A football team loses 2 yards every 5 minutes. How many yards did the team lose after 15 minutes?

The value of d²y/dx² at the point defined by t = -π/6 is 0.

To find an equation for the line tangent to the curve at the point defined by t = -π/6, we first need to find the derivatives of x and y with respect to t, and then evaluate them at t = -π/6.

Given:

x = sin^2(t) - 1

y = csc(t)

Taking the derivatives with respect to t:

dx/dt = 2sin(t)cos(t)

dy/dt = -csc(t)cot(t)

Now we can evaluate the derivatives at t = -π/6:

dx/dt = 2sin(-π/6)cos(-π/6) = -√3/2

dy/dt = -csc(-π/6)cot(-π/6) = -2√3

The slope of the tangent line is given by dy/dx, so we can find it by dividing dy/dt by dx/dt:

dy/dx = (dy/dt) / (dx/dt) = (-2√3) / (-√3/2) = 4

To find the equation of the tangent line, we need a point on the line. We already know that the point is on the curve defined by x and y, so we substitute t = -π/6 into x and y: x = sin^2(-π/6) - 1 = 1/4 - 1 = -3/4

y = csc(-π/6) = -2√3

Using the point-slope form of a line, where (x₁, y₁) is a point on the line, and m is the slope: y - y₁ = m(x - x₁)

Substituting the values:

y - (-2√3) = 4(x - (-3/4))

y + 2√3 = 4(x + 3/4)

y + 2√3 = 4x + 3

y = 4x + 3 - 2√3

Therefore, the equation of the tangent line to the curve at the point defined by t = -π/6 is y = 4x + 3 - 2√3.

To find the value of d²y/dx² at this point, we need to take the second derivative of y with respect to x and evaluate it at the point. First, let's find dy/dx: dy/dx = dy/dt / dx/dt = (-2√3) / (-√3/2) = 4

Now, let's find d²y/dx²:

d²y/dx² = d/dx(dy/dx) = d/dx(4) = 0

Therefore, the value of d²y/dx² at the point defined by t = -π/6 is 0.

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Answer:

20

Step-by-step explanation:

20 - 14= 6

6 * -3= -18

The closed formula of h(t) and f(t) for

h(0)=f(0)=100b => h(t) = 100(2t+1), f(t) = 100(2t-1) ,

h(0)=200, f(0)=100 => h(t) = 200(2t+1), f(t) = 100(2t-1)

h(0)=600, f(0)=500 =>h(t) = 300 + 200(2t+\((-1)^{t}\)), f(t) = 200 - 100\((-1)^{t}\)

The recursive equations for the given two interacting population of hares and foxes are

h(t+1)=4h(t)-2f(t)

f(h+1)=h(t)+f(t)

for the given initial population in parts from a to c we need to create a close formula for h(t) and f(t)

h(t) = 100(2t+1)

f(t) = 100(2t-1)

h(t) = 200(2t+1)

f(t) = 100(2t-1)

h(t) = 300 + 200(2t+\((-1)^{t}\))

f(t) = 200 - 100\((-1)^{t}\)

The closed formula of h(t) and f(t) for

h(0)=f(0)=100b => h(t) = 100(2t+1), f(t) = 100(2t-1) ,

h(0)=200, f(0)=100 => h(t) = 200(2t+1), f(t) = 100(2t-1)

h(0)=600, f(0)=500 =>h(t) = 300 + 200(2t+\((-1)^{t}\)), f(t) = 200 - 100\((-1)^{t}\)

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Answer:

SO I know y=7.5

z=square root(5/3)

Step-by-step explanation:

2y+23=4y+8

2y+15=4y

15=2y

7.5=y

3z^2 -5=0

3z^2=5

z^2=5/3

z=square root of 5/3

Answer:

What we need to do is visualize what the problem says. We know there's a tower of 100 feets which has a support cable at the top which measures 140 feet, and we need to calculate how far from the tower is the cable anchored.

What we need to do is using the Pythagorean Teorem, as we have a rectangular triangle (we assume the tower is vertical).

We know the hypotenuse is 140 feets, as it's the lenght of teh cable, and one of the triangle sides is 100 feets, as it's the tower height.

As the Pythagorean Teorem says \(a^2 + b^2 = c^2\) (being c the hypotenuse)

We can now replace on \(a^2 + b^2 = c^2\) the numbers we have \(100^2 + b^2 = 140^2\)

Now, we solve \(100^2 + b^2 = 140^2\) by operating:

\(100^2 + b^2 = 140^2\);  \(b = \sqrt{140^2-100^2}\); b = 98

Now, we know the cable is 98 feets far from it

The distance base of the tower to the base cable is 97.97 ft

A right-angled triangle is a triangle, that has one of its interior angles equal to 90 degrees or anyone angles is a right angle.

Given that, A radio tower is 100 feet high. A support cable 140 feet long is fastened to the top of the tower and is anchored in the ground. We need to find how far from the base of the tower will the cable be anchored,

As we can see (refer to the figure), the whole scene is creating a right triangle,

Let the distance base of the tower to the base cable be x

Therefore, using Pythagoras theorem,

140² = 100 + x²

x = \(\sqrt{140^2 - 100^2}\)

x = \(\sqrt{19600-10000}\)

x = \(\sqrt{9600}\)

x = 97.97

Hence, the distance base of the tower to the base cable is 97.97 ft

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Answer:

(-8;7) ---> (8;7)

x changes sign. y stays with the same sign

............

There are infinitely many possible Jordan normal forms for a non-diagonalizable 5x5 complex matrix.

Given that A is a 5x5 complex matrix, the possible characteristic polynomial will have degree 5, and the minimal polynomial will divide the characteristic polynomial and have degree at most 5.

If A is not diagonalizable, then there will be at least one Jordan block in the Jordan normal form of A. The size of the largest Jordan block will be equal to the algebraic multiplicity of the corresponding eigenvalue. Since the characteristic polynomial has degree 5, there can be at most 5 Jordan blocks, and their sizes must sum to 5.

Therefore, the possible Jordan normal forms for A are:

A single 5x5 Jordan block

Two Jordan blocks, one of size 4 and one of size 1

Two Jordan blocks, one of size 3 and one of size 2

Three Jordan blocks, one of size 3 and two of size 1

Three Jordan blocks, one of size 2 and two of size 1

Four Jordan blocks, each of size 1

The minimal polynomial will be the product of linear factors corresponding to the distinct eigenvalues of A, and each factor will have multiplicity equal to the size of the largest Jordan block corresponding to that eigenvalue.

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Answer:

B.) The interquartile range of the data is 2

Step-by-step explanation:

By answering the above question, we may state that The circle's radius is  radius 8.5 feet as a result.

In more modern use, a circle's or sphere's length is equal to its radius, and it is one of the line segments connecting the object's centre and circumference. The phrase is derived from the Roman word circle, which also describes a waggon wheel's spokes. The radius of a circle is the separation of any points on its circumference from its centre. Often, it is denoted by "R" or "r". A line segment with one termination in the centre and one on the circle's perimeter is called a radius. Radius = circular diameter A circle's diameter is the portion that passes through its centre and has ends on the circle.

The formula for calculating a circle's circumference is:

C = 2πr

When r denotes the radius, C denotes the circumference, and denotes a mathematical constant roughly equal to 3.14159.

We are informed that the circle's diameter is 17 feet. We may solve for r by setting this equal to the circumference formula:

17π = 2πr

By multiplying both sides by 2, we obtain:

r = 17π / (2π)

The units are cancelled, leaving:

r = 17 / 2

Examining this expression results in:

r = 8.5 ft

The circle's radius is 8.5 feet as a result.

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4x² +x +19, is the standard equation. of the quadratic equation

Equatiοns are statements in mathematics that have twο algebraic expressiοns οn either side οf the equals (=) sign.

It shοws that the expressiοns printed οn the left and right sides have an equal relatiοnship.

In any mathematical equatiοn, we have LHS = RHS (left hand side = right hand side).

Equatiοns can be sοlved tο find the value οf an unknοwn variable that represents an unknοwn quantity.

If there is nο "equal tο" symbοl, a statement is nοt an equatiοn.

When twο expressiοns have equal values, a mathematical statement knοwn as an equatiοn includes the symbοl "equal tο" between them.

Hence, 4x² +x +19, is the standard equatiοn

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The number of plants Ethan has are 5.

Two or more expressions with an Equal sign is called as Equation.

Let x be the number of plants Ethan has.

Ethan uses 3.5 ounces of water for each plant, so he will use a total of 3.5p ounces of water.

If he starts with 32 ounces of water and ends up with 14.5 ounces

Total of 32 - 14.5 = 17.5 ounces of water.

As given the amount of water used is equal to the amount of water per plant times the number of plants:

3.5x = 17.5

Divide both sides by 3.5

x=5

Hence, , Ethan has 5 plants.

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Answer:

-4, and (a+b) are the two factors

Step-by-step explanation:

-4(a+b)

We have two factors

-4, and (a+b)

Answer:

-4 and a and b/(a+b)

Step-by-step explanation:

When there is a number outside of a parentheses, you want to distribute it inside of the parentheses.  So in this case, -4 is on the outside, so it usually gets distributed it in, which makes it a factor.

Since a and b are getting multiplied by the -4, they are also factors in the equation.  

In a problem like this, if you want to solve it, the number outside the parentheses gets distributed into the numbers in the parentheses.  (It gets multiplied by the numbers).

-4 times a and -4 times b

-4 times a is -4a

-4 times b is -4b

The answer to this problem, if you need it is -4a-4b.  :)

53 inches is the mean height of the students in the group.

Given data: \(54,48,52,56,55\)

We know that mean of the heights =  \(\frac{Sum of all the heights}{No. of students}\)

                                                         \(= \frac{54+48+52+56+55}{5}\)

                                                         \(= \frac{265}{5}\)

                                                         \(= 53\) inches

Thus, the mean height of the students is 53 inches

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Answer:

5d+4

Step-by-step explanation:

Number of ticket sold by Daniel = d .... 1

If Sara sold 4 more tickets to the school play than the number Danielle sold, the total number sold by Sarah is expressed as d+4 .... 2

If Brett sold 3 times as many as Danielle sold, the amount sold by Brett is 3×d = 3d ..... 3

The number of tickets that the 3 students sold altogether can be gotten by adding equation 1, 2 and 3 together as shown;

d+(d+4)+3d

Collect like terms

= d+d+3d+4

= 2d+3d+4

= 5d+4

Hence the number of tickets that the 3 students sold altogether is represented as 5d+4

Answer:

5d+4

Step-by-step explanation:

Have a good day

Answer:

21

Step-by-step explanation:

An isosceles triangle has 2 sides of the same length, those sides being the sides that aren't the base. The perimeter is the total length of all 3 sides of the triangle. We know that the base is 5 inches, and that one side is 8. Because the triangle is isosceles, we know that the others ide is also 8 inches. Therefore, the perimeter is 8+8+5, which is 21.

Answer:

21 in.

Step-by-step explanation:

If the triangle is isosceles, then two of its three sides are of equal length.  We can assume that the side lengths are 5 in., 8 in and 8 in.  Summing these up, we get total length 21 in.  That's the perimeter of the triangle.

The equation of the line in point-slope form and in​ slope-intercept form are both y = 1/2x.

1. Point-Slope Form: y - y1 = m(x - x1), where m is the slope of the line and (x1, y1) is a point on the line.

2. Slope-Intercept Form: y = mx + b, where m is the slope of the line and b is the y-intercept.

3. Standard Form: Ax + By = C, where A and B are coefficients that define the slope and y-intercept of the line.

If a line has a slope of 1/2 and passing through the origin, then:

m = 1/2

(x1, y1) = (0,0)

Plug in the values in the point-slope form and in​ slope-intercept form.

point-slope form

y - y1 = m(x - x1)

y - 0 = 1/2(x - 0)

y = 1/2x

slope-intercept form

y = mx + b

y = 1/2x + b

Substitute the values of x and y and solve for the y-intercept, b.

0 = 1/2(0) + b

b = 0

y = 1/2x + 0

y = 1/2x

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Answer:

slope = - 3

Step-by-step explanation:

Calculate the slope m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (- 6, 6) and (x₂, y₂ ) = (- 3, - 3)

m = \(\frac{-3-6}{-3-(-6)}\) = \(\frac{-9}{-3+6}\) = \(\frac{-9}{3}\) = - 3

Answer:

Step-by-step explanation:

2 * (n - 1) represents "the product of 2 and the difference of a number and 1.​"

Answer:

2*{n-1} represents the product of 2 and the difference of number and 1.

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The calculated value of the tenth term, b₁₀ of the sequence is 78732

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

b₁ = -4

bₙ = 3bₙ₋₁

The above means that

We multiply the current term by 4 to get the next term

So, we have

b₂ = 3 * 4 = 12

b₃ = 3 * 12 = 36

b₄ = 3 * 36 = 108

b₅ = 3 * 108 = 324

b₆ = 3 * 324 = 972

b₇ = 3 * 972 = 2916

b₈ = 3 * 2916 = 8748

b₉ = 3 * 8748 = 26244

b₁₀ = 3 * 26244 = 78732

Hence, the tenth term, b₁₀ of the sequence is 78732

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Answer:

−7k^4−11k^2+6

Step-by-step explanation:

−4k^4+14+3k^2−3k^4−14k^2−8

(−4k^4+−3k^4)+(3k^2+−14k^2)+(14+−8)

−7k^4−11k^2+6

...

Answer:

46 degrees

Step-by-step explanation:

you know that if you add 134 and x  it will equal a straight line or 180 degrees. So set it up as an addition problem.

134 + x =180   subt. 134 from both sides

x=180-134

x=46 degrees

Answer:

46

Step-by-step explanation:

Answer:The function is nonlinear

Step-by-step explanation:

A P E X

Answer:

47 and 34

Step-by-step explanation:

x+x-13=81

2x-13=81

2x=94

x=47

y=34

34+47=81

Answer: 4/1

Step-by-step explanation: Find the reciprocal of the divisor

Reciprocal of 5/24: 24/5

Now, multiply it with the dividend

So,

5/6 ÷ 5/24= 5/6 × 24/5= 5 × 24/ 6 x 5 = 120/30

After reducing the fraction, the answer is

4/1

The end behaviour of the graph of the Polynomial as required to be determined in the task content is; As x tends negative infinity, y tends to negative infinity and As x tend to infinity, y tends to infinity.

By observation of the polynomial equation; the degree is 3 which is odd and the leading coefficient is; positive.

Therefore, it follows that the end behaviour is; As x tends negative infinity, y tends to negative infinity and As x tend to infinity, y tends to infinity.

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The end behavior of the polynomial y = 2x³ + x² - 45 is:

As x approaches negative infinity, y approaches negative infinity. As x approaches positive infinity, y approaches positive infinity.

The degree of the polynomial and the sign of the leading coefficient  describe the end behavior.

Below are rules for determining the end behavior of a function:

a. Even and Positive: As x approaches negative infinity, y approaches positive infinity. Also, as x approaches positive infinity, y approaches positive infinity

b. Even and Negative: As x approaches negative infinity, y approaches negative infinity. Also, as x approaches positive infinity, y approaches negative infinity

c. Odd and Positive: As x approaches negative infinity, y approaches negative infinity. Also, as x approaches positive infinity, y approaches positive infinity.

d. Odd and Negative: As x approaches negative infinity, y approaches positive infinity. Also, as x approaches positive infinity, y approaches negative infinity.

Given: y = 2x³ + x² – 45

The degree (largest exponent) of the polynomial = 3 (odd)

Leading coefficient (coefficient of largest exponent) = 2 (positive)

Since the degree and leading coefficient are positive and negative respectively.

Therefore, the end behavior of the graph of the polynomial is:

As x approaches negative infinity, y approaches negative infinity. Also, as x approaches positive infinity, y approaches positive infinity.

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Step-by-step explanation:

an object and its shadow create a right-angled triangle.

2 objects and their shadows create 2 similar right-angled triangles.

that means the angles are the same, and the side lengths of one triangle all correlate with the corresponding side lengths of the other triangle via the same factor.

so,

42 × f = 6

f = 6/42 = 1/7

the length of Joel's shadow is then

20 × f = 20 × 1/7 = 2.857142857... ft