A bike tire has a diameter of 14 inches. It runs over a piece of gum that sticks to the tire. Write a cosine function that describes the height of the gum above the ground as a function of angular distance.




a. y = -7 cos x + 7


b. y = 7 cos x + 14


c. y = -7 cos x + 14


d. y = 14 cos x + 28

Answer:

  b.  10

Step-by-step explanation:

For the most part, these are problems in addition. The measures of the different angles add up according to the relationships given in the problem statement.

From the picture, you can tell that ∠JKN is the sum of ∠1 and ∠2, which are said to be equal (congruent). That is, ∠1 has a measure that is half of that of ∠JKN.

Since ∠JKN is a right angle, 90°, and the measure of ∠1 is half that, m∠1 is 45°.

So, to find t, we equate the given expression for m∠1 to 45 and solve.

  4t +5 = 45

  4t = 40 . . . . . subtract 5

  t = 10 . . . . . . . divide by 4 . . . . . matches answer choice B

First you must know that the sides 2x and x + 8 are equal to each other and sides x and 3x - 16 are equal to each other.

This means you can make a formula like so:

2x = x + 8

and

x = 3x - 16

Now you may solve for x for both of them (you should get the same answer for both x's)

2x - x = (x - x) + 8

x = 8

and

x - 3x = (3x - 3x) - 16

-2x = -16

-2x/-2 = -16/-2

x = 8

To find the length of each side just replace x with 8!

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

  d.  (3, 7, -3)

Step-by-step explanation:

The reduced row-echelon form of the augmented matrix has 1s on the diagonal and zeros off-diagonal, except for the answer in the last column. It can be convenient to start by writing the augmented matrix using the second equation first:

[tex]\left[\begin{array}{ccc|c}-1&2&-3&20\\9&-4&1&-4\\4&4&-1&43\end{array}\right] \\\\\text{Add 9 times the first row to the second, and 4 times the first row to the third}\\\\\left[\begin{array}{ccc|c}-1&2&-3&20\\0&14&-26&176\\0&12&-13&123\end{array}\right][/tex]

[tex]\text{Subtract 2 times the third row from the second}\\\\\left[\begin{array}{ccc|c}-1&2&-3&20\\0&-10&0&-70\\0&12&-13&123\end{array}\right] \\\\\text{Divide the second row by -10}\\\\\left[\begin{array}{ccc|c}-1&2&-3&20\\0&1&0&7\\0&12&-13&123\end{array}\right][/tex]

[tex]\text{Subtract 2 times the second row from the first, and}\\\text{subtract 12 times the second row from the third}\\\\\left[\begin{array}{ccc|c}-1&0&-3&6\\0&1&0&7\\0&0&-13&39\end{array}\right] \\\\\text{Divide the third row by -13}\\\\\left[\begin{array}{ccc|c}-1&0&-3&6\\0&1&0&7\\0&0&1&-3\end{array}\right][/tex]

[tex]\text{Add 3 times the third row to the first, then multiply the result by -1}\\\\\left[\begin{array}{ccc|c}1&0&0&3\\0&1&0&7\\0&0&1&-3\end{array}\right][/tex]

The method may not be strictly according to some algorithm, but it avoids fractions and gives the correct result: (x, y, z) = (3, 7, -3).

Answer:

The answer is d. (3, 7, -3)

Step-by-step explanation:

100% sure I got a 100 on review exam

Answer:

  29 × 51 inches

Step-by-step explanation:

If the scale is ...

  photo : painting = 1 : 3

then each dimension of the painting is 3 times the corresponding dimension of the photo. The painting is (3×13) by (3×17) inches, or 39 × 51 inches.

Answer: Lena eats 1/4 of the whole bar

Step-by-step explanation:

Half of the bar is 50. A full bar would be 100%. If Phillip has half, amd Lena eats half of that half, she eats 0.25 out of 0.5. 0.5 is half of the whole bar, so 0.5×0.5 is 1, and if lena ate 0.25 of 1, that is 1/4.

TRUE IT IS REALLY TRUEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE

Answer:

True, all points to the of zero on a horizontal number line are negative.

Step-by-step explanation:

Detailed explanation is as follows:

* All points to the left of zero on a horizontal number line are negative.

* A number line is a picture of a graduated straight line that serves as abstraction for real numbers.

* This number line can be extended to the left to represent numbers which are smaller than 0.

Tags: horizontal number line, points to the zero

Answer: I think is A

Step-by-step explanation:

You do y2-y1/x2-x1 and get a slope of 3 and according to the graph when the x is 3 the y is about 2 hope this help

Answer:

A

Step-by-step explanation:

if you do all the math will see that A is correct and the other guy said its A so its defently A

Answer:

B. infinite solutions along a line

Step-by-step explanation:

The matrix is equivalent to the equations ...

x = 2

y = 9

0z = 0 . . . . . . true for any z

This tells you the solutions are ...

(x, y, z) = (2, 9, z)

This defines a line parallel to the z-axis.

Answer:

it would be 3.33%

Step-by-step explanation:

Answer:

  about 5.55%

Step-by-step explanation:

The interest formula is ...

  i = Prt

where i is the interest earned, P is the principal amount, r is the annual rate, and t is the number of years. Fill in the given information and solve for the remaining variable.

  5000 = 15000·r·6

  5000/90000 = r = 1/18 ≈ 5.55% . . . . . divide by the coefficient of r

____

Comment on the answer

The decimal value of 1/18 is 0.0555555... repeating indefinitely. Rounded to 3 digits, it would be 5.56%. The offered answer choices seem to give more attention to the repeating digits than to proper rounding.

Answer:

11/381

Step-by-step explanation:

Not sure what the ? after each number means but I'm going to assume they aren't there

so we need find the number of tokens in all which is

44+1414+66=1524

P(red)=44/1524 now reduce giving P(red)=11/381

Moderators please delete this answer.

Looks like [tex]f(x,y)=x^2+y^2-x^2y+7[/tex].

[tex]f_x=2x-2xy=0\implies2x(1-y)=0\implies x=0\text{ or }y=1[/tex]

[tex]f_y=2y-x^2=0\implies2y=x^2[/tex]

The latter two critical points occur outside of [tex]D[/tex] since [tex]|\pm\sqrt2|>1[/tex] so we ignore those points.

The Hessian matrix for this function is

[tex]H(x,y)=\begin{bmatrix}f_{xx}&f_{xy}\\f_{yx}&f_{yy}\end{bmatrix}=\begin{bmatrix}2-2y&-2x\\-2x&2\end{bmatrix}[/tex]

The value of its determinant at (0, 0) is [tex]\det H(0,0)=4>0[/tex], which means a minimum occurs at the point, and we have [tex]f(0,0)=7[/tex].

Now consider each boundary:

[tex]f(1,y)=8-y+y^2=\left(y-\dfrac12\right)^2+\dfrac{31}4[/tex]

which has 3 extreme values over the interval [tex]-1\le y\le1[/tex] of 31/4 = 7.75 at the point (1, 1/2); 8 at (1, 1); and 10 at (1, -1).

[tex]f(-1,y)=8-y+y^2[/tex]

and we get the same extrema as in the previous case: 8 at (-1, 1), and 10 at (-1, -1).

[tex]f(x,1)=8[/tex]

which doesn't tell us about anything we don't already know (namely that 8 is an extreme value).

[tex]f(x,-1)=2x^2+8[/tex]

which has 3 extreme values, but the previous cases already include them.

Hence [tex]f(x,y)[/tex] has absolute maxima of 10 at the points (1, -1) and (-1, -1) and an absolute minimum of 0 at (0, 0).

The function must first have its partial derivatives set to zero to find its critical points. Also, considering the given domain's boundaries with Lagrange multipliers can establish the function's maximum and minimum points.

This function is a multivariable function and to find its extreme values within a specified domain you would use multivariable calculus methods. For the given function f(x, y) = x2 + y2 − x2y + 7, we first find its critical points by setting its partial derivatives equal to zero and then solve for x and y. Additionally, we need to consider the boundaries of the set {|x| ≤ 1, |y| ≤ 1} by using the method of Lagrange multipliers. The extreme values are obtained at the critical points within the domain, including the boundary.

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Answer:

  "halfway between"

Step-by-step explanation:

The zero crossings are symmetrical about the line of symmetry, which is a vertical line through the vertex. The x-coordinate of the vertex s the average of the two x-intercepts, so lies between them--exactly halfway between them.

Answer:

Between

Step-by-step explanation:

The Vertex is a point where two or more curve meets. In the case of a quadratic equation, the vertex is at the minimum point (if a is positive) or at the maximum point (if a is negative).

When the graph of a quadratic function crosses the x-axis twice, the x-coordinate of the vertex lies between the two x-intercepts.

Note that the two x-intercepts are the roots of the quadratic function.

Answer:

  [tex]\dfrac{r_s}{r_r}\approx 6.3346[/tex]

Step-by-step explanation:

The ratio of the radii is the square root of the ratio of the areas:

  [tex]\dfrac{r_s}{r_r}=\sqrt{\dfrac{22680}{565.2}}\approx 6.3346[/tex]

The radius of sphere s is about 6.3346 times as large as the radius of sphere r.

To determine the ratio of the sizes of the radii of the two spheres based on their surface areas, you can use the ratios of the square roots of the surface areas. Using this method, the radius of Sphere S is found to be roughly 8 times larger than Sphere R

The subject topic of this question is related to geometry, specifically looking at the relationship between the surface areas of two spheres and their respective radii. Given that the surface area (SA) of a sphere is given by the formula SA=4πr², you can set up a ratio for the radii.

The square roots of the ratios of the surface areas of the spheres will give us the ratio of the radii. In other words, sqrt(SA of sphere S/ SA of sphere R) = ratio of the radii. Substituting the given values, we get sqrt(22680/565.2) which approximately equals to 8.

Therefore, the radius of Sphere S is approximately 8 times larger than Sphere R.

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If you translate circle 1 with the vector (6,-4), the center will become

[tex](-4,5)+(6,-4) = (-4+6,5-4)=(2,1)[/tex]

So, circles 1 and 2 are now concentric. The radii are, respectively, 2 and 6. This means that, if we dilate circle 1 with a scale factor of 3, its radius will become 6 as well.

After this two transformations, both circles will have center (2,1) and radius 6.

The transformation rule is (x+6, y-4).

We dilate by a factor of 3.

A circle is a perfectly round shape meaning any point around its curve is the same distance from its central point called the center

Firstly we need to shift the center.

Again we need to dilate the circle.

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Answer:

Step-by-step explanation:

121b^4 - 49 is a "difference of squares."

Formula for factoring a "difference of squares:"

 a² - b² =  (a - b)(a + b)

So:  rewrite your 121b4 - 49 as 11²b^4 - 7² = (11b²)² - 7²

                                                                  = (11b² - 7)(11b² + 7)

This answer matches the last of the four given answer choices.

Answer:

b

Step-by-step explanation:

(625x¹²y⁸)^¼

(5⁴x¹²y⁸)^½

5×x³×y²

5x³y²

5|x³|y²

For it to be positive,

x³ should be positive because 5 and y² already are positive.

Answer:

4.6

Step-by-step explanation:

Formula: Range = highest value - lowest value

Step 1: List all the data in ascending order

1.8, 2.4, 3.5, 4.9, 5.2, 6.4

Step 2: Identify the lowest and highest number

Lowest number : 1.8

Highest number : 6.4

Step 3 : Substitute the values in the formula

Range = highest value - lowest value

6.4 - 1.8 = 4.6

!!

Answer:  $67.20

Step-by-step explanation:

store buys jacket at 60 dollars and marks it up 12%

$60 x .12% = $7.20

$60 + $7.20 = $67.20

Answer:

(- 1, 4)

Step-by-step explanation:

The line x = 1 is a vertical line.

The point P(3, 4) is 2 units to the right of x = 1 ( 3 - 1 = 2 )

Hence the reflection will be 2 units to the left of x = 1, that is  (1 - 2)

P'(- 1, 4)

The reflection of point P(3, 4) about the vertical line x = 1 is P'(-2, 4).

Reflection is a transformation that flips a figure over a line or a plane. It is a type of symmetry transformation that maintains the same shape and size of the object but changes its orientation with respect to the line or plane of reflection.

Given: Point P(3, 4).

The line x = 1 is a vertical line.

Now, let's find the reflection of point P(3, 4) about the vertical line x = 1:

To reflect a point about a vertical line, we reverse the sign of the x-coordinate while keeping the y-coordinate the same.

So, the reflection of P(3, 4) will be (-2, 4).

Hence, the reflection of point P(3, 4) is P'(-2, 4).

Learn more about Reflection here:

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Answer:I=103395.6

Step-by-step explanation:

Using the formula for calculating interest (I) which is PRT, you substitute the given values for principal (P), rate (R), and time (T) respectively. First, calculate the product of principal P and rate R, then multiply this result by the time (T). Hence, the estimated interest is $103,396.54.

The formula for calculating interest (I) is I = PRT. In your case, the principal (P) is $49,236.45, the rate (R) is 105% or 1.05 (we use decimal form for this calculation), and the time (T) is 2 years. To calculate interest, we substitute these values into the formula as follows:

I = $49,236.45 * 1.05 * 2

First, calculate the product of principal and rate: $49,236.45 * 1.05 = $51,698.27

Next, multiply this result by the time: $51,698.27 * 2 = $103,396.54

Therefore, the estimated interest is $103,396.54

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Answer:

[tex]\displaystyle r=\sqrt{\frac{539}{\pi\cdot h}}[/tex]

Step-by-step explanation:

Fill in the value of the volume and solve for r.

[tex]539=\pi\cdot r^2\cdot h\\\\\dfrac{539}{\pi\cdot h}=r^2 \quad\text{divide by the coefficient of $r^2$}\\\\r=\sqrt{\dfrac{539}{\pi\cdot h}} \quad\text{take the square root}[/tex]

In the context of mathematical geometry, if 'A⊥Y and X || Y', it means that A is perpendicular to Y and X is parallel to Y. In such a scenario, A would also be perpendicular to X.

In mathematical terms, the symbols used in this question represent geometric relationships. Here, 'A⊥Y' means that A is perpendicular to Y, meaning A intersects with Y at a right angle (90 degrees). 'X || Y' signifies that X and Y are parallel, meaning they are in the same plane never intersect or meet, regardless of how far extended.

When it is given 'A⊥Y and X || Y', this suggests a specific geometric condition. In such a case, the vector A (or line/segment) is perpendicular to the vector Y. Also, the Vector X is parallel to Y. From these conditions, if one line is perpendicular to a second line, and a third line is parallel to the second line, then the first and third lines are also perpendicular to each other. Therefore, the conclusion in this case would be 'A is perpendicular to X' or 'A⊥X'.

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Answer:

4.) 2.5%

Step-by-step explanation:

1/20 = 5/100 = 5%

If that value is cut in half, it becomes ...

(1/2)×5% = 2.5%

Answer:

The correct option is 4) 2.5%

Step-by-step explanation:

Consider the provided information.

One of every 20 customers reports poor customer service on your company’s customer satisfaction survey.

First find the 1 is how much percent of 20.

[tex]\frac{1}{20}\times 100=1\times 5=5\%[/tex]

That means 5% of customers reports for poor customer services.

It is given that, You have just created a new process that should cut the number of poor customer service complaints in half.

Previously 5% of customers was not satisfy with the customer services, now only half of it not satisfy the customer service.

[tex]\frac{1}{2}\times 5\%=2.5\%[/tex]

Hence, the correct option is 4) 2.5%

Answer:

1\2

Step-by-step explanation:

draw a circle split it where there are 6 slices color half red and white now color one of the slices green and the rest blue there are 2 slices out of 6 colored blue. Hope it helped! make sure to reduce

Final answer:

The spinner is half RED and WHITE, and the other half is BLUE and GREEN. With 1/6 of it being GREEN, the remaining fraction 1/3 of the spinner is BLUE.

Explanation:

To determine how much is BLUE on the mystery spinner, we must calculate the portions of each color. We know that the spinner is 50% RED and WHITE combined and the remainder is BLUE and GREEN. Since 1/6 of the spinner is GREEN, we have to find out what fraction is left for BLUE.

Firstly, we calculate what 50% is in fraction form, which is 1/2 of the spinner. Now, knowing that 1/6 of the spinner is GREEN, we subtract the GREEN fraction from the half not covered by RED and WHITE:

1/2 (portion of BLUE and GREEN) - 1/6 (portion of GREEN) = (3/6 - 1/6) = 2/6, which simplifies to 1/3.

Therefore, 1/3 of the spinner is BLUE.

Answer:

D (1,0)

Step-by-step explanation:

Let the coordinates of D be (a,b).

The diagonals of a parallelogram bisect each other.

The midpoint of AC should be the same as the midpoint of BD.

[tex](\frac{-2+4}{2},\frac{4+-1}{2}) =(\frac{1+a}{2} ,\frac{3+b}{2})[/tex]

[tex](\frac{2}{2},\frac{3}{2}) =(\frac{1+a}{2} ,\frac{3+b}{2})[/tex]

Compare corresponding coordinates

This implies that:

[tex]1+a=2[/tex], [tex]3+b=3[/tex]

[tex]a=2-1[/tex], [tex]b=3-3[/tex]

[tex]a=1[/tex], [tex]b=0[/tex]

Therefore the coordinates of D are: (1,0)

Answer:

Option D for plato users

Step-by-step explanation:

D.  (1, 0)

Answer:

t = 11,794 years

Step-by-step explanation:

If you are looking for a confirmation that your answer is correct, it is.

i dont quite get the question but...

i guess this is how it is.

Take the mirror image of∆ABC Through the a line through the point y=3.

The new ∆ABC would have point C=(4,2)

B=(3,-6) A=(1,-3)

Now shifting the ∆ABC one unit (i.e. 2 acc. to the graph as scale is 1 unit =2) towards right ( or adding 2 to the x coordinates of ∆ABC)

We get the Coordinates of triangle ABC as A=(3,-3) B=(5,-6) C=(6,2).

This coordinate is the same coordinates of ∆A"B"C".

Hope it helps...

Regards;

Leukonov/Olegion.

Answer:

x={-2,2}

Step-by-step explanation:

Graph them when intersecting.

Algebraically:

x^2 + 1 = -x^2 + 9

Add x^2 on both sides and subtract 1 on both sides.

2x^2 = 8

Divide 2 on both sides

x^2 = 4

Square root on both sides

|x| = 2

Remove abs value by putting + or - on the other side

x = {-2,2}

Please mark for Brainliest!!  :D Thanks!!

For more information or any questions, please comment below and I'll respond as soon as possible!! :)

2,2

B in edge

I am taking the test

Answer:

(1,6)

Step-by-step explanation:

In this question, the point (1,2) is first reflected on the line y=0 then followed by line y=2

In the first reflection, y=0, the line is the x-axis, so the point (1,2) is reflected on the x-axis. The law here is that reflection of a point (x,y) on the x-axis, will result to an image of (x,-y)

The point is (1,2), its image will be (1,-2)

The new image (1, -2) is then reflected on the line y=2 but you should be aware that the x-coordinate will remain the same, but the y-coordinate will change. This is to say that the y coordinate value will shift the same number of units above the line y=2 as it is below the line y=2

Point (1,-2) reflected on line y=2 will result to an image (1,6). The x-coordinate value has remained the same, where as the y coordinate value has shifted 4 units above the line y=2 because it was 4 units below the line y=2.

Final image will be (1,6)