Given:
The expression is:
[tex](5^2)(7^2)(3^2)[/tex]
To find:
The value of the given expression.
Solution:
We have,
[tex](5^2)(7^2)(3^2)[/tex]
On simplification, we get
[tex](5^2)(7^2)(3^2)=(25)(49)(9)[/tex]
[tex](5^2)(7^2)(3^2)=11025[/tex]
Therefore, the value of the given expression is 11025.
What is the common ratio for the geometric sequence below, written as a fraction?
768, 480, 300, 187.5, …
/
Answer:
5/8
Step-by-step explanation:
Find the common ratio by dividing one of the numbers in the sequence by the previous one:
480/768
= 0.625
Convert this to a fraction:
0.625
= 5/8
So, the common ratio is 5/8
Help me wit this rq…………..
Let W be part of the solid sphere of radius 4, centered at the origin, that lies above the plane z = 2. Set up an integral in cylindrical coordinates to find the volume of the region. Do NOT actually integrate.
Answer:
V = ∫∫∫rdrdθdz integrating from z = 2 to z = 4, r = 0 to √(16 - z²) and θ = 0 to 2π
Step-by-step explanation:
Since we have the radius of the sphere R = 4, we have R² = r² + z² where r = radius of cylinder in z-plane and z = height² of cylinder.
So, r = √(R² - z²)
r = √(4² - z²)
r = √(16 - z²)
Since the region is above the plane z = 2, we integrate z from z = 2 to z = R = 4
Our volume integral in cylindrical coordinates is thus
V = ∫∫∫rdrdθdz integrating from z = 2 to z = 4, r = 0 to √(16 - z²) and θ = 0 to 2π
Answer:
[tex]\displaystyle V = \int\limits^{2 \pi}_{0} \int\limits^{2\sqrt{3}}_{0} \int\limits^{\sqrt{16 - r^2}}_2 {r} \, dz \, dr \, d\theta[/tex]
General Formulas and Concepts:
Multivariable Calculus
Cylindrical Coordinate Conversions:
[tex]\displaystyle x = r \cos \theta[/tex][tex]\displaystyle y = r \sin \theta[/tex][tex]\displaystyle z = z[/tex][tex]\displaystyle r^2 = x^2 + y^2[/tex][tex]\displaystyle \tan \theta = \frac{y}{x}[/tex]Volume Formula [Cylindrical Coordinates]:
[tex]\displaystyle V = \iiint_T \, dV \rightarrow V = \iiint_T {r} \, dz \, dr \, d\theta[/tex]
Step-by-step explanation:
Step 1: Define
Identify given.
Solid sphere w/ radius 4 centered at (0, 0, 0) → x² + y² + z² = 4²
Plane z = 2
Step 2: Find Volume Pt. 1
Find bounds of z.
[Sphere] Substitute in plane z:∴ 0 ≤ r ≤ 2√3
Step 2: Find Volume Pt. 2
[Sphere] Substitute in plane z:∴ 0 ≤ θ ≤ 2π
Step 3: Find Volume Pt. 3
[Sphere] Substitute in cylindrical conversions:∴ 2 ≤ z ≤ √(16 - r²)
Step 4: Find Volume Pt. 4
Substitute in variables [Volume Formula - Cylindrical Coordinates]:∴ the volume of the region is found with the integral above.
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Learn more about multivariable calculus: https://brainly.com/question/17203772
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Topic: Multivariable Calculus
Unit: Triple Integral Applications
Find the value of x for which WXYZ must be a parallelogram.
Answer:
[tex](5x - 4) \degree = (2x + 14)\degree \\ 3x = 18\\ x = 6[/tex]
helppp please i need this answered fast please :⊂
Answer:
dang good luck
Step-by-step explanation:
Can someone please help me? thank you
Answer:
c = (ef-ab)/d
Step-by-step explanation:
ab+cd = ef
Subtract ab from each side
ab+cd -ab = ef-ab
cd = ef-ab
Divide by d
cd /d =(ef-ab)/d
c = (ef-ab)/d
50 POINTS!!!!!!!!!!!!!!!
28,45,12,34,36,45,19,20
Find the mean absolute deviation of this set of data. PLEASE PUT STEPS
Answer:
10.125
Step-by-step explanation:
Given the data :
28,45,12,34,36,45,19,20
The mean absolute deviation of the data is :
Σ|x - mean| / n
n = number of values = 8
Mean = Σx / n = 239 / 8
Mean = 29.875
Take the sum of the absolute value if the difference between each data value and the mean, then divide by the data size
Using a mean absolute deviation calculator ;
Mean absolute deviation = Σ|x - mean| / n = 10.125
What is the value of y - X?
A. 20
D
B. 30
O
E.
о O
C. 45
Answer:
30
Step-by-step explanation:
that is the procedure above
I am majorly stuck lol
The area of a rectangle is given by the expression 8x3 + 26x2 + 31x + 15. If the width of the rectangle is 2x + 3, what is the expression that represents the length of the rectangle?
A medical researcher is studying the spread of a virus in a population of 1000 laboratory mice. During any week, there is a 70% probability that an infected mouse will overcome the virus, and during the same week there is a 40% probability that a noninfected mouse will become infected. Four hundred mice are currently infected with the virus. How many will be infected next week and in 3 weeks?
(a) next week mice rilex
(b) in 3 weeks mice
Answer:
a) 360 mice
b) 364 mice
Step-by-step explanation:
Assume :
A = number of infected mice , B = number of non-infected mice
P( infected mice overcoming infection ) = 70% = 0.7
P ( Infected mice not overcoming infection ) = 1 - 0.7 = 0.3
P( mice becoming infected ) = 40% = 0.4
P ( mice not becoming infected ) = 1 - 0.4 = 0.6
Number of infected mice = 400
Number of non-infected mice = 1000 - 400 = 600
step 1 ; express the probabilities in matrix form
[tex]P = \left[\begin{array}{ccc}0.3&0.4&\\0.7&0.6&\\\end{array}\right][/tex]
[tex]X = \left[\begin{array}{ccc}400\\600\\\end{array}\right][/tex]
step 2 : multiply the matrix above to determine the number of mice that will be infected
a) For next week
PX = [tex]\left[\begin{array}{ccc}360\\640\\\end{array}\right][/tex]
i.e. 360 mice will get infected next week
next 2 week = P ( PX )
= [tex]\left[\begin{array}{ccc}0.3&0.4&\\0.7&0.6&\\\end{array}\right][/tex] * [tex]\left[\begin{array}{ccc}360\\640\\\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}364\\636\\\end{array}\right][/tex]
b) In 3 weeks time
P ( P(PX) = [tex]\left[\begin{array}{ccc}0.3&0.4&\\0.7&0.6&\\\end{array}\right][/tex] * [tex]\left[\begin{array}{ccc}364\\636\\\end{array}\right][/tex]
= [tex]\left[\begin{array}{ccc}363.6\\636.4\\\end{array}\right][/tex]
i.e. 364 mice will get infected in 3 weeks time
Please help me with this I need it bad
Answer:
1
Step-by-step explanation:
The average rate of change is the gradient _
Gradient = Rise / Run = (y2 - y1) / (x2 - x1)
From the table ;
x2 = 4 ; x1 = - 1 ; y2 = 5 ; y1 = 0
Gradient = (y2 - y1) / (x2 - x1) = (5-0) / (4 - - 1) = 5/5 = 1
Necesito ayuda con este ejercicio hay que determinar el valor de la a: [tex]a^{20} : a^{2x} = a^{12}[/tex]
Answer:
x = 10 + log(1/a^12)/(2 log(a)) + (i π n)/log(a) for n element Z
Step-by-step explanation:
Solve for x:
a^(20 - 2 x) = a^12
Take reciprocals of both sides:
a^(2 x - 20) = 1/a^12
Take the logarithm base a of both sides:
2 x - 20 = log(1/a^12)/log(a) + (2 i π n)/log(a) for n element Z
Add 20 to both sides:
2 x = 20 + log(1/a^12)/log(a) + (2 i π n)/log(a) for n element Z
Divide both sides by 2:
Answer: x = 10 + log(1/a^12)/(2 log(a)) + (i π n)/log(a) for n element Z
The cost C of manning household is partly constant and partly varies as the number of people, the cost is 70,000 and for 10 people, the cost is 90,000 find the expression for C in terms of n ii. The weekly cost for 12 people
Answer:
4.196.754
Step-by-step explanation:
god bless stay safe po
Please help me with this as quickly as possible
3 hour 30 minutes : 36 minutes
1 hour = 60 minutes
3 hour = 3×60 minutes = 180 minutes
3hour 30 minutes = 180 minutes + 30 minutes
= 210 minutes
210 minutes : 60 minutes
3 hours 30 minutes : 60 minutes = 6:2
Is this quadratic? If so what form is it?
Answer:
Yes. Factored form.
Step-by-step explanation:
Answer:
yes, and it's in intercept form
Step-by-step explanation:
Hi there!
We are given the function f(x)=-2(x-4)(x+3)
A quadratic function is a function that has a degree of 2 (the highest exponent in the function is to the 2nd power)
There are 3 forms to write a quadratic function:
standard form, which is f(x)=ax²+bx+c, where a, b, and c are free coefficients (numbers)
vertex form, which is f(x)=a(x-h)²+k, where a is a free coefficient and (h,k) is the vertex
intercept form, which is f(x)=a(x-[tex]x_{1}[/tex])(x-[tex]x_{2}[/tex]), where a is a free coefficient and [tex]x_{1}[/tex] and [tex]x_{2}[/tex] are the x intercepts
You may notice that f(x)=-2(x-4)(x+3) is actually in intercept form; a is -2 and [tex]x_{1}[/tex] and [tex]x_{2}[/tex] are 4 and -3 respectively (remember: the formula for intercept form has -[tex]x_{1}[/tex] and -[tex]x_{2}[/tex], but the x intercepts are [tex]x_{1}[/tex] and [tex]x_{2}[/tex]. Therefore, the x intercepts should be the opposites of -[tex]x_{1}[/tex] and -[tex]x_{2}[/tex]).
If the formula is in intercept form, it should be quadratic.
However, if you want to be sure it's quadratic, you can expand the function.
f(x)=-2(x-4)(x+3)
first, multiply the binomials together using FOIL
(x-4)(x+3)
x²-x-12
now multiply x²-x-12 by -2
-2(x²-x-12)
do the distributive property
-2x²+2x+24
It's a quadratic function! The value of the highest exponent is 2 :)
Hope this helps!
y-4=7(x-6)y−4=7(x−6)
Answer:
I believe the question was written twice on accident
y=7x-38
Step-by-step explanation:
y-4=7(x-6)
y-4=7x-42
y=7x-38
Which one hurry
A.2 unit sides
B.3 unit sides
C.4 unit sides
D.5 unit sides
Answer:
4 units
Step-by-step explanation:
P of a square is P =4s
A of a square is A = s^2
4s = s^2
Divide each side by s
4s/s = s^2/s
4 =s
I needddd helpppp
Which point is a representation of -(-3)???
Answer:
Point a
negative means on a number line to the left side
Step-by-step explanation:
Find the area of the triangle.
24 in.
32 in.
Answer:
A = 384 inches^2
Step-by-step explanation:
The area of a triangle is given by
A = 1/2 bh where b is the length of the base and h is the height
A = 1/2 ( 32) *(24)
A = 384 inches^2
Answer:
The area of triangle is 384 inches².
Step-by-step explanation:
Given : -Base of triangle = 24 inchesHeight of triangle = 32 inches To Find :-Area of triangleFormula Used :-Area of triangle = 1/2 × base × height
Solution :-Using Formula
Area of triangle = 1/2 × base × height
substitute the values into the formula
Area of triangle = 1/2 × 32 inches × 24 inches.
multiply,
Area of triangle = 1/2 × 768 inches ²
Divide, we get
Area of triangle = 384 inches ²
Therefore, The area of triangle is 384 inches².
Please help due today
Answer:
55
Step-by-step explanation:
all of the angles in a triangle ALWAYS add up to 180 degrees.
do the math.
Write the equation of the line parallel to y=1/2x−6 that passes through (−10,4).
Answer:
y = 1/2 x + 9
Step-by-step explanation:
y = 1/2 x + b
4 = (1/2)(-10) + b
4 = -5 + b
b = 9
Translate and solve: twenty-three greater than b is at least −276.
Answer:
b+23≥-276
b≥-276-23
b≥-299
Step-by-step explanation:
hope this is helpful
Which scenario is modeled by the equation (x) (0.6) = 86 dollars and 46 cents?
Answer:
Answer: (C)A picnic table is on sale for 60 percent off.
Step-by-step explanation:
well someone copied me but okay :[
CAN SOMEONE HELP ME PLS
solve the literal equation for C. -3x+2c=-3
Step-by-step explanation:
I'm sorry I can't answer that but I know something so you can answer that. search Chrome quickmath all your problems, equations and more can be solved
Answer:
c = 3/2x + −3/2
Step-by-step explanation:
Let's solve for c
-3x+2c=-3
Step 1: Add 3x to both sides.
2c −3x + 3x = −3 + 3x
2c = 3x −3
Step 2: Divide both sides by 2.
2c = 3x−3
2 2
c = 3/2x + −3/2
Answer:
c = 3/2x + −3/2
Let g(x) be the indicated transformation of f(x). Write the rule for g(x) f(x)=3x + 1: translation 2 units right
Answer:
3x +3
Step-by-step explanation:
3x + 1 + 2units(on the x axis)= 3x +3
Solve for x in the equation x squared + 2 x + 1 = 17.
Step-by-step explanation:
quadratic formula
-b+-√b^2
2a
-2+-√2^2-4×1×-16
2×1
-2+-√68
2
either
x= 3.125
or
x= -5.125
Write an equivalent expression for: 5(5x - 9) *
Answer:
25x - 45
Step-by-step explanation:
5(5x - 9)
Distribute
5*5x - 5* (9)
25x - 45
Answer:
➛ 25 x - 45
Step-by-step explanation:
➛ 5 ( 5 x - 9 )
Using distributive property multiply both by 5
➛ 5 × 5 x - 5 × -9
➛ 25 x - 45
Please help it’s summer school and i need serious help
Answer:
B
Step-by-step explanation:
guys please help me :(((((((((( crying
Answer:
18
Step-by-step explanation:
2/6
4/12
6/18
Answer:
x = 18
Step-by-step explanation:
We can write ratios
2 2+4
---- = -----
6 x
Using cross products
2x = 6(2+4)
2x = 6(6)
2x = 36
Divide by 2
2x/2 = 36/2
x = 18
