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2 years ago

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The minimum length L of a highway sag curve can be computed by where θ 1 is the downhill grade in degrees (θ 1 < 0°), θ 2 is

the uphill grade in degrees (θ 2 > 0°), S is the safe stopping distance for a given speed limit, h is the height of the headlights, and α is the alignment of the headlights in degrees. Compute L for a 55-mph speed limit, where and Round your answer to the nearest foot.

1 answer:

8_murik_8 [283]2 years ago

5 0

Answer:

The answer to the nearest foot is = 15 feet

Step-by-step explanation:

Solution

The first set taken is to Compute L for a 55-mph speed limit

Given that

L =(θ2 -θ1)/200 (h +S Tan ∝) =

= ( u + 5) 336²/200 (1.9 +336 tan 0.7°)

= 9° (336)²/200 (1.9 +336 tan 0.7°) = 14.7652094

= 15 feet { 9° = 9*π/180 = π/20}

Note: Kindly find an attached image for the complete question given and answered

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(b) For those values of k, verify that every member of the family of functions y = A sin(kt) + B cos(kt) is also a solution. y =

frutty [35]

Answer:

Check attachment for complete question

Step-by-step explanation:

Given that,

y=Coskt

We are looking for value of k, that satisfies 4y''=-25y

Let find y' and y''

y=Coskt

y'=-kSinkt

y''=-k²Coskt

Then, applying this 4y'"=-25y

4(-k²Coskt)=-25Coskt

-4k²Coskt=-25Coskt

Divide through by Coskt and we assume Coskt is not equal to zero

-4k²=-25

k²=-25/-4

k²=25/4

Then, k=√(25/4)

k= ± 5/2

b. Let assume we want to use this

y=ASinkt+BCoskt

Since k= ± 5/2

y=A•Sin(±5/2t)+ B •Cos(±5/2t)

y'=±5/2ACos(±5/2t)-±5/2BSin(±5/2t)

y''=-25/4ASin(±5/2t)-25/4BCos(±5/2t

Then, inserting this to our equation given to check if it a solution to y=ASinkt+BCoskt

4y''=-25y

For 4y''

4(-25/4ASin(±5/2t)-25/4BCos(±5/2t))

-25A•Sin(±5/2t)-25B•Cos(±5/2t).

Then,

-25y

-25(A•Sin(±5/2t)+ B •Cos(±5/2t))

-25A•Sin(±5/2t) - 25B •Cos(±5/2t)

Then, we notice that, 4y'' is equal to -25y, then we can say that y=Coskt is a solution to y=ASinkt+BCoskt

4 0

2 years ago

Translate triangle a by vector (-3/1)to give triangle b. Then rotate your triangle b 180 degrees around the origin to give trian

Dmitrij [34]

Answer:

Rotation of triangle A across a point (1.5, -0.5) by 180°.

Step-by-step explanation:

Translation of a figure about a vector $\binom{-3}{1}$ means translation of a figure by 3 units to the left on x-axis and 1 unit in the positive direction of the y-axis.

Rule for the translation will be,

(x, y) → [(x - 3), (y + 1)]

From the figure attached,

Vertices of the triangle A are A(1, -1), B(1, -4) and C(3, -4)

After translation new image points will be A'(-2, 0), B'(-2, -3), C'(0, -3).

After rotation of these image points 180° about the origin will be,

Rule for the rotation,

(x, y) → (-x, -y)

A'(-2, 0) → A"(2, 0)

B'(-2, -3) → B"(2, 3)

C'(0, -3) → C"(0, 3)

Therefore, A(1, -1) → A"(2, 0) is the single transformation.

Rule for this transformation which maps triangle C to A will be defined by,

Rotation of triangle A across a point (1.5, -0.5) by 180°.

8 0

2 years ago

Suppose that 20% of the adult women in the United States dye or highlight their hair. We would like to know the probability that

Rasek [7]

Answer:

71.08% probability that pˆ takes a value between 0.17 and 0.23.

Step-by-step explanation:

We use the binomial approxiation to the normal to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

In this problem, we have that:

$p = 0.2, n = 200$ . So

$\mu = E(X) = np = 200*0.2 = 40$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{200*0.2*0.8} = 5.66$

In other words, find probability that pˆ takes a value between 0.17 and 0.23.

This probability is the pvalue of Z when X = 200*0.23 = 46 subtracted by the pvalue of Z when X = 200*0.17 = 34. So

X = 46

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{46 - 40}{5.66}$

$Z = 1.06$

$Z = 1.06$ has a pvalue of 0.8554

X = 34

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{34 - 40}{5.66}$

$Z = -1.06$

$Z = -1.06$ has a pvalue of 0.1446

0.8554 - 0.1446 = 0.7108

71.08% probability that pˆ takes a value between 0.17 and 0.23.

6 0

2 years ago

Gareth has $2,000 to invest. Putting the money in a savings account at his local bank will earn him 2.2% annual interest and giv

Alenkinab [10]

Answer:

Option c. 18 withdrawals is correct

Step-by-step explanation:

Gareth has to invest = $2,000

His local bank gives 2.2% annual interest and gives him the ability to make ATM withdrawals without any charges.

In an online savings gives 4.85% annual interest, but charges $3 every time he makes an ATM withdrawal.

Let us find the amount of interest earned from the local bank.

The amount of interest earned from Local Bank = 2.2% of 2000

= $\frac{22}{100}$ × 2000

= 0.022 × 2000 = $44

The amount of interest earned from online savings = 4.85% of 2000

= $\frac{4.85}{100}$ × 2000

= 0.0485 × 2000 = $97

As it is given that savings account has no ATM withdrawal charges but online savings account charge $3.00 per withdrawal.

so we need to make x withdrawals from both accounts such that:

97 - 3x = 44

Let us solve for x.

Upon subtracting 97 from both sides of or equation we will get,

97 - 97 - 3x = 44 - 97

3x = -53

$\frac{3x}{-3}=\frac{-53}{-3}$

x = 17.666 rounded to 18

Therefore, Gareth must make 18 ATM withdrawals every year for the local savings account to be a better deal than the online savings account.

4 0

2 years ago

ou have two parents, four grandparents, eight great-grandparents, and so forth. (a) If all your ancestors were distinct, what wo

Maslowich

Answer:

Part A:

$2^{40}-2\\=1.0995*10^{12} ancestors$

Part B:

Generations Age=25*39=975 years

Part C:

Some ancestors on different branches of the family tree must be the same.
There could not have been 39 generations in my line of ancestry.

Step-by-step explanation:

Given Data:

Two Parents, Four Grand Parents, Eight great Grand Parents.

Generation=39

Solution:

Part A:

From given data Following series is made:

$2+2^2+2^3+.........+2^{39}$

Now, Above series will become:

$2[1+2+2^2+......+2^{38}]$

From geometric Sequence:

$2[\frac{2^{38+1}-1}{2-1} ]$

$2^{40}-2\\=1.0995*10^{12} ancestors$

Part B:

Generations Age=years*Number of generations

Generations Age=25*39=975 years

Part C:

Number of people lived= 10^11

Ancestors= $1.0995*10^{12} ancestors$

$10^{11}$

It means ancestors are not distinct, it means:

Some ancestors on different branches of the family tree must be the same.
There could not have been 39 generations in my line of ancestry.

5 0

2 years ago