The square root of 576 is the inverse of the mathematical operation of squaring the number 24. The square root of a number implies a number whose product with itself gives the initial number. Now we will calculate the square root of 576 using various methods and a few interesting facts and problems too.
Square root of 576: 24Square of 576: 331776What Is the Square Root of 576?The square root of 576 can be written as √576 and (576)1/2
The square of 576 will be a number(a) such that a × a = 576
And 24 × 24 = 576 also -24 × -24 = 576
Therefore, +24 and -24 are the square root of 576
Is Square Root of 576 Rational or Irrational?The square root of 576 are +24 and -24.
Both numbers are integers and we know that all integers are rational numbers.
Hence, the square root of 576 is a rational number.
Solve the following quadratic equation: x^2-10x+25=51
please show steps i don’t understand
1. Simplify the quadratic equation into its standard form
Formula : ax^2+bx+c=0
Subtract from both sides:
x^2-10x+25=51
x^2-10x+25-51=0
x^2-10x-26=0
Use the standard form, ax^2+bx+c=0, to find the coefficients of our equation.
x^2-10x-26=0
a=1
b=-10
c=-26
The quadratic formula gives us the roots for ax^2+bx+c=0, in which a, b and c are numbers (or coefficients), as follows :
x=(-b±sqrt(b^2-4ac))/(2a)
to get the result :
x=(10±sqrt(204))/2
Simplify 204 by finding its prime factors:
The prime factorization of 204 is 2^2*3*17
x_2=-2.141
Answer:
x = 5 ± √51
Step-by-step explanation:
x² - 10x + 25 = 51
x² - 10x + 25 - 51 = 51 - 51
x² - 10x - 26 = 0
Factors with a product of -26 and a sum of -10:
NONE! Solve by completing the square (see attachment)
Step 1: Rearrange
x² - 10x + 25 = 51
x² - 10x = 26
Step 2: Add (b/2)² to both sides
x² - 10x + (-10/2)² = 26 + (-10/2)²
x² - 10x + 25 = 51
Step 3: Factor and solve
(x - 5)² = 51
x - 5 = √51
x = 5 ± √51
BRAINLIEST please if this helped!" Laurent Series "
Expand:
[tex] f(z) = \frac{ {e}^{ {z}^{2} } }{ {z}^{3} } [/tex]
Recall that for all [tex]z\in\Bbb C[/tex],
[tex]\displaystyle e^z = \sum_{n=0}^\infty \frac{z^n}{n!}[/tex]
Then
[tex]\displaystyle \frac{e^{z^2}}{z^3} = \frac1{z^3} \sum_{n=0}^\infty \frac{z^{2n}}{n!} = \boxed{\sum_{n=0}^\infty \frac{z^{2n-3}}{n!}}[/tex]
If csc ( x ) = 4, for 90 ∘ < x < 180, then sin ( x /2 ) = ? cos ( x /2 ) = ? tan ( x/ 2 ) = ?
Answer:
see below
Step-by-step explanation:
cscx=4
sinx=1/4
cosx=-√(1-sin^2x)=-√(1-(1/16))=-√(15/16)=-√15/4
note: cos<0,sin>0 in quadrant II
sin(x/2)= [tex]\sqrt{\frac{1+cos(x)}{2} } =\sqrt\frac{1+\sqrt{\frac{15}{4} } }{2} =\sqrt{\frac{4+\sqrt{15} }{8} }[/tex]
cos(x/2)= [tex]\sqrt{\frac{1-cos(x)}{2} } =\sqrt{\frac{1-\sqrt{\frac{15}{4} } }{2} } =\sqrt{\frac{4-\sqrt{15} }{8} }[/tex]
tan(x/2)= [tex]\frac{sin(x)}{1-cos(x)} =\frac{\frac{1}{4} }{(1-\frac{\sqrt{15} }{4} )} =\frac{\frac{1}{4} }{\frac{4-\sqrt{15} }{4} } =\frac{1}{4-\sqrt{15} }[/tex]
Calculator check:
[tex]sinx=\frac{1}{4}[/tex]
[tex]x\neq 165.52[/tex]˚ in quadrant II
[tex]\frac{x}{2} \neq 82.76[/tex] ˚
sin(x/2)≈sin(82.76)≈0.9920..
exact value=√(4+√15)/8≈0.9920..
..
cos(x/2)≈cos(82.76)≈0.1260..
exact value=√(4-√15)/8≈0.1260..
..
tan(x/2)=tan(82.76)≈7.872..
exact value=1/(4-√15)≈7.872..
If the area of the rectangle is twenty-four-and-thirty-two-hundredths square inches, what’s the measurement of the width?
Answer:
Can't answer this without knowing the height of the rectangle ...
Step-by-step explanation:
Answer: 3.2
Step-by-step explanation: Trust me, I got it right.
A sequence can be generated by using
an=an-1-5 where
a1 = 100 and n is a whole number greater
than 1.
(a) What are the first five terms in the sequence?
(b) Write an iterative rule for the sequence. Show your work
a) The first five terms in the sequence is 100, 95, 90, 85 and 80
b) The nth term of the sequence will be 100 + (n - 1)(5) = 5n + 95
Iterative rule for a sequenceSequences are set of values arranged in a particular order. Given the recursive formula for a sequence expressed as;
an=an-1-5
If the first term a1 = 100, then;
a2 = a1 - 5
a2 = 100 - 5
a2 = 95
For the third term
a3= a2 - 5
a3= 95 - 5
a3 = 90
The other two terms will be 85 and 80
a) The first five terms in the sequence is 100, 95, 90, 85 and 80
b) The nth term of the sequence will be 100 + (n - 1)(5) = 5n + 95
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Find the maximum rate of change of the function f (x, y) = x^2y^2 + xy −10 at the
point (1, 1), and the direction in which it occurs.
Answer:
The maximum rate of change of the given function is equal to 3√2.
The direction at which the vector points is given by the unit vector [tex]\displaystyle \frac{\sqrt{2}}{2} \hat{\i} + \frac{\sqrt{2}}{2} \hat{\j}[/tex].
General Formulas and Concepts:
Pre-Calculus
Vectors
Unit Vector:Calculus
Differentiation
DerivativesDerivative NotationDerivative Property [Addition/Subtraction]:
[tex]\displaystyle (u + v)' = u' + v'[/tex]
Derivative Rule [Basic Power Rule]:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Multivariable Calculus
Partial Derivatives
Gradient:
[tex]\displaystyle \nabla f(x, y, z) = \frac{\partial f}{\partial x} \hat{\i} + \frac{\partial f}{\partial y} \hat{\j} + \frac{\partial f}{\partial z} \hat{\text{k}}[/tex]
Gradient Property [Addition/Subtraction]:
[tex]\displaystyle \nabla \big[ f(x) + g(x) \big] = \nabla f(x) + \nabla g(x)[/tex]
Step-by-step explanation:
Step 1: Define
Identify given.
[tex]\displaystyle f(x, y) = x^2y^2 + xy - 10[/tex]
[tex]\displaystyle \text{Point} \ (1, 1)[/tex]
Step 2: Find Maximum Rate of Change
[Function] Take gradient:∴ the maximum rate of change of the given function f(x, y) is equal to 3√2.
Step 3: Find Direction
[Gradient] Convert to unit vector:∴ we have found the direction of the gradient.
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Topic: Multivariable Calculus
Unit: Directional Derivatives
A 9 ft. ladder leans against the side of a house. The bottom of the ladder is 6 ft. from the side of the house. How high is the top of the ladder from the ground? If necessary, round your answer to the nearest tenth.
Answer:
15 ft
Step-by-step explanation:
I'm not sure but I think u add them together to get ur answer
hope it helps
(12-3)\times6+(3\times7)
Answer:
The answer is 75
Step-by-step explanation:
Subtract: 12 - 3 = 9Consider the equation v+4+v=8. What is the resulting equation after the first step in the solution?
0v+4=8-v
Ov+4=8
04+v=8-v
O2v + 4 = 8
The resulting equation after the first step in the solution is:
2v + 4 = 8.
What is Equation?An equation is a mathematical statement that asserts the equality between two expressions. It typically contains one or more variables and may involve mathematical operations such as addition, subtraction, multiplication, division, or exponentiation.
we have the Equation v + 4 + v =8
Now, simplifying we get
2v + 4= 8
2v = 4
v =2
To obtain this equation, we combined the like terms "v" on the left side of the equation, which gives us 2v. The rest of the equation remains unchanged.
Therefore, the correct answer is : 2v + 4 = 8.
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Keith is the owner of a cafe. He bought 28.6 pounds of apples for making pies. Apples cost$1.75 per pound. He also bought a can of chocolate syrup for $27.75. What was the amount that Keith spent?
Answer:
$77.514
Step-by-step explanation:
28.6 x 1.74 + 27.75 = 77.514
Suppose that y is inversely proportional to the 4th power of x, and that y=16 when x=6. What is y when x=3? Round your answer to two decimal places if necessary.
Answer:
y = 1
Step-by-step explanation:
Given
y ∝ x⁴⇒ y = kx⁴
Finding the proportionality constant, k
y = 16 and x = 316 = k (6)⁴16 = 1296kk = 16/1296k = 1/81Finding y
y = 1/81 x (3)⁴y = 1/81 x (81)y = 1In a line of boys,Peter is the 11th from either side of the line. how many boys are in the line 5pionts because its simple
Answer: 21
Step-by-step explanation:
Someone please help!
Step-by-step explanation:
<1 = 180°-102° = 78° (the extended angle is 180°)
<2 = <5 = 58°
<3 = 180° - 78° - 58° = 44° (the sum of the angles inside of a triangle is 180°)
<4 = 180° - 44° - 58° = 78° = <1 (the extended angle is 180°)
solve the following inequality
4x+15≥x+6
Answer:
[tex]\boxed{\sf{x\geq -3}}[/tex]Step-by-step explanation:
The following inequality can be solved by separating the term x from one side.
4x+15≥x+6
First, subtract by 15 from both sides.
4x+15-15≥x+6-15
Solve.
4x≥x-9
Then, you subtract by x from both sides.
4x-x≥x-9-x
Solve.
3x≥-9
Divide by 3 from both sides.
3x/3≥-9/3
Solve.
Divide the numbers from left to right.
-9/3=-3
[tex]\Longrightarrow: \boxed{\sf{x\geq -3}}[/tex]
Therefore, the correct answer is x≥-3.I hope this helps, let me know if you have any questions.
Answer:
x ≥ -3
Step-by-step explanation:
To determine the solution to the inequality, we need to isolate the variable and its coefficient on one side of the equation. Furthermore, isolate the variable by dividing the coefficient by both sides of the equation. The inequality obtained after doing these steps is the solution to the inequality.
Given inequality:
4x + 15 ≥ x + 6As said above, let's isolate "x" and it's coefficient on one side of the equation. This can be done by subtracting "x + 15" to both sides of the equation.
⇒ 4x + 15 - (x + 15) ≥ x + 6 - (x + 15)⇒ 4x + 15 - x - 15 ≥ x + 6 - x - 15⇒ 3x ≥ -9As said above, let's further isolate "x" by dividing the coefficient of "x" to both sides of the equation.
⇒ 3x/3 ≥ -9/3⇒ x ≥ -3Therefore, the solution is x ≥ -3.
What is the solution to the inequality |2x – 3| > 5?
Answer:
x > 4 or x < -1
Step-by-step explanation:
[tex]2x - 3 > 5[/tex]
[tex]2x > 8[/tex]
[tex]x > 4[/tex]
[tex]2x - 3 < - 5[/tex]
[tex]2x < - 2[/tex]
[tex]x < - 1[/tex]
what is the median of 7,3,4,7,5,6,5,5,4
Your median is 5 because that is the number that is mentioned the most.
A median is a number that i said the most.
And in the pic your median is 7.
Hope this helps you :0
what digit 5 sits in this number 725,069
Answer:
The digit 5 is equal to is 5,000 :)
Have an amazing day!!
Please rate and mark brainliest!!
Answer:
The thousandth digit!
Step-by-step explanation:
Write an equation in slope-intercept form of the line shown.
An equation is
Using the slope intercept formula, the equation for the line in slope intercept form is y = -x - 4
Slope intercept equationThe slope intercept equation can be describe as follows:
y = mx + b
where
m = slopeb = y-interceptTherefore,
(-4, 0)(1, -5)
m = -5 - 0 / 1 + 4 = -5 / 5 = -1
Therefore, let's find b using (1, -5)
-5 = -1(1) + b
-5 = -1 + b
b = -5 + 1
b = -4
Therefore, the equation is y = -x - 4
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How do I find the mean of these numbers
Answer:
add all of them together (x and y’s) the divide the sum by the amt of numbers
Step-by-step explanation:
Answer:
1. 0
2. -2.5
3. 5
4. -2.5
5. -4
Step-by-step explanation:
Did this by adding the scores together and then dividing by the number of scores added
Please help now, I will give Brainliest!!! :D
Peter is 19 years old. He lives at home with his parents and goes to college part time. He recently started working as a server, working 40 hours per week.
Where Peter lives, the minimum wage for tipped and non tipped employees is $7.25 per hour.
In the average week, he serves 90 tables whose typical bill is $21 with an average tip of 15%.
How much money does he make in a typical week??
Answer:
$573.50 per week
Step-by-step explanation:
wages = 40 hr/wk * 7.25 $/hr $290 per week
tips 90 tables * ( 21*.15) = 283.50
total 290 + 283.5 = 573.50
In your own words describe how to find the area of a composite
figure? What are the steps you would take to solve a problem like
this?
HELP PLS ILL MAKE THE BRAINIEST SAY THANKS AND RATE 5 STARS JUST HELP ME IN LIKE 5 - 10 MIN PLS!
Answer:
A=LxW
Step-by-step explanation:
cut the shape into easier pieces then go to one piece and x the W with the L for example 4x5 then x them and youll get your area like this A=LxW = 20=4x5 like that then do the same for the other pieces then once you x them all add them and youll get the whole area for your shape
hoped it helped :)
can someone help me with this?
Answer:
f(x) = 2 -2^x
Step-by-step explanation:
The graph has a horizontal asymptote at y = 2. It has a slope that doubles in each unit interval. This tells you it is an exponential function with a base of 2, and a vertical translation of 2. The curve downward, rather than upward, means the function has been reflected across a horizontal line.
__
vertical shiftAn exponential function of the form ...
y = a·b^x
will have a horizontal asymptote at y=0. The asymptote here is y=2, so 2 has been added to the function value.
base valueThe slope of the above function (y=a·b^x) will be multiplied by a factor of 'b' when x increases by 1. Your graph has a slope (rise/run) of -1 for x between 0 and 1, a slope of -2 for x between 1 and 2, and a slope of -4 between x=2 and 3. This behavior indicates that b=-2/-1 = -4/-2 = 2.
scale factorThe function so far looks like ...
y = a·2^x +2
Using x=0, we can find the value of 'a'.
1 = a·2^0 +2
-1 = a . . . . . . . . subtract 2
Then the function is ...
f(x) = -2^x +2
2/4×5/2
please answer fast
Answer: 10/8 = 1 1/4
Step-by-step explanation:
2x5 =10
4x2 =8
10/8= 1 2/8 = 1 1/4
Determine the period
Answer: 8
just guessed it
37+6x-33-7x
i need help i cant find the answer
Answer:
By simplifiying the expression we get
−x+4
Answer:
-x+4
Step-by-step explanation:
Subtract: 37-33
Combine like terms: 6x-7
Rearrange terms: -x+4
Forces with magnitudes of 2000 newtons and 900 newtons act on a machine part at angles of +45degrees and -60degrees respectively, with the right side of the x-axis. Find the direction and magnitude of the resultant of these forces.
Answer:
First,you need to find the components of each force.
I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER
Answer:
here
Step-by-step explanation:
if you need more explanation comment on this
Course challenge
You might need: Calculator
Figure A is a scale image of figure B.
Figure A
Figure B
16
Figure A maps to figure B with a scale factor of 4/9
What is the value of X?
Answer:
x=36
Divide the corresponding side (16) by 4/7
Answer:
x=36
Divide the corresponding side (16) by 4/7
Step-by-step explanation:
x=16×9/4=36
I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER
Answer:
24:37
Simplify the ratio by dividing by the GCF, in this case, two.
[tex]\frac{48 / 2}{74 / 2} = \frac{24}{37}~also~known~as~24:37[/tex]
Refer to attachment for question
Answer:
Below!
Step-by-step explanation:
Let the irrational number be known as "x".
[tex]\implies -\sqrt{41} \times x = 1[/tex]
Divide both sides by -√41.
[tex]\implies \dfrac{(-\sqrt{41} \times x)}{-\sqrt{41} } = \dfrac{1}{\sqrt{-41} }[/tex]
[tex]\implies x = \dfrac{1}{-\sqrt{41} }[/tex]
Take the "-" to the numerator:
[tex]\implies x = \dfrac{-1}{\sqrt{41} }[/tex]
Use parenthesis to isolate the "-"
[tex]\implies x = -\huge\text{(}\dfrac{1}{\sqrt{41} } \huge\text{)}[/tex]
Note: 1 can also be written as √1. (√1 = √1 × √1 = 1)
[tex]\implies {x = -\huge\text{(}\dfrac{\sqrt{1}}{\sqrt{41} }\huge\text{)}}[/tex]
Combine the roots in the equation:
[tex]\implies {x = -\huge\text{(}\sqrt{\dfrac{1}{41} }} \huge\text{)}}[/tex]
Remove the parenthesis:
[tex]\implies {x = -\sqrt{\dfrac{1}{41} }}[/tex]
Thus, Option C is correct.