Step-by-step explanation:
p³ + 1/p³
or, (p+1/p) (p²-p.1/p+1/p²)
or, (p+1/p) (p²-1+1/p²)
Given the first four terms of a linear sequence : 3,x,y,30 a) Calculate the value of x and y
Answer:
Step-by-step explanation:
It should be noted that based on the information given, the values of x and y in the linear pattern will be 12 and 21.
How to illustrate the information?
It should be noted that since this is a linear pattern, it should be noted that it illustrates that the values in between them are the same.
It should be noted that the numbers that fits into the scenario are 3, 12, 21 and 30. There's a difference of 9 between them.
Therefore, it should be noted that based on the information given, the values of x and y in the linear pattern will be 12 and 21.
GREAT IM DONE
a square is inscribed in a circle. how fast is the area of the square changing when the circel is increasing at 1 in/min
The area of the square is changing at 12√2 + 2√2t square inches/minute when the circle is increasing at 1 in/min.
Let us find the relationship between r and s using the Pythagorean theorem. Since the square is inscribed in the circle, the diameter of the circle is equal to the diagonal of the square.
2r = s√2
Squaring both sides, we get:
4r² = 2s²or s² = 2r²
Dividing by 2 on both sides, we get:
s²/2 = r²
Differentiating both sides with respect to t, we get:
ds²/dt = 2r (dr/dt)
Dividing both sides by 2s, we get:
ds/dt = r (dr/dt) / s
Substituting r² = s²/2,
\(ds/dt = r (dr/dt) / √2s2s ds/dt = r (dr/dt)s ds/dt = (r/2) (dr/dt)2s ds/dt = r (dr/dt) or dA/dt = 2s ds/dt = 2r (dr/dt)\)
Now, substituting r² = s²/2,
dA/dt = 2s ds/dt = 2(√2 s) (dr/dt) = 2(√2) r (dr/dt)
Now, substituting dr/dt = 1 in/min and r = 6 in (since the circle is increasing at 1 in/min, the radius after t minutes is 6 + t),
dA/dt = 2(√2) (6 + t) (1) = 12√2 + 2√2t square inches/minute
Therefore, the area of the square is changing at a rate of 12√2 + 2√2t square inches/minute.
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What I'm doing was correct?
Answer:
The distance between points R and S is \(\sqrt{ 29 }\) units
Step-by-step explanation:
Coordinates of point R = (-1, 3)
Coordinates of point S = (4, 1)
Now, by distance formula:
\(d(R, S) = \sqrt{ \{4 -( - 1) \}^{2} + {(1 - 3)}^{2} } \\ \\ = \sqrt{ \{4 + 1 \}^{2} + {( - 2)}^{2} } \\ \\ = \sqrt{ \{5 \}^{2} + {( - 2)}^{2} } \\ \\ = \sqrt{ 25 + 4 } \\ \\ \implies \huge \orange{d(R, S) = \sqrt{ 29 } \: units}\)
So, you are correct.
Determine the value of Cin on the antiderivative of F(x) = sin³(x)cos^5(x) for x = 0.406 and y = 1.6. Note : Use 3 decimal places and angle in radian form.
The value of Cin on the antiderivative of F(x) = sin³(x)cos^5(x) for x = 0.406 and y = 1.6 is 3.575.
To find the value of Cin on the antiderivative of F(x) = sin³(x)cos^5(x), we need to evaluate the definite integral of F(x) with respect to x, and then use the given values of x and y to solve for Cin.
Using the product-to-sum identities, we can rewrite F(x) as:
F(x) = (sin²(x)cos^4(x))(sin(x)cos(x))
Then, using the power-reducing identity sin²(x) = (1-cos(2x))/2, we can simplify F(x) as:
F(x) = [(1-cos(2x))/2]^2(sin(x)cos(x))
Expanding the square and using the double angle identity sin(2x) = 2sin(x)cos(x), we get:
F(x) = [1-2cos(2x)+cos²(2x)]/4(sin(2x)/2)
Simplifying further, we get:
F(x) = [1/8]sin(2x) - [1/4]cos(2x)sin²(2x) + [1/8]cos³(2x)
Now, we can evaluate the definite integral of F(x) from 0 to 0.406:
∫[0.406,0] F(x) dx = [-1/16]cos(0.812) + [1/32]sin(0.812) - [1/32]cos³(0.812)
Using the given value of y = 1.6, we can solve for Cin:
Cin = (y - ∫[0.406,0] F(x) dx) / [sin(0.812)]^3
Substituting the values and evaluating, we get:
Cin = (1.6 - (-0.223)) / [sin(0.812)]^3 = 3.575 (rounded to 3 decimal places)
Therefore, the value of Cin on the antiderivative of F(x) = sin³(x)cos^5(x) for x = 0.406 and y = 1.6 is 3.575.
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whats the square root of 7, then move the decimal points over 2?
Answer:
264.575131
Step-by-step explanation:
PLEASE MARK BRAINLIEST
Answer:
264.5751311
Step-by-step explanation:
The square root of 7 is 2.645751311
Move the decimal point two to the right to get your answer:
264.5751311
I Hope That This Helps! :)
which value is higher -30 or -70? explanation
Simplify the expression k^4⋅ k^7
Answer:
Step-by-step explanation:
you muiltiply k^ 4x7
k^28
Select all the expressions that are equivalent to 4-3.
A) -12
B) (-4) - (-4).(-4)
C) 2-6
D (1/4) • (1/4) • (1/4)
E) (1) · (1). (1)
F) 8-1/ 2 to the power of 2
G) 12
Answer:
See below.
Step-by-step explanation:
4*-3
A) -12
C) 2*-6
-hope it helps
The expressions that are equivalent to 4 × -3 are A) -12 and C) 2 × -6.
What is the expression?Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.
Option A is a straightforward multiplication of 4 and -3, which gives -12.
Option C (2 × -6) is equal to -12.
Option B can be simplified as follows: (-4) - (-4) · (-4) = (-4) - 16 = -20.
Therefore, option B is not equivalent to 4 × -3.
Option D is equal to 1/64.
Option E is equal to 1.
Option F is equal to 2, and option G is equal to 12.
Options B, D, E, F, and G are not equivalent to 4 × -3.
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Write down the inequality described by "half of x is no more than six", and solve it
Given the ordered pair (5, -4), where will the transformed image be after the following
composition: r(180, O) o T(-1,2)
A.) (-4,2)
B.) (-4,-2)
C.) (6,2)
D.) (-6, 6)
Using translation concepts, it is found that the transformed image of (5,-4) after the composition will be given by:
D.) (-6, 6)
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
In this problem, first the image is rotated 180º around the origin, hence:
(x,y) -> (-x, -y), then:
(5,-4) -> (-5, 4).
Then, T(-1,2) means that:
(x,y) -> (x - 1, y + 2).
Then:
(-5,4) -> (-5 -1, 4 + 2) -> (-6,6)
Hence option D is correct.
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PLZ help!! will give brainliest!!!
Options for x- (-19
(-1/3
(0
(19
Answer:
2/3=-1/3x+7
-19/3.-3=x
19=x
x=19
The variance of a sample or a population cannot be _____. a. zero b. calculated c. negative d. less than1
The variance of a sample or a population cannot be negative. This means that option c, negative, is the correct answer.
Variance is a statistical measure that quantifies the dispersion or spread of data points around the mean. It tells us how much the individual data points deviate from the average. The variance is always a non-negative value because it is calculated by summing the squared differences between each data point and the mean, divided by the total number of data points.
If the variance were negative, it would imply that the sum of the squared differences between each data point and the mean is less than zero. However, this is not possible because squared differences are always positive or zero.
On the other hand, options a, zero, and d, less than 1, are incorrect. The variance can be zero if all the data points in the sample or population are the same, indicating no dispersion. Additionally, the variance can be any positive value, including values less than 1.
To summarize, the variance of a sample or a population cannot be negative, making option c, negative, the correct answer.
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The teacher could buy the shirts online for $3. 50 each. She would also pay a fee of $9. 50 for shipping the shirts. Write a function that can be used to find y, the total cost, in dollars, of buying x shirts online.
Enter your function in the space provided
The function with y and x, representing cost and shipping charges will be y = 3.50x + 9.50.
The express that can be used to write the function is as follows-
Total amount = number of shirts × cost of shirts + shipping fee
Write the function based on the formula -
y = 3.50×x + 9.50
As stated x represents the number of shirts bought online. We know that shipping charges will be calculated once while cost of shirt will vary according to the number of shirts.
Hence the function will be -
y = 3.50x + 9.50
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A triangle has sides with lengths of 4 yards, 6 yards, and 7 yards. Is it a right triangle?
Find the lengths of the diagonals of rectangle QRST when QS = 20x - 5 and RT = 14x + 7.
A) 70
B) 99. 7
C) 17. 5
D) 35
The correct option is D i.e.35. A line segment connecting the rectangle's two opposed vertices is known as the diagonal.
The rectangle is split into two identical right triangles by its diagonal. The two-dimensional shape of a rectangle has four sides, four vertices, and four angles. A rectangle's two diagonals are the same length.
Two diagonals divide a rectangle into two right-angled triangles, with the diagonal serving as the hypotenuse on each diagonal. The diagonals cut each other in half, creating an acute angle and an obtuse angle respectively. The diagonal of the rectangle form two congruent triangles.
Since the diagonals of a rectangle are equal
∴ QS = RT
20x - 5 = 14x + 7
6x = 12
x = 2
QS = RT = 35
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Find the slope of the line y=1 over 6 x + 3 over 2
Answer:
1/6x
Step-by-step explanation:
the slope intercept form is: y = mx + b
m = slope
b = y-intercept.
When you already have in the form the slope is where m is, so the number that's is with x. In this case it's 1/6x.
Give a geometric explanation of why a homogenous linear system consisting of two equations in three unknowns must have infinitely many solutions. What are the possible numbers of solutions of a nonhomogeneous 2 X 3 linear system? Give a geometric explanation of your answer.
Geometrically, a system of two linear equations in three unknowns can be interpreted as two planes in three-dimensional space. If the two planes are not parallel, they will intersect in a line, which corresponds to the solution set of the system. If the two planes are parallel, they will either coincide (in which case there are infinitely many solutions) or be distinct and parallel (in which case there are no solutions).
For homogeneous system (i.e., a system with all zero constants on the right-hand side), the planes must intersect at the origin (the point where all three coordinates are zero), since this is the only point that satisfies both equations. Therefore, there must be infinitely many solutions, since any multiple of the solution vector will also satisfy the system.
For a nonhomogeneous system (i.e., a system with nonzero constants on the right-hand side), the two planes will either intersect in a line (in which case there are infinitely many solutions) or be parallel but not coincide (in which case there are no solutions). However, in this case, the line of intersection will not necessarily pass through the origin (unless the constant terms happen to be zero), so the solutions will not be multiples of a single vector. Therefore, the number of solutions can be either zero (if the planes are parallel and distinct) or infinitely many (if the planes intersect in a line).
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00
3 A total of 30 shirts were recently sold at Friday night's football game. Each adult shirt cost
$11.50 and each youth shirt cost $9.45. The total revenue was $324.50.
of two equations that can be used to solve for the number of A (adult) shirts
Answer:
number of adult shirts sold (a) = 20
number of youth shirts sold (b) = 10
Step-by-step explanation:
a = number of adult shirts sold
y = number of youth shirts sold
30 = a + y
$324.50 = 11.50a + 9.45y
This is the resulting system of equations from the given information in the problem.
Solve for y in the first equation and then substitute the equation for y into the second equation :
a+y=30 --> y=30-a
324.50 = 11.50a + 9.45(30-a)
Solve for a.
324.50 = 11.50a + 283.5 - 9.45a
41 = 2.05a
a = 20
Now that we have solved for a, we can back substitute into our equation for y and solve.
y=30-(20)
y = 10
CHECK:
(20)+(10) = 30 True
(11.50)(20) + (9.45)(10) = 324.5 True
evaluate the limit, if it exists. (if an answer does not exist, enter dne.) lim t→4 t2 − t − 12 t − 4
The limit of the given function as t approaches 4 is 7.
To evaluate the limit, we substitute the value of 4 into the function. By direct substitution, we get (4*2 - 4 - 12) / (4 - 4). Simplifying this expression, we have (16 - 4 - 12) / 0, which equals 0 / 0. This is an indeterminate form, which means we need to apply further algebraic manipulation to determine the limit.
To find the limit, we can factor the numerator as (t - 4)(t + 3). This allows us to cancel out the common factor of (t - 4) in the numerator and denominator. After canceling out (t - 4), the expression becomes (t + 3). Now we can evaluate the limit by substituting the value of t as it approaches 4 into the simplified expression.
Taking the limit as t approaches 4 of (t + 3), we get (4 + 3), which equals 7. Therefore, the limit of the given function as t approaches 4 is 7.
In summary, by factoring the numerator and canceling out the common factor of (t - 4), we simplified the expression to (t + 3). Substituting the value of t as it approaches 4 into the simplified expression gives us the limit of 7.
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HELP I NEES ANSWER NOW PLS HELP IF YOU KNOW
Answer:
1. THERE S NO JI ON THE FIGURE???
2. 2/3 is scale factor
Step-by-step explanation:
pls mark brainliest and hope this helps :)
Solve the equations for the bolded variables.
By solving the given equations for the bolded variables, we have the following:
s = L/Z P - 2l = 2wR = V/Ih = (S - 3πr²)/2πrWhat is an expression?An expression can be defined as a mathematical equation which is used to show the relationship existing between two or more variables and numerical quantities.
In this exercise, you're required to describe the steps that should be taken to rearrange and make bolded variables the subject of formula. Therefore, the appropriate and required steps are listed as follows:
Z = sL
You should divide both sides by L, to make s the subject of formula:
s = L/Z
Question 12.P = 2l + 2w
You should subtract 2l from both sides, to make w the subject of formula:
P = 2l + 2w
P - 2l = 2l + 2w - 2l
P - 2l = 2w
Rearranging the equation, we have:
2w = P - 2l
Dividing both sides by 2, we have:
w = (P - 2l)/2
Question 13.I = V/R
You should cross-multiply, to make R the subject of formula:
IR = V
R = V/I
Question 14.S = 3πr² + 2πrh
You should subtract 3πr² from both sides, to make h the subject of formula:
S - 3πr² = 3πr² + 2πrh - 3πr²
S - 3πr² = 2πrh
Rearranging the equation, we have:
2πrh = S - 3πr²
Dividing both sides by 2πr, we have:
h = (S - 3πr²)/2πr
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HELP!! I WILL GIVE BRAINLIEST TO THE PERSON WHO ANSWERED IT CORRECTLY AND GAVE A GREAT EXPLANATION!!! PLEASE ANSWER THE QUESTION!! IT IS ALGEBRA AND I AM NO GOOD AT IT!!!
( Hello! I'm bo)red....Can someone talk to me.....anyone...please???
Answer:
I believe the correct answer would be C.
Step-by-step explanation:
Have a great day! :)
What number would that be??
Suppose a 95% confidence interval for μ turns out to be (1000, 2100). Give a definition of what it means to be 95% confident in an inference.
Being 95% confident in an inference means that, based on the statistical analysis performed, there is a 95% probability that the true population parameter (in this case, μ) falls within the calculated confidence interval (in this case, (1000, 2100)).
Confidence intervals are used in statistics to estimate the true value of a population parameter (such as the mean, μ) based on a sample of data. In this case, the confidence interval is (1000, 2100).
The confidence level, in this case, 95%, represents the probability that the calculated confidence interval contains the true population parameter. This means that if the same statistical analysis were repeated multiple times, we would expect the true population parameter to fall within the confidence interval in approximately 95% of those repetitions.
The confidence interval is calculated based on the sample data and the chosen confidence level. In this case, the interval (1000, 2100) was calculated based on the sample data and a 95% confidence level.
The interpretation of the confidence interval (1000, 2100) is that there is a 95% probability that the true population parameter, μ, falls within this interval. It does not mean that there is a 95% probability that the interval contains the true value of μ; rather, the confidence level reflects the long-term frequency of intervals that will contain the true value of μ when similar analyses are repeated.
Therefore, based on the given information, we can conclude that being 95% confident in an inference means that there is a 95% probability that the true population parameter, μ, falls within the calculated confidence interval of (1000, 2100).
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How do you solve inequality questions?
An inequality like the statement, x + 3 > 5, can be solved by finding the value of the variable, "x", which is x > 2.
How to Solve an Inequality Question?Inequalities are used to express relationships between quantities or values that are not equal. They can be used to describe constraints or limitations on a solution to a problem, or to represent a range of possible values.
Inequality can also be used to describe relationships between variables in algebraic expressions or equations.
To solve an inequality, we need to isolate the variable in the given statement to determine the value of the variable.
For example, given the inequality, x + 3 > 5, in order to solve this inequality, we need to find the value of x by subtracting 3 from both sides:
x + 3 - 3 > 5 - 3
x > 2.
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In a certain triangle one side has a measure of 12 and another side has a measure of 18. If the triangle is isosceles, then which of
the following could be the measure of the third side?
Answer:
20 inches feet long
Step-by-step explanation:
add 12+8
A kangaroo hops 9 kilometers in 3 minutes. at this rate how far does the kangaroo travel in 2 minutes
Answer: If a kangaroo hops 9km in 3 minutes, that means he runs 3km every minute, which we can multiply by 2 in order to get 6km in the first 2 minutes. [EXTRA: In one hour, the kangaroo can hop 180km, which means his top speed is 180km/h without accounting for fatigue]
Step-by-step explanation: a
Pre-Algebra
Solve for x
Answer:
x=5
Step-by-step explanation:
multiply three to both sides to get rid of the fraction bar
5x+ 2= 9*3
5x+2=27
subtract 2 from both sides
5x=27-2
5x=25
divide by 5 to solve for x
x= 25/5
x=5
Hope this helps have a great day
can somebody please answer this asap
Answer:
you have to add all of them up it will get you some of your awner
find the area of the surface. z = 2 3 x3/2 + y3/2 , 0 ≤ x ≤ 1, 0 ≤ y ≤ 1
The area of the surface is S = \(\frac{-4}{15}(-1+8\sqrt{2}-9\sqrt{3} )\)
Now, According to the question:
The given equation is:
\(z = \frac{2}{3}(x^\frac{3}{2}+y^\frac{3}{2} )\),
0 ≤ x ≤ 1 , 0 ≤ y ≤ 1
Let's know:
Surface Area:
To surface area of a solid E, defined by z = f(x , y) can be found by integrating\(\int\limits \int\limits_R \sqrt{(z_x)^2+(z_y)^2+1},dA\) where R is the rectangular region
[0,1] × [0, 1] and \(z_x,z_y\) corresponds to the partials of z w.r.t x and y.
Now,
\(\sqrt{(z_x)^2+(z_y)^2+1}\) = \(\sqrt{1+(\sqrt{x} )^2+(\sqrt{y} )^2}\) = \(\sqrt{1+x+y}\)
S = \(\int\limits \int\limits_R \sqrt{(z_x)^2+(z_y)^2+1},dA\)
= \(\int\limits^1_0\int\limits^1_0 \sqrt{x+y+1}dy dx\)
[Integrate with respect to y ]
= \(\int\limits^1_0 (\frac{2}{3}(x + y + 1)^\frac{3}{2} )|^1_0 dx\)
= \(\int\limits^1_0 (\frac{2}{3}(x + (1) + 1)^\frac{3}{2}-\frac{2}{3}(x + (0) + 1)^\frac{3}{2} )dx\)
= \(\int\limits^1_0 ((\frac{2}{3}(x +2)^\frac{3}{2} ) - (\frac{2}{3}(x +1)^\frac{3}{2} ) , dx\)
= \(\int\limits^1_0 (\frac{2}{3}((x +2)^\frac{3}{2} - (x +1)^\frac{3}{2} )) , dx\)
[Integrate with respect to x ]
= \(\frac{2}{3} (\frac{2}{5}(x + 2)^\frac{5}{2} - \frac{2}{5}(x +1)^\frac{5}{2} )|^1_0\)
= \(\frac{2}{3}(\frac{2}{5}((1)+2 )^\frac{5}{2}-\frac{2}{5}((1)+1)^\frac{5}{2})-\frac{2}{3}(\frac{2}{5}((0)+2 )^\frac{5}{2} -\frac{2}{5}((0)+1)^\frac{5}{2}\)
= \(\frac{2}{3}(\frac{18\sqrt{3}}{5} -\frac{8\sqrt{2} }{5} )-\frac{2}{3} (\frac{8\sqrt{2} }{5} -\frac{2}{5} )\)
= \(\frac{-4}{15}(-1+8\sqrt{2}-9\sqrt{3} )\)
Hence, The area of the surface is S = \(\frac{-4}{15}(-1+8\sqrt{2}-9\sqrt{3} )\)
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