A steep mountain is inclined 75 degree to the horizontal and rises 3900 ft above the surrounding plain. A cable car is to be installed by connecting a cable from the top of the mountain to a spot on the plain that is 910 ft from the base of the mountain. Find the shortest length of cable needed.

Answer:

y''=(4-3t)/[16 t^3 (2-t)^(3/2)]

Step-by-step explanation:

x = t², y = (2 - t)^1/2

dy/dx=dy/dt×dt/dx by chain rule

dy/dt=1/2 (2-t)^(1/2-1) × (-1)

dy/dt=-1/2 (2-t)^(-1/2)

dy/dt=-1/[2(2-t)^(1/2) ]

dx/dt=2t

dy/dx=-1/[2(2-t)^(1/2) ] × 1/[2t]

dy/dx=-1/[4t (2-t)^(1/2) ]

We need to find the second derivative now.

That is we calculate d/dt(dy/dx in terms of t) then divide by derivative of x in terms of t).

dy/dx=-1/[4t (2-t)^(1/2) ]

Let's find derivative of this with respect to t.

d/dt(dy/dx)=

[0[4t (2-t)^(1/2)]-(-1)(4(2-t)^(1/2)+-4t(1/2)(2-t)^(-1/2))]/ [4t (2-t)^(1/2) ]^2

Let's simplify

d/dt(dy/dx)=

[(4(2-t)^(1/2)+-4t(1/2)(2-t)^(-1/2))]/ [4t (2-t)^(1/2) ]^2

Continuing to simplify

Apply the power in the denominator

d/dt(dy/dx)=

[(4(2-t)^(1/2)+-4t(1/2)(2-t)^(-1/2))]/ [16t^2 (2-t) ]

Multiply by (2-t)^(1/2)/(2-t)^(1/2):

d/dt(dy/dx)=

[(4(2-t)+-4t(1/2)]/ [16t^2 (2-t)^(3/2)]

Distribute/multiply:

d/dt(dy/dx)=

[(8-4t+-2t)]/ [16t^2 (2-t)^(3/2)]

Combine like terms:

d/dt(dy/dx)=

[(8-6t)]/ [16t^2 (2-t)^(3/2)]

Reducing fraction by dividing top and bottom by 2:

d/dt(dy/dx)=

[(4-3t)]/ [8t^2 (2-t)^(3/2)]

Now finally the d^2 y/dx^2 in terms of t is

d/dt(dy/dx) ÷ dx/dt=

[(4-3t)]/ [8t^2 (2-t)^(3/2)] ÷ 2t

d/dt(dy/dx) ÷ dx/dt=

[(4-3t)]/ [8t^2 (2-t)^(3/2)] × 1/( 2t)

d/dt(dy/dx) ÷ dx/dt=

[(4-3t)]/ [16t^3 (2-t)^(3/2)]

Or!!!!!!

x = t², y = (2 - t)^1/2

Since t>0, then t=sqrt(x) or x^(1/2).

Make this substitution into the equation explicitly solved for y:

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

Differentiate:

y' =(1/2) (2 - x^1/2)^(-1/2) × -1/2x^(-1/2)

y'=-1/4(2 - x^1/2)^(-1/2)x^(-1/2)

y'=-1/4(2x-x^3/2)^(-1/2)

Differentiate:

y''=1/8(2x-x^3/2)^(-3/2)×(2-3/2x^1/2)

y''=(2-3/2x^1/2)/[8 (2x-x^3/2)^(3/2)]

Replace x with t^2

y''=(2-3/2t)/[8 (2t^2-t^3)^(3/2)]

Multiply top and bottom by 2

y''=(4-3t)/[16 (2t^2-t^3)^(3/2)]

Factor out t^2 inside the 3/2 power factor:

y''=(4-3t)/[16 (t^2)^(3/2) (2-t)^(3/2)]

y''=(4-3t)/[16 t^3 (2-t)^(3/2)]

Answer:

I don't know what to do so I just answered the volume of this tell me if I am wrong

Step-by-step explanation:

radius : 3.5 cm

volume : ?

now,

volume (v) : π × r (2)

: 22/7 × 3.5(2)

:22×3.5×3.5 by 7

therefore,

the volume is 38.5

Answer:

45

Step-by-step explanation:

9 x 5 = 45

it's a multiplication question

Answer:

y = -26.059x + 722.63

Step-by-step explanation:

The equation that represents the approximate line of best fit for data will be D. y = –26x + 723.

It should be noted that an equation is simply used to illustrate the mathematical expressions between variables.

To find an equation of a line, it's important to identify the slope, the point, and then substitute the values into the point-slope form.

Using the given data you can build the linear regression that is described by the linear function y=ax+b, you can see that a = -26 and b = 723 in the attached diagram.

In this case, the equation that represents the approximate line of best fit for data will be y = –26x + 723. The line expresses the relationship between the points.

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The partial fraction expansion will look like

(x - 2)/((x ² + 1) (x - 1)²) = (ax + b)/(x ² + 1) + c/(x - 1) + d/(x - 1)²

Get everything in terms of a common denominator, and compare the numerators on both sides:

x - 2 = (ax + b) (x - 1)² + c (x ² + 1) (x - 1) + d (x ² + 1)

Expand the right side:

x - 2 = (ax + b) (x - 1)² + c (x ² + 1) (x - 1) + d (x ² + 1)

x - 2 = (a + c) x ³ + (-2a + b - c + d) x ² + (a - 2b + c) x + b - c + d

Match up the coefficients and solve the resulting system of equations:

a + c = 0

-2a + b - c + d = 0

a - 2b + c = 1

b - c + d = -2

==>   a = -1, b = -1/2, c = 1, d = -1/2

So the expansion into partial fractions is

(x - 2)/((x ² + 1) (x - 1)²) = (-x - 1/2)/(x ² + 1) + 1/(x - 1) - 1/(2 (x - 1)²)

… = -(2x + 1)/(2 (x ² + 1)) + 1/(x - 1) - 1/(2 (x - 1)²)

Answer:

Yes

Step-by-step explanation:

-10x+4y ≥-4

Plug in (0,-1)

-10(0) +4(-1) ≥-4

-4 ≥ -4

This is a true statement so the point is a solution

Answer:

Yes

Step-by-step explanation:

Substitute x = 0 and y = -1

Then

[tex] - 10(0) + 4( - 1) \geqslant - 4 \\ - 4 \geqslant - 4[/tex]

Answer:

Timed test.

Step-by-step explanation:

An operational definition gives exactly what the independent variable means and its mode of measurement. The Independent variable is the variable in a research or experimental study which causes a change in the the measured variable. Hence, the independent variable is the predictor variable. In the study above, the independent variable is the timed test which is used to observe changes in the heart rate of the test taker (test anxiety). The change innheartrate of the test taker is the dependent variable.

Answer:

7 and 1 respectively

Step-by-step explanation:

1/7= 7 ) 1 (, the basic definition of division

Answer:

option A. twelve because hypotenuse angle is equal to perpendicular to the sum base

The function written in the rational form is, C. F(x) = (x - 5)/3x

Rational numbers are subsets of real numbers which can be written in the form of p/q, where q ≠ 0. As at q = 0 it is undefined.

Similarly, A rational expression is also written in the form of p/q, where p and q are algebraic expressions and q ≠ 0.

From the given options, F(x) is written in the form p/q,

Where, p = x - 5 and q = 3x.

Therefore, The rational function is, F(x) = (x - 5)/3x, where x ≠ 0.

As at x = 0 the function is undefined.

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Answer:

X = 50; Y = 50

Answers are the same by following the correct order of operations.

Step-by-step explanation:

This problem deals with the correct order of operations. Multiplication is done before addition.

22 * 2 + 6 = X

44 + 6 = X

X = 50

6 + 22 * 2 = Y

6 + 44 = Y

Y = 50

The answers are the same despite the order in which the operations were written since by following the correct order of operations, you must do the multiplication first in each chase.

Answer:

5

Step-by-step explanation:

median means the number in the middle

The question isn't well formatted ; however, from what can be deduced from the question posted :

Answer:

- 10.071

Step-by-step explanation:

Given the expression :

Solve for hhh: h-\left(-2.22\right)=-7.851h−(−2.22)=−7.851h, minus, left parenthesis, minus, 2, point, 22, right parenthesis, equals, minus, 7, point, 851 h =h=h, equals

Expressing Mathematically :

h - (- 2.22) = - 7.851

Opening the bracket :

h + 2.22 = - 7.851

Subtract 2.22 from both sides :

h + 2.22 - 2.22 = - 7.851 - 2.22

h = - 10.071

Explanation:

When multiplying fractions, we multiply the numerators together, and the denominators are handled separately.

The numerators in this case are -1 and 3. They multiply to -3

The denominators multiply to 2*4 = 8

So that's how we end up with -3/8 as the final answer

This fraction cannot be reduced any further, because 3 and have 8 no factors (other than 1) in common.

Answer:

C

Step-by-step explanation:

The center of the base is the center of the circle

The center of the circle is C

According to the information we can infer that the correct inequality that represents the given situation is D.) X - 27 < 400.

Let's break down the information provided: Steve gained some points, lost 27 points, and finished with less than 400 points. To represent the number of points Steve had initially, let's use 'X'.

Since he finished with less than 400 points, we can express this as X + G - 27 < 400.

According to the above we can conclude that the correct inequality that represents the given situation is D.) X - 27 < 400.

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Answer:

45.1

Step-by-step explanation:

m<A = 51°

For angle A, BC is the opposite leg.

AB is the hypotenuse.

sin A = opp/hyp

sin 51° = BC/58

BC = 58 * sin 51°

BC = 45.1

Answer:

True

Step-by-step explanation:

If you don't pay by the deadline, interest rate will contribute to your finance charge.

Answer:

Step-by-step explanation:

This is the problem we need to solve:

[tex]z=\frac{x_i-\bar{x}}{\sigma}[/tex] and we have everything but the z-score (which we find from a table) with our main unknown being the standard deviation.

If the probability that a random variable that is less than 11 is .67, we first have to find the z-score from the table that is closest to .67, and there are 2:

P(z < .43) = .66640 and P(z < .44) = .67003

We'll use z = .44

[tex].44=\frac{11-10}{\sigma}[/tex] and

[tex].44=\frac{1}{\sigma}[/tex] and

[tex]\sigma=\frac{1}{.44}[/tex] so

σ = 2.27 (check it; it works!)

Answer:

-3

Step-by-step explanation:

k/-11

Let k =33

33/ -11

-3

Answer:

-3

Step-by-step explanation:

33/-11 = -3

NOTE

division and multiplication = negative

addition and subtraction are a pair.

I hope this helped!

Answer:

Step-by-step explanation:

Xét tam giác DAB có: P là trung điểm AD, M là trung điểm AB

=> MP là đường trung bình của tam giác DAB => MP//BD và MP=[tex]\frac{1}{2}[/tex]BD  (1)

Xét tam giác DBC có: N là trung điểm DC, Q là trung điểm BC

=> QN là đường trung bình của tam giác DBC => QN//BD và QN=[tex]\frac{1}{2}[/tex]BD  (2)

Từ (1) và (2) => vecto MP song song cùng chiều với vecto QN

và độ dài MP = độ dài QN = [tex]\frac{1}{2}[/tex]BD

=> vecto MP = vecto QN

Tương tự xét các tam giác DAC và tam giác ABC => vecto MQ = vecto PN

Answer:

19

Step-by-step explanation:

Add 7 onto 12 to find answer.

Answer:

b = 19

Step-by-step explanation:

b = 12 + 7

Simplify 12+7 to 19.

Answer: No real solution

Step-by-step explanation:

Answer:

72

The result is rational because it can be written as the ratio of two integers and its decimal expansion can terminate or repeat.

Answered by GAUTHMATH

Answer:

y - 4 = 1/3 (x + 2)

3 y - 12 = x + 2

3y = x + 14

y = x / 3 + 14 / 3

Using y = m x + b    as the equation for a standard line

We see that equation represents a line with slope of 1/3

When x = 0  the y-intercept is 14 /3