqrt[3]{343} = 7[/tex]
7 + 4 = 11
f(-64) = ?
[tex] \sqrt[3]{ - 64} = - 4[/tex]
-4 + 4 = 0
Find the real-number root.
√1.44
1.2
no real roots
2.07
0.72
Answers
Answer: A. 1.2
Step-by-step explanation:
The principal, real, root of:
2^√1.44
=1.2
All roots:
1.2
−1.2
1.44 is not a perfect square
A tree casts a shadow of 24 ft. At the same time, a 6 ft adult casts a shadow of 2 ft. what is the hight of the tree?
Answers
Answer: 8ft tall
Step-by-step explanation:
6/2=3
24/3=8
so the tree is 8ft tall
The standard deviation for u(90, 230)
Answers
Answer:
Standard deviation is 70
Step-by-step explanation:
square root of 4,900= 70 (solved using standard deviation formula)
Ivan said that if a number ends in 0 both 2 and 5 are factors of the number. Is he correct? Why of why not?
Answers
Answer:
yes he is correct bc the number will always be divisive by 2 and 5
Jack is 4 times as old as Lacy. 9 years from now the sum of their ages will be 63. How old are they now?
Jack is
years old while Lacy is
years old.
Answers
Answer:
jack is 54 and lacey is 13.5. I think
Step-by-step explanation:
Let Jack be J and Lacy be L.
First equation: J=4L
Second equation: (J+9)+(L+9)=63
Solving using substitution:
4L+9+L+9=63
5L+18=63
5L= 45
L = 9
L=9 and J=4L = 4*9 = 36
So Jack is 36 years old and Lacy is 9 years old.
I need help please due in a hour
Answers
Answer:
so easy ....dude
Step-by-step explanation:
you can do it..
What are m and b in the linear equation 15 + 9x + 3 + 7x = y?
Answers
15 + 3 + 9x + 7x = y
18 + 16x = y
Recall
b + mx = y
m = 16
b = 18
I need help please ASAP !!
Answers
Answer:
Step-by-step explanation:
5) ∠1
6) ∠2 and ∠3
7) ∠1
The ratio of dogs to cats at the veterinarian's office on Saturday. was 6 to 5. If there were 15 cats at the office, how many dogs and cats were there altogether?
Answers
Answer:
33 total cats and dogs
Step-by-step explanation:
15/5=3
3*6=18
18+15=33
hope this helps
Answer:
Dogs: 18Cats: 15In total: 33Step-by-step explanation:
Set up a proportion: [tex]\frac{6}{5} = \frac{x}{15}[/tex] Cross multiply, then divide: 15 × 6 = 90, 90 ÷ 5 = 18So, there are 18 dogs in total.Add the dogs and cats together: 18 + 15 = 33I hope this helps!
Practice Translate Expressions
Write an algebraic expression that models the given word phrase.
1) 15 divided by d ________________________
2) seven fewer than a number n ________________________
3) two times the sum of a and b ________________________
4) nine less than 5 multiplied by the number p ________________________
5) the product of 15 and x ________________________
6) quotient of 4 more than the number z and the number y decreased by _________
Answers
2) n - 7
3) (a + b) x 2
4) 5p - 9
5) 15x
6) 4 + z / y
lf x = 4 and y = 7, evaluate the following expression:
3(x + y)
Answers
3(4+7)
Simplify
3(11)
Multiply
3 x 11 = 33
So, the answer is 33.
What is a savings goal? PLS I NEED HELP QICK PLSSS nvm
Answers
Answer:
A goal for the amount of money being saved.
Step-by-step explanation:
Please help ASAP marking brainly
Answers
Answer:
y = 2
Step-by-step explanation:
We are given the value of x (second equation). Let's substitute the value of x into the first equation to find y.
[tex]\rightarrow \dfrac{x}{y} = 6[/tex]
[tex]\rightarrow \dfrac{4(y + 1)}{y} = 6 \ \ \ \ \ \ \ \ \ \ \ \ \ \text{\large{[}x = 4(y + 1)]}[/tex]
Use cross multiplication.
[tex]\rightarrow 4(y + 1) = 6 \times y[/tex]
[tex]\rightarrow 4(y + 1) = 6 y[/tex]
Simplify the distributive property.
[tex]\rightarrow 4(y + 1) = 6 y[/tex]
[tex]\rightarrow 4y + 4 = 6 y[/tex]
Subtract 4y both sides.
[tex]\rightarrow 4y - 4y + 4 = 6 y - 4y[/tex]
[tex]\rightarrow 4 = 2y[/tex]
Divide both sides by 2.
[tex]\rightarrow \dfrac{4}{2} = \dfrac{2y}{2}[/tex]
[tex]\rightarrow 2 = y[/tex]
Thus, the value of y is 2.
X + 14 = 21 what should be done to solve this equation
Answers
Answer:
x+14=21 Add 14 to both sides of the equation. Subtract 14 from the left side of the equation. Add 14 to the left side and subtract 14 from the right side of the equation.
Step-by-step explanation:
Answer: x = 7
Step-by-step explanation:
U first subtract 14 from both sides
x + 14 - 14 = 21 - 14
And then u simplify
and get 7
whats 1.07 x 30 in standard form
Answers
Answer:
The simple answer is 32.1
Step-by-step explanation:
It might look easier if you add 1 x 30 and 0.07 x 30.
Answer:
The correct answer is 32.1
Step-by-step explanation:
Solve the following equations for x (5 points each). (a) -3x+10=34 and (b) 13x-4=11x+10-8
please show work
Answers
Answer:
A)x=-8 B)x=3
Step-by-step explanation:
A)-3x+10=34 -3x+10-10=34-10 -3x/-3=24/-3 x=-8
B) 13x-4=11x+10-8 13x-4+4=11x+10-8+4 13x-11x=11x-11x+6 2x/2=6/2 x=3
AHIJ has coordinates H(0, 0), I(-3, -1), and J-1, -2). Graph the triangle and its translation 3 units to the right and 2 units down. What are the coordinates of J'
Answers
The coordinates of the triangle is plotted on the graph and the translated triangle is H' ( 3 , -2 ) , I' ( 0 , -3 ) and J' ( 2 , -4 )
Given data ,
Let the triangle be represented as ΔHIJ
Let the coordinates of the triangle be H(0, 0), I(-3, -1), and J(-1, -2)
Now , the translation rule is
The triangle is translated 3 units to the right and 2 units down
So , add 3 to the x-coordinates and subtract 2 from the y-coordinates of each point
So , the translated triangle is H' ( 3 , -2 ) , I' ( 0 , -3 ) and J' ( 2 , -4 )
Hence , the translated triangle is H' ( 3 , -2 ) , I' ( 0 , -3 ) and J' ( 2 , -4 )
To learn more about translations click :
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What are the coordinates of the vertex for f(x) = x2 + 4x + 10?
A- (−2, 2)
B- (2, 2)
C- (−2, 6)
D- (2, 6)
Answers
Answer:
I believe the answer is C (-2,6)
[tex]\\ \rm\rightarrowtail y=x^2+4x+10[/tex]
Add and subtract 4[tex]\\ \rm\rightarrowtail y=x^2+4x+4+10-4[/tex]
[tex]\\ \rm\rightarrowtail y=x^2+4x+2^2+6[/tex]
[tex]\\ \rm\rightarrowtail y=(x+2)^2+6[/tex]
Vertex form
y=a(x-h)^2+kVertex:-
(h,k)=(-2,6)In this image, what is the value of C? Round your answer to the nearest tenth.
Answers
Answer:
C = 7.2
Step-by-step explanation:
What's Pythagorean Theorem?
Pythagorean Theorem is a theorem in which it states that the sum of the squares of the legs of a right triangle is equal to the square of the hypotenuse. This can be represented as an equation of a² + b² = c².To find the value of C, we're going to use Pythagorean Theorem! We're given the legs as 4 and 6.
Step 1: Simplify.
[tex]4^2+6^2=c^2[/tex][tex]16+36=c^2[/tex] [tex]52=c^2[/tex]Step 2: Take square root of both sides.
[tex]\sqrt{c^2}=\sqrt{52}[/tex] C ≈ 7.2Therefore, the value of C is 7.2.
I need help doing this I don't pay attention in class now I'm lost
Answers
Answer:
i think the answer is 6498
Step-by-step explanation:
Answer:
6498
Step-by-step explanation:
Pay attention in class :)
Okay, so basically, you just need to replace x and y with the corresponding numbers.
So our equation would be:
9 * 2(5 * 7 - 8 * 2) squared
Now we solve with PEMDAS:
9 * 2(35 - 16)squared
9 * 2(19)squared
9 * 2(361)
18 * 361
6498
Let me know if I did something wrong!
PLEASE HELP
Write a story problem to go with the multiplication problem 5 x 3/4 . Then solve the problem.
Answers
Story:
John is baking a cake. He need to feed 5 people with the cake but the recipe is only designed for 1 serving. In the regular recipe, it required 3/4 cups of sugar. How much sugar does he need for the new recipe?
Answer:
3.75 or 3 3/4
Answer:
A store has 5 oranges then a customer buys 3/4 of them. How many is left
Step-by-step explanation:
5x3/4=3.75 if it was in decimal but in fraction it is 23/4
5x3/4=3.75
3/4 is 0.75
0.75 x 5=3.75
Which set of ordered pairs represents a function?
{(2, –2), (1, 5), (-2, 2), (1, –3), (8, –1)}
{(-3, –1), (-7, 1), (–6, –1), (-8, 1), (2, –1)}
{(1, 8), (5, 2), (2, –5), (1, –3), (–2, 9)}
{(–3, 1), (6, 3), (4, 2), (6, –3), (1, –1)}
Answers
Answer:
A
Step-by-step explanation:
A function is a relation for which each value from the set the first components of the ordered pairs is associated with exactly one value from the set of second components of the ordered pair.
Emma measured a line to be 16 inches long. If the actual length of the line is 15.3 inches, then what was the percent error of the measurement, to the nearest tenth of a percent?
Answers
Answer:
4.6% (nearest tenth)
Step-by-step explanation:
percent error = (|approx - actual| ÷ actual) × 100
percent error = (|16 - 15.3| ÷ 15.3) × 100
= 4.6% (nearest tenth)
[tex] \sf\% \: error = \frac{ |approx - actual| }{actual} \times 100[/tex]
Approx = 16Actual = 15.3[tex] \tt\% \: error = \frac{ |16 - 15.3| }{15.3} \times 100[/tex]
[tex] \tt\% \: error = \frac{ |0.7| }{15.3} \times 100[/tex]
[tex] \tt\% \: error = \frac{ |0.7| }{ \frac{153}{10} } \times 100[/tex]
[tex] \tt\% \: error = \frac{0.7}{ \frac{153}{10} } \times 100[/tex]
[tex] \tt\% \: error = \frac{ \frac{7}{10} }{ \frac{153}{10} } \times 100[/tex]
[tex] \tt\% \: error = \frac{7 }{ 153 } \times 100[/tex]
[tex] \tt\% \: error = \frac{7 00}{ 153 } [/tex]
[tex] \tt\% \: error =4.57\%[/tex]
Thus, The % error is 4.6% when rounded off to the nearest tenth!!~A rectangle has a length of 3x – 1 and a width of 2x + 4. Find the perimeter of this rectangle. Then find the area of the rectangle.
Answers
Answermmm
Step-by-step explanation:
fff
Answer:
Area:
(3x-1) * (2x+4) = 6x² + 10x - 4
Perimeter:
((3x-1)*2) + ((2x+4)*2) = 10x + 6
100points please help
Image attached
Find x
Answers
180 -190