[tex] \frac{dr}{dt} = 6.79 \: \frac{m}{s} [/tex]
Step by Step Explanation:
The area a is defined as
[tex]a = \pi {r}^{2} [/tex]
Now take derivative of the above expression with respect to time:
[tex] \frac{da}{dt} = 2\pi r \frac{dr}{dt} [/tex]
Solving for dr/dt, we then get
[tex] \frac{dr}{dt} = \frac{1}{2\pi r} \frac{da}{dt} [/tex]
Note that da/dt = 900 m^2/s and when the area of the oil slick is 1400 m^2, the radius r is r = √(1400/π) = 21.1 m. Therefore,the rate at which the radius is increasing dr/dt is
[tex] \frac{dr}{dt} = \frac{1}{2\pi(21.1 \: m)}(900 \frac{ {m}^{2} }{s} ) = 6.79 \frac{m}{s} [/tex]
2. Evaluate the expression when x = 7 and y = 4 x * y - 4(2)
Answer:
20
Step-by-step explanation
7*4=28
28-4=24
4(2)=8
28-8=20
hope that helped!!
Answer:
y = 8/27
Step-by-step explanation:
given
x = 7
y = 4x*y - 4(2)
y = 4*7*y - 8
y = 28y - 8
8 = 28y - y
8 = 27y
8/27 = y
to prove
y = 4x*y - 4(2)
8/27 = 4*7*y - 8
8/27 = 28*8/27 - 8
8/27 = 224/27 - 8
8/27 = 224 - 27*8/27
8/27 = 8/27
hence it is proved that y is 8/27 .
The area of a sector created by a 120° angle is 4 pi in squaredWhat is the area of a sector created by an angle of 30°
in the same circle
Answer:
π in²
Step-by-step explanation:
We'll begin by calculating the radius of the circle. This can be obtained:
Area of sector (A) = 4π in²
Angle (θ) = 120 °
Radius (r) =?
The radius of the circle can be obtained by using the formula for calculating the area of a sector. This is illustrated below:
A = θ/360 × πr²
4π = 120/360 × πr²
4π = ⅓ × πr²
Cross multiply
3 × 4π = πr²
12π = πr²
Divide both side by π
r² = 12π / π
r² = 12
Take the square root of both side
r = √12 in
Thus, the radius is √12 in.
Finally, we shall determine the area of the sector created by 30 °. This can be obtained as follow:
Radius (r) = √12 in
Angle (θ) = 30 °
Area of sector (A) = ?
A = θ/360 × πr²
A = 30/360 × π(√12)²
A = 1/12 × 12π
A = π in²
Therefore, the area of the sector created by 30 ° us π in².
What is the value of ?
Answer:
x=3
Step-by-step explanation:
Log base 5 of 125=x
that is equal to 5x5x5 which is 125
5 is multiplied 3 times so x is 3
if x=-4 then what is x^2? in an equation for my homework, they have the solution as positive instead of negative and I don’t understand why.
Answer:
see explanation
Step-by-step explanation:
Given
x² , then when x = - 4
x² = - 4 × - 4 = + 16
[ the product of a negative and a negative results in a positive ]
Which of the following is geometric sequence
A. 1,1/2,1/4,1/8
B.2,4,6,8
C.1,1,2,3,5
D.7,4,1,-2
Answer:
A
Step-by-step explanation:
...................
Answer:
here's the whole unit test
Step-by-step explanation:
ur welcomeeeee ;)
solve
(3431)−2/3÷(491)3/2
a. 16807
b.343
c.49
d.2401
4th grade math question
Answer:
1 1/6
Step-by-step explanation:
the problem is asking you to do 1/6 7 times. Lets break it down and make it 1/6 plus 1/6 plus 1/6 plus 1/6 plus 1/6 plus 1/6 plus 1/6
so lets add the all the numerators 1 plus 1 plus 1 plus 1 plus 1 plus 1 plus 1 is 7
the numerator value is 7 and you dont add the denominator so it stays as 6
so the answer is 7/6 or 1 1/6 as a mixed number
Answer:1 1/6
Step-by-step explanation: The answer is one and one sixth because when you imagine that the 7 is over one, when you times it you get 7/6 and that is 1/ 1/6
Which of the following are the domain and range that represent the inverse of the function f(x), given the mapping diagram of f(x) below? 1 AWN O 2. 4 6 8
Answer:b
Step-by-step explanation:
Find Z for the following sequence:
210, 209, 213, 186, 202, Z
Answer:
77
Step-by-step explanation:
as far as I can tell the steps between the given numbers are
-1
+4
-27
+16
1 can be expressed as 1³
4 can be expressed as 2²
27 can be expressed as 3³
16 can be expressed as 4²
my best guess is that next one is minus 5³ = -125
edit: technically the given steps can be expressed as
(-1)³
(-2)²
(-3)³
(-4)²
somewhat nicer pattern there
{3/4 x (3/3/4 ÷ 5/16)} -3/1/3
An airplane flying at an altitude of 37,000 feet is still A horizontal distance of 100 miles (100 miles = 5280 ft) from the airport. What angle of depression does the airplane need to use to reach the runway?
Given :
An airplane flying at an altitude of 37,000 feet is still A horizontal distance of 100 miles (100 miles = 5280 ft) from the airport.
To Find :
What angle of depression does the airplane need to use to reach the runway?
Solution :
Let, angle of depression is [tex]\theta[/tex] .
So,
[tex]tan\ \theta = \dfrac{ Altitude \ in \ which \ plane \ is \ flying}{Horizontal \ Distance}\\\\tan \ \theta = \dfrac{37000}{5280}\\\\tan \ \theta = 7.00\\\\\theta = tan^{-1} 7\\\\\theta = 81.87^o[/tex]
Hence, this is the required solution.
I need help with this with work asap thank you
Answer:
multiply all sides (5.5 x 6 x 8.5) which results to 261.5 ft squared
Can someone help me? Question attached, 20 points.
Answer:
6
Step-by-step explanation:
[tex]V = A * b = 5A[/tex]
[tex]5A = 141.3[/tex]
[tex]A = 28.26[/tex]
[tex]\pi r^2 = 28.26[/tex]
[tex]3.14 r^2 = 28.26[/tex]
[tex]r^2 = 9[/tex]
[tex]r = 3[/tex]
[tex]D = 2r = 2 * 3 = 6[/tex]
- Leona Bahr is paid a commission of 12% on all sales above $7,000 for the week. She is also paid a weekly salary of $380. What are her total earnings for a week in which her sales were $9,800?
Answer:
716
Step-by-step explanation:
9800-7000=2800 sales over 7000
2800 x .12=336 commission
380 (salary) + 336 (commission)=716 Total earnings
accounting equation is what
Help me...!
!!
!!
!!
!!
The answer to this question is:
2 ¾ inches.
Can anyone solve this?
Answer:
They are congruent
Step-by-step explanation:
The reason that WK is congruent to WL is because both come from the same origin of W and they both end up in the same place on their side. Which means if WK and WL are congruent, that means that AK and AL are congruent as well.
Which choice is equivalent to the fraction below when x is an appropriate
value? Hint: Rationalize the denominator and simplify.
4
4 - 6x
A. 8+226x
16 - 6x
B. 8+ 2162
846
C.
2 + V6
4- 6x
D. 8. 216
8 - 3x
UN
1. 8^3 * 8^2, 8^5, and (2^3)^5
2. 6^9, and 6^5 x 6^4
Answer:
8+2√6x / 8-3x
Step-by-step explanation:
yes
Sarah can do 68 push ups in 4 minutes . At this rate how many push ups can she do each minute?
Answer:
Sarah can do 17 push-ups each minute.
Step-by-step explanation:
4 minutes = 68 push ups
68 divided by 4 = 17 push ups
1 minute = 17 push ups
- 12. What is the greatest common factor of 120 and 84?
e.
a. 3
b. 6
12
18
d.
Answer:
12 (the third one is the greatest common factor of 120 and 84)
Answer:
12
Step-by-step explanation:
factors of 120. 1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,80,120
factors of 84: 1,2,3, 4,6,7,12,14,28,42,84
greatest common factor=12
The area of A PQR is 15 m², and p = 5 m, q = 10 m.
Find the possible measure of angle R (in degrees)
PLEASE HELP i dont know the answer for: Chose an equivalent ratio 15 cats to 20 dogs. choices: A. 4 to 5. B. 3 to 4. C. 3 to 5. D. 10 to 15.
Answer:
D 10 to 15 is the answer correct
Someone tell me what the answer
Answer:
can you please put a better picture?
11x+x^2= 2y
Y + x = 19
Answer:
x = -15,46 thì y ≈ 34,46
x = 2,46 thì y ≈ 16,54
Step-by-step explanation:
x + y = 19 => x = 19 - y (1)
thay x = 19 -y vào phương trình 11x + x^2 = 2y ta có:
11 * (19 - y) + (19 - y)^2 =2y
=> 209 - 11y + 361 - 38y + y^2 = 2y
=> y^2 - 51y + 570 = 0
=> y ≈ 34,46 và y≈16,54
thay y ≈ 34,46 vào phương trình (1) có:
x = 19 - 34,46 = -15,46
thay y ≈ 16,54 vào phương trình (1) có:
x = 19 - 16,54 = 2,46
Answer:
Step-by-step explanation:
11x+x^2= 2y
Y + x = 19
Multiply and re-arrange second equation:
2y = 38 - 2x
Substitute into first equation:
11x + x^2 = 38 - 2x
Re-arrange:
x^2 + 13x - 38 = 0
Solve using quadratic formula:
x = (-13+(13^2-4*(-38))^(1/2))/2 or (-13-(13^2-4*(-38))^(1/2))/2
x = 2.46 or -15.46
Substitute back to solve for y:
y = 19 - 2.46 or 19 + 15..46
y= 16.54 or 34.46
A.3 1/4
B.1 3/4
C.2 1/4
D.3/3
Answer:
A. 3 [tex]\frac{1}{4}[/tex]
Step-by-step explanation:
Which is an asymptotic of the graph of the function y=cot [x- 2pi/3]
Answer:
B
Step-by-step explanation:
The asymptote of the function [tex]y = cot(x - \frac{2\pi}{3})[/tex] is at x = - π/3.
What are periodic functions?A periodic function has a range that is determined for a fixed interval and a domain that includes all real number values.
Any function that has a positive real integer p such that f (x + p) = f (x), with all x being real values, is said to be periodic.
We know, tan = sin/cos.
Hence 1/tan = cos/sin = cot.
So, The denominator sin can not be zero, And sin is zero on π and - π.
Given, A function [tex]y = cot(x - \frac{2\pi}{3})[/tex].
At, x = - π/3.
Therefore, [tex]y = cot(\frac{\pi}{3} - \frac{2\pi}{3})[/tex].
[tex]y = cot(-\pi)[/tex], Which is undefined.
learn more about asymptotes here :
https://brainly.com/question/17767511
#SPJ7
Solve for x. Round to the nearest tenth, if necessary. C С B x 25 34° А
Help with this problem please.
Answer:
59 or I’m wrong
Step-by-step explanation:
Answer:
x=20.7
Step-by-step explanation:
using cosine...
cos 34=adjacent/hypotenuse
cos 34=x/25
Cross multiply
x=cos 34 ×25
x=20.72593931
x≈20.7(to the nearest tenth)
Find the mean for the given sample data. Unless indicated otherwise, round your answer to one more decimal place than is present in the original data values. The local Tupperware dealers earned these commissions last month: $1077.28, $2661.13, $4642.11, $4264.15, $1019.55, $3444.20, $2525.92, $3740.26, $3533.07, $1633.84 What was the mean commission earned? Round your answer to the nearest cent.
Answer:
the mean commission earned is 2854.15
Step-by-step explanation:
The computation of the mean commission earned is shown below'
The mean is
= ($1077.28 + $2661.13 + $4642.11 + $4264.15 + $1019.55 + $3444.20 + $2525.92 + $3740.26 + $3533.07 + $1633.84) ÷ 10
= 2854.15
Hence, the mean commission earned is 2854.15
The same should be considered and relevant
Student spend 5 minutes of every 60 minutes at school moving from class to class. Which fraction is equivalent to the number of minutes student spend moving from class to class?
Answer:
10/120
Step-by-step explanation:
Twice a number divided by 5 gives 4
simple equations
Answer:
x=10
Step-by-step explanation:
Let the number = x
∴ 2x/5=4
∴2x=5*4
∴2x=20
∴x=20/2
∴x=10
Hope it helps you!
Mark as brainliest if you like it
Answer:
2x / 5 = 4
x = 10
Step-by-step explanation:
Twice a number divided by 5 gives 4
2x / 5 = 4
2x / 5 = 4
Multiply both sides by 5
2x = 20
Divide both sides by 2
x = 10