Answer:
The rate of change is of of the area when the radius is 4 centimeters [tex]48\pi[/tex] square centimeters.
Step-by-step explanation:
Area of a circle:
The area of a circle of radius r is given by:
[tex]A = \pi r^2[/tex]
Implicit derivative:
To solve this question, we have to derivate implictly the equation as a function of t. Thus:
[tex]\frac{dA}{dt} = 2\pi r \frac{dr}{dt}[/tex]
The radius of a circle is increasing at a rate of 6 centimeters per minute.
This means that [tex]\frac{dr}{dt} = 6[/tex]
Find the rate of change of the area when the radius is 4 centimeters.
This is [tex]\frac{dA}{dt}[/tex] when [tex]r = 4[/tex]. Thus
[tex]\frac{dA}{dt} = 2\pi r \frac{dr}{dt} = 2\pi(4)(6) = 48\pi[/tex]
The rate of change is of of the area when the radius is 4 centimeters [tex]48\pi[/tex] square centimeters.
Please help with 15, 17 and 19
Given:
15. [tex]\log_{\frac{1}{2}}\left(\dfrac{1}{2}\right)[/tex]
17. [tex]\log_{\frac{3}{4}}\left(\dfrac{4}{3}\right)[/tex]
19. [tex]2^{\log_2100}[/tex]
To find:
The values of the given logarithms by using the properties of logarithms.
Solution:
15. We have,
[tex]\log_{\frac{1}{2}}\left(\dfrac{1}{2}\right)[/tex]
Using property of logarithms, we get
[tex]\log_{\frac{1}{2}}\left(\dfrac{1}{2}\right)=1[/tex] [tex][\because \log_aa=1][/tex]
Therefore, the value of [tex]\log_{\frac{1}{2}}\left(\dfrac{1}{2}\right)[/tex] is 1.
17. We have,
[tex]\log_{\frac{3}{4}}\left(\dfrac{4}{3}\right)[/tex]
Using properties of logarithms, we get
[tex]\log_{\frac{3}{4}}\left(\dfrac{4}{3}\right)=-\log_{\frac{3}{4}}\left(\dfrac{3}{4}\right)[/tex] [tex][\because \log_a\dfrac{m}{n}=-\log_a\dfrac{n}{m}][/tex]
[tex]\log_{\frac{3}{4}}\left(\dfrac{4}{3}\right)=-1[/tex] [tex][\because \log_aa=1][/tex]
Therefore, the value of [tex]\log_{\frac{3}{4}}\left(\dfrac{4}{3}\right)[/tex] is -1.
19. We have,
[tex]2^{\log_2100}[/tex]
Using property of logarithms, we get
[tex]2^{\log_2100}=100[/tex] [tex][\because a^{\log_ax}=x][/tex]
Therefore, the value of [tex]2^{\log_2100}[/tex] is 100.
Write the augmented matrix for each system of equations.
5x - 4y - 62 = -3
x - 3y +z = -1
-3x - 6y + 72 = 1
a.
C.
5
-4
-6
5 -4.
-6
Ou
1
-3
1
0
1
-1
-3
-6
0
0
0
1
b.
d.
5
-4 - 6
-3
5
1
o w
1
-3
-1
-4
-3
7
-6
-6
9514 1404 393
Answer:
see below
Step-by-step explanation:
The augmented matrix is the 3×4 matrix of the coefficients in the standard-form equations.
[tex]\left[\begin{array}{ccc|c}5&-4&-6&-3\\1&-3&1&-1\\-3&-6&7&1\end{array}\right][/tex]
2. The cost of oranges varies directly with the total mass bought. 2 kg of oranges costs $4.50. Describe the relationship between cost and mass in words. You may want to calculate a unit rate first.
Answer:
The relationship between the cost/mass is $2.25/kg.
Step-by-step explanation:
You first need to divide $4.50 / 2, to know what a single kilogram mass costs.
$4.50 / 2 = $2.25
Now that you have this unit rate $2.25, You can multiply/add it.
$4.50 + $2.25 is $6.75, + another $2.25 = $9.00, and so on.
can someone write me this?
Answer:
write me the question oñ
What is the solution set for the quadratic inequality x2 – 5 ≤ 0?
Answer: -4...?
Step-by-step explanation:
31vw+41uvw+9uvw–11uvw
Combine any like terms in the expression. If there are no like terms, rewrite the expression.
Answer:
31vw+39uvw . yes we will rewrite the expression
Step-by-step explanation:
41uvw+9uvw=50uvw-11uvw=39uvw
a number of rounded to the nearest hundred thousand 400,000. the same number ro u nded to the nearest rounded to the nearest ten thousand is 350,000. what could be the number?
9514 1404 393
Answer:
354,998
Step-by-step explanation:
If the number is less than 350,000, it will not round to 400,000.
If the number is 355,000 or more, it will not round to 350,000.
The number (n) must satisfy ...
350,000 ≤ n < 355,000
__
If we're restricted to integers, the number could be any between 350,000 and 354,999, inclusive. One possibility is 354,998.
I need help please anyone
Answer:
base: 3units
height: 5units
Area:15units square
Step-by-step explanation:
you can count the squares in the figure to know the base and hight.
Area of parallelogram= base x height= 3x5= 15 units square.
please give me brainliest, thanks!
what is the answer to this? i can’t figure it out.
9514 1404 393
Answer:
25 +0i
Step-by-step explanation:
The conjugate of a complex number is that number with the sign of the imaginary part reversed.
For z = -3+4i, its conjugate z* is -3-4i. The product of z and z* is ...
(-3 +4i)(-3 -4i) = -3(-3 -4i) +4i(-3 -4i)
= 9 +12i -12i -16i² = 9 +16 = 25
The real part of the product is 25; the imaginary part is 0.
(-3 +4i)(-3 -4i) = 25 +0i
_____
You may have noticed that (z)(z*) = |z|², the sum of the squares of the real and imaginary parts. It is always a non-negative real number.
Help please (pre algebra)
Answer:
Step 1: 3t = 51
Step 2: 3t/3 = 51/3
Step 3: t = 17
Step 4: The Green Garage has 17 tires
Hope this helps!
Answer:
3t=51
[tex]\frac{3t}{3}[/tex]=[tex]\frac{51}{3}[/tex]
t=17
The Green Garage has 17 tires.
Step-by-step explanation:
Look at the question carefully
for the function x^2+8x+7
evaluate f(4)
Answer:
I think you would have to plug in 4 as X so it would be 4^2 +8(4)+ 7
that would be 16+ 32 +7 and that would equal 55
Your cell phone plan costs 55 dollars a month, plus 35 cents per minute. Write an equation to represent the monthly bill of the cell phone plan.
Answer: Umm lemme try this
Step-by-step explanation:
55+35=x
Suppose you pay $3.00 to roll a fair die with the understanding that you will get back $5 (and your wager) for rolling a 5 or a 2, nothing otherwise. What are your expected net winnings, to the nearest cent?
Which equation represents a circle with a center at (–3, –5) and a radius of 6 units?
Answer:
Step-by-step explanation:
The general equation of the circle is:
(x-h)²+(y-k)²=r²
(h, k)=(-3,-5) are the coordinates of the center of the circle.
r=6 is the radius
The equation of the circle is:
(x+3)²+(y+5)² = 36
Each book weighs 6 ounces. Which Ordered pair is a visible solution if X represents the number of books he orders NY represents the total weight of the books in ounces
Miss Smith save 5% on her recent Starbucks order because she is a Starbucks Rewards member if the cost of per purchase before the discount was $5.20 how much did Miss smith save
Answer:
$4.94
Step-by-step explanation:
O 5.20 100%
P - 5
N 95%
0.95 x 5.20 = 4.94
Ms. Smith saved $4..94.
Can someone help me with this question please..
Answer:
The ordered pair would be (2,3)
2 in the first Box
3 in the second
if sec theta = - √30 / 3, find cos theta.
if sin(-theta) = -0.97, find cos (π/2 - theta).
Step-by-step explanation:
[tex] \cos \theta = \frac{1}{ \sec\theta } = - \frac{3}{ \sqrt{30} } = - \frac{3 \sqrt{30} }{30} = - \frac{ \sqrt{30} }{10} [/tex]
[tex] \cos( \frac{\pi}{2} - \theta )= \cos \frac{\pi}{2} \cos \theta + \sin \frac{\pi}{2} \sin \theta [/tex]
Note that
[tex] \sin( - \theta) = - \sin \theta[/tex]
[tex] \cos \frac{\pi}{2} = 0 \: \: \: \: \: \sin \frac{\pi}{2} = 1[/tex]
Therefore,
[tex] \cos( \frac{\pi}{2} - \theta ) = 0.97[/tex]
(-5,-12) find cot???????
In Unit Circle, we know that x-term = cos and y-term = sin
[tex] \large \boxed{(x,y) = (cos \theta , sin \theta)}[/tex]
Recall the cotangent ratio:
[tex] \large \boxed{cot \theta = \frac{cos \theta}{sin \theta} }[/tex]
Because cotangent is reciprocal of tangent which is sin/tan so cotangent is 1/(sin/cos) = cos/sin.
Substitute the point in.
[tex] \large{cot \theta = \frac{ - 5}{ - 12 } \longrightarrow \frac{5}{12} }[/tex]
Answer
cot theta = 5/12Let me know if you have any doubts!
Solve the following system. If the system's equations are dependent or if there is no solution, state this.
12a+35b= 19
24a+8c= 1
28b+8c= 5
A) There is one solution. The solution is (__,__,__)
B) The system is dependent
C) There is no solution
Answer:
the answer is c .no solution
Find an equation for the line that passes through the points (-2,-6) and (6,4).
Step-by-step explanation:
Line P passes through POINTS (-2,6) and (6,4). Using y=mx + b where m is the SLOPE(rise divided by the run), and b is the Y-INTERCEPT. Pick the POINT (6,4) and plug into the Y-INTERCEPT EQUATION above to determine the Y-INTERCEPT
I need to know the answer this is confusing
Answer:
46
Step-by-step explanation:
102 + 32 = 134
180 - 134 = 46
x = 46
I need help ASAP please anyone
Answer:
112
Step-by-step explanation:
Answer:
112
Step-by-step explanation:
4×4= 16×2=32
5×4= 20×2=40
5×4= 20×2=40
Total = 112
what is not an angle pair?
Answer:
A pair of angles whose sum is not 90 or 180 is not an angle pair.
The formula s = sqrt((SA)/6) gives the length of the side, sof a cube with a surface area, SA. How much longer is the side of a cube with a surface area of 180 square meters than a cube with the surface area of 120 square meters?
Answer:B
Sqt 30 - 2 sqt 5 m
Step-by-step explanation:
Edge
The graph shown below expresses a radical function that can be written in
the form f(x) = a(x+k)1/*+c
value of k in this function?
What does the
graph tell you about the value of k in this function
A 90% confidence interval for the
population mean
?is 18
Answer:
With a 90 percent confidence interval, you have a 10 percent chance of being wrong.
Step-by-step explanation:
If using the method of completing the square to solve the quadratic equation x^2+8x+11=0, which number would have to be added to "complete the square"?
Answer:
4
Step-by-step explanation:
x²+8x+11=0
x²+8x+(+4)²-(+4)²+11=0
Answer:
16
Step-by-step explanation:
x2+8x= −11−11
28=4→(4)2=16
x2+8x+16=x2+8x+16= −11+16−11+16
(x+4)2= 55
16
2(x+3)=x-4
please help me <3
At Misu's Ice Cream Parlor, their famous 4-layer ice cream cake consists of four layers of ice
cream alternating with layers of cake. If there are 8 flavors of ice cream, and we count
different cakes based on the order of ice cream layers from top to bottom:
a) how many different cakes can be made if flavors can be repeated?
Answer:
4096 different cakes can be made if flavors can be repeated.
Step-by-step explanation:
Since at Misu's Ice Cream Parlor, their famous 4-layer ice cream cake consists of four layers of ice cream alternating with layers of cake, if there are 8 flavors of ice cream, and we count different cakes based on the order of ice cream Layers from top to bottom, to determine how many different cakes can be made if flavors can be repeated, the following calculation must be performed:
8 x 8 x 8 x 8 = X
64 x 64 = X
4.096 = X
Therefore, 4096 different cakes can be made if flavors can be repeated.
