Answer:
For a) $A(r(t))=π(4t)^2.$
For b) 803.84
Step-by-step explanation:
For a) we can do a simple substitution on the variable r. Notice that $A=πr^2$ make $A$ a function of $r.$ Then, $A(r(t))=\pi (r(t))^2=\pi (4t)^2.$
For b) you only need to substitute the value $t=4$ on the expresión $A(r(t)).$
what should be added to 4x get 9X please help me in this pic also all
Answer:
[tex]thank \: you[/tex]
Givenf (x) = { (+ 6) whatisf (-6)?
Answer:
[tex]f(x) = 6 \\ f( - 6) = 6 \\ because \: here \: function \: is \: \\ independent \: of \: x \\ thank \: you[/tex]
Answer:
f(x) = +6f(-6) = +6Because, function f(x) is independent of x
So, the value of f(x) is +6 everywhere
Therefore, f(-6) = +6
How do i work out the area of a circle that equals 5000
Answer:
Radius is 39.89422804 units
Step-by-step explanation:
Area of circle can be calculated with the formula: [tex]\pi r^{2}[/tex]
The area of the circle is 5000.
[tex]\pi r^{2}[/tex]= 5000
If you're looking for the radius, solve for r.
[tex]r^{2}[/tex]= [tex]\frac{5000}{\pi }[/tex]
r= [tex]\sqrt{\frac{5000}{\pi} }[/tex]
r= 39.89422804 units
Sketch a linear graph given the following key features
Answer:
Step-by-step explanation:
Simplify: y^-3
a) 3/y
b) - 1/y^3
c) -3y
d) 1/y^3
Answer:
1/y^3
Step-by-step explanation:
We know that a^-b = 1/a^b
y ^-3 = 1/y^3
Simplify the expression.
Please add an explanation if you understand how to do this.
Answer:
2x^31
Step-by-step explanation:
~Simplify the expression
2x^29/x^-2
~Apply quotient rule [ a^b/a^c = a^b-c ]
2x^31
Best of Luck~
Answer:
2x³¹Step-by-step explanation:
(x¹⁶ + x⁴x¹²)x⁹x⁴/x⁻² =(x¹⁶ + x¹⁶)x¹³x² = 2x¹⁶x¹⁵ =2x³¹Used identities:
nᵃnᵇ = nᵃ⁺ᵇ1/n⁻ᵃ = nᵃdy/dx(2x^2+2y^2-3x+2y=1)
Answer:
[tex]{ \bf{ \frac{dy}{dx} = \frac{3 - 4x}{4y + 2} }}[/tex]
Step-by-step explanation:
[tex]{ \sf{ \frac{dy}{dx} (2 {x}^{2} + 2 {y}^{2} - 3x + 2y = 1) }} \\ \\ { \sf{4x + 4y \frac{dy}{dx} - 3 + 2 \frac{dy}{dx} = 0 }} \\ \\ { \sf{ 4y\frac{dy}{dx} + 2 \frac{dy}{dx} = 3 - 4x }} \\ \\ { \sf{ \frac{dy}{dx}(4y + 2) = 3 - 4x }} \\ \\ { \sf{ \frac{dy}{dx} = \frac{3 - 4x}{4y + 2} }}[/tex]
[tex]{ \underline{ \tt{ \blue{christ \:† \: alone }}}}[/tex]
How is the series 6+13+20+...+111 represented in summation notation?
Notice that
6 + 7 = 13
13 + 7 = 20
so if the pattern continues, the underlying sequence in this series is arithmetic with first term a = 6 and difference d = 7. This means the k-th term in the sequence is
a + (k - 1) d = 6 + 7 (k - 1) = 7k - 1
The last term in the series is 111, which means the series consists of 16 terms, since
7k - 1 = 111 ==> 7k = 112 ==> k = 16
Then in summation notation, we have
[tex]\displaystyle 6+13+20+\cdots+111 = \boxed{\sum_{k=1}^{16}(7k-1)}[/tex]
Which of the fractions below are less than 2/5? Select two.
Answer:
1/8 is less than
Step-by-step explanation:
i dont see any fractions below gona have to edit your answer
A grocery store buys cereal using the cost function
c(n) = { 2n when n < 100 1.9n when 100
Sn = 500 1.8n when n > 500 where n is
the number of boxes of cereal the grocery store
buys and c(n) is the cost of the cereal. The grocery
store then sells the cereal using the sales function
s(c) = 1.3c. What is the cost of the cereal if the
grocery store buys 250 boxes?
The cost of the cereal if the grocery store buys 250 boxes is $475
We know that:
The cost function is:
c(n) = 2*n if n < 100
c(n) = 1.9*n if 100 ≤ n ≤ 500
c(n) = 1.8*n if n > 500.
(we can assume that the cost function is in dollars)
This is a piecewise function, this means that we need to see in which interval we have the number n, and then select the correct function to use.
Now, we want to find the cost of the cereal if the store buys 250 boxes.
Then we have n = 250.
We can see that n = 250 is in the second interval, 100 ≤ n ≤ 500, then we will use the second function to find the cost.
We will get:
c(250) = 1.9*(250) = $475
We can conclude that the cost if the store buys 250 boxes is 475
If you want to learn more, you can read:
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Select the correct answer from each drop-down menu.
The table represents function f, and the graph represents function g.
-2
- 1
1
2
3
4
0
х
Ax)
7
0
-5
-8
-9
-8
-5
у
A
6
4
2
g
X
.
-21
2
2
The line of symmetry for function fis
and the line of symmetry for function gis
The y-intercept of function fis
the y-intercept of function g.
Over the interval [2, 4], the average rate of change of function fis
the average rate of change of function g.
Answer:
Line of symmetry of f is x=2 and the line of symmetry for function g is x=1 as the graph starts repeating itself after x=1. Y intercept is the point at which x is 0, for f it is - 5 and for g it is - 6. Rate of change in interval [2,4] is given by (f(4)-f(2))/2=2 for f and for g it is, (g(4)-g(2))/2=-4
The true statements are:
The line of symmetry for function f is x = 2The line of symmetry for function g is x = 1The y-intercept of function f is -5The y-intercept of function g is -6Over the interval [2, 4], the average rate of change of function f is half the average rate of change of function g.Line of SymmetryThis is the point where the function is divided into equal halves.
From the figure, the table and graph are divided at points x = 2, and x = 1.
So, the line of symmetry for function f is x = 2 and the line of symmetry for function g is x = 1
Y-InterceptThis is the point where the function has an x value of 0
From the figure, the y values when x = 0 are -5 and -6
So, the y-intercept of function f is -5 and the y-intercept of function g is -6
Average rate of changeThis is calculated as:
[tex]m = \frac{y_2 - y_1}{x_2 -x_1}[/tex]
For function f, we have:
[tex]m = \frac{-5 + 9}{4-2}[/tex]
[tex]m = \frac{4}{2}[/tex]
[tex]m = 2[/tex]
For function g, we have:
[tex]m = \frac{2+ 6}{4-2}[/tex]
[tex]m = \frac{8}{2}[/tex]
[tex]m = 4[/tex]
By comparison,
[tex]m_f = 0.5 \times m_g[/tex]
Hence, over the interval [2, 4], the average rate of change of function f is half the average rate of change of function g.
Read more about functions and graphs at:
https://brainly.com/question/13136492
please help me
no links or files
thank you !
Jane is saving to buy a cell phone. She is given a $100 gift to start and saves $35 a month from her allowance. So after one month, Jane has saved $135. Does it make sense to represent the relationship between the amount saved and the number of months with one constant rate? Why or why not? Explain your answer.
Jane is given a $100 gift to start and saves $35 a month from her allowance.
After 1 month, Jane has saved
After 2 months, Jane has saved
After three months, Jane has saved
and so on
In general, after x months Jane has saved
This means that it makes sense to represent the relationship between the amount saved and the number of months with one constant rate (in this case the constant rate is 35). It makes sense because the amount of money increases by $35 each month. Since the amount of increase is constant, we get constant rate. Also the initial amount is known ($100), so there is a possibility to write the equation of linear function representing this situation.
Step-by-step explanation:
Suppose you are conducting a study about how the average US worker spends time over the course of a workday. You are interested in how much time workers spend per day on personal calls, emails, and social networking websites, as well as how much time they spend socializing with coworkers versus actually working.
The most recent census provides data for the entire population Of U.S. workers on variables such as travel time to work, time spent at work, and break time at work. The census, however, does not include data on the variables you are interested in, so you obtain a random sample of 82 full-time workers in the United States and ask about personal calls, e-mails, and so forth. You are curious about how your sample compares with the census, so you also ask the workers the same questions about work that are asked in the census.
Suppose the mean break time per day from the most recent census is 29.6 minutes, with a standard deviation of 16.0 minutes. Your sample of 82 U.S. workers provides a mean break time per day of 31.9 minutes with a sample standard deviation of 22.4 minutes.
Organize this information by completing the following table.
μ = _________ M= __________
σ= _________ s= ___________
σM = _______ sM = _________
Answer:
lol
Step-by-step explanation:
Now don't get us wrong – not all of these answers raise this excellent question
The value of [tex]\mu[/tex] = 29.6, M = 31.9, [tex]\sigma[/tex] = 16 , s = 22.4, [tex]\sigma_m[/tex] = 3.121, and [tex]\rm S_m[/tex] = 2.473.
It is given that the mean break time per day from the most recent census is 29.6 minutes with a standard deviation of 16 minutes.
It is required to organize the information in a table if the sample size is 82.
What is the margin of error(MOE)?It is defined as an error that gives an idea about the percentage of errors that exist in the real statistical data.
The formula for finding the MOE:
[tex]\rm MOE = Z_{score}\frac{s}{\sqrt[]{n} }[/tex]
Where is the z score at the confidence interval
s is the standard deviation
n is the number of samples.
We know:
[tex]\rm \sigma_m= \frac{\sigma^2}{n}[/tex]
We have,
[tex]\rm \sigma = 16 \ and \ n = 82[/tex]
[tex]\rm \sigma_m= \frac{16^2}{82}[/tex]
[tex]\rm \sigma_m= 3.121[/tex]
For [tex]\rm S_m[/tex]
[tex]\rm S_m = \frac{s}{\sqrt{n} }[/tex]
We have,
s = 22.4 and n = 82
[tex]\rm S_m = \frac{22.4}{\sqrt{82} }[/tex]
[tex]\rm S_m = 2.473[/tex]
Thus, the value of [tex]\mu[/tex] = 29.6, M = 31.9, [tex]\sigma[/tex] = 16 , s = 22.4, [tex]\sigma_m[/tex] = 3.121, and [tex]\rm S_m[/tex] = 2.473.
Learn more about the Margin of error here:
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Solve the following equation for the given variable.
-6x - 6 - 2x = 40
Round your answers to the nearest tenths place.
Step-by-step explanation:
- 6x - 6 - 2x = 40. collect the like terms
- 6x - 2x - 6 = 40
- 8x - 6 = 40 take 6 to the right
- 8x = 40 + 6
- 8x/ -8 = 46/ - 8
x = - 5.75
I hope this answers your question
Megan has earned a total of 67.50 in interest on her savings account. It is the third year she has had her 900.00 deposit in her savings account. What is the interset rate on this account? List your answer as a percent to the nearest tenth
9514 1404 393
Answer:
2.5%
Step-by-step explanation:
Simple interest is computed using the formula ...
I = Prt . . . . for principal P invested at rate r for t years
Using the given values, we can solve for r ...
67.50 = 900r·3
r = 67.50/2700 = 0.025 = 2.5%
Megan's account earned 2.5% interest.
what percent is 50cent of 50cent
what
Step-by-step explanation:
pretty sure its 25 percent
Answer:
25%
Step-by-step explanation:
if you take half of 50 it is 25 so all of it is used or 25%
Hope this helps <3 Comment if you want more thanks and be sure to give brainliest (4 left) <3
what is the gcf of 10 and 62
The table above shows some values of the functions f
and g. What is the value of f(g(1)) ?
A) 2
B) 3
C) 4
D) 5
Answer:
a
Step-by-step explanation:
g(1)=5
f(g(1))=f(5)
f(5)=2
Determine what type of model best fits the given situation:
The temperature of a cup of coffee decreases by 5 F every 20 minutes.
5, 10, 12, 4, 6, 11, 13,5
calculate the mode
Answer:
5
Step-by-step explanation:
Mode is which number occurs most, and in this set of data, 5 occurs two times.
pls find the volume :))
Answer:
The volume can be found by multiplying these two numbers, which is
65/4 x 1/2
65/8 units^3
Let me know if this helps!
Answer:
8 1/8 units ^3
Step-by-step explanation:
The volume is given by
V = Bh where B is the area of the base and h is the height
V = 16 1/4 * 1/2
Changing to an improper fraction
V = ( 4*14+1)/4 * 1/2
= (65/4) * 1/2
= 65/8
Changing back to a mixed number
= 8 1/8
Use Green's Theorem to evaluate the line integral along the given positively oriented curve. ∫C (3y +5e√x)dx + (10x + 3 cos y2)dy C is the boundary of the region enclosed by the parabolas y = x2 and x = y2
By Green's theorem, the line integral
[tex]\displaystyle \int_C f(x,y)\,\mathrm dx + g(x,y)\,\mathrm dy[/tex]
is equivalent to the double integral
[tex]\displaystyle \iint_D \frac{\partial g}{\partial x} - \frac{\partial f}{\partial y} \,\mathrm dx\,\mathrm dy[/tex]
where D is the region bounded by the curve C, provided that this integrand has no singularities anywhere within D or on its boundary.
It's a bit difficult to make out what your integral should say, but I'd hazard a guess of
[tex]\displaystyle \int_C \left(3y+5e^{-x}\right)\,\mathrm dx + \left(10x+3\cos\left(y^2\right)\right)\,\mathrm dy[/tex]
Then the region D is
D = {(x, y) : 0 ≤ x ≤ 1 and x ² ≤ y ≤ √x}
so the line integral is equal to
[tex]\displaystyle \int_0^1\int_{x^2}^{\sqrt x} \frac{\partial\left(10x+3\cos\left(y^2\right)\right)}{\partial x} - \frac{\partial\left(3y+5e^{-x}\right)}{\partial y}\,\mathrm dy\,\mathrm dx \\\\ = \int_0^1 \int_{x^2}^{\sqrt x} (10-3)\,\mathrm dy\,\mathrm dx \\\\ = 7\int_0^1 \int_{x^2}^{\sqrt x} \mathrm dy\,\mathrm dx[/tex]
which in this case is 7 times the area of D.
The remaining integral is trivial:
[tex]\displaystyle 7\int_0^1\int_{x^2}^{\sqrt x}\mathrm dy\,\mathrm dx = 7\int_0^1y\bigg|_{y=x^2}^{y=\sqrt x}\,\mathrm dx \\\\ = 7 \int_0^1\left(\sqrt x-x^2\right)\,\mathrm dx \\\\ = 7 \left(\frac23x^{3/2}-\frac13x^3\right)\bigg|_{x=0}^{x=1} = 7\left(\frac23-\frac13\right) = \boxed{\frac73}[/tex]
Charlie is watching hot air balloons. Balloon A has risen at a 56° angle. Balloon B has risen at an 81° angle. If the distance from balloon A to the ground is 1,200 feet, how far is balloon B from balloon A? Round your answer to the nearest whole number. Two points labeled Balloon A and Balloon B are connected to a point labeled Charlie, which is on a straight line labeled ground. A dashed line connects point Balloon A to line Ground; another dashed line connects point Balloon B to line ground; both dashed lines form a right angle with line Ground; the angle formed from point Balloon A, point Charlie, and line ground measures x degrees; and the angle formed by point Balloon B, point Charlie, and line Ground measures y degrees.
A) 999 feet
B) 1,005 feet
C) 1,052 feet
D) 1,102 feet
The distance between Balloon B and Balloon A is 999 feet (correct to the nearest whole number); that is, Balloon B is 999 feet from balloon A
The diagram for the question is shown as described in the question in the attachment below.
From the diagram,
Let the height from balloon A to the ground be /AG/ and the height from balloon B to the ground be /BD/ and the point where Charlie is be C
/AG/ = 1200 feet
/AG/ = /BD/ = 1200 feet ( as shown in the diagram)
The distance between the two balloons is equal to /GD/
Also, from the diagram, /GD/ = /GC/ + /CD/
To find /GC/,
Consider ΔAGC
/AG/ = 1200 feet
/GC/ = ?
From the question, "Balloon A has risen at a 56° angle"
∴ x° = 56°
Using the formula
[tex]tan(x^{o} ) = \frac{/AG/}{/GC/}[/tex]
[tex]tan(56^{o}) = \frac{1200}{/GC/}[/tex]
[tex]/GC/ = \frac{1200}{tan(56^{o}) }[/tex]
/GC/ = 809.41 feet
To find /CD/
Consider ΔBCD
/BD/ = 1200 feet
/CD/ = ?
From the question, "Balloon B has risen at a 81° angle"
∴ y° = 81°
Using the formula
[tex]tan(y^{o} ) = \frac{/BD/}{/CD/}[/tex]
[tex]tan(81^{o}) = \frac{1200}{/CD/}[/tex]
[tex]/CD/ = \frac{1200}{tan(81^{o}) }[/tex]
/CD/ = 190.06 feet
Now, recall that /GD/ = /GC/ + /CD/
∴ /GD/ = 809.41 feet + 190.06 feet
/GD/ = 999.47 feet
/GD/ ≅ 999 feet (to the nearest whole number)
Hence, the distance between the two balloons is 999 feet
Balloon B is 999 feet from balloon A.
Learn more here: https://brainly.com/question/15979174
Answer:
999 Units
Step-by-step explanation:
Find f(-2) given f(x) = –x^3 – 3x^2 +8
Answer:
Option A, 4
Step-by-step explanation:
f(-2) = -(-2)³-3×(-2)²+8
= 8-12+8
= 16-12
= 4
Richland's Real GDP per person is #10b and poorland's Real GDP per person is #5b. However, Richland's Real GDP per person is growing at 1% per year and poorland's Real GDP per person is growing at 3% per year. Compare real GDP per person in the two countries after ten years and after twenty years. Approximately how many years will it take poorland to catch up with Richland?
Answer:
after 5 years, rich : poor = 11.0 : 6.7after 10 years, 12.2 : 9.035.3 yearsStep-by-step explanation:
It is convenient to let a graphing calculator show the answers to these questions.
The exponential equation modelling the growth will be of the form ...
f(x) = (initial value) × (1 +growth rate)^x
Richland's GDP/person can be modeled by r(x) = 10·1.01^x
Poorland's GCP/person can be modeled by p(x) = 5·1.03^x
The attached graph shows values for x=5, 10 and r(x)=p(x).
It will take about 35.3 years for Poorland to catch up.
What’s v=(324pie)(3)
The minimum point of the graph y = 2x^2 + 2x +1 is located at:
Answer:
A
Step-by-step explanation:
By completing the square, y = 2x^2 + 2x +1 will be y=2(x+1/2)^2+(1/2) the minimum point is the vertex of the parabola which is (-1/2, 1/2)
26) What is the perimeter of a rectangle whose
lengths are 9x + 5 and widths are 7x + 2?
Answer:
32х+14
Step-by-step explanation:
[tex]2(9x + 5 + 7x + 2) \\ 18x + 10 + 14x + 4 \\ 32x + 14[/tex]
Answer:
32x + 14
Step-by-step explanation:
The opposite sides of a rectangle are equal, so
perimeter = 2(9x + 5) + 2(7x + 2) ← distribute parenthesis
= 18x + 10 + 14x + 4 ← collect like terms
= 32x + 14
What is the value of n to the nearest whole number?
O 10
o 13
18
o
21
Answer:
n is 13
Step-by-step explanation:
[tex] {n}^{2} = {12}^{2} + {6}^{2} - (2 \times 12 \times 6) \cos(90 \degree) \\ {n}^{2} = 180 \\ n = 13.4[/tex]
Answer:
n is 13
Step-by-step explanation:
The number 42 has the prime factorization 2.3.7. Thus 42 can be written in four ways as a product of two positive integer factors (without regard to the order of the factors):
1.42, 2 · 21,3 · 14, and 6. 7.
Required:
List the distinct ways the number 770 can be written as a product of two positive integer factors.
Answer:
Step-by-step explanation:
770 = 2*5*7*11
So they are:
2*385
10*77
5*154
7*110
14*55
11*70
22*35
