Answer:
(a) 9800π cm²/s
(b) 39200π cm²/s
(c) 58800π cm²/s
Step-by-step explanation:
As we know,
The area of circle is:
[tex]A= \pi r^2[/tex]
[tex]\frac{dA}{dt}=2 \pi r\frac{dr}{dt}[/tex]
The given value is:
[tex]\frac{dr}{dt} =70 \ cm/s[/tex]
Now,
(a)
After 1 second,
r = 70×1
= 70 cm
⇒ [tex]\frac{dA}{dt}=2\pi(70)\times (70)[/tex]
[tex]=9800 \pi \ cm^2/s[/tex]
(b)
After 2 second,
r = 70×4
= 280 cm
⇒ [tex]\frac{dA}{dt}=2\pi \ (280)\times (70)[/tex]
[tex]39200\pi \ cm^2/s[/tex]
(c)
After 6 seconds,
r = 70×6
= 420 cm
⇒ [tex]\frac{dA}{dt}=2\pi \ (420)\times (70)[/tex]
[tex]58800\pi \ cm^2/s[/tex]
The rate will be:
(a) 9800 π cm²/s
(b) 39200 π cm²/s
(c) 58800 π cm²/s
Circle:A circle seems to be a closed object or structure generated by tracing a point that travels together in plane at quite a constant distances from either a specific location.
According to the question,
Speed, [tex]\frac{dr}{dt}[/tex] = 70 cm/s
We know,
The area of circle:
→ A = πr²
[tex]\frac{dA}{dt}[/tex] = 2πr[tex]\frac{dr}{dt}[/tex]
(a) After 1 s, the rate be:
r = 70 × 1
= 70 cm
[tex]\frac{dA}{dt}[/tex] = 2π(70) × 70
= 9800 π cm²/s
(b) After 2 s, the rate be:
r = 70 × 4
= 280 cm
[tex]\frac{dA}{dt}[/tex] = 2π(280) × 70
= 39200 π cm²/s
(c) After 6 s, the rate be:
r = 70 × 6
= 420 cm
[tex]\frac{dA}{dt}[/tex] = 2π(420) × 70
= 58800 π cm²/s
Thus the response above is correct.
Find out more information about area of circle here:
https://brainly.com/question/12069107
Given that z is a standard normal random variable, what is the value of z if the area to the left of z is 0.9382:
a. 1.8
b. 1.54
c. 2.1
d. 1.77
Answer: 1.54
Step-by-step explanation:
Given that :
Z = normal random variable
Area to the left of z = 0.9382
For a random normal distribution ;
P(Z < x) = 0.9382
Using the Z table (standard normal distribution table) ;
Locating the probability value (0.9382) on the table and picking the intersecting z value both horizontally and vertically :
Horizontal value = 1.5
Vertical value = 0.04
Horizontal + vertical = (1.5 + 0.04) = 1.54
What is the correct value of d?
if [tex]x\leq cy+D[/tex], solve for y in terms of x, c and d? (c>0)
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
[tex]x \leqslant cy + D[/tex]
Subtract sides D
[tex]x - D \leqslant cy + D - D[/tex]
[tex]x - D \leqslant cy[/tex]
Divide sides by c
[tex] \frac{x - D }{c} \leqslant \frac{cy}{c} \\ [/tex]
[tex] \frac{x -D}{c} \leqslant y \\ [/tex]
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
How much is 0 x , where x is any non-zero number? How much is 0 x for any positive power of x? How much is 0 0 ? Explain.
Answer:
Step-by-step explanation:
The value X° where x is non zero number will give a value of 1 because any value raise to the power of zero gives 1.
For example if X = 2, 2° = 1
For the expression 0^x, this will result into zero for any positive power of x. Let x be 3 for example,
0³ = 0×0×0
0³ = 0
Also if x = 4
0⁴ = 0×0×0×0 = 0
Therefore, no matter the value of x, rge value 0^x will return back zero.
For 0^0 this value is an indeterminate function i.e we cannot determine the the value. The value cannot return Amy positive or negative real number on the number line. Hence 0^0 is indeterminate.
Help with number 1 please
Answer:
you could stay there 6 nights
Step-by-step explanation:
to solve this you would do 825$ ÷ by the amout which is 134$ and then you get 6.15671641791 then you would round it which give you 6 nights.
A random sample of 114 observations produced a sample mean of 30. Find the critical and observed values of z for the following test of hypothesis using The population standard deviation is known to be 5 and the population distribution is normal.
Complete Question
A random sample of 114 observations produced a sample mean of 30. Find the critical and observed values of z for the following test of hypothesis using α=0.01. The population standard deviation is known to be 5 and the population distribution is normal.
[tex]H_o: \mu =28[/tex] versus H1: μ>28.
Round your answers to two decimal places.
[tex]z_{critical} =[/tex]
Answer:
[tex]z_{critical} = 2.33[/tex]
The observed value is [tex] z = 4.27 [/tex]
Step-by-step explanation:
From the question we are told that
The sample size is n = 114
The sample mean is [tex]\= x = 30[/tex]
The significance level is [tex]\alpha = 0.01[/tex]
The population standard deviation is [tex]\sigma = 5[/tex]
The null hypothesis is [tex]H_o: \mu =28[/tex]
The alternative hypothesis is H1: μ>28.
Generally the test statistics (observed value ) is mathematically represented as
[tex] z = \frac{ \= x - \mu }{ \frac{\sigma }{\sqrt{n} } } [/tex]
=> [tex] z = \frac{ 30- 28 }{ \frac{5}{\sqrt{114} } } [/tex]
=> [tex] z = 4.27 [/tex]
From the normal distribution table the critical value of [tex]\alpha = 0.01[/tex] is
[tex]z_{critical} = 2.33[/tex]
find the value of x !!!!
What is 34.567 rounded to the tenths place
Answer:
34.57 I'm pretty sure yayyy
Answer:
34.567 rounded to tenths is 34.6
Step-by-step explanation:
because if you look at the number to the right it five or more so you raise the score and the five turns to a 6 so 34.567 = 34.6
Imaginary Numbers (File attached)
I WILL AWARD EXTRA 50 POINTS AND BRAINLIEST
Raise the monomial to a power:
5x2y3 to the power of 2
–4ax3 to the power of 3
–2m3n2t the power of 4
–a2bc3 to the power of 5
Answer
1. 52x4y6
2. −2 2 ax 27
3.-2m3n2t4
4.−a 2 bc 243
I dont have an explination sorry
and maybe no spaces
Eve saw 715 cars in her front yard. 2/5 of the cats were black. How many black cats were in Eves front yard.
PLZZZ HELPS ME I WILL GIVE BRAINLIEST!
Which relations are functions?
Select Function or Not a function for each graph.
Answer: The first 3 are functions. The last one is not a function
Step-by-step explanation: What you can do is the line test. If you draw a line through it, the line shouldn't touch the arrow twice. Like the last one, it touches the line twice, so it is not a function
I have a small dog and a big dog. My big dog weighs 50 pounds more than twice the weight of my small dog. The sum of their weght is 68 pounds. How much do they weigh?
Answer:
Small dog =18
Big dog=50
Step-by-step explanation:
68-50=18
Answer:
75+68
Step-by-step explanation:
how to get domain and range from a table of values.
Answer: The domain is all of the possible values for the input (x) axis. The range is the possible values for the output (y).
Step-by-step explanation: You will have to subtract the least value from the greatest value for both your x and y.
find the value of X and Y if (2x + 3) + i(x – 2y) = 5 – 7i
Answer:
x = 1, y = 4
Step-by-step explanation:
Given
(2x + 3) + i(x - 2y) = 5 - 7i
Equate the real parts on both sides
2x + 3 = 5 ( subtract 3 from both sides )
2x = 2 ( divide both sides by 2 )
x = 1
Equate the coefficients of the imaginary terms
x - 2y = - 7 , that is
1 - 2y = - 7 ( subtract 1 from both sides )
- 2y = - 8 ( divide both sides by - 4 )
y = 4
Sarah babysat for 3 hours and earned $24. At this rate, how much money will Sarah earn if she babysits for 8 hours?
о
Translate the phrase into an algebraic expression.
y more than 4
Answer:
y+4
Step-by-step explanation:
NEED HELP WITH MATH! Will Give Brainliest! Image is below.
The answer is number 4. x=1 x=2 x=-2
Solve for x? -10x-(-4)=14
Q: -10x-(-4)=14
A: x=-1
Process:
-Subtracting a negative is just like adding 10x+4=14
-Subtract 4 from both sides -10x=10
Divide -10 from both sides x=-1
The percent of fat calories that a person in America consumes each day is normally distributed with a mean of about 36 and a standard deviation of about 10. Suppose that 16 individuals are randomly chosen. For the group of 16, find the probability that the average percent of fat calories consumed is more than thirty-five (Round to 3 decimal places)
Answer:
Step-by-step explanation:
Mean μ = 36
standard deviation σ = 10
n = 16
standard deviation of the group σ₁ = σ / √n
σ₁ = 10/ √16
= 10 / 4 = 2.5
σ₁ = 2.5
P ( x > 35 ) = 1 - P ( x < 35 )
P ( x < 35 ) = P( z < (35 - 36) / 2.5 ) = P( z < (35 - 36) / 2.5 )
= P( z < 0.4 )
= .3446
P ( x > 35 ) = 1 - .3446
= .6554 .
It has been debated for years as to whether or not Descartes's Rule of Signs is helpful when working with Polynomial Functions. In your own words:
a) explain the purpose in using Descartes's Rule of Signs
b) state whether or not you think it is helpful or simply a waste of time, then explain your answer.
Use the graph of the line to answer the questions.
What is an equation of the line in point-slope form?
y-1=3(x+0)
y-0=3(x-1)
y+1=(1/3)(x+2)
y+2=(1/3)(x+1)
How can the point-slope form be written in function notation?
f(x)=(1/3)x-(5/3)
f(x)=(1/3)x-(1/3)
f(x)=3x-3
f(x)=3x+1
Answer: Use the graph of the line to answer the questions.
What is an equation of the line in point-slope form?
✔ y + 1 = (1/3)(x + 2)
How can the point-slope form be written in function notation?
✔ f(x) = (1/3)x – (1
Suppose the difference between actual and predicted weekly sales of a company follows a uniform distribution between -$4000 and $4000. Determine the probability that the actual sale is within $1500 of the predicted sale (which means P(-1500
Answer: 0.375
Step-by-step explanation:
Given: The difference between actual and predicted weekly sales of a company follows a uniform distribution between -$4000 and $4000.
Probability density function: [tex]f(x)=\dfrac{1}{b-a}=\dfrac{1}{4000-(-4000)}=\dfrac{1}{8000}[/tex]
The probability that the actual sale is within $1500 of the predicted sale = [tex]\int^{1500}_{-1500}f(x)dx=\int^{1500}_{-1500}\dfrac{1}{8000}dx=\dfrac{1}{8000}[x]^{1500}_{-1500}\\\\= \dfrac{1}{8000}(1500-(-1500))\\\\= \dfrac{1}{8000}(3000)=0.375[/tex]
Hence, Required probability =0.375
4- Employees at a certain company currently have to pay 7% of their health care costs,
while the company pays the rest. Next year, however, employees will have to pay 14%
of their health care costs. Express this change as:
absolute change (in percentage points) =
relative change =
Answer:
The absolute change would be 3 percentage points.
The relative change would be 100%
Step-by-step explanation:
You purchase 3 items for $4.23. About how much did you spend?
Answer:
4.23 rounded to the nearest whole number is 4.
Answer:
4.23 2.115 per item
Step-by-step explanation:
what is i^30
Math is killing me and i have no real help someone save me!!! I cant even start to understands this concept so if you could explain and give the answer that'd be great bunch of points if you do!!!
Answer:-1
Step-by-step explanation: It’s seen as a pattern going back and forth between a few answers.
Answer:
It's -1.
Step-by-step explanation:
i has no value but if you multiply it by itself 30 times you get -1. Imaginary numbers are great, I know.
649+n= 700 +27
295-38 =n-24
Question 1
[tex]649+n=700+27\\ \\649+n=727\\ \\ n=\boxed{78}[/tex]
Question 2
[tex]295-38=n-24\\\\257=n-24\\\\n=\boxed{281}[/tex]
What is the slope of the line that goes through the points (1,-2) and (3,6)?
Question 1 options:
-4
4
1
2
Answer: 4
Step-by-step explanation: Brainliest plz!!
Which best explains the forces acting on the objects?
Answer:
this answer is not avaliable because i didnt have any options.
Step-by-step explanation:
Answer:
The answer is B: Objects W and Y have balanced forces, and objects X and Z have unbalanced forces.
Step-by-step explanation:
A polynomial, P(x) = x2 + 2x + k has (x – 2) as a factor. What is
the value of k?
Answer:
x-2 =0
x=2
now
putting the x value in p
we have,
p(2) = x2 + 2x +k
= 2×2 +2×2+k
= 4+4+k
= 8+k
so,
Either
8+k =0
k= - 8