I'm going to assume the limit is
[tex]\displaystyle \lim_{x\to3} \frac{\sqrt{x+1} - 2}{x - 3}[/tex]
since problems like this usually involve indeterminate forms, and
√(x + 1) - 2 = x - 3 = 0
when x = 3.
To get around the discontinuity in the limand at x = 3, rationalize the numerator:
[tex]\dfrac{\sqrt{x+1} - 2}{x - 3} \times \dfrac{\sqrt{x + 1} + 2}{\sqrt{x + 1} + 2} = \dfrac{\left(\sqrt{x+1}\right)^2 - 2^2}{(x-3) \left(\sqrt{x+1}+2\right)} = \dfrac{x-3}{(x-3)\left(\sqrt{x+1}+2\right)}[/tex]
Now as x approaches 3, the factors of x - 3 cancel, the resulting limand is continuous at x = 3, and we have
[tex]\displaystyle \lim_{x\to3} \frac{\sqrt{x+1} - 2}{x - 3} = \lim_{x\to3} \frac1{\sqrt{x+1}+2} = \boxed{\frac14}[/tex]
the lenth of a rectangle is twice the width if the permeter is 20 cm find the width
L = 2W
perimeter = 2( L + W ) = 20 .
2 ( 2W + W ) = 20
6 W = 20
W = 20/6
= 10/3
L = 20/3
Answer:
10/3
Step-by-step explanation:
Given properties of the rectangle:
The length is twice the width ( So we can say l = 2w ) The perimeter is 20cmGiven this we want to find the width of the perimeter.
Creating a system of equation:
First off we know that perimeter = 2L + 2W
We also know that the perimeter of this rectangle is 20 cm
So we can say that 20 = 2L + 2W
We also know that the length of this rectangle is twice the width or in other words l = 2w
So we have the two equations, 20 = 2l + 2w and l = 2w
Solving the system:
We are going to use the substitution method to solve this system.
The substitution method works when you have two equations, one can be just a plain equation but the other must have one of the variables defined ( by itself on either side of the equal sign )
If you have one of the variables defined, you can plug it in ( substitute ) into the other equation and solve for the other variable.
Plugging in the defined variable into the other equation
Equation : 20 = 2l + 2w
Defined variable : l = 2w
==> plug in l = 2w
20 = 2(2w) + 2w ( now we solve )
==> multiply 2 and 2w
20 = 4w + 2w
==> combine like terms
20 = 6w
==> divide both sides by 6
20/6 = w
==> simplify fraction
10/3 = w
The width = 10/3
Checking our work:
First we must solve for length as well
Solving for length by plugging in width into either equation
l = 2w
==> plug in w = 10/3
l = 2(10/3)
==> multiply 2 and 10/3
l = 20/3
Now to check our we we plug in the length and width into both equations, if both are true then our answer is correct
Equation 1 : 2l + 2w = 20
==> plug in l = 20/3 and w = 10/3
2(20/3) + 2(10/3) = 20
==> simplify multiplication
40/3 + 20/3 = 20
==> add fractions
20 = 20
Equation 2 : l = 2w
==> plug in l = 20/3 and w = 10/3
20/3 = 2(10/3)
==> multiply 2 and 10/3
20/3 = 20/3
Both are correct so our final answer is correct as well! :)
The compound interest formula can be rewritten as
P = A/(1 + r/n)nt.
Find the principal P that you need to invest on the day your child is born at 4.2% annual interest compounded quarterly to make your child a millionaire on his or her 21st birthday. (Round your answer to the nearest cent.)
Answer:
Compound interest, or 'interest on interest', is calculated using the compound interest formula.
The formula for compound interest is A = P(1 + r/n)^nt, where P is the principal balance, r is the interest rate, n is the number of times interest is compounded per time period and t is the number of time periods.
Step-by-step explanation:
What is the approximate solution to this equation? 15(3)^2x=90
Answer:
x ≈ 0.67
Step-by-step explanation:
[tex]15(3)^2x = 90\\\\15(9)x = 90\\\\135x = 90\\\\x = 90/135\\\\ x = 2/3\\\\x = 0.666...\\\\x = 0.67 \ (rounded \ to \ nearest \ hundredth )[/tex]
Jordan ran 7/8 mile on Monday and 5/6 mile on Tuesday.
How much farther did Jordan run on Monday than on Tuesday?
Enter your answer as a fraction in simplest form
Answer:
[tex] \frac{1}{24} miles \\ [/tex]
Step-by-step explanation:
[tex] \frac{7}{8} - \frac{5}{6} = \frac{1}{24} [/tex]
Find the volume of rectangular pyramid 5in 5 in 2 in
Answer:
16.67
Step-by-step explanation:
formula for a rectangular pyramid =
lengthxwidth= base area x height/3
2x5=10x5=50
50/3=16.67
(04.02 mc)
segment ab falls on line 6x + 3y = 9. segment cd falls on line 4x + 2y = 8. what is true about segments ab and cd?
You can see that both lines have the same slope showing that they are both parallel
Linear equationsThese are equations that has a degree of 1. Given the equation of the lines
ab = 6x + 3y = 9
cd: 4x + 2y = 8
Write then in slope-intercept form
ab: y = -2x + 3
cd = y = -2x +8
You can see that both lines have the same slope showing that they are both parallel
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Answer:
They are parallel because they have the same slope of −2.
Step-by-step explanation:
Type the correct answer in the box. Use numerals Instead of words. If necessary, use / for the fraction bar.
David invested $230 in a savings account that offers a 3% return on the Investment. The value of David's Investment will be at least $415 after a
period of
years.
Hint: Use the formula A= P1+, where A is the amount after tyears, Pls the amount Invested, r is the rate of interest, and t is the time period.
Use a calculator to compute the answer, and round It off to the nearest year.
Reset
Next
Using an exponential function, it is found that the value of David's Investment will be at least $415 after a period of 20 years.
What is an exponential function?An increasing exponential function is modeled by:
[tex]A(t) = A(0)(1 + r)^t[/tex]
In which:
A(0) is the initial value.r is the growth rate, as a decimal.In this problem, the initial value and the growth rate for his investment are given by:
A(0) = 230, r = 0.03.
Hence, the value after t years is given by:
[tex]A(t) = 230(1.03)^t[/tex]
Then, the value will be of at least $415 when:
[tex]A(t) \geq 415[/tex]
[tex]230(1.03)^t \geq 415[/tex]
[tex](1.03)^t \geq \frac{415}{230}[/tex]
[tex]\log{(1.03)^t} \geq \log{\frac{415}{230}}[/tex]
[tex]t\log{1.03} \geq \log{\frac{415}{230}}[/tex]
[tex]t \geq \frac{\log{\frac{415}{230}}}{\log{1.03}}[/tex]
[tex]t \geq 20[/tex]
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what is the value of x
Answer:
Should be 60°
Step-by-step explanation:
Since each interior angle in an octagon is 120°, you would subtract 120° from 180° (which is the angle of a line). This would get you 60 °.
I want to know the answer of these questions and the questions are
2 + 7
6 + 4
2 + - 7
- 2 + 7
- 2 + - 7
6 + - 4
- 6 + 4
- 6 + -4
2 + 7 = 9
6 + 4 = 10
2 + - 7 = -5
- 2 + 7 = 5
- 2 + - 7 = -9
6 + - 4 = 2
- 6 + 4 = - 2
- 6 + - 4 = -10
HELPP PLEASE ILL MAKE YOU THE BRAINIEST Find the area of the rhombus
Answer:
D1×D2/2sq
445×5= 225
225/2
=112.5
What are the fourth roots of 2√3 −2i? Enter your answer by filling in the boxes. Enter the roots in order of increasing angle measure.
By using the De Moivre's formula, the quartic roots of the complex numbers (in polar form) are z₁ = (√2, π/6), z₂ = (√2, 2π/3), z₃ = (√2, 7π/6), z₄ = (√2, 5π/3).
How to find the roots of a complex number
Complex numbers are numbers of the form a + i b, where a and b are the real and imaginary component, respectively. In other words, complex numbers are an expansion from real numbers. The n-th root of a complex number is found by using the De Moivre's formula:
[tex]\sqrt[n]{z} = \sqrt[n]{r}\cdot \left[\cos \left(\frac{\theta + 2\pi\cdot k}{n} \right) + i\,\sin \left(\frac{\theta + 2\pi\cdot k}{n}\right)\right][/tex], for i = {0, 1, 2, ..., n - 1}.
Where:
r - Norm of the complex number.θ - Direction of the complex number, in radians.The norm of the complex number is found by Pythagorean theorem:
[tex]r = \sqrt{(2\sqrt{3})^{2}+(-2)^{2}}[/tex]
r = 4
And the direction is determined below:
[tex]\theta = \tan^{-1} \left(\frac{2\sqrt{3}}{-2} \right)[/tex]
θ = 2π/3 rad
Then, the quartic roots of the complex numbers (in polar form) are z₁ = (√2, π/6), z₂ = (√2, 2π/3), z₃ = (√2, 7π/6), z₄ = (√2, 5π/3).
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PLS HELP!!! WILL GIVE A LOT OF POINTS!!!
dont forget the show your work pls
Answer: it might be 8
Step-by-step explanation: Write a distance formula: x^2 - x^1
substituted -3.8, 4.2 into x^2 - x^1 and u will get 4.2 + 3.8 and u will calculate and it gets 8
I hope its right
help please!!!!!!!^3
Answer:
36
Step-by-step explanation:
[tex]-2[-6(-4+7)]\\\\=(-2)(-6)(3)\\\\=12(3)\\\\=36[/tex]
Find the center and radius of the circle whose equation is x2 + y2 + 8x - 2y + 15 = 0
(4, 1) r = 2
(-16, 1), r = 4
(-4, 1),
(-4, -1),
The equation represents a circle whose center is (-4, 1) and has a radius r = √2
How to find the center and radius of the circle?We have the equation:
[tex]x^2 + y^2 + 8x - 2y + 15 = 0[/tex]
We can rewrite this as:
[tex](x^2 + 8x ) + (y^2 - 2y ) + 15 = 0\\\\\\\\(x^2 + 8x + 16) - 16 + (y^2 - 2y + 1) - 1 + 15 = 0\\\\(x + 4)^2 + (y - 1)^2 - 16 - 1 + 15 = 0\\\\(x + 4)^2 + (y - 1)^2 = 2[/tex]
Where we just completed squares.
Comparing this with the general circle equation, we can see that the center is the point (-4, 1) and the radius is √2.
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Can someone simplfy to me why we use different formula in some equations for sin cos tan? Like in some instances we swap variables and in others we just divide and stuff and I don't understand why we do that
3+x=7 what is x .........................
Answer:
4
Step-by-step explanation:
x = 7 - 3
x = 4
Answer:
x = 4
Step-by-step explanation:
3+x = 7
Subtract 3 from each side
3+x-3 = 7-3
x = 4
what is nine minus one third?
Answer:
[tex]\frac{26}{3}[/tex]=[tex]8.6...[/tex]=[tex]8\frac{2}{3}[/tex]
Step-by-step explanation:
You multiply 9 x 3=27
(leave 1/3 alone, it's already good)
you have a 27/3-1/3
(subtract those)
your answer is 26/3
(see answer above for decimal form and mixed fraction form)
Help please this is due today
The experimental probability that in a group of 4 students, at least one of them has brown eyes is 95%.
What is Experimental Probability?
Experimental probability is a probability that is determined on the basis of a series of experiments. A random experiment is done and is repeated many times to determine their likelihood and each repetition is known as a trial. The experiment is conducted to find the chance of an event to occur or not to occur.
Here , Favorable Outcome = 19
Total outcomes = 20
Probability = Favorable Outcome/ Total Outcome
= 19 / 20
= 95%
Thus, the experimental probability that in a group of 4 students, at least one of them has brown eyes is 95%.
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If y=3x+4 we’re changed to y=5x+4 how would the graph of the new function compare with the first one
Answer:
t would be steeper
Step-by-step explanation:
Find a polynomial f(x) of degree 3 with real coefficents and following zeros. -4,4i
Answer:
[tex]f(x)=x^3 +4x^2 +16x +64[/tex]
Step by step explanation:
[tex]\text{Given that, two roots are}~ -4~ \text{and}~ 4i.\\\\\text{Let,}\\\\~~~~~~~x = 4i\\\\\implies x^2 = 16i^2~~~~~~~;[\text{Square on both sides}]\\\\\implies x^2 = -16~~~~~~~~;[i^2 = -1]\\\\\implies x^2 +16 = 0\\\\\text{So,}~ x^2 +16~ \text{ is a factor of the 3 degree polynomial}.\\ \\ \text{The polynomial is ,}\\\\ f(x) = (x+4)(x^2 +16)\\\\~~~~~~~=x^3 +16x +4x^2 +64\\\\~~~~~~~=x^3 +4x^2 +16x +64[/tex]
Find the length of the third side. If necessary, write in simplest radical form.
find m ab in the figure below a90 b108 c72 d162
STATISTICS!!!! PLEASE HELP ASAP
Answer: they can conclude the distributions are different at the 95% confidence interval. Compute the z test statistic to solve this.
Step-by-step explanation: to get the 95% confidence interval on the mean take the mean value (984) +/- (2*standard deviation divided by the square root of the number of samples) (I.e. 984 +/- (2*267/sqrt(501)))
Solve the system of equations using substitution.
Y= 2x - 10
Y= 4x - 8
Answer:
Step-by-step explanation:
4x - 8 = 2x - 10
2x - 8 = -10
2x = -2
x = -1
y = 4(-1) - 8 = -4 -8 = -12
(-1, -12)
can anyone please explain me why DB=DP instead of DB=AD?
I am finding it difficult to understand
Step-by-step explanation:
In given, it's said that D is a midpoint, which mean DP == AD, DP is the same as DP because isosceles triangle properties said that two-length are equal when their base angle are equal. In a right triangle, the midpoint D, draws a line to the "90 degree" angle is always a isosceles
What is the surface area of the cylinder? Please show work.
Answer:
Surface area is 288π cm² (exact solution), which is approximately 904.78 cm² (if you use pi on calculator) or 904.32 cm² (if you use 3.14 for pi).
Step-by-step explanation:
Surface area of cylinder
[tex]SA = 2 \times \text{area of base} + \text{lateral area}\\SA = 2 \pi r^2 + 2 \pi r h[/tex]
SA ... surface area
r ... radius
h ... height of cylinder
Given:
d = 12 cm
h = 18 cm
Since diameter d is 12 cm, that means that radius is half of that, so 6 cm.
r = 6 cm
Insert in formula:
[tex]SA = 2 \pi r^2 + 2 \pi r h\\SA = 2 \pi (6)^2 + 2 \pi (6)(18)\\SA = 72 \pi + 216 \pi\\SA = 288 \pi \text{ cm}^2 \approx 904.78 \text{ cm}^2[/tex]
PLEASE HELP!!!!!!!!!!!!
Answer:
see explanation
Step-by-step explanation:
PQRS is a cyclic quadrilateral.
the opposite angles in a cyclic quadrilateral sum to 180° then
∠ Q + ∠ S = 180 ( substitute values )
3x - 8 + 3x + 8 = 180
6x = 180 ( divide both sides by 6 )
x = 30
Then
∠ Q = 3x - 8 = 3(30) - 8 = 90 - 8 = 82°
∠ S = 3x + 8 = 3(30) + 8 = 90 + 8 = 98°
∠ P = x + 15 = 30 + 15 = 45°
∠ R = 180° - ∠ P = 180° - 45° = 135°
A bag contains pennies, nickels, dimes, and quarters. There are 50 coins in all. Of the coins, 16% are pennies and 34% are dimes. There are 3 more nickels than pennies. How much money does the bag contain?
see the attachment for solution
hope it helps...!!!
Answer:
$5.83
Step-by-step explanation:
The total amount of money is the sum of the values of the various denomination coins.
__
setupLet p, n, d, q represent the numbers of pennies, nickels, dimes, and quarters, respectively.
p + n + d + q = 50 . . . . . . there are 50 coins in all
16% × 50 = p . . . . . . . . . . 16% are pennies
34% × 50 = d . . . . . . . . . . 34% are dimes
n = p +3 . . . . . . . . . . . . . . there are 3 more nickels than dimes
The total value is ...
v = 0.01p +0.05n +0.10d + 0.25q
__
solutionThe numbers of pennies and dimes are found easily:
0.16 × 50 = p = 8
0.34 × 50 = d = 17
Then the number of nickels can be found:
n = p +3 = 8 +3 = 11
Finally, the number of quarters is found from the total number of coins:
p + n + d + q = 50
8 + 11 + 17 + q = 50 . . . substitute known values
q = 14 . . . . . . . . . . . . . subtract 36 from both sides
The total value is then ...
v = 0.01(8) +0.05(11) +0.10(17) +0.25(14) = 0.08 +0.55 +1.70 +3.50
v = 5.83
The bag contains $5.83.
math hw please answer quickly i dont understand
Answer:
See explanation
Step-by-step explanation:
Since she used only 1/2 of the recipe and the full recipe uses 1 cup, divide 1 by 2. The equation is 1/2=0.5.
For the lemon juice, the equation is 1/4 divided by 2. On the number line, make a dot at 1/4, and then travel backwards halfway. 1/4 divided by 2 is 1/8, or 0.125.
Hope this helps!
Convert 0.0150 km to meters and express the answer to the correct number of significant digits. a. 150 m b. 15 m c. 15.0 m d. 150.0 m
The correct answer is option C which is 15 meters.
What is unit conversion?
Unit conversion is a multi-step process that entails multiplying or dividing by a numerical factor, selecting the correct number of significant digits, and then multiplying or dividing by another numerical factor.
The unit conversion will be done as:-
1 km = 1000 meters
0.0150 Km = 0.0150 x 1000 meters
0.0150 Km = 15 meters
Therefore the correct answer is option C which is 15 meters.
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