does the point (-4, 2) lie inside or outside or on the circle x^2 + y^2 = 25?
Answers
Answer:
The points lie INSIDE THE CIRCLE
hope it helps
have a nice day
Given equation of the Circle is ,
[tex]\sf\implies x^2 + y^2 = 25 [/tex]
And we need to tell that whether the point (-4,2) lies inside or outside the circle. On converting the equation into Standard form and determinimg the centre of the circle as ,
[tex]\sf\implies (x-0)^2 +( y-0)^2 = 5 ^2[/tex]
Here we can say that ,
• Radius = 5 units
• Centre = (0,0)
Finding distance between the two points :-
[tex]\sf\implies Distance = \sqrt{ (0+4)^2+(2-0)^2} \\\\\sf\implies Distance = \sqrt{ 16 + 4 } \\\\\sf\implies Distance =\sqrt{20}\\\\\sf\implies\red{ Distance = 4.47 }[/tex]
Here we can see that the distance of point from centre is less than the radius.
Hence the point lies within the circle .
Related Questions
If each side of a cube is doubled, its volume?
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If you double each side the volume is 8 times
Must click thanks and mark brainliest
help me out .... I will mark u as brilliant students
Answers
oe which question are you figure it out
Help me quick i need helppp
Answers
[tex]\\ \sf\longmapsto (m-8)+(m-8)+(m-8)+(m-8)+(m-8)+(m-8)=12[/tex]
[tex]\\ \sf\longmapsto 6(m-8)=12[/tex]
[tex]\\ \sf\longmapsto 6m-48=12[/tex]
[tex]\\ \sf\longmapsto 6m=12+48[/tex]
[tex]\\ \sf\longmapsto 6m=60[/tex]
[tex]\\ \sf\longmapsto m=\dfrac{60}{6}[/tex]
[tex]\\ \sf\longmapsto m=10[/tex]
Answer:
M=14
Step-by-step explanation:
First make an equation - m÷6 =8Then shift 6 to 8 - m=6×8Answer - m=14There were 642 students enrolled in a freshman-level chemistry class. By the end of the semester, the number of students who passed was 5 times the number of students who failed. Find the number of students who passed and the number who failed.
Answers
Answer:
535 students passed and 107 students failed
Step-by-step explanation:
Create a system of equations where p is the number of students who passed and f is the number of students who failed:
p + f = 642
p = 5f
Solve by substitution by plugging in 5f as p into the first equation, then solving for f:
p + f = 642
5f + f = 642
6f = 642
f = 107
So, 107 students failed.
Find how many students passed by multiplying this by 5:
107(5)
= 535
535 students passed and 107 students failed.
Calculus!
The volume of a substance, A, measured in cubic centimeters increases according to the exponential growth model dA/dt = 0.3A, where t is measured in hours. The volume of another substance, B, also measured in cubic centimeters increases at a constant rate of 1 cm^3 per hour according to the linear model dB/dt = 1. At t = 0, substance A has a volume A(0) = 3 and substance B has size B(0) = 5. At what time will both substances have the same volume?
Would it be correct to write the growth model of substance B as x + 5? And how could I write the growth model of substance A? Thank you in advance, and sorry for the poor formatting.
Answers
Answer:
The two substances will have the same volume after approximately 3.453 hours.
Step-by-step explanation:
The volume of substance A (measured in cubic centimeters) increases at a rate represented by the equation:
[tex]\displaystyle \frac{dA}{dt} = 0.3 A[/tex]
Where t is measured in hours.
And substance B is represented by the equation:
[tex]\displaystyle \frac{dB}{dt} = 1[/tex]
We are also given that at t = 0, A(0) = 3 and B(0) = 5.
And we want to find the time(s) t for which both A and B will have the same volume.
You are correct in that B(t) is indeed t + 5. The trick here is to multiply both sides by dt. This yields:
[tex]\displaystyle dB = 1 dt[/tex]
Now, we can take the integral of both sides:
[tex]\displaystyle \int 1 \, dB = \int 1 \, dt[/tex]
Integrate. Remember the constant of integration!
[tex]\displaystyle B(t) = t + C[/tex]
Since B(0) = 5:
[tex]\displaystyle B(0) = 5 = (0) + C \Rightarrow C = 5[/tex]
Hence:
[tex]B(t) = t + 5[/tex]
We can apply the same method to substance A. This yields:
[tex]\displaystyle dA = 0.3A \, dt[/tex]
We will have to divide both sides by A:
[tex]\displaystyle \frac{1}{A}\, dA = 0.3\, dt[/tex]
Now, we can take the integral of both sides:
[tex]\displaystyle \int \frac{1}{A} \, dA = \int 0.3\, dt[/tex]
Integrate:
[tex]\displaystyle \ln|A| = 0.3 t + C[/tex]
Raise both sides to e:
[tex]\displaystyle e^{\ln |A|} = e^{0.3t + C}[/tex]
Simplify:
[tex]\displaystyle |A| = e^{0.3t} \cdot e^C = Ce^{0.3t}[/tex]
Note that since C is an arbitrary constant, e raised to C will also be an arbitrary constant.
By definition:
[tex]\displaystyle A(t) = \pm C e^{0.3t} = Ce^{0.3t}[/tex]
Since A(0) = 3:
[tex]\displaystyle A(0) = 3 = Ce^{0.3(0)} \Rightarrow C = 3[/tex]
Therefore, the growth model of substance A is:
[tex]A(t) = 3e^{0.3t}[/tex]
To find the time(s) for which both substances will have the same volume, we can set the two functions equal to each other:
[tex]\displaystyle A(t) = B(t)[/tex]
Substitute:
[tex]\displaystyle 3e^{0.3t} = t + 5[/tex]
Using a graphing calculator, we can see that the intersect twice: at t ≈ -4.131 and again at t ≈ 3.453.
Since time cannot be negative, we can ignore the first solution.
In conclusion, the two substances will have the same volume after approximately 3.453 hours.
pls help me asap !!!!
Answers
Answer:
9--7
Step-by-step explanation:
distance = √74
Step-by-step explanation:
d = √((x2 - x1)²+(y2 - y1)²)
Where the first point = (x1, y1) and the second point = (x2, y2)
First point: (2, -2)
Second point: (7, -9)
Step 1. Plug these points into the formula
d = √((7 - 2)² + (-9 - -2)²)
Step 2. Subtract
d=√(( 5 )² + ( -7 )²)
Step 3. Simplify the exponents
d=√(25) + (49)
Step 4. Add
d=√74
Will Mark Brainnlest Please help me
Answers
Answer:
l = 2, m = - 1, n = - 6
Step-by-step explanation:
A scalar matrix has its diagonal elements equal and all other elements zero, so
2l - 4 = 0 ( add 4 to both sides )
2l = 4 ( divide both sides by 2 )
l = 2
---------------------------------------
3l + n = 0
3(2) + n = 0
6 + n = 0 ( subtract 6 from both sides )
n = - 6
--------------------------------------
3m - n = 3
3m - (- 6) = 3
3m + 6 = 3 ( subtract 6 from both sides )
3m = - 3 ( divide both sides by m )
m = - 1
Condition for increasing decreasing and concavity of function
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Answer:
If the concavity of f changes at a point (c,f(c)), then f′ is changing from increasing to decreasing (or, decreasing to increasing) at x=c. That means that the sign of f″ is changing from positive to negative (or, negative to positive) at x=c. This leads to the following theorem
Step-by-step explanation:
The previous section showed how the first derivative of a function, f′ , can relay important information about f . We now apply the same technique to f′ itself, and learn what this tells us about f . The key to studying f′ is to consider its derivative, namely f′′ , which is the second derivative of f . When f′′>0 , f′ is increasing. When f′′<0 , f′ is decreasing. f′ has relative maxima and minima where f′′=0 or is undefined. This section explores how knowing information about f′′
Let f be differentiable on an interval I . The graph of f is concave up on I if f′ is increasing. The graph of f is concave down on I if f′ is decreasing. If f′ is constant then the graph of f is said to have no concavity.
Note: We often state that " f is concave up" instead of "the graph of f is concave up" for simplicity.
The graph of a function f is concave up when f′ is increasing. That means as one looks at a concave up graph from left to right, the slopes of the tangent lines will be increasing. Consider Figure 3.4.1 , where a concave up graph is shown along with some tangent lines. Notice how the tangent line on the left is steep, downward, corresponding to a small value of f′ . On the right, the tangent line is steep, upward, corresponding to a large value of f′ .
Deion is saving up to buy a new phone. He already has $95 and can save an additional $7 per week using money from his after school job. How much total money would Deion have after 6 weeks of saving? Also, write an expression that represents the amount of money Deion would have saved in w weeks.
Answers
$95 + 7 x 6= 137
The expression that represents the amount of money Deion would have saved in w weeks is 95 + 7w and the total savings after 6 weeks will be $137.
What is an expression?A statement expressing the equality of two mathematical expressions is known as an equation.
A mixture of variables, numbers, addition, subtraction, multiplication, and division are called expressions.
An expression is a mathematical proof of the equality of two mathematical expressions.
As per the given,
Initial fixed money = $95
Per week saving $7/week
Total money = fixed money + money in w weeks.
⇒ 95 + 7w
For 6 weeks, w = 6
⇒ 95 + 7× 6 = $137.
Hence "The expression that represents the amount of money Deion would have saved in w weeks is 95 + 7w and the total savings after 6 weeks will be $137".
To learn more about expression,
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Geometry I need help someone help me
Answers
Answer:
fohohcoufohohcouvhop
Step-by-step explanation:
typing mistake sorry
[tex]\\ \sf\longmapsto x+73=90[/tex]
[tex]\\ \sf\longmapsto x=90-73[/tex]
[tex]\\ \sf\longmapsto x=17[/tex]
Why?
Sum of two complementary angles is 90°
Which polynomial is a binomial?
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Find the values of the missing sides. You must use exact answers! PLEASE HURRY AND HELP
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Answer:
x=4sqrt3 a=4 b=3 ,y=8sqrt3 c=8 d=3
Step-by-step explanation:
because this is a 30-60-90 triangle, it is easy to find the side lengths. the longer leg is sqrt(3) times the shorter leg so x= 12/sqrt(3) or 4sqrt(3). the hypotenuse is 2 times the shorter leg so y= 8sqrt(3)
What is the value of x?
Answers
Answer:
x = 54.6 m
Step-by-step explanation:
Δ MAB and Δ MNP are similar, then corresponding sides are in proportion, that is
[tex]\frac{MA}{MN}[/tex] = [tex]\frac{MB}{MP}[/tex] , substitute values
[tex]\frac{80.5-35}{80.5}[/tex] = [tex]\frac{x}{96.6}[/tex]
[tex]\frac{45.5}{80.5}[/tex] = [tex]\frac{x}{96.6}[/tex] ( cross- multiply )
80.5x = 4395.3 ( divide both sides by 80.5 )
x = 54.6
Answer:
Answer:
Answer:x = 25°
Answer:x = 25°Step-by-step explanation:
Answer:x = 25°Step-by-step explanation:The secant- secant angle FGE is one half the difference of the intercepted arcs, that is (135 - x) = 55 ( multiply both sides by 2 to clear the fraction )
Answer:x = 25°Step-by-step explanation:The secant- secant angle FGE is one half the difference of the intercepted arcs, that is (135 - x) = 55 ( multiply both sides by 2 to clear the fraction )135 - x = 110 ( subtract 135 from both sides )
Answer:x = 25°Step-by-step explanation:The secant- secant angle FGE is one half the difference of the intercepted arcs, that is (135 - x) = 55 ( multiply both sides by 2 to clear the fraction )135 - x = 110 ( subtract 135 from both sides )- x = - 25 ( multiply both sides by - 1 )
Answer:x = 25°Step-by-step explanation:The secant- secant angle FGE is one half the difference of the intercepted arcs, that is (135 - x) = 55 ( multiply both sides by 2 to clear the fraction )135 - x = 110 ( subtract 135 from both sides )- x = - 25 ( multiply both sides by - 1 )x = 25°
Hence the answer is 25.
Determine the period
Answers
Answer:
16 units
Step-by-step explanation:
period = length of an interval that contains exactly one copy of the repeating pattern, so from one peak to another peak.
in this graph its the peaks are 1 and 17, hence the period is 16
Help me ? :( no spam or
Answers
Now
[tex]\\ \sf\longmapsto tan(\alpha+\beta)=\sqrt{3}[/tex]
[tex]\\ \sf\longmapsto \alpha+\beta=60\dots(1)[/tex]
And
[tex]\\ \sf\longmapsto tan(\alpha-\beta)=\dfrac{1}{\sqrt{3}}[/tex]
[tex]\\ \sf\longmapsto \alpha-\beta=30\dots(2)[/tex]
Adding both
[tex]\\ \sf\longmapsto 2\alpha=30+60=90[/tex]
[tex]\\ \sf\longmapsto sin2\alpha=sin90[/tex]
[tex]\\ \sf\longmapsto sin2\alpha=1[/tex]
Please help me solve this question!
Answers
Write the ratio: 3 1/6 to 17/6
as a fraction in lowest terms.
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Answer: [tex]\frac{19}{6} : \frac{17}{6}[/tex]
Step-by-step explanation:
Let us first represent the ratio.
3[tex]\frac{1}{6} : \frac{17}{6}[/tex]
Now we need to convert 3[tex]\frac{1}{6}[/tex] into a improper fraction.
[tex]\frac{19}{6} : \frac{17}{6}[/tex]
Now it is in its simplest form.
The final answer is [tex]\frac{19}{6} : \frac{17}{6}[/tex]
Solve the equation by completing the square.
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2t(t-1)-t+1 factorise
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Answer:
this is the answer of this question
hoping it will help u
What is the shaded area of the figure?
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Answer:
Step-by-step explanation:
The idea here is to find the area of the circle and then subtract from it the area of the triangle. That will give you the area of what's left in the circle (the shaded part). The area of a circle is:
[tex]A_c=\pi r^2[/tex] so
[tex]A_c=(3.14)(12.4)^2[/tex] where 12.4 is the radius.
[tex]A_c=482.81[/tex] rounded to the nearest tenth. I used 3.14 for pi.
Now for the area of the triangle. The formula is
[tex]A_t=\frac{1}{2}bh[/tex] where h is the height of 12.4 and the base is the diameter which is 12.4 * 2 = 24.8
[tex]A_t=\frac{1}{2}(24.8)(12.4)[/tex] so
[tex]A_t=153.76[/tex]
Now subtract the triangle's area from the circle's area:
482.81 - 153.76 = 329.05 mm²
a random number generator is used to model the patters of animals in the wild. this type of study is called
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Answer:
This type of study is called a simulation
Step-by-step explanation:
answer please lol so uh yeah
Answers
Answer:
5x=20
5x/5=20/5
x=4
Step-by-step explanation:
substitute the 5x
divide both sides by 5 it will be 20 divide by 5
answer is x =4
With the aid of an illustrative example, discuss the relationship between the area of a region and the definite integral. *
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Suppose there is a function f(x), the definite integral of the function is the difference between the upper and lower x-values.
There are three relationships between the definite integral and the area of the region. The relationships are:
Positive functionNegative functionRegion between two functionsPositive function
The area between the function itself and the x-axis represents the definite integral.
Negative function
The area between the function itself and the x-axis, multiplied by -1 represents the definite integral.
Region between two functions
The definite integral of the function is the difference between the region of both functions.
See attachment for further illustration
Learn more about area of a region and the definite integral at:
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which exponential expression is equivalent to
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Answer:
B
Step-by-step explanation:
(y^(4))^(1/5)=y^(4/5)
What is 55 increased by 10%?
Answers
Answer:
10% of 55
=> 10/100 × 55
=> 1/10×55
=> 5.5
55 increased by 10% => 55 + 5.5
=> 60.5
hope that helps ✌
Answer:
Step-by-step explanation:
10% of 55
10/100*55
1/10*55
5.5 <--- That is 10% of 55
55+5.5 = 60.5
Given 4 points A, B, C, D where no 3 points are collinear, any 2 points have a distance greater than 10. Prove that there exist two points out of 4 given points with greater distance 14.
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Answer:
idea how to tell your loved one how you feel? How about a love song?
Given the a center (-1, -2) and a radius r = 2. Identify the circle.
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Answer:
1st option
1st graph has the centre on (-1,-2) and the distance of the circumference from the centre is 2
Answered by GAUTHMATH
hlpppppppppppppppppppppppppppppppp
Answers
Answer:
c
Step-by-step explanation:
-7.5 is less than 6.5
Please help solve for x
Answers
Answer:
8.49
Step-by-step explanation:
there is a little formula related to the famous formula of Pythagoras.
it says that the height of a triangle is the square root of the product of both segments of the baseline (the segments the height splits the baseline into).
so, x is actuality the height of the triangle.
x = sqrt(3×24) = sqrt(72) = 8.49
Chris drives 240 miles from his home in Atlanta, Georgia, at 60 miles per hour. How many minutes longer would the return trip take if he travels at 50 miles per hour
Answers
Answer:
48 minutes
240 at 60mph = 4 hrs.
240 at 50 mph = 4.8 hrs.
it would take an extra 60*.8 or 48 minutes
Step-by-step explanation:
The trip will be of 48 minutes longer when the speed is decreased by 10 miles per hour.
What is the formula for time?
The time is given by distance/speed. The unit of time is minutes or seconds.
What will be the time difference?When distance of 240 miles is cover by the speed of 60 miles per hour then the time take to travel this distance will be 240/60=4 hours
When distance of 240 miles is cover by the speed of 50 miles per hour then the time take to travel this distance will be 240/50=4.8 hours
The difference between 4.8 hours and 4 hours is of 0.8 hours or 0.8*60=48 minutes.
Therefore, the trip will be of 48 minutes longer.
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