Answer: 1.
Step-by-step explanation: 1^5 is really just 1, 5 times.
1*1*1*1*=1
The radius of the circle is increasing at a rate of 1 meter per day and the sides of the square are increasing at a rate of 3 meters per day. When the radius is 3 meters, and the sides are 20 meters, then how fast is the AREA outside the circle but inside the square changing
Answer:
The area inside the square and outside the circle is changing at a rate of 101.150 square meters per day.
Step-by-step explanation:
According to the statement of the problem, the circle is inside the square and the area inside the square but outside the circle, measured in square meters, is represented by the following formula. It is worth to notice that radius ([tex]r[/tex]) is less than side ([tex]l[/tex]), both measured in meters:
[tex]A_{T} = A_{\square} -A_{\circ}[/tex]
[tex]A_{T} = l^{2}-\pi\cdot r^{2}[/tex]
Now, the rate of change of the total area is calculated after deriving previous expression in time:
[tex]\frac{dA_{T}}{dt} = 2\cdot l\cdot \frac{dl}{dt} -2\pi\cdot r\cdot \frac{dr}{dt}[/tex]
Where [tex]\frac{dl}{dt}[/tex] and [tex]\frac{dr}{dt}[/tex] are the rates of change of side and radius, measured in meters per day.
Given that [tex]l = 20\,m[/tex], [tex]r = 3\,m[/tex], [tex]\frac{dl}{dt} = 3\,\frac{m}{day}[/tex] and [tex]\frac{dr}{dt} = 1\,\frac{m}{day}[/tex], the rate of change of the total area is:
[tex]\frac{dA_{T}}{dt} = 2\cdot (20\,m)\cdot \left(3\,\frac{m}{day} \right)-2\pi\cdot (3\,m)\cdot \left(1\,\frac{m}{day} \right)[/tex]
[tex]\frac{dA_{T}}{dt} \approx 101.150\,\frac{m^{2}}{day}[/tex]
The area inside the square and outside the circle is changing at a rate of 101.150 square meters per day.
the circumference of a circle is 20 pi. what is the radius of this circle?
Work Shown:
C = circumference = 20pi
d = diameter
C = pi*d
pi*d = 20pi
d = 20 after dividing both sides by pi
The radius is half the diameter, so r = d/2 = 20/2 = 10.
As an alternative, you can use the formula C = 2*pi*r
Using the circumference of the circle formula to solve the problem. Then the radius of the circle is 10 units.
What is a circle?It is a locus of a point drawn at an equidistant from the center. The distance from the center to the circumference is called the radius of the circle.
Given
The circumference of a circle is 20π.
We know that the circumference of the circle is given by
[tex]\rm Circumference\ of\ the\ circle = 2\pi r[/tex]
Where r is the radius of the circle.
Then the radius of the circle will be
[tex]\begin{aligned} 20 \pi &= 2 * \pi * r \\r &= 10\end{aligned}[/tex]
Thus, the radius of the circle is 10 units.
More about the circle link is given below.
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HELLLPPP 31 kilograms is the same as how many pounds? Hint: 1 kg = 2.2 lb Round your answer to the nearest tenth.
Hi! I'm happy to help!
To solve this, we need to turn all the kilograms into pounds. We know that to turn 1 kg into a pound, you multiply the amount of kilograms by 2.2.
Knowing this, we can multiply our 31 kilograms by 2.2.
31×2.2=68.2
This means that 31 kilograms is equal to 68.2 pounds.
I hope this was helpful, keep learning! :D
The graph of y=√x is translated 5 units to the left and 7 units up. What is the equation of the graph that results from this translation?
Answer:
y = [tex]\sqrt{x+5}[/tex] + 7
Step-by-step explanation:
Given the graph of f(x) then f(x + k) is a horizontal translation of f(x)
• If k > 0 then a shift to the left of k units
• If k < 0 then a shift to the right of k units
Thus a translation of 5 units to the left
y = [tex]\sqrt{x+5}[/tex]
Given the graph of f(x) then f(x) + c is a vertical translation of f(x)
• If c > 0 then shift up by c units
• If c < 0 then shift down by c units
Thus
y = [tex]\sqrt{x+5}[/tex] + 7 ← translated equation
A small toy car costs $3. A large toy car costs 5 times as much as the small one. Aaron wants to buy one of each. Which equation can he use to find the cost (a) of the two cars?
Answer: He can use 3 x 5 = 15 and 15 + 3.
Step-by-step explanation:
Since a small car is $3, and the large car is 5x the price of the small car, he can use the equation 3 x 5 = 15, because the small car is $3, and the large car is 5x the price. You can use 15 + 3 = 18, because the small car is $3, so you also have to add that.
Here to help!
The equation is x + 5x = 18 , where x is the cost of small toy car and the total cost of the two cars = $ 18
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the total cost of the two cars be A
Now , the equation will be
Let the cost of the small toy car be = x
The cost of small toy car = $ 3
The cost of the large car = 5 x cost of small toy car
Substituting the values in the equation , we get
The cost of the large car = 5 x 3
The cost of the large car = $ 15
So , the cost of two cars = x + 5x
Substituting the values in the equation , we get
The total cost of the two cars A = 15 + 3
The total cost of the two cars A = $ 18
Therefore , the value of A is $ 18
Hence , the equation is A = x + 5x
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I NEED HELP ON THIS QUESTION!!!!! I WILL GIVE BRAINLIEST TO THE BEST ANSWER!!!!
Answer:
D
Step-by-step explanation:
Both are exponential decay.
Answer:
D.Step-by-step explanation:
f(0) = 24, f(1) = 6 and f(2) = 0 means f(x) > 0 in (0,2)
and f(0) > f(1) > f(2) means f is decreasing in (0,2)
g(0) = 15 and g(2) = 0 means g(x) > 0 in (0,2)
and g(0) > g(2) means g is decreasing in (0,2)
cost of putting a fence around a square field rupees 35 rupees is
4480 find the each side of the field
Answer:
cost of one side= 1120
Step-by-step explanation:
Given. total cost=4480
cost per meter=35
So,perimeter=total cost/cost per metre
perimeter=4480/35
perimeter=128
perimeter of square=4*side
128/4=side
side=32
given cost of one meter=35
So,cost of 32 meter=35*32
So,cost of one side=1120
Answer:
the cost of fencing a square field at the rate of ₹35 per m is ₹4480.
so the perimeter of the square field = 4480/35
= 128m
Length of each side = 128/4
= 32m
Hope this helps! （づ￣3￣）づ╭❤～
Carey earns $9.75 working part time on weekends. The table below shows the amount, a, Carey earns for working h hours. Carey’s Earnings h 0 1 3 a $0 $9.75 ? Which value completes the table to show the amount Carey earns for working 3 hours?
Answer:
$29.25
Step-by-step explanation:
For every 1 hour, Carey earns $9.75. Multiply $9.75 by 3 to find out how much she earns for 3 hours of work.
$9.75 × 3 = $29.25
Carey earns $29.25 for working 3 hours.
Answer:
29.25
Step-by-step explanation:
I got it right on edge!! trust me
Factor 75 - 95. a. 5(15 - 19) b. 5(19 - 15) c. 25(3 - 4) d. 25(4 - 3)
Answer:
a. 5(15-19)
Step-by-step explanation:
to factor out this expression you need to find the greatest common factor (GCF) in order to fully factor out the expression
the GCF of the number 75 and -95 is 5
divide both numbers by 5 to get 15 and -19
to finish out with the fully factored expression put 15-19 inside parenthesis and put a 5 outside of the parenthesis as shown below:
5(15-19)
Answer:
a. 5(15 -19)
Step-by-step explanation:
15*5 = 75
-19*5 = -95
Factor is:
5(15 -19)
4x + 5 = x + 26 need help
Answer:
x = 7
Step-by-step explanation:
4x + 5 = x + 26
4x - x = 26 - 5
3x = 21
x = 21/3
x = 7
Check:
4*7 + 5 = 7 + 26
28 + 5 = 33
Top Hat Soda has 300,000 milliliters of cola to bottle. Each bottle holds 500 milliliters. How many bottles will the cola fill?
Answer:600
Step-by-step explanation:
300,000/ 500 =600
Helpp pleasee asap!!
Answer:
114,112,coA,ce 58,124,DFA,EOB
2x - 3y = -5
5x - 22 = -4y
Solve In Multiplication Method
Answer:
(2, 3 )
Step-by-step explanation:
Given the 2 equations
2x - 3y = - 5 → (1)
5x + 4y = 22 → (2) [ rearranged equation ]
Multiplying (1) by 4 and (2) by 3 and adding will eliminate the term in y
8x - 12y = - 20 → (3)
15x + 12y = 66 → (4)
Add (3) and (4) term by term to eliminate y, that is
23x = 46 ( divide both sides by 23 )
x = 2
Substitute x = 2 in either of the 2 equations and evaluate for y
Substituting into (2)
5)2) + 4y = 22
10 + 4y = 22 ( subtract 10 from both sides )
4y = 12 ( divide both sides by 4 )
y = 3
Solution is (2, 3 )
Find the measure of FG.
Answer:
8
Step-by-step explanation:
By power of a point, (x-2)(x+13) = (x-3)(x+16). Solving, we find that x=11, so FG= 11-3 = 8
HELP ME ASAP I DONT UNDERSTAND
Answer
False
Step-by-step explanation:
3 is an element of A but {3} is not so it is false.
Let P be a non zero polynomial such that P(1+x)=P(1−x) for all real x, and P(1)=0. Let m be the largest integer such that (x−1) m divides P(x) for all such P(x). Then m equals
Answer:
m = 0, P(3)/2, P(4)/6, P(5)/12 ..........
Step-by-step explanation:
For non zero polynomial, that is all real x as follows:
x = 1, 2, 3, 4 ............
Using, P(1 + x) = P(1 - x)
For x = 1: P(2) = P(0) = 1
For x = 2: P(3) = P(-1) = 2
Hence, P(x)/m(x - 1) can be solved as follows:
When = 1
P(2)/0 = 1
∴ m = 0
When x = 2
P(3)/m = 2
∴ m = P(3)/2
When x = 3
P(4)/2m = 3
∴ m = P(4)/6
When x = 4
P(5)/3m = 4
∴ m = P(5)/12
Hence, m = 0, P(3)/2, P(4)/6, P(5)/12......
Given: cos(3x – Pi) = Negative StartFraction StartRoot 3 EndRoot Over 2 EndFraction, where 0 ≤ x < 180° Which values represent the solutions to the equation? {10°, 110°, 130°} {20°, 100°, 140°} {30°, 330°, 390°} {60°, 300°, 420°}
Answer:
Step-by-step explanation:
Given the expression cos(3x-π) = -√3/2, we are to find the values of x that represent the solutions to the equation.
cos(3x-π) = -√3/2
take inverse cos of both sides
cos⁻¹[cos(3x-π)] = cos⁻¹[-√3/2]
3x-π = cos⁻¹[-√3/2]
3x-π = -30°
since 180° = π rad
Hence;
3x- 180° = -30°
3x = -30°+ 180°
3x = 150°
x = 150°/3
x = 50°
Since cos is negative in the first second and 3rd quadrant;
3x-180° = -30°
In the second quadrant;
3x-180° = 180-30
3x - 180 = 150
3x = 150+180
3x = 330
x = 110°
In the third quadrant;
3x-180° = 270+30
3x - 180 = 300
3x = 300+180
3x = 480
x = 480/3
x = 160
4.257 inches rounded to the nearest tenth is
[tex]4.257\approx4.3[/tex]
[tex]\text{Round to the nearest tenths place}\\\\4.257\\\\\text{"2" would be the number in the tenth place}\\\\\text{We would need to round up if the number to the right of the number is}\\\text{5 or greater}\\\\\text{In this case, the next number "5", so we would round up}\\\\\text{Therefore, your answer should be:}\\\\\boxed{4.3\,\, in}[/tex]
A train covered a certain distance at a uniform speed. If the train would have been 6km/h faster, it would have taken 4 hours less than the scheduled time. And, if the train were slower by 6km/h, it would have taken 6 hours more than the scheduled time. Find the length of the journey.
Answer:Let x km/hr be the speed of train
Let y be the time taken by the train
Distance = speed x time
= x y
To form the first equation let us consider the given information from the question that is If the train had been 6 km/hr faster,it would have taken 4 hours less than the scheduled time.
it clearly says that speed is increased by 6 and time is reduced by 4
So , (x + 6) (y - 4) = x y
x y - 4 x + 6 y - 24 = x y
x y - x y - 4 x + 6 y = 24
- 4 x + 6 y = 24
divided by (-2) => 2 x - 3 y = -12 ----- (1)
To form the second equation let us consider the given information from the question that is If the train were slower by 6km/hr, then it would have taken 6 hours more than the scheduled time.
it clearly says that speed is reduced by 6 and time is increased by 6
So , (x - 6) (y + 6) = x y
x y + 6 x - 6 y - 36 = x y
x y - x y + 6 x - 6 y = 36
6 x - 6 y = 36
divided by (6) => x - y = 6 ----- (2)
2 x - 3 y = -12
(2) x 2 => 2 x - 2 y = 12
(-) (+) (-)
---------------
- y = -24
y = 24
Now we have to apply the value of y in the first equation to get value of x
Substitute y = 24 in the first equation we get
2 x - 3 (24) = -12
2 x - 72 = -12
2 x = -12 + 72
2 x = 60
x = 60/2
x = 30
Speed of the train = 30 km/hr
Time taken by the train = 24 hours
Distance covered by the train = x y = 30 x 24 = 720 km
Verification:
2 x – 3 y = -12
2(30) - 3(24) = -12
60 - 72 = -12
-12 = -12
What is the solution to this system of equations? 2x + 3y = 7 and -4x - 6y = -2
Answer:
No Solution
Step-by-step explanation:
I used a graphing tool to graph the lines. When graphed, the lines are parallel, and they do not intercept at a point.
There is no solution to the system.
Answer:
Step-by-step explanation:
We will use the graphing method.
Graph the both equations. The intersection point coordinates are the solution of the system.
● 2x + 3y = 7
● -4x -6y = -2
The two lines are parallel. So the system has no real solution. If we tried solve it with calculations we will find an impossible result ( 12 = 0)
2c+17.6 =6 SOLVE --------------- 4 give your answer as a decimal get brainly
Answer:
[tex]\huge\boxed{x = -5.8}[/tex]
Step-by-step explanation:
2x + 17.6 = 6
Subtracting both sides by 17.6
2x = 6 - 17.6
2x = -11.6
Dividing both sides by 2
x = -11.6 / 2
x = -5.8
If today is Friday, what day will it be in 51 days?
Show your thinking.
Answer:
SundayStep-by-step explanation:
Each weekday repeats every 7 days.
51 = 49 + 2 = 7•7 + 2
So 49 days from now also will be Friday .
Two days later will be Sunday.
So in 51 days will be Sunday.
0.008 x 2.5 in standard form is (A) 2 x 10-² (B) 2 x 10 (C) 2 x 10-¹ (D) 2 x 10²
Answer:
(D) 2 x 10²
Step-by-step explanation:
Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the 10. If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.
Hope it is helpful.....Answer:
2 × 10 ^2
Step-by-step explanation:
(d) option is correct
(85^4 - 75^4)/(85^3 + 85*75^2 + 75*85^2 + 75^3).=
Answer:
10
Step-by-step explanation:
(85^4 - 75^4)/(85^3 + 85*75^2 + 75*85^2 + 75^3)=10
What is 33⁄5 as an improper fractions
Answer:
6 3/5
Step-by-step explanation:
33/5 = 6 R3
Answer:
6.6
Step-by-step explanation:
33÷5=6.6
33 divided by 5equal
Write the other side of this equation so it's true for all values of x: 1/2(6x-10)-x=?
Answer:
2x 5
Step-by-step explanation:
1/2(6x - 10) - x =
= 3x - 5 - x
= 2x - 5
The other side of the given equation so it's true for all values of x is 2x-5.
Given that, 1/2(6x-10)-x.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Now, 6x/2 - 10/2 -x
= 3x-5-2
= 2x-5
Therefore, the other side of the given equation so it's true for all values of x is 2x-5.
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plz help.. plzz if you can
Answer:
C is a function
Step-by-step explanation:
We can use the vertical line test. If a vertical straight lines passes through the graph more than one, it is not a function
A and B are not functions
C is a function
Answer ASAP please!
Which of the following statements is not true?
A. Pythagoras' can be used to find an unknown angle of a right-angle triangle
B. Pythagoras' theorem can be used to find an unknown side length of a right-angle triangle
C. Pythagoras' theorem can only be used on right-angle triangles
D. Trigonometry can be used to find an unknown angle of a right-angle triangle
E. Trigonometry can be used to find an unknow side length of a right-angle triangle
TRIGONOMETRY CAN BE USED TO FIND AN UNKNOWN SIDE LENGTH OF A RIGHT ANGLE TRIANGLE
NEED ASAP What is the quotient and remainder of 8,595 ÷ 24?
Answer:
358.125
Step-by-step explanation:
Answer:
358 3/24
Step-by-step explanation:
rationalise the following 1/√7
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Hi my lil bunny!
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
[tex]1\sqrt{7}[/tex]
[tex]= \frac{1}{7} \sqrt{7}[/tex] (Decimal: 0.377964)
OR
[tex]\frac{1}{\sqrt{7} }[/tex]
[tex]= \frac{1}{\sqrt{7} } X \frac{\sqrt{7} }{\sqrt{7} }[/tex]
[tex]= \frac{\sqrt{7} }{(\sqrt{7})^{2} }[/tex]
[tex]= \frac{\sqrt{7} }{\sqrt{7} }[/tex]
I don't really know because both of them seem right..
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
If this helped you, could you maybe give brainliest..?
❀*May*❀