Answer:
Step-by-step explanation:
The question is incomplete. Here is the complete question.
Find the average rate of change of the area of a circle with respect to its radius r as r changes from 3 to each of the following.
(i) 3 to 4
(ii) 3 to 3.5
(iii) 3 to 3.1
(b) Find the instantaneous rate of change when r = 3. A'(3)
Area of a circle A(r)= πr²
The average rate of change of the area of a circle with respect to its radius
ΔA(r)/Δr = πr₂²-πr₁²/r₂-r₁
ΔA(r)/Δr = π(r₂²-r₁²)/r₂-r₁
i) If the radius changes from 3 to 4
ΔA(r)/Δr = π(r₂²-r₁²)/r₂-r₁
ΔA(r)/Δr = π(4²-3²)/4-3
ΔA(r)/Δr = π(16-9)/1
ΔA(r)/Δr = 7π
Hence, average rate of the area of a circle when the radius changes from 3 to 4 is 7π
ii) If the radius changes from 3 to 3.1
ΔA(r)/Δr = π(r₂²-r₁²)/r₂-r₁
ΔA(r)/Δr = π(3.5²-3²)/3.5-3
ΔA(r)/Δr = π(12.25-9)/0.5
ΔA(r)/Δr = 3.25π/0.5
ΔA(r)/Δr = 6.5π
Hence, average rate of the area of a circle when the radius changes from 3 to 3.5 is 6.5π
iii) If the radius changes from 3 to 3.1
ΔA(r)/Δr = π(r₂²-r₁²)/r₂-r₁
ΔA(r)/Δr = π(3.1²-3²)/3.1-3
ΔA(r)/Δr = π(9.61-9)/0.1
ΔA(r)/Δr = 0.61π/0.1
ΔA(r)/Δr = 6.1π
Hence, average rate of the area of a circle when the radius changes from 3 to 3.1 is 6.1π
iv) Instantaneous rate of change A'(r) = 2πr
When r = 3;
A'(3) = 2π(3)
A'(3) = 6π
Hence, the instantaneous rate of change when r = 3 is 6π
Answer:A number decreased by 4 is the same as 12.5
Step-by-step explanation:
Two pence coins are used to make a square. If one millioncoins were used, what would be the length of the sides of the square?
How many square metres would these one million coins cover?
(The diameter of a 2p coin is 25mm to the nearest millimetre.
Answer:
i dont know the answer
Step-by-step explanation:
just put a random answer and hope for the best
Evaluate the line integral ∫CF⋅dr, where F(x,y,z)=−xi−2yj−zk and C is given by the vector function r(t)=⟨sint,cost,t⟩, 0≤t≤3π/2.
Answer:
[tex]\mathbf { \int _ c Fdr= - \dfrac{9 \pi ^2}{8} - \dfrac{3}{2} }[/tex]
Step-by-step explanation:
GIven that:
[tex]r(t) = (sin \ t, cos \ t, t)[/tex]
[tex]r' (t) = (cos \ t, -sin \ \ t, 1)[/tex]
[tex]F(x, y, z) = ( -x, -2y , - z)[/tex]
[tex]F(r(t)) = ( sin \ t , - 2 cos \ t, - 1 t)[/tex]
[tex]F(r(t)) \times r'(t) = (sin \ t, - 2 \ cos \ t , -1 \ t)( cos \ t , - sin \ t , 1 )[/tex]
[tex]= sin t \ cos t + 2 \ sin t \ cos t - 1t[/tex]
[tex]= 3sint \ cost - 1 t[/tex]
[tex]\int _ c Fdr = \int ^b_a f(r(t)) \times r'(t) \ dt[/tex]
[tex]= \int^{3 \pi/2}_0 \ [3 sin \ t \ cos \ t - 1 \ t ] \ dt[/tex]
[tex]= 3 \int ^{3 \pi/2} _0 \ cos \ t ( sin \ t \ dt ) - 1 \int ^{3 \pi/2}_0 \ (t) \ dt[/tex]
Let cos t = u &
sint dt = du
[tex]= 3 \int ^{3 \pi/2_} } _0 \ udu - 1 \int ^{3 \pi/2}_0 \ (t) \ dt[/tex]
[tex]= 3 [ \dfrac{u^2}{2}]^{3 \pi/2}_0 - 1 [ \dfrac{t^2}{2}]^{3 \pi/2}_0[/tex]
[tex]= \dfrac{3}{2} [ cos ^2 \ t ] ^{3 \pi/2} _0- \dfrac{1}{2} ( \dfrac{ 3 \pi }{2 })^2 - 0^2[/tex]
[tex]= \dfrac{3}{2} [ cos ^2 \ \dfrac{3 \pi}{2} - cos ^2 \ 0 ] - \dfrac{1}{2}( \dfrac{9 \pi^2}{4})[/tex]
[tex]= \dfrac{3}{2} ( 0 -1 ) - \dfrac{9 \pi^2}{8}[/tex]
[tex]= - \dfrac{3}{2} - \dfrac{9 \pi ^2}{8}[/tex]
[tex]\mathbf { \int _ c Fdr= - \dfrac{9 \pi ^2}{8} - \dfrac{3}{2} }[/tex]
To answer this question, we apply:
∫CF×dr = ∫ c F (r(t)) × dr
Solution is:
( 1/2) - (9/8)×π
We know r(t) = sint i + cost j + t k
Then dr = ( cost i - sint j + k ) dt
And F ( x , y , z ) = -x i - 2y j - z k
Then F ( r(t)) = - sint i - 2 × cost j - t × k
And F ( r(t)) × dr = (- sint×cost + 2 ×sint ×cost - t ) dt
∫F (r(t)) × dr = ∫ (- sint×cost + 2 ×sint ×cost - t ) dt
Integration limits 0≤ t ≤ ( 3/2 ) π
∫ (- sint×cost + 2 ×sint ×cost - t ) dt = ∫ ( sint ×cost - t ) dt
∫ sint ×cost × dt - ∫ t × dt
∫F (r(t)) × dr = (1/2) sin²t - ( 1/2) × t² | 0 y (3/2) π
∫F (r(t)) × dr = (1/2)× ( -1)² - 0 - ( 9/8 ) × π - 0
∫F (r(t)) × dr = ( 1/2) - (9/8)×π
Related Link :https://brainly.com/question/3645828
Will GIVE 75 POINTS PLZ HELP!!!
Joey owns a small bakery and today Phoebe has ordered 100 cookies. If Joey boxes the cookies by the dozen, which of the following equations describes how many boxes of cookies Phoebe will have? Let b represent the number of boxes. (HINT: All of the cookie boxes are not necessarily full.)
A. 100 = b/12
B. 12b + 4 = 100
C. 12b = 100 – 4
D. 100/b = 12
E. (100-4)/12=b-1
F. 12 + b = 100
Answer:
A
Step-by-step explanation:
x^2 -9 divided by x+3
Answer:
x-3
Step-by-step explanation:
x²-9÷x+3=x-3
2-(3x2)➗6 solve this asap pls (I just need the number) ty <3
Answer:
1
Step-by-step explanation:
If 7x + 4 = -19 + 5x, then 2x – 14 equals
A-23
B 23
C-37
D-14
Answer:
C
Step-by-step explanation:
Here we have the question,
7x+4 = -19 + 5x
Now we add 19 to both sides,
7x + 4 + 19 = -19 + 19 + 5x
7x + 23 = 5x
Now we subtract 7x from both sides,
23 = -2x
We divide -2 from both sides,
x = -23/2
Now we plug this in into 2x - 14,
2(-23/2) - 14 = -23-14 = -37
Our answer is C
Please Help. Will give brainlleast.
Answer:
(-1, 0), (-1, -5)
Step-by-step explanation:
The initial translation transformation was ...
(x, y) ⇒ (x +4, y)
Then the reflection across the line y=x added the transformation ...
(x, y) ⇒ (y, x)
So, the result of the composition of transformations was ...
(x, y) ⇒ (y, x+4)
Then the reverse transformation, the one that gets from the image back to the pre-image, will be ...
(y, x+4) ⇒ (x, y)
(x, y) ⇒ (y-4, x)
The points A", B", C", D" will be transformed back to pre-image points ...
A"(-4, 5) ⇒ A(1, -4)
B"(-1, 5) ⇒ B(1, -1)
C"(0, 3) ⇒ C(-1, 0) . . . . . . matches an answer choice
D"(-5, 3) ⇒ D(-1, -5) . . . . . matches an answer choice
Evaluate the expression. 202 + 6(9 + 3)
Answer:
= 274
Step-by-step explanation:
202 + 6(9 + 3)
= 202 + 9 * 12
= 202 + 72
= 274
Answer:
Its is actually 472
Step-by-step explanation:
Please help ASAP. Worth 50 points
Answer:
the anser is 9.5+1.5n and the second ansr is 48x+16
Answer:
a
Step-by-step explanation:
How are I supposed to do this ?
Answer:
Step-by-step explanation:
1. binomial polynomial
2. 2 terms
3. 4 is the constant term
4. - 1/10 x^3 is the leading term
5. -1/10 is the leading coefficient.
can some one plzz answer this fastttttt plzzz
Answer:
Please see attached picture
hope it helped you:)
Harper deposited $110 into a savings account that earns 3.5% interest a year. The function (R)t models the amount of money Raymond has in his savings account as a function of time (t) in years. R(t)=110(1.025)^t How much more money will Harper have in his savings account than Raymond after two years? A: $2.26 B: $7.83 C: $5.57 D: $3.37
Answer:
A. $2.26
Step-by-step explanation:
An equation for Harper's balance can be written similar to the one written for Raymond's balance. It will be ...
H(t) = 110(1.035)^t
For t = 2, the two balances will be ...
H(2) = 110(1.035^2) = 117.83
R(2) = 110(1.025^2) = 115.57
The difference is ...
$117.83 -115.57 = $2.26
Harper's account will have $2.26 more.
_____
As a quick estimate or sanity check, you can see that Harper's interest rate is 1% more than Raymond's. So, in 2 years, he will earn a little more than 2% more on his investment than Raymond earns. 2% of $110 is $2.20, so the difference can be expected to be slightly more than this.
2564.0 millimeters tall. If the boards are too long they must be trimmed, and if the boards are too short they cannot be used. A sample of 26 is made, and it is found that they have a mean of 2559.5 millimeters with a standard deviation of 15.0. A level of significance of 0.05 will be used to determine if the boards are either too long or too short. Assume the population distribution is approximately normal. Find the value of the test statistic. Round your answer to three decimal places.
Answer:
We conclude that the board's length is equal to 2564.0 millimeters.
Step-by-step explanation:
We are given that a sample of 26 is made, and it is found that they have a mean of 2559.5 millimeters with a standard deviation of 15.0.
Let [tex]\mu[/tex] = population mean length of the board.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 2564.0 millimeters {means that the board's length is equal to 2564.0 millimeters}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] [tex]\neq[/tex] 2564.0 millimeters {means that the boards are either too long or too short}
The test statistics that will be used here is One-sample t-test statistics because we don't know about the population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{s }{\sqrt{n}} }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample mean length of boards = 2559.5 millimeters
s = sample standard deviation = 15.0 millimeters
n = sample of boards = 26
So, the test statistics = [tex]\frac{2559.5-2564.0}{\frac{15.0 }{\sqrt{26}} }[/tex] ~ [tex]t_2_5[/tex]
= -1.529
The value of t-test statistics is -1.529.
Now, at a 0.05 level of significance, the t table gives a critical value of -2.06 and 2.06 at 25 degrees of freedom for the two-tailed test.
Since the value of our test statistics lies within the range of critical values of t, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region.
Therefore, we conclude that the board's length is equal to 2564.0 millimeters.
A magnitude 6.7 earthquake struck the SanFernando valley region of Los Angeles in 1994, causing widespread damage. Suppose another region with more active earthquakes and the number of earthquakes in this region is a random variable (binomial) distribution. Use a normal distribution approximation to find standard deviation if the probability is 0.87 that there will be at least 15 earthquakes with mean=17.6.
Answer: 2.308 .
Step-by-step explanation:
Let X denotes the number of earthquakes in SanFernando valley region of Los Angeles in 1994.
Given: [tex]\mu=17.6[/tex]
Probability is 0.87 that there will be at least 15 earthquakes .
i.e. [tex]P(X\geq15)=0.87[/tex]
[tex]\Rightarrow\ P(\dfrac{X-\mu}{\sigma}\geq\dfrac{15-17.6}{\sigma})=0.87\\\\ \Rightarrow\ P(Z\geq\dfrac{-2.6}{\sigma})=0.87\ \ \ [Z=\dfrac{X-\mu}{\sigma}][/tex]
Z-value corresponding to p-value 0.87 is -1.1263 .
So, [tex]\dfrac{-2.6}{\sigma}=-1.1263[/tex]
[tex]\sigma= \dfrac{-2.6}{-1.1263}\approx2.308[/tex]
Hence, the required standard deviation = 2.308 .
PLease help i dont know how to do this please explain too!!
Answer:
6.25
Step-by-step explanation:
The perimeter is the sum of the lengths of the sides.
For a rectangle, it's the two widths plus the two heights.
P = 2W + 2H
Plugging in values:
52 = 2(3x − 1) + 2(x + 2)
52 = 6x − 2 + 2x + 4
52 = 8x + 2
50 = 8x
x = 6.25
Find the value of x.
Formula used:-Perimeter of rectangle = 2 ( l + b )
Solution:-We know that,
Perimeter of rectangle = 52 [ Given ]
⇒ 2 ( l + b ) = 52
⇒ 2 ( 3x - 1 + x + 2 ) = 52
⇒ 2 ( 4x + 1 ) = 52
⇒ 8x + 2 = 52
⇒8x = 52 - 2
⇒ 8x = 50
⇒ x = 50/8
⇒ x = 6.25 inches
Find the sum of x^2 + 3x and – 2x^2 +9x + 5.
Answer:
-x² + 12x + 5
Step-by-step explanation:
Step 1: Write out expression
x² + 3x - 2x² + 9x + 5
Step 2: Combine like terms
-x² + 3x + 9x + 5
Step 3: Combine like terms
-x² + 12x + 5
Answer:
-x² + 12x + 5
Step-by-step explanation:
pls help im stuck on this
The -2/5 means we go to the left 2/5 of a full unit. So we take 2 small little steps (going over 2 little tickmarks), then we move 4 small steps to the right due to the +4/5 portion. Ultimately, we end up at 2/5 as the answer
So -2/5 + 4/5 = 2/5
This can be thought of as -2+4 = 2, then you just stick 5 in the denominator for each term.
A highway sign in Canada gives the speed limit as 100 kilometers per hour. If you are driving 62 miles per hour are you driving under the speed limit? (1mi=1.6km)
As we know that 1 mile=1.6km
then,
62 miles=62*1.6km
=99.2km/hour
so, yes we are driving under the speed limit.
Answer:
Yes
Step-by-step explanation:
Convert 62 mph to kph by multiplying it by 1.6
62(1.6)
= 99.2
Yes, you are driving under the speed limit
Rhonda is building a rectangular patio. The perimeter of the patio is to be 96 feet. Determine the dimension of the patio if the length is to be 6 feet less than twice the width
Answer:
Length= 30 ft
Width= 18ft
Step-by-step explanation:
The perimeter of the rectangular patio is to be 96 feet.
the length is to be 6 feet less than twice the width
Perimeter=2(length+width)
But
Length= 2(width)-6
Substituting in perimeter equation
Perimeter=2(length+width)
Perimeter=2((2(width)-6)+width)
Perimeter= 96 feet
Let width= x
Perimeter=2((2(width)-6)+width
96=2((2(x)-6)+x)
96= 4x-12+2x
108= 6x
18= x
Width= 18ft
Length= 2(width)-6
Length= 2(18)-6
Length= 36-6
Length= 30 ft
HELP PLEASE ASAP !!!!
-3h -6(5h/3 + 7/2) +9h = -53
Find the value for h.
Answer: h= 8
Step-by-step explanation:
-3h - 6(5h/3 + 7/2) + 9h = -53 Distribute on the left
-3h - 10h - 21 + 9h = -53 combine like terms on the left side
-4h -21 = -53 Now add 21 to both sides
+21 +21
-4h = -32 Divide both sides by -4
h = 8
root 2+ root 32+ root 64
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Hi my lil bunny!
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
Let's simplify step-by-step.
[tex]root^2 + root^{32} + root^{64}[/tex]
[tex]= o^2 rt^2 + o^2 rt^{32} + o^2 rt^{64}[/tex]
Answer : [tex]\boxed{o^2 rt^2 + o^2 rt^{32} + o^2 rt^{64}}[/tex]
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Have a great day/night!
❀*May*❀
**Will mark brainilest, please help!** A rectangular piece of metal is 10 in longer than it is wide. Squares with sides 2 in long are cut from the four corners and the flaps are folded upward to form an open box. If the volume of the box is 598 in3, what were the original dimensions (width and length) of the piece of metal?
Answer:
The dimensions of the piece of metal can be represented by x and x+10.
Now, 2 in squares are being cut out of each corner.
So the new dimensions are x-4 (2in from each side) and x+10-4 or x+6.
When you fold it up, the height becomes 2 and the base has dimensions x-4 and x+6. Now plug this into the volume formula.
V=l*w*h
1302 = (x+6)(x-4)(2)
651 = x2+2x-24
0 = x2 + 2x-675
0 = (x+27)(x-25)
x=-27 reject since lengths cannot be negative or x=25.
So your original dimension for the piece of metal are 25 by 35.
Step-by-step explanation:
1. The x-intercept of the equation 5x - 2y = 10 is
Answer:
x =2
Step-by-step explanation:
The x- intercept is when y = 0
Hence, 5x - 2y = 10
5x - 2(0) = 10
5x = 10
Therefore, x = 2
some please help me
It looks like you want to find the height of the green region. If so then that would be about 5.2 mL since the top part of the green area is around the first smaller tick above the 5.
Each smaller tickmark is 1/5 = 0.2 of a full unit. Note how there are 5 smaller tickmark spaces to make up a full unit (when we go from 5 to 6, there are 5 smaller tickmark spaces we have to move)
Answer: 5.2 mLSarah saw seven sharks while swimming now how many S is in the sentence
Answer:
6 S's in the sentence
Step-by-step explanation:
23×99×90+54+23-12321
answer please
Answer:
[tex]192686[/tex]
Step-by-step explanation:
23×99×90+54+23-12321
=2277×90+54+23-12321
=204930+54+23-12321
=204984+23-12321
=205007-12321
=192686
Answer:
192686 is answer.
Step-by-step explanation:
= 23*99*90+54+23-12321
= 204930 +77-12321
= 205007 -12321
= 192686.
Solve 5g = 20
Please and thank u
Answer:
g = 4
Step-by-step explanation:
5g = 20
Divide each side by 5
5g/5 = 20/5
g = 4
Answer:
g= 4
Step-by-step explanation:
5g = 20
5g /5 = 20 /5
g =4
Scores on a college entrance examination are normally distributed with a mean of 500 and a standard deviation of 100. What percent of people who write this exam obtain scores between 350 and 650?
Answer:
86.64%
Step-by-step explanation:
We solve for the above question using z score formula
z score formula = z = (x - μ)/σ
where
x is the raw score
μ is the population mean
σ is the population standard deviation.
For x = 350, μ = 500, σ = 100
z score = 350 - 500/100
= -150/100
= -1.5
Using the z score for normal distribution
Probability (z = -1.5) = P(x = 350).
= 0.066807
For x = 650, μ = 500, σ = 100
z score = 650 - 500/100
= 150/100
= 1.5
Using the z score for normal distribution
Probability (z = 1.5) = P(x = 650).
= 0.93319
The probability of people who write this exam and obtain scores between 350 and 650
P < 350 < x < 650 = P(x ≤ 650) - P(x ≤ 350)
= P(z = 1.5) - P(z = -1.5)
= 0.93319 - 0.066807
= 0.866383
Therefore, the percent of people who write this exam and obtain scores between 350 and 650 is
0.866383 × 100
= 86.6383%
Approximately ≈ 86.64%
The measures of the angles of a triangle are in the ratio 2 : 3 : 4. The simplified ratio of the measures of the exterior angles of the triangle is a : b : c. Find a + b + c.
Answer:
Step-by-step explanation:
2x+3x+4x=180 degrees
9x=180 fdegrees
x=180/9
x=20
2x=40
3x=60
4x=80
Answer:
18
Step-by-step explanation:
The measures of the angles of a triangle are in the ratio 2:3:4 means we have one interior angle measuring 2x, another measuring 3x, and the last one measuring 4x. We know the sum of the measures of the interior angles of a triangle is 180 degrees.
We need to solve the following equation to find first x, and then find the measurement of each interior angle of the triangle.
2x+3x+4x=180
(2+3+4)x=180
(9)x=180
x=180/9
x=20
So one interior angle measures 2x=2(20)=40.
Another measures 3x=3(20)=60.
The last measuring 4x=4(20)=80.
The exterior angles of this triangle therefore measure the following:
180-40=140
180-60=120
180-80=100
So the un-simplified ratio of the measures of the exterior angles is as follows:
140:120:100.
Let's simplify that.
It is easy to see each number is divisible by 10.
Let's reduce it by dividing each by 10:
14:12:10
Let's simplify more (as we want the most simplified ratio).
Each number is divisible by 2 since they are all even.
Let's reduce again but not by dividing by 2:
7:6:5
So the simplified ratio of the measures of the exterior angles of the triangle is a:b:c=7:6:5 and so a+b+c=7+6+5=18.
Answer is 18.
Assume that the Poisson distribution applies and that the mean number of hurricanes in a certain area is 6.2 per year. a. Find the probability that, in a year, there will be 5 hurricanes. b. In a 35-year period, how many years are expected to have 5 hurricanes? c. How does the result from part (b) compare to a recent period of years in which years had hurricanes? Does the Poisson distribution work well here?
Answer: Try to use socratic
Step-by-step explanation: