Answer:
110 feet
Step-by-step explanation:
Take x as the width of the field.
4x = 440 feet
x = 440 feet ÷ 4
x = 110 feet
So, the field is 110 feet wide #
What is the smallest positive three-digit number that is a multiple of 4 and whose digits' sum is 23?
Answer:
the number is 788......
help with 4b thank you.
First let's compute dx/dt
[tex]x = t - \frac{1}{t}\\\\x = t - t^{-1}\\\\\frac{dx}{dt} = \frac{d}{dt}\left(t - t^{-1}\right)\\\\\frac{dx}{dt} = 1-(-1)t^{-2}\\\\\frac{dx}{dt} = 1+\frac{1}{t^{2}}\\\\\frac{dx}{dt} = \frac{t^2}{t^{2}}+\frac{1}{t^{2}}\\\\\frac{dx}{dt} = \frac{t^2+1}{t^{2}}\\\\[/tex]
Now compute dy/dt
[tex]y = 2t + \frac{1}{t}\\\\y = 2t + t^{-1}\\\\\frac{dy}{dt} = \frac{d}{dt}\left(2t + t^{-1}\right)\\\\\frac{dy}{dt} = 2 - t^{-2}\\\\\frac{dy}{dt} = 2 - \frac{1}{t^2}\\\\\frac{dy}{dt} = \frac{2t^2}{t^2}-\frac{1}{t^2}\\\\\frac{dy}{dt} = \frac{2t^2-1}{t^2}\\\\[/tex]
From here, apply the chain rule to say
[tex]\frac{dy}{dx} = \frac{dy*dt}{dx*dt}\\\\\frac{dy}{dx} = \frac{dy}{dt} \times \frac{dt}{dx}\\\\\frac{dy}{dx} = \frac{dy}{dt} \div \frac{dx}{dt}\\\\\frac{dy}{dx} = \frac{2t^2-1}{t^2} \div \frac{t^2+1}{t^{2}}\\\\\frac{dy}{dx} = \frac{2t^2-1}{t^2} \times \frac{t^{2}}{t^2+1}\\\\\frac{dy}{dx} = \frac{2t^2-1}{t^2+1}\\\\[/tex]
We could use polynomial long division, or we could add 2 and subtract 2 from the numerator and do a bit of algebra like so
[tex]\frac{dy}{dx} = \frac{2t^2-1}{t^2+1}\\\\\frac{dy}{dx} = \frac{2t^2-1+2-2}{t^2+1}\\\\\frac{dy}{dx} = \frac{(2t^2+2)-1-2}{t^2+1}\\\\\frac{dy}{dx} = \frac{2(t^2+1)-3}{t^2+1}\\\\\frac{dy}{dx} = \frac{2(t^2+1)}{t^2+1}-\frac{3}{t^2+1}\\\\\frac{dy}{dx} = 2-\frac{3}{t^2+1}\\\\[/tex]
This concludes the first part of 4b
=======================================================
Now onto the second part.
Since t is nonzero, this means either t > 0 or t < 0.
If t > 0, then,
[tex]t > 0\\\\t^2 > 0\\\\t^2+1 > 1\\\\\frac{1}{t^2+1} < 1 \ \text{ ... inequality sign flip}\\\\\frac{3}{t^2+1} < 3\\\\-\frac{3}{t^2+1} > -3 \ \text{ ... inequality sign flip}\\\\-\frac{3}{t^2+1}+2 > -3 + 2\\\\2-\frac{3}{t^2+1} > -1\\\\-1 < 2-\frac{3}{t^2+1}\\\\-1 < \frac{dy}{dx}\\\\[/tex]
note the inequality signs flipping when we apply the reciprocal to both sides, and when we multiply both sides by a negative value.
You should find that the same conclusion happens when we consider t < 0. Why? Because t < 0 becomes t^2 > 0 after we square both sides. The steps are the same as shown above.
So both t > 0 and t < 0 lead to [tex]-1 < \frac{dy}{dx}[/tex]
We can say that -1 is the lower bound of dy/dx. It never reaches -1 itself because t = 0 is not allowed.
We could say that
[tex]\displaystyle \lim_{t\to0}\left(2-\frac{3}{t^2+1}\right)=-1\\\\[/tex]
---------------------------------------
To establish the upper bound, we consider what happens when t approaches either infinity.
If t approaches positive infinity, then,
[tex]\displaystyle L = \lim_{t\to\infty}\left(2-\frac{3}{t^2+1}\right)\\\\\\\displaystyle L = \lim_{t\to\infty}\left(\frac{2t^2-1}{t^2+1}\right)\\\\\\\displaystyle L = \lim_{t\to\infty}\left(\frac{2-\frac{1}{t^2}}{1+\frac{1}{t^2}}\right)\\\\\\\displaystyle L = \frac{2-0}{1+0}\\\\\\\displaystyle L = 2\\\\[/tex]
As t approaches infinity, the dy/dx value approaches L = 2 from below.
The same applies when t approaches negative infinity.
So we see that [tex]\frac{dy}{dx} < 2[/tex]
---------------------------------------
Since [tex]-1 < \frac{dy}{dx} \text{ and } \frac{dy}{dx} < 2[/tex], those two inequalities combine into the compound inequality [tex]-1 < \frac{dy}{dx} < 2[/tex]
So dy/dx is bounded between -1 and 2, exclusive of either endpoint.
strontium-90 is a radioactive material that decays according to the function A(t)=A0e−0.0244t, where A0 is the initial amount present and A is the amount present at time t (in years). Assume that a scientist has a sample of 400 grams of strontium-90.
(a) What is the decay rate of strontium-90?
(b) How much strontium-90 is left after 30 years?
(c) When will only 100 grams of strontium-90 be left?
(d) What is the half-life of strontium-90?
(a) The decay rate of strontium-90 is nothing%.
(Type an integer or a decimal. Include the negative sign for the decay rate.)
Answer:
Step-by-step explanation:
The decay rate of strontium-90 is -.0244 as given.
For b., we have to use the formula to find out how much is left after 30 years. This will be important for part d.
[tex]A(t)=400e^{-.0244(30)}[/tex] which simplifies a bit to
A(t) = 400(.4809461353) so
A(t) = 192.4 g
For c., we have to find out how long it takes for the initial amount of 400 g to decay to 100:
[tex]100=400e^{-.0244t}[/tex]. Begin by dividing both sides by 400:
[tex].25=e^{-.0244t[/tex] and then take the natural log of both sides:
[tex]ln(.25)=lne^{-.0244t[/tex] . The natural log and the e cancel each other out since they are inverses of one another, leaving us with:
ln(.25) = -.0244t and divide by -.0244:
61.8 years = t
For d., we figured in b that after 30 years, 192.4 g of the element was left, so we can use that to solve for the half-life in a different formula:
[tex]A(t)=A_0(.5)^{\frac{t}{H}[/tex] and we are solving for H. Filling in:
[tex]192.4=400(.5)^{\frac{30}{H}[/tex] and begin by dividing both sides by 400:
[tex].481=(.5)^{\frac{30}{H}[/tex] and take the natural log of both sides, which allows us to pull the exponent out front. I'm going to include that step in with this one:
ln(.481) = [tex]\frac{30}{H}[/tex] ln(.5) and then divide both sides by ln(.5):
[tex]\frac{ln(.481)}{ln(.5)}=\frac{30}{H}[/tex] and cross multiply and isolate the H to get:
[tex]H=\frac{30ln(.5)}{ln(.481)}[/tex] and
H = 28.4 years
PLEASE ANSWER
For a parabola where p > 0, the curve will open
Options
To the left
Up
Down
To the right
Answer:
‼️D) To the right‼️
Explanation
There is an easy way to tell whether the graph of a quadratic function opens upward or downward: if the leading coefficient is greater than zero, the parabola opens upward, and if the leading coefficient is less than zero, the parabola opens downward.
please help, will give brainliest!!
Answer:
3
Step-by-step explanation:
[tex] \frac{3x - 3}{x} \div \frac{x - 1}{x} [/tex]
[tex] \frac{3(x - 1)}{x} \times \frac{x}{x - 1} = 3[/tex]
The number of dollars in x quarters
Answer:
There are four quarters in one dollar, so 4x quarters in x dollarsA walking path across a park is represented by the equation y = -4x+10. A
new path will be built perpendicular to this path. The paths will intersect at
the point (4.-6). Identify the equation that represents the new path.
102
10
10
O A. y -**-5
B. y --4x+10
C. y - 4x-22
O D. v-**-7
first invert fraction of the slope from 4/1 to 1/4 and switch sign. then figure out the y-intercept
the algebraic approach would work like this:
-4x + 10 = 1/4x + b
plug in what you got, here: the intersection information
-4*(4) + 10 = 1/4*(4) + b
-16 + 10 = 1 + b
-6 = 1 + b
-7 = b
A park is 5 miles east of Roxana's home. A library is 4 miles north of the park. How far is Roxana's home from the library?
Answer: 9 miles I think but I dont know where her house is exactly.
18 Geometry question: Use an algebraic equation to find the measure of each angle that is representative in terms of X
Answer:
12x - 28° = 116°
7x + 32° = 116°
Step-by-step explanation:
12x - 28° and 7x + 32° are vertical angles. Vertical angles are congruent.
Therefore, to find the measure of each angle, we have to set each equation equal to each other as follows:
12x - 28° = 7x + 32°
Collect like terms
12x - 7x = 28 + 32
5x = 60
Divide both sides by 5
5x/5 = 60/5
x = 12
✔️12x - 28°
Plug in the value of x
12(12) - 28
= 144 - 28
= 116°
✔️7x + 32°
7(12) + 32
= 84 + 32
= 116°
Which equation has the same solution as 10(x) - x + 5 = 41
Step-by-step explanation:
if that is truly the full problem description, then we have
10x - x + 5 = 41
=>
9x = 36
our simply
x = 4
so, I am not sure, what your teacher wants to see as result.
there is an infinite number of equations I could find, all with the solution x = 4.
I’m new to this app and I need help with those two questions please help!!
y=x²-10x-7
a>0 so we will be looking for minimum
x=-b/2a=10/2=5
y=25-50-7=-32
Answer: (5;32)
y=-4x²-8x+1
а<0 so we will be looking for maximum
х=-b/2a=8/-8=-1
у=4+8+1=13
Maximum point (-1;13)
for any Integer 'a',a ÷ 0 is _______
give me answer
Answer:
undefined, invalid
and for a limit expression like a/x, x->0 we also say this is infinite.
Algebra word problem plz help me
Step-by-step explanation:
here's the answer to your question
Use the given conditions to write an equation for each line in point-slope form and slope-intercept form.
Slope= 1/3, passing through the origin
Answer:
[tex](y - 0) = \frac{1}{3} (x - 0)[/tex]
[tex]y = \frac{1}{3} x[/tex]
Put the following equation of a line into slope-intercept form, simplifying all
fractions.
3x + 6y = -42
Answer:
y = -1/2x -7
Step-by-step explanation:
3x + 6y = -42
Slope intercept form is
y = mx+b where m is the slope and b is the y intercept
Subtract 3x from each side
3x-3x+6y = -3x-42
6y = -3x-42
Divide each side by 6
6y/6 = -3x/6 - 42/6
y = -1/2x -7
Which of the following is equivalent to the expression below
Answer:
Could you add a picture or answer choices so we know what to choose from?
Bà B đến ngân hàng ngày 05/05/2019 để gửi tiết kiệm 250 triệu đồng thời hạn 3 tháng, lãi suất 7%/năm, NH trả lãi định kỳ hàng tháng (kỳ lĩnh lãi đầu tiên là ngày 05/05/2019). Đến ngày 05/08/2019, bà B tất toán sổ tiết kiệm trên. Tính số tiền bà B nhận được vào ngày đáo hạn sổ tiết kiệm là? (Cơ sở công bố lãi suất là 365 ngày)
Answer:
Ask in English then I can help u
Find the distance across the lake, assume the triangles are similar
Answer:
C
Step-by-step explanation:
Since the triangles are similar, the scale factor is 100/5=20. So L/15=20, L=300
Question 1 (Fill-In-The-Blank Worth 4 points)
(05.02)The area of the parallelogram below is
square meters
6 m
7 m
2 m
Numerical Answers Expected!
Answer for Blank 1
Step-by-step explanation:
we don't see the parallelogram nor any description of it.
so, it is impossible to tell you the right answer.
as I only answer questions by don't ask any, I don't know how you can add a picture.
The graph below shows two polynomial functions, f(x) and g(x): Graph of f of x equals x squared minus 2 x plus 1. Graph of g of x equals x cubed plus 1 Which of the following statements is true about the graph above? (4 points) g(x) is an even degree polynomial with a positive leading coefficient. g(x) is an odd degree polynomial with a negative leading coefficient. f(x) is an even degree polynomial with a positive leading coefficient. f(x) is an odd degree polynomial with a negative leading coefficient.
9514 1404 393
Answer:
(c) f(x) is an even degree polynomial with a positive leading coefficient.
Step-by-step explanation:
The leading terms of the two functions are ...
f(x): x² (even degree, positive coefficient: 1)
g(x): x³ (odd degree, positive coefficient: 1)
Then it is true that ...
f(x) is an even degree polynomial with a positive leading coefficient
Suppose that a group of 10 people join a weight loss program for 3 months. Each person's weight is recorded at the beginning and at the end of the 3-month program. To test whether the weight loss program is effective, the data should be treated as:
To test the effectiveness of the weight loss program, a PAIRED SAMPLE test distribution is used.
The weight loss data collated for the program for both the beginning and end of the program period was obtained with one subject or person having two separate readings, these shows that the samples are NOT INDEPENDENT.
When performing a test which involves DEPENDENT or MATCHED samples, whereby means of two measurements taken from the SAME subject are involved, a PAIRED SAMPLE TEST DISTRIBUTION IS ADOPTED.
Therefore, the effectiveness of the weight loss programme will be accurately evaluated using a PAIRED SAMPLE TEST.
Learn more : https://brainly.com/question/17143411
I really need the help please and thank you
Answer:
Answer is D.
Step-by-step explanation:
Let the inverse be m:
[tex]{ \sf{m = \sqrt{x} - 8 }} \\ { \sf{m + 8 = \sqrt{x} }} \\ { \sf{x = {(m + 8)}^{2} }} \\ { \bf{f {}^{ - 1} (x) = {(x + 8)}^{2} }}[/tex]
Domain:
[tex]{ \sf{x \geqslant - 8}}[/tex]
the guys is wrong i checked
Step-by-step explanation:
the guys is wrong i checked
A line contains the points (4, 5) and (3,-9). Write the equation of the line using slope-intercept form. A. y=-2x - 3 B. y = 2x – 15 C. 1 yax +3 2 1 V= -X-7 2
Answer:
Y =-4X +21
Step-by-step explanation:
x1 y1 x2 y2
4 5 3 9
(Y2-Y1) (9)-(5)= 4 ΔY 4
(X2-X1) (3)-(4)= -1 ΔX -1
slope= -4
B= 21
Y =-4X +21
10. cos c plz help me
Answer:
cos C = 12/13
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
Cos theta = adj/ hyp
cos C = 36/39
Dividing the top and bottom by 3
cos C = 12/13
CosØ=Base/Hypotenuse
cosC=BC/ACcosC=36/39cosC=12/13The sum of one and three times a number is -89. What is the number?
A) Translate the statement above into an equation that you can solve to answer this question. Do not solve it yet. Use
x
as your variable.
The equation is
B) Solve your equation in part [A] for
Answer:
A. 1 + 3x = -89
B. x = -30
Step-by-step explanation:
Let the unknown variable be x.
A. Translating the word problem into an algebraic expression, we have;
1 + 3x = -89
B. To solve for the unknown variable;
1 + 3x = -89
3x = -89 -1
3x = -90
x = -90/3
x = -30
Check:
1 + 3x = -89
Substituting the value of x;
1 + 3(-30) = -89
1 + (-90) = -89
1 - 90 = -89
-89 = -89
3 1/2 of 4.4 of 1.1 of 5 WILL GIVE BRAINLIEST
Answer:
84.7
Step-by-step explanation:
of is another way to say multiply so what your doing is muliplying all the numbers
Answer:
84.7
Step-by-step explanation:
SEE THE IMAGE FOR SOLUTION
HOPE IT HELPS
HAVE A GREAT DAY
Find the missing side lengths
I need help in y = ( it's not 6 I put every number and still got it wrong)
Answer:
y = 9√3
x = 18
Step-by-step explanation:
taking 30 as reference angle
b = y
p = 9
h = x
so
tan30 = p/b
1/√3 = 9/b
or, b = 9√3
so
[tex]h^2 = p^2 + b^2\\x^2 = 9^2 + y^2\\or, x^2 = 81 + (9\sqrt{3} )^2\\or, x^2 = 81 + 243\\or, x ^2 = 324\\or, x =\sqrt{324} \\\\so x = 18[/tex]
A small airplane flies 750 miles with an average speed of 250 miles per hour. 1.75 hours after the plane leaves, a Boeing 747 leaves from the same point. Both planes arrive at the same time; what was the average speed of the 747?
Answer:
The average speed of the 747 was of 600 miles per hour.
Step-by-step explanation:
A small airplane flies 750 miles with an average speed of 250 miles per hour.
Velocity is distance divided by time, and here, we find the time of the small airplane. So
[tex]v = \frac{d}{t}[/tex]
[tex]250 = \frac{750}{t}[/tex]
[tex]250t = 750[/tex]
[tex]t = \frac{750}{250}[/tex]
[tex]t = 3[/tex]
1.75 hours after the plane leaves, a Boeing 747 leaves from the same point. Both planes arrive at the same time;
This means that it traveled 750 miles in 3 - 1.75 = 1.25 hours.
What was the average speed of the 747?
[tex]v = \frac{d}{t} = \frac{750}{1.25} = 600[/tex]
The average speed of the 747 was of 600 miles per hour.
Please answer all of these
Answer:
1a 300
b 180
c 330
d 1470
e 180
f 7344
Step-by-step explanation:
