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We obtain x1=10 and x2=10 by solving the one-step matrix equation.

A matrix is a set of numbers arranged in rows and columns. Learn about the dimensions and components of matrices by starting your first introduction. A rectangular grid of numbers organized into rows and columns is known as a matrix. Matrix A, as an illustration, has two rows and three columns.

An arrangement of numbers, occasionally expressions and symbols, in rows and columns is called a matrix. Quantum mechanics, optics, mathematics, and other mathematical functions are all solved using matrix formulas.

Matrices are very expensive items that are used in a variety of applications. Matrix applications are employed in a variety of scientific disciplines in addition to mathematics.

x1 + (-2) = 8

x2 +( 5) = 15

solve 1

x1 - 2 = 8

On both sides of the equation, add 2.

⇒ x1 -2 + 2 = 8 +2

⇒ x1 =8 +2

⇒ x1 = 10

Equation 2 resolution

x2 + 5 = 15

On both sides of the equation, deduct 5

⇒x2 + 5 -5 = 15 - 5

⇒ x2 = 15 - 5

⇒ x2 = 10

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The 95% confidence interval estimate of the population mean is 98.10< μ < 98.30.

Given that

sample mean = ~x = 95.2

sample standard deviation = s = 0.7

sample size = n = 175

Degrees of freedom = d.f = n - 1 = 175 - 1 = 174

αt /2,d.f = 1.974.

The explanation for step 1

At 95% confidence level

 α= 1-0.95% =1-0.95 =0.05

α /2=0.05/ 2= 0.025

αt /2,d.f = t0.025,174 = 1.974

αt /2,d.f = 1.974

The explanation of Step 2

Margin of error = E = t/2,df x (s /Vn )    =  1.974 x ( 0.7/ V175)   = 0.10

Margin of error = E = 0.10

The 95% confidence interval estimate of the population mean is,

~x- E < μ < ~x + E

98.2 - 0.10< μ < 98.2 + 0.10

98.10< μ < 98.30

Margin of error = E = 0.10

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The approximate total length of iron edging needed to create the square frame and the two diagonals is 43.5 inches. So, option A is correct.

When two vertices of a polygon or polyhedron are not on the same edge, a diagonal in geometry is a line segment that connects them. The term "diagonal" is a colloquial term for any sloping line.

The elements on the line connecting the top left corner and bottom right corner of a square matrix make up the diagonal of a matrix in matrix algebra.

Given, The diagonal of a square is 9 inches.

The side of the square be x as we have assumed.

We have to apply Pythagoras theorem for Δ ABC

AB²+BC²=AC²

x²+x²=9²

x=9/√2

We know that the diagonals in the square bisect each other.

OA = 4.5 inches=OC

OD = 4.5 inches=OB

Therefore, the total length of iron edge that is required for the window is:

=4×Length of square+2 diagonals

= 4×6.36+2×9=43.46 inches

The approximate total length of iron edging needed to create the square frame and the two diagonals is 43.5 inches.

Hence, option A is correct.

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Consequently, we deduce that the typical output voltage is under 130.

In statistics, the standard deviation measures how widely distributed or how much a bunch of values can vary. While a big standard deviation shows that values are scattered throughout a wider range, a low standard deviation suggests that values are frequently close to the set's mean.

Here,

A defined output voltage of 130 is offered for an electrical circuit.

The voltage for this circuit was measured 40 times independently, with a sample mean of 128.6 and a standard deviation of 2.1.

Let's say the average output voltage.

Null Hypothesis, [tex]H_{0}[/tex]:  = 130 denotes that the average output voltage is 130.

A Different Hypothesis, [tex]H_{A}[/tex] :  < 130  ( it indicates that the average output voltage is below 130.)

One-sample t test statistics will be employed in this case because we are unsure about the population standard deviation;

            T.S.  =   ~ [tex]\frac{X^{'}-u }{\frac{s}{\sqrt{n} } }[/tex]

In this case, sample mean output voltage equals 128.6

Sample standard deviation equals 2.1, or s.

n = 40 for the sample of independent readers.

Thus, test statistics equal.

So, test statistics  =    ~[tex]\frac{128.6-130 }{\frac{2.1}{\sqrt{40} } }[/tex]

                              =  -4.216

Now, for a left-tailed test with a 0.05 level of significance, the t table provides a critical value of -1.685 at 39 degrees of freedom. We have enough data to reject our null hypothesis because it will fall in the rejection region because our test statistics are smaller than the crucial value of t, which is -4.216 -1.685.

Consequently, we deduce that the typical output voltage is under 130.

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The simplified form can be written as -

7.8y + 1.4z

We have the following expression -

6(0.7y + 0.8z) − 4z − 6(−0.1z − 0.6y)

We have -

6(0.7y + 0.8z) − 4z − 6(−0.1z − 0.6y)

(6 x 0.7y + 6 x 0.8z) - 4z + 6 x 0.1z + 6 x 0.6y

4.2y + 4.8z - 4z + 0.6z + 3.6y

7.8y + 4.8z - 3.4z

7.8y + 1.4z

Therefor, the simplified form can be written as -

7.8y + 1.4z

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In the given diagram, the measure of diagonal EG is 80

From the question, we are to determine the measure of diagonal EG

From the given diagram,

We have a parallelogram.

Since the diagonals of a parallelogram bisect each other, we can write that

EJ = JG

Thus,

4w + 4 = 2w + 22

Solve for w

4w - 2w = 22 - 4

2w = 18

w = 18/2

w = 9

But

EG = EJ + JG

EG = 4w + 4 + 2w + 22

Substitute the value of w

EG = 4(9) + 4 + 2(9) + 22

EG = 36 + 4 + 18 + 22

EG = 80

Hence, the measure of EG is 80

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Answer:

The Pacific Ocean is approximately 4.9 times larger than Lake Superior in terms of volume. This can be shown through the following mathematical argument:

First, divide the volume of the Pacific Ocean by the volume of Lake Superior to determine the size ratio:

6 x 10^8 cubic kilometers / 1.22 x 10^4 cubic kilometers = 4.9

This shows that the Pacific Ocean is approximately 4.9 times larger than Lake Superior.

To defend this solution, we can use the concept of ratio and proportion. We know that the ratio of the volumes of the two bodies of water is equal to the ratio of their respective sizes. Therefore, by finding the ratio of the volumes, we can determine the size ratio.

In this case, the ratio of the volumes is 6 x 10^8 cubic kilometers / 1.22 x 10^4 cubic kilometers, which simplifies to 4.9. This means that the Pacific Ocean is 4.9 times larger than Lake Superior in terms of volume.

This solution can be further supported by the fact that the Pacific Ocean is the largest ocean in the world, while Lake Superior is one of the Great Lakes and is much smaller in size.

Step-by-step explanation:

SELF EXPLANATORY

Answer:

The correct answer is (0) and (-10)

Step-by-step explanation:

The standard form of this equation is (x-a)(x-b)=0

so, here given equation is : x(x+10)=0

For solving the equation, equate both the LHS parts equals to RHS i.e. :

x(x+10)=0

x=0 &                          (x+10)=0 or x=(-10)

Answer: m = 1, b = 7.

Step-by-step explanation:

First, you must convert 2 + 3x + 5 - 2x = y to slope-intercept form. (y = mx + b)

y = mx + b
y = x + 7

The slope (m) is 1

The y-intercept (b) is 7

413 bricks are needed to build a wall whose area is equivalent to 10.32 m².

Given is that a brick wall of dimension 4.3 m by 2.4 m is to be built. There are 40 bricks per m².

The area of the wall will be -

[A] = 4.3 x 2.4 = 10.32 m²

[A] = 10.32 m²

Now, for the area of 1 m², 40 bricks are needed. So, for 10.32 m², we can say that -

10.32 x 40

412.8

413 bricks.

Therefore, for the area of 10.32 m², to only 413 bricks are needed to build it.

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The graph of Stewart's assignment added as an attachment

From the question, we have the following parameters that can be used in our computation:

Number of assignments = 36

Rate of assignment per day = 4

This means that the equation of the scenario is

Number of assignments remaining = Initial number of assignments - Rate of assignment per day * Number of days

Represent the number of assignments remaining with y and the number of days with x

So, we have the following representation

y = Initial number of assignments - Rate of assignment per day * x

Substitute the known values in the above equation, so, we have the following representation

y = 36 - 4 * x

Evaluate the products

y = 36 - 4x

So, the equation is y = 36 - 4x and the graph is added as an attachment

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A dealer bought some 9-volt batteries for $2,400. She sold them for $5,600, making a profit of $1.60 on each battery. 2,500 batteries were involved in the deal.

The dealer bought some 9-volt batteries for $2,400 and she sold them for $5,600. To find out how many batteries were involved, we need to calculate how much she made from each battery. We can do this by subtracting the cost of the batteries from the selling price and then dividing it by the number of batteries. Profit per battery = $5,600 - $2,400 = $3,200. Number of batteries = $3,200/$1.60 = 2,500. Therefore, the dealer bought 2,500 batteries.

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If the farmer plans to fence a rectangular pasture adjacent to a river than the dimensions that is required for the least amount of fencing is  length = 900 m and width = 450 m  .

In the question ,

it is given that ,

the farmer is planning to fence the rectangular pasture adjacent to the river ,

the area of the pasture is = 405000 square meter .

let the length of the pasture = "y"

let the width of the pasture be = "x" ,

since only three side is fenced , the required perimeter is = 2x + y ;

given that area ⇒ x*y = 405000

y = 405000/x  ;

So , the perimeter equation becomes ;

p = 2x + 405000/x

differentiating and equation to 0 we get ;

p' = 2 - 405000/x²

2 - 405000/x² = 0 ;

2x² = 405000

x² = 202500 ;

x = 450 , putting in perimeter equation ,

we get ; y = 900 .

Therefore , the dimension is length = 900 m and width = 450 m.

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An element with mass 420 grams decays by 11.8% per minute. the amount of the element remaining after 16 minutes is 56.3 grams

This is a type of function that are of 3 main parts

A mathematical function called an exponential function is employed frequently in everyday life. It is mostly used to compute investments, model populations, determine exponential decay or exponential growth, and so forth.

Considering the given problem,  

the starting = 420 grams

the base = 1 - r = 1 - 11.8% = 1 - 0.118 = 0.882

the exponents = 16

amount remaining = 420 (0.882)^16

= 56.330895

= 56.3 to the nearest tenths

the amount left is 56.3 g

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Answer:

around 8,000 or 100,000 is the answer

The number on round off to each place will be 45,621.

The decimal number is rounded to any place by the following concept -

We look at the number to the right of concerned digit. If that number is more than five or exactly five, then we add 1 to our number. However, if it is less than five, then the number remains same.

For instance, if we round 45.621 to nearest tenth, we will get 45.6. This is because on right to it, the number 2 is less than 5. Now, in the mentioned digit which is 45,621, we see there is no decimal and number after that. So, as the digits are 0 which is less than 5, the number will remain as it is.

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The mean yield for the three temperatures are equal.

Temperature is a unit used to express how hot or cold something is. It can be expressed using the Celsius or Fahrenheit scales, among others. Temperature shows which way heat energy will naturally flow, i.e., from a hotter (body with a higher temperature) to a colder (body with a lower temperature) (one at a lower temperature).

Given:

Number of groups [tex]k=3[/tex]

Number of observation in group 50°C, [tex]n_{1} =5[/tex]

Number of observation in group 60°C, [tex]n_{2} =5[/tex]

Number of observation in group 70°C, [tex]n_{3} =5[/tex]

Total number of observation [tex]N=15[/tex]

Null hypothesis [tex]H_{0}[/tex] :

The mean yield for the three temperatures are equal.

Alternative hypothesis [tex]H_{1}[/tex] : The mean yield for the three temperatures are not equal.

Now, Sum of the squares of between groups:

⇒∑  [tex]n_{i} (X_{i} -X)^{2}[/tex]

Here, [tex]X_{i}[/tex] is the mean of the jth group, [tex]X[/tex] is the overall mean and [tex]n_{1}[/tex] is the sample size of the jth group.

[tex]X=\frac{X_{1} +X_{2}+...+X_{i} }{i}[/tex]

[tex]X_{1} =34+24+36+39+32=165\\X_{2} =30=31+34+23+27=145\\X_{3} =23+28+28+30+31=140[/tex]

[tex]X_{i} =\frac{X_{i} }{n_{i} }[/tex]

⇒ [tex]X_{1} =\frac{165}{5} =33[/tex]

⇒ [tex]X_{2} =\frac{145}{5} =29[/tex]

⇒ [tex]X_{3} =\frac{140}{5} =30[/tex]

[tex]=n_{1} (X_{i} -X)^{2}+n_{2} (X_{2} -X)^{2}+n_{3} (X_{3} -X)^{2}[/tex]

SSB= 5 × [tex](33-30)^{2}[/tex]+ 5 × [tex](29-30)^{2}[/tex] + 5 × [tex](28-30)^{2}[/tex]

      = 5 × [tex]3^{2}[/tex] + 5 × [tex]1^{2}[/tex] + 5 × [tex]2^{2}[/tex]

      = 5 × 9 + 5 × 1 + 5 × 4

      = 45 + 5 + 20

      = 70

Now, Sum of difference between each element and grand mean squared (SST)

⇒ [tex](34-30)^{2} +(34-30)^{2}+(36-30)^{2} +...+(31-30)^{2}[/tex]

⇒ 306

Now, SSE = SST - SSB

= 306 - 70 = 236

Therefore,

Source of         Sum of                 Degrees of                   Mean

variation         squares             freedom                    square

Between      [tex]SSB=70[/tex]           [tex]df_{1} =k-1=2[/tex]            [tex]MSB=\frac{SSB}{df_{1} } =\frac{70}{2} =35[/tex]          

groups

Error    [tex]SSE=236[/tex]        [tex]df_{2} =N-k=12[/tex] [tex]MSE= \frac{SSE}{df_{2} } =\frac{236}{2} =19.67[/tex]                                          

Total                [tex]306[/tex]

Given .05 level of significance. i.e, [tex]F(0.05,2,12)=3.8853[/tex] tabulated value.

As [tex]1.7794 < 3.8853[/tex], tabulated value is higher than calculated value.

So, the null hypothesis is accepted.

Hence, the mean yield for the three temperatures is equal.

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Answer:

(c) 13 cm, 7 cm, 6 cm

Step-by-step explanation:

To determine which of the given sets of measurements cannot be the sides of a triangle, we can use the triangle inequality. The triangle inequality states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

In other words, if the sides of the triangle are a, b, and c, then a + b > c.

In answer choice c: 7 + 6 = 13, meaning that it does not satisfy the above inequality.

Therefore, the answer is (c) 13 cm, 7 cm, 6 cm

if this helps you, it would help me a lot if you could mark this as brainliest :)

As a set of inputs with one output for each, a function is defined as a relationship between them.

An equation, rule, or law in mathematics that establishes the link between the independent variable and the dependent variable (the dependent variable). Mathematics is rife with functions, and the sciences depend on them for constructing physical relationships.

We have given, f(0) = 3 for all parts.

a) f(n+1) = -2 f(n)

For f(1) put f(n) = f(0), f(0+1) = -2 f(0)

f(1) = -2(3) = -6

For f(2) put f(n = 1), f(1+1) = -2 f(1)

f(2) = -2(-6) = 12

For f(3) put f(n) = f(2),  f(2+1) = -2 f(2)

f(3) = -2(12) = -24

For f(4) put n = 3, f(3+1) = -2 f(3)

f(4) = -2(-24) = 48

For f(5) put n = 4, f(4+1) = -2 f(4)

f(5) = -2(48) = -96

b) f(n+1) = 3, f(n) + 7

For f(1) put n = 0, f(0+1) = 3 f(0)+7

f(1) = 3(3)+7 = 16

For f(2) put n = 1, f(1+1) = 3 f(1)+7

f(2) = 3(16)+7 = 55

For f(3) put f{n}=f{2}, f(2+1)=3 f(2)+7

f(3) = 3(55) + 7 = 172

For f(4) put n = 3, f(3+1) = 3 f(3)+7

f(4) = 3(172)+7 = 523

For f(5) put n = 4, f(4+1) = 3 f(4)+7

f(5) = 3(523)+7 = 1576

c) f(n+1) = f(n)²-2 f(n)-2

For f(1) put n = 0, f(0+1) = f(0)²-2 f(0)-2

f(1) = 3²-2(3)-2 = 1

For f(2) put n = 1, f(1+1) = f(1)²-2 f(1)-2

f(2) = 1²-2(1)-2 = -3

For f(3) put n = 2, f(2+1) = f(2)² - 2 f(2) - 2

f(3) = -3² - 2(-3) - 2 = 13

For f(4) put n = 3, f(3+1) = f(3)² - 2 f(3) - 2

f(4) = 13² - 2(13) - 2 = 141

For f(5) put n=4, f(4+1) = f(4)² - 2 f(4) - 2

f(5) = 141² - 2(141) - 2 = 19597

d) f(n+1)[tex]=3^{\frac{f(n)}{3}}$[/tex]

For f(1) put n = 0, f(0+1) [tex]$=3^{\frac{f(0)}{3}}$[/tex]

f(1) = [tex]3^{\frac{3}{3}}[/tex] = 3

For f(2) put n = 1, f(1+1) [tex]=3^{\frac{f(1)}{3}}$[/tex]

f(2) [tex]=3^{\frac{3}{3}}[/tex] = 3

For f(3) put n = 2, f(2+1) [tex]=3^{\frac{f(2)}{3}}$[/tex]

f(3) [tex]=3^{\frac{3}{3}}[/tex] = 3

For f(4) put n = 3, f(3+1) [tex]$=3^{\frac{f(3)}{3}}$[/tex]

[tex]$f(3)=3^{\frac{3}{3}}=3$[/tex]

For f(4) put n = 3, f(3+1) = [tex]$3^{\frac{f(3)}{3}}$[/tex]

f(4) [tex]$=3^{\frac{3}{3}}[/tex] = 3

For f(5) put n = 4, f(4+1) = [tex]3^{\frac{f(4)}{3}}$[/tex]

f(5) [tex]=3^{\frac{3}{3}}[/tex] = 3

The complete question is:

Find f( 1 ) , f( 2 ) , f( 3 ) , f( 4 ) , and f( 5 ) if f(n) is defined recursively by f( 0 ) = 3 and for n = 0 , 1 , 2 ,... a) f(n + 1 ) = − 2 f(n) . b) f(n + 1 ) = 3 f(n) + 7. c) f(n + 1 ) = f(n) 2 − 2 f(n) − 2. d) f(n + 1 ) = 3 f( slader

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f(2)=4, f(3)=7, f(4)=19, f(5)=40

What is a function?

In mathematics, a function is an expression, rule, or law that establishes the relationship between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences. German mathematician Peter Dirichlet initially provided the contemporary concept of function in 1837.

Given, the function is  f(n+1) = f(n) + 3f(n-1)

Calculating f(2) by substituting n=1 in the above equation.

f(2) = f(1) + 3f(0)

⇒f(2) = 1 + 3

⇒f(2) = 4

f(3) is calculated by substituting n=2

f(3) = f(2) + 3f(1)

⇒f(3) = 4 + 3

⇒f(3) = 7

f(4) is calculated by substituting n=3

f(4) = f(3) + 3f(2)

⇒f(4) = 7 + 12

⇒f(4) = 19

f(5) is calculated by substituting n=4

f(5) = f(4) + 3f(3)

⇒f(5) = 19 + 21

⇒f(5) = 40

f(2)=4, f(3)=7, f(4)=19, f(5)=40

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The equation of the line perpendicular to y=-3x-1 that passes through the point (3,4) is y = (1/3)x + 3.

What do you mean by equation of line?

The slope of the line and a point on the line can be used to create the equation of a line. The slope of the line, which can be stated as a numeric integer, fraction, or the tangent of the angle it forms with the positive x-axis, is the line's inclination with respect to the positive x-axis.

The slope of the line given in the question is: -3,

The slope of perpendicular line is negative reciprocal of the slope of other line,

So,

The slope of perpendicular line is: 1/3.

The equation of the line is generally in the form:

y = mx + c

So, the equation of line becomes:

y = (1/3)x + c

We have given that the line passes through the point (3,4).

Putting the values of x and y in the above equation to get the value of c.

4 = (1/3)(3) + c

c = 3

Putting the value of c in the equation,

y = (1/3)x + 3

This is the required equation.

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Answer:

(-3,-4) and (3,4).

Step-by-step explanation:

Answer:

Measures are SV=9 units., SY=14 units, YW= [tex]\sqrt{75units}[/tex], YW=[tex]\sqrt{27units}[/tex]

Step-by-step explanation:

===================================================

Explanation:

The circumcenter is found by intersecting the perpendicular bisectors of the triangle.

Segments VY, WY, and XY are perpendicular bisectors of triangle STU.

A perpendicular bisector has two properties:

Perpendicular bisector WY divides side TU into equal pieces TW and WU

In short:

TW = WU

So

TW = 11

since WU is equal to 11 as well

---------------------------------------

Focus on triangle TWY.

This is a right triangle with the sides of...

We'll use the pythagorean theorem to determine the unknown leg.

Plug in a = 11 and c = 14. Then let's solve for b.

[tex]a^2+b^2 = c^2\\\\11^2+b^2 = 14^2\\\\121+b^2 = 196\\\\b^2 = 196-121\\\\b^2 = 75\\\\b = \sqrt{75}\\\\b \approx 8.66025\\\\b \approx 8.7\\\\[/tex]

Therefore, segment YW is roughly 8.7 units.

Answer:

-------------------------------------

Set equation for area of given shape:

Simplify and solve for x:

Answer:

x = 2.5 mm

Step-by-step explanation:

A compound shape is made up of two or more basic shapes.

From inspection of the given compound shape, we can see that it is made up of two rectangles.

[tex]\boxed{\begin{minipage}{4 cm}\underline{Area of a rectangle}\\\\$A=w \cdot l$\\\\where:\\ \phantom{ww}$\bullet$ $w$ is the width. \\ \phantom{ww}$\bullet$ $l$ is the length.\\\end{minipage}}[/tex]

Dimensions of the smaller rectangle:

Dimensions of the larger rectangle:

Therefore, the equation for the area of the compound shape is:

[tex]\begin{aligned}\implies \textsf{Area}&=x \cdot 4 + x \cdot (2x+3)\\&=4x+x(2x+3)\\&=4x+2x^2+3x\\&=2x^2+7x\end{aligned}[/tex]

Given the area of the compound shape is 30 mm², substitute this value into the found equation for area and solve for x:

[tex]\begin{aligned}\implies 2x^2+7x &=30\\2x^2+7x-30&=0\\2x^2+12x-5x-30&=0\\2x(x+6)-5(x+6)&=0\\(2x-5)(x+6)&=0\\\\2x-5&=0 \implies x=2.5\\x+6&=0 \implies x=-6\end{aligned}[/tex]

As length is positive, x = 2.5 mm only.

Answer:

x^2 - x +3, aka the last option

Step-by-step explanation: y intercept is positive in the table, and leaves us with the first option and the last option. plugging in 3 gets the right answer of 9 for the last choice and gives 15 for the first choice

C. Albino alligators are very rare.

What is crocodiles ?

Crocodiles are large reptiles found in tropical regions of Africa, Asia, the Americas and Australia. They are members of the order Crocodilia, which also includes caimans, gharials and alligators.

crocodiles are more than alligators in the reptile tent because Albino alligators are very rare. according to the passage there are more types of crocodiles ans less alligators.

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Answer:

8750 Rs

Step-by-step explanation:

Saves

12.5 : 100 = x : 10 000

x = 10 000 * 12.5 / 100

x = 100 * 12.5

x = 1250 Rs

Total he spends

10 000 - 1250 = 8750 Rs

Answer:

infinite number of solutions

Step-by-step explanation:

5x - 4y = 10 → (1)

10x - 8y = 20 → (2)

multiply (1) by - 2

- 10x + 8y = - 20 → (3)

ad (2) and (3) term by term

0 + 0 = 0

0 = 0 ← true statement

this indicates the system has an infinite number of solutions

The 2.5kg of potatoes cost £1.40 so the cost of 4.25 kg of potatoes is £2.38.

A cost is an outlay needed to create, market, or prepare an asset for regular use. In other words, it's the cost incurred to produce a good, buy inventory, sell goods, or prepare equipment for use in a business process.

Given,

2.5 kg of potatoes = £1.401 kg of potatoes

cost = 1.40/2.5

       = £0.56

To find the cost of 4.25 kg of potatoes is: Then,

1 kg = £0.564.25 kg

      = 0.56 x 4.25

      = £2.38

Thus from the above conclusion we can say that the cost is £2.38.

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The angular velocity of the sphere at the bottom of the incline is 88.1 rad/s.

In physics, angular velocity or angular speed, also recognized as angular frequency vector, is a pseudovector portrayal of how fast the angular position or orientation of an object changes over time.

So, angular velocity will be:

mg(h sinθ) = 1/2 Iω² + 1/2mv²

I of solid sphere = 2/5 mr²

Hence,

mg(h sinθ) = 1/2 (2/5 mr²) ω² + 1/2 mv²

Now remove the mass:

g h sin θ = 1/5 r² ω² + 1/2 v²

ω = v/r, v = ωr

Now, calculate angular velocity as follows:
g h sin θ = 1/5 r² ω² + 1/2 (ωr)²

g h sin θ = (7/10) r² ω²

ω² = 10 g h sin θ/7 r²

ω = √10 g h sin θ/7 r²

  = √10 (9.8) (2.1) sin 25° / 7 (0.04)²

  = 88.1 rad/s

Therefore, the angular velocity of the sphere at the bottom of the incline is 88.1 rad/s.

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Complete question:
An 8.0 cm diameter, 400 g sphere is released from rest ta the tip of a 2.1 m long, 25-degree incline. It rolls, without slipping, to the bottom. What is the sphere's angular velocity at the bottom of the incline?

Answer:

should be option 2, but im sorry if it isnt.

Step-by-step explanation: