Answer:
If the radius is 6mm, the diameter is 12mm.
If the diameter is 22 ft, the radius is 11 ft.
Step-by-step explanation:
1st one) When you try to find the diameter of any circle, and you already have the radius, you need to multiply it by two (double it)
6 x 2 = 12mm
2nd one) Then to do the opposite, you need to divide the diameter by 2.
22/2 = 11 ft
Hope this helped :)
Solve for z.
x + y + z = 4
4x - y - z = 1
x + z = 2
Answer:
z= 4-x-y
z= -1+4x-y
z= 2-x
Step-by-step explanation:
z = 2-x
y = -1-z +4x
substitute
x -1 -2+x +4x + 2 -x = 4
-1 + 5x = 4
5x = 5
x = 1
z = 1
1+y+1 = 4
y = 2
(a) Calculate sinh (log(6) - log(5)) exactly, i.e. without using a calculator Answer: (b) Calculate sin(arccos(76)) exactly, i.e. without using a calculator.
(a) The exact value of sinh(log(6) - log(5)) is 11/60.
To calculate sinh(log(6) - log(5)), we can use the identity: sinh(x) = ([tex]a^n[/tex] - [tex]e^-x[/tex])/2
So, substituting x = log(6) - log(5), we get:
sinh(log(6) - log(5)) = ([tex]e^(log(6)[/tex] - log(5)) - [tex]e^-(log(6)[/tex] - log(5)))/2
= (([tex]e^log(6)[/tex])/([tex]e^log(5)[/tex]) - ([tex]e^-log(6)[/tex])/([tex]e^-log(5)[/tex]))/2
= ((6/5) - (5/6))/2
= (36/30 - 25/30)/2
= 11/60
Therefore, sinh(log(6) - log(5)) = 11/60.
(b) The exact value of sin(arccos(76)) is undefined.
To calculate sin(arccos(76)) exactly, we can use the Pythagorean identity [tex]sin^2[/tex](x) + [tex]cos^2[/tex](x) = 1.
Let's assume arccos(76) = x. Applying the cosine function to both sides, we have cos(arccos(76)) = cos(x).
Since arccos and cosine are inverse functions, cos(arccos(76)) simplifies to 76.
Now, using the Pythagorean identity, we can calculate sin(x):
sin(x) = sqrt(1 - [tex]cos^2[/tex](x)) = sqrt(1 - 76^2) = sqrt(1 - 5776) = sqrt(-5775).
The square root of -5775 is an imaginary number, which cannot be expressed exactly without using complex numbers or numerical methods.
Therefore, the exact value of sin(arccos(76)) cannot be determined without using a calculator or numerical methods.
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Use the Ratio Test to determine the convergence or divergence of the series. If the Ratio Test is inconclusive, determine the convergence or divergence of the series using other methods. (If you need to use or –, enter INFINITY or –INFINITY, respectively.)
[infinity] (n − 1)!
5n
n = 0
lim n → [infinity]
an + 1
an
=
Using the Ratio Test the series ∑(n³ / [tex]4^n[/tex]) converges. Option A is the correct answer.
To determine the convergence or divergence of the series ∑(n³ / [tex]4^n[/tex]), we can apply the Ratio Test.
The Ratio Test states that if the limit of the absolute value of the ratio of consecutive terms in a series is less than 1, then the series converges. If the limit is greater than 1 or it does not exist, the series diverges.
Let's apply the Ratio Test to the given series:
lim n → ∞ |([tex]a_n[/tex] + 1) / [tex]a_n[/tex]| = lim n → ∞ |((n + 1)³ / [tex]4^{(n + 1)[/tex]) / (n³ / [tex]4^n[/tex])|
We simplify the expression by multiplying by the reciprocal:
lim n → ∞ |((n + 1)³ / [tex]4^{(n + 1)[/tex]) × ([tex]4^n[/tex] / n³)|
Next, we simplify the expression inside the absolute value:
lim n → ∞ |((n + 1)³ × [tex]4^n[/tex]) / ([tex]4^{(n + 1)[/tex] × n³)|
Now, we can cancel out the common factors:
lim n → ∞ |(n + 1)³ / (4 × n³)|
Simplifying further:
lim n → ∞ |(n + 1) / (4n)|³
Taking the limit as n approaches infinity:
lim n → ∞ |(1 + 1/n) / 4|³
Since the limit of the absolute value of the ratio is less than 1 (as n approaches infinity), the series converges.
Therefore, the answer is:
A. Converges
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The question is -
Use the Ratio Test to determine the convergence or divergence of the series. If the Ratio Test is inconclusive, determine the convergence or divergence of the series using other methods.
∑ n = 1 to ∞ (n³ / 4^n)
lim n → ∞ |(a_n + 1) / a_n| = _______
A. Converges
B. Diverges
an object is traveling on a circle with a radius of 5 cm. if in 20 seconds a central angle of 1/3 radian is swept out, what is the angular speed of the object? what is the linear speed?
Let C be a relation defined on R as follows: For all x,y∈R,xCy iff x 2 +y2 =1. Determine if C is reflexive, symmetric, transitive, or none of these.
The relation C is defined on the set of real numbers (R) as xCy if [tex]x^2[/tex] + [tex]y^2[/tex] = 1 is not reflexive, not symmetric, and not transitive.
To determine if the relation C is reflexive, we need to check if every element x in R is related to itself. However, for any real number x, [tex]x^2[/tex] + [tex]x^2[/tex] = 2[tex]x^2[/tex] ≠ 1. Therefore, C is not reflexive.
For symmetry, we need to check if whenever xCy, then yCx. However, if we take x = 0 and y = 1, we have [tex]x^2[/tex] + [tex]y^2[/tex] = [tex]0^2[/tex]+ [tex]1^2[/tex] = 1, which satisfies the condition for C. But for yCx, we have [tex]y^2[/tex] + [tex]x^2[/tex] = [tex]1^2[/tex] + [tex]0^2[/tex] = 1, which also satisfies the condition. Therefore, C is symmetric.
To test for transitivity, we need to check if whenever xCy and yCz, then xCz. However, if we consider x = 0, y = 1, and z = -1, we have [tex]x^2[/tex] +[tex]y^2[/tex] = [tex]0^2[/tex]+ [tex]1^2[/tex] = 1 and [tex]y^2[/tex] + [tex]z^2[/tex] =[tex]1^2[/tex] + [tex](-1)^2[/tex] = 2. Since 1 + 2 ≠ 1, the condition for transitivity is not satisfied. Thus, C is not transitive.
In conclusion, the relation C is not reflexive, symmetric, or transitive.
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hlp help help plsssssssssssss
Answer:
A
Step-by-step explanation:
Think about the square root of 64, which is 8. It will only be slightly higher than 8, which will not even be .5, so 8 is the closest number.
which of the following equations are linear? a. y = 6x 8 b. y 7 = 3x c. y – x = 8x 2 d. 4y = 8
A linear equation is an equation in which the highest power of an unknown quantity is 1. Among the given options, the equation y = 6x + 8 is linear.
Hence, the correct option is a. y = 6x + 8.
An equation is linear if and only if it can be written in the form y = mx + c, where m and c are real numbers. In the given options, the equation y = 6x + 8 can be written in the form y = mx + c where m = 6 and c = 8, so it is linear. On the other hand, the equation y – x = 8x2 can be rearranged to give y = 8x2 + x, so the highest power of x is 2. Hence, this equation is not linear.Similarly, the equation 4y = 8 can be rearranged to give y = 2, which is a constant, and so it is also not linear.Finally, the equation y7 = 3x is not linear because the exponent 7 on y is greater than 1 and makes the equation non-linear. Therefore, the correct answer is option a. y = 6x + 8.
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Kendra dives off a diving board into the water and then comes back up to the surface. Her dive can be modeled by the equation: , where "h" is the height in feet and "x" is the horizontal distance in feet from the diving board. 1) How high is the diving board? 2) How deep does the diver dive into the water? 3) At what horizontal distance from the board does the diver enter the water? 4) At what horizontal distance from the board does the diver come to the surface of the water after the dive?
Answer:
1. 6 feet
2. 6.25 feet
3. 1 feet
4. 6 feet
Step-by-step explanation:
The equation is : [tex]$h(x)=x^2-7x+6$[/tex]
1. The diving board is where Kendra dives off. Here, the horizontal distance, x from the diving board is 0.
So, substituting x = 0 in the equation, we get
[tex]$h(0)=0^2-7(0)+6$[/tex]
[tex]$=0-0+6$[/tex]
[tex]$=6$[/tex]
So, the diving board is 6 feet above the surface of the water.
2. From the equation, we known that it is a parabola and the vertex is minimum.
It is the minimum height which represents the depth Kendra dives into the water.
So the [tex]$x$[/tex] coordinate of the vertex is = [tex]$\frac{-b}{2a}$[/tex]
Here, a and b are the coefficients of linear term and the quadratic terms in the equation. Therefore,
a = 1 and b = -7
∴ x coordinate = [tex]$\frac{-(-7)}{2 \times 1} $[/tex]
[tex]$\frac{7}{2}=3.5$[/tex]
Now substituting to find f(x),
[tex]$h(3.5)=(3.5)^2-7(3.5)+6$[/tex]
= -6.25
Therefore, the diver dives 6.25 feet below the water surface.
3. The horizontal distance from the board the diver enters into the water.
This is the y-intercept and it is the value of x when h(x)=0.
∴ [tex]$0=x^2-7x+6$[/tex]
Factorizing, we get [tex]$(x-1)(x-6)=0$[/tex]
∴ [tex]$x=1 \text{ or}\ x=6$[/tex]
So there are two solutions that are the two x intercepts of the function. Here at x = 1 shows the horizontal distance from the board from where Kendra dives into the water.
4. We know that the equation given has [tex]$\text{two}$[/tex] x intercepts. These two x intercepts are the points where the parabola crosses the x-axis, which is the height [tex]$h(x)=0$[/tex]. The height is the water surface level.
The first x intercept represents the points where Kendra dives into the water.
And the second x intercept is the point where Kendra comes out of the water surface. This this is [tex]$x=6$[/tex] for [tex]$h(x)=0$[/tex].
Thus Kendra dives out of the water surface at 6 feet from the board.
which expression is equivlent to 12(2x-3y+4)
Answer:
24x-36y+48
hope this helps :)
24x - 36y + 48 is equivalent to 12(2x-3y+4)
Need help with this question thank you!
Answer:
Step-by-step explanation:
(5,3) should be your slope. Start from the bottom of the line and go up. Use the X axis slope 1st because of the x1 y1 coordinates.
Answer:
(5,-1)
(-4,0)
Step-by-step explanation:
5 is in the X axis
-1 is in the Y axis
-4 is in the Y axis
0 is in the X axis
Someone please help me I’ll give out brainliest please dont answer if you don’t know
Answer:
[tex]15c - 1[/tex]
Step-by-step explanation:
[tex]3(5c + 3) - 10[/tex]
Apply the distributive property.
[tex]3(5c) + 3 \times 3 - 10[/tex]
Multiply 5 by 3.
[tex]15c + 3 \times 3 - 10[/tex]
Multiply 3 by 3.
[tex]15c + 9 - 10[/tex]
Subtract 10 from 9.
[tex]15c - 1[/tex]
Hope it is helpful....Two numbers are randomly selected from the following set without replacement.
{3, 16, 2, 11, 15, 6, 14, 7, 10, 1}
a. What is the probability that they are both even?
b. What is the probability that they are both prime? Note: 1 is not prime.
c. What is the probability of the sum of the two numbers being even?
d. What is the probability of the product of the two numbers being odd?
The last two problems are based on a single draw from the set.
e What is the probability that a prime number was drawn from the set, given that it
is an odd number.
f. What is the probabilityselected from the set. that a prime number was drawn from
the set, given that it is an even number.
Answer:
I dot know good luck
Step-by-step explanation:
Paola wants to measure the following dependent variable: happiness. How could you measure happiness in a way:
a) physiological?
b) observation?
c) self-report? Search for a scale that already exists.
What is the scale called? :
APA citation:_____
1. She would use Facial electromyography
2. She would use smiling
3. She would use Subjective Happiness Scale
How do you measure happiness?It is common practice to evaluate subjective experiences, including happiness, using self-report measures. The Subjective Happiness Scale (SHS) is a popular tool for gauging happiness.
The SHS is a self-report survey that asks participants to rate how much they agree with statements about their personal experiences of happiness. It consists of four things and is frequently utilized in studies.
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Find z1/z2 in polar form. The angle is in degrees. z1= 15 cis (83) and z2 = 6 cis (114).
To find the division of z1 by z2 in polar form, where the angles are given in degrees, we have z1 = 15 cis (83°) and z2 = 6 cis (114°). The polar form of the division of z1 by z2 is 2.5 cis (329°).
To divide complex numbers in polar form, we can divide their magnitudes and subtract their angles. Let's start by dividing the magnitudes:
|z1/z2| = |z1|/|z2| = 15/6 = 2.5
Next, we subtract the angles:
θ = θ1 - θ2 = 83° - 114° = -31°
Since the angle is negative, we add 360° to it to get a positive angle in the standard range:
θ = -31° + 360° = 329°
Therefore, the division of z1 by z2 in polar form is given by:
z1/z2 = 2.5 cis (329°)
So, the polar form of the division of z1 by z2 is 2.5 cis (329°).
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Help ASAP ASAP please please help ASAP ASAP please please help please
Answer:
XY = 9
Step-by-step explanation:
Similar polygons have corresponding sides with proportional lengths.
WX/AB = XY/BC
12/8 = XY/6
8XY = 12 * 6
8XY = 72
XY = 9
Solve for x: 3x + 2 = 2x + 8.
Answer:
x = 6
hope this is the answer you are looking for
Step-by-step explanation:
Answer:
X=6
Step-by-step explanation:
Firstly subtract 2x from both sides = x+2=8
Then subtract 2 from both sides and you'll get x=6.
Mr. Johnson drove 4 1/3 miles on Monday and 5 1/2 miles on Tuesday, How many miles did Mr. Johnson drive altogether?
Answer:
9 [tex]\frac{5}{6}[/tex]
Step-by-step explanation:
Help pleas ? Brainliest as prize
Answer:
9
Step-by-step explanation:
There are 9 x's above 1 letter mailed.
Pls help me guysss !!!!
Answer:
First answer choice
Step-by-step explanation:
Answer:
The answer would be A
Step-by-step explanation:
Solve for x.
x = ln e
x =
Answer:
x = 1
Step-by-step explanation:
simplify this number 27:81
Answer:
I believe the simplified form of this ratio is 1:3
*The common factor to both numbers is 27.
27÷27=1 and 81÷27=3
So, that's where the 1:3 came from
Which table represents a linear equation
If the volume of the cylinder is 502.4 in?, what is the radius of
the base of the cylinder? Use 3.14 for i and enter your answer
as a whole number.
h=10 in
r= in.
Answer:
radius of the base of cylinder = 4 in
Step-by-step explanation:
Volume of cylinder = pi x r² × h
502.4 = 3.14 x r² x 10
502.4 = 31.4 x r²
r² = 502.4/31.4
r² = 16
r = 4 in
Mhanifa can you please help? This is due soon. Look at the picture attached. I will mark brainliest!
Answer:
84° 125°Step-by-step explanation:
Sum of the interior angles of a regular polygon:
S(n) = 180°(n - 2), where n- number of sidesExercise 4Pentagon has sum of angles:
S(5) = 180°(5 - 2) = 540°Sum the given angles and find x:
x° + 122° + 100° + 90° + 144° = 540°x° + 456° = 540°x° = 540° - 456°x° = 84°Exercise 5Hexagon has sum of angles:
S(6) = 180°(6 - 2) = 720°Sum the given angles and find x:
x° + 110° + 160° + 105° + 105° + 115° = 720°x° + 595° = 720°x° = 720° - 595°x° = 125°The discrete-time system is described by yik-11 + 2y[k] = Fiki, with fiki = [k] and y(0) = 0. Solve the above equation iteratively to determine yll] and y[2] values.
Value of y[1] = 0.5 and y[2] = 0.5.
The given discrete-time system is:
y[k-1] + 2y[k] = [k]with y(0) = 0.
Substituting k = 0 in the above equation:
y[-1] + 2y[0] = [0] y[-1] = 0
Substituting k = 1 in the given equation:
y[0] + 2y[1] = [1]
Substituting the value of y[0] from the above equation in this equation, we get:
2y[1] = [1] - y[0]
Substituting the value of y[0] = 0 in the above equation:
2y[1] = [1]y[1] = [1]/2 = 0.5
Substituting k = 2 in the given equation:
y[1] + 2y[2] = [2]
Substituting the value of y[1] from the above equation in this equation, we get:
2y[2] = [2] - y[1]
Substituting the value of y[1] = 0.5 in the above equation:
2y[2] = [2] - 0.5y[2] = [2]/2 - 0.5 = 0.5
Therefore, y[1] = 0.5 and y[2] = 0.5.
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the price of a jacket was reduced from $50 to $30. by what percentage was the price of the jacket reduced?
Answer:
the jacket price was reduced by 40%.
Step-by-step explanation:
if $50 is 100% then every one dollar is 2%.
Percentage of the reduction of price of the jacket is 40%.
What is Percentage?Percentage is defined as the parts of a number per fraction of 100.
Percentage is usually denoted by the symbol '%'.
We have to divide a number with it's whole and then multiply with 100 to calculate the percentage of any number.
Given that,
Original price of the jacket = $50
Let x be the percentage of reduction of the price of the jacket.
50 - (x × 50) = 30
50x = 50 - 30
50x = 20
x = 20 / 50
x = 0.4
Percentage = 0.4 × 100 = 40%
Hence the percentage reduction is 40%.
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List three examples of aa variable costs
Answer:
utility cost, direct labor costs, cost of raw materials used in production
A grain silo is built from two right circular cones and a right circular cylinder with internal measurements represented by the figure below. Of the following, which is closest to the volume of the grain silo, in cubic feet?
A) 261.8
B) 785.4
C) 916.3
D) 1047.2
Answer:
A. 261.8
Step-by-step explanation:
espero ayudar sorry
Consider the set F of continuous functions f with the property that f'(2) = 0. a. Name a larger real vector space we've studied this semester that F is a subset of. b. Prove whether F is a subspace of the vector space you named in part a. C. We learned this semester that if something is a subset of a known vector space, we only need to check two axioms instead of 10. Explain why we can get away with not checking the other 8 axioms. Don't just quote the rule we learned-try to explain the logic behind it. d. Why was it not ok to only check the two subspace axioms on problem 8 from exam 2? Why wasn't it a subspace?
The set in problem 8 was not a subspace because one of the subspace axioms requires that the zero vector, which is the additive identity element, is included in the set. In the given problem, the zero vector was not part of the set, so it failed to satisfy this axiom
a. The set F is a subset of the vector space of continuous functions on some interval, which we have studied this semester.
b. To prove whether F is a subspace of the vector space of continuous functions, we need to check if F satisfies the three subspace axioms: closure under addition, closure under scalar multiplication, and the zero vector property.
Let f and g be two functions in F, and let c be a scalar. To show closure under addition, we need to prove that f + g is also in F. Since both f and g have the property that f'(2) = 0 and g'(2) = 0, their sum (f + g) will also have the property that (f + g)'(2) = f'(2) + g'(2) = 0 + 0 = 0. Therefore, f + g is in F.
To show closure under scalar multiplication, we need to prove that cf is also in F. Again, since f has the property that f'(2) = 0, multiplying f by any scalar c will not change the derivative at 2. Therefore, (cf)'(2) = c × f'(2) = c × 0 = 0, and cf is in F.
Finally, the zero vector property states that the zero function, denoted as 0, must be in F. The zero function has the property that its derivative is always zero, including at 2. Therefore, 0'(2) = 0, and the zero function is in F.
Since F satisfies all three subspace axioms, we can conclude that F is a subspace of the vector space of continuous functions.
c. We can get away with not checking the other eight axioms (associativity, commutativity, distributivity, etc.) because F is a subset of a known vector space. By being a subset of a vector space, F inherits those axioms from the larger vector space. The other eight axioms are properties of vector spaces that hold true for all vectors in the larger vector space, including the vectors in F. Therefore, if F satisfies the subspace axioms, it automatically satisfies the other eight axioms by virtue of being a subset of a vector space.
d. It was not okay to only check the two subspace axioms on problem 8 from exam 2 because the set in that problem did not satisfy the zero vector property. One of the subspace axioms requires that the zero vector, which is the additive identity element, is included in the set. In the given problem, the zero vector was not part of the set, so it failed to satisfy this axiom. As a result, the set in problem 8 was not a subspace.
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which angle pair represents corresponding angles?
options on picture
Answer: b
Step-by-step : not needed