A 92-ft tree casts a shadow that is 120 ft long. What is the angle of elevation of the sun?

Answer:

[tex]\mathbf{ - \dfrac{3 \pi^2}{2}}[/tex]

Step-by-step explanation:

Given that:

F(x, y, z) = 5xi - 5yj - 3zk

The objective is to evaluate the [tex]\int _c F \ dr .C[/tex]

and C is given by the vector function  r(t) = (sin t, cost, t) where  0 ≤ t ≤ π

[tex]F(r(t)) = 5 \ sint \ i - 5 \ cost \ j - 3t \ k[/tex]

∴

[tex]\int_c F . \ dr = \int ^{\pi}_{0} ( 5 \ sint \ i - 5 cos t \ j - 3 t \ k ) ( cos \ t , - sin \ t , 1 ) \ dt[/tex]

[tex]=\int ^{\pi}_{0} ( 5 \ sint \ cost+ 5 cos t \ sin t - 3 t) dt[/tex]

[tex]=\int ^{\pi}_{0} ( 10 \ sint \ cost) \ dt -3 \int ^{\pi}_{0} \ dt[/tex]

[tex]= \int ^{\pi}_{0} ( 10 \ sint \ cost) \ dt - 3 [\dfrac {t^2}{2}]^{\pi}_{0} \ \ dt[/tex]

[tex]= 10 [\dfrac{sin^2 \ t}{2}]^{\pi}_{0} - \dfrac{3}{2}(\pi)^2[/tex]

By dividing 2 with 10 and integrating [tex]= 10 [\dfrac{sin^2 \ t}{2}]^{\pi}_{0}[/tex]; we have:

[tex]=5(sin^2t -sin^2 0) -\dfrac{3 \pi^2}{2}[/tex]

[tex]=5(0) -\dfrac{3 \pi^2}{2}[/tex]

[tex]= 0 - \dfrac{3 \pi^2}{2}[/tex]

[tex]\mathbf{= - \dfrac{3 \pi^2}{2}}[/tex]

Answer:

  -7

Step-by-step explanation:

As x increases by 1, y decreases by 7, so the "rise"/"run" is ...

  slope = rise/run = -7/1 = -7

*Correct Question:

Based on the similar triangles shown below, Theodore claims that ∆TUV is transformed to ∆WXY with a scale factor of 3/2. Is Theodore correct?

A. Yes, the triangles are similar with a scale factor of 3/2.

B. No, the triangles are similar with a scale factor of 2/1.

C. No, the triangles are similar with a scale factor of 2/3.

D. No, the triangles are similar with a scale factor of 4/3.

Answer:

C. No, the triangles are similar with a scale factor of 2/3.

Step-by-step explanation:

∆TUV is the original triangle. After transformation, the size reduced to give us ∆WXY. This means ∆TUV was reduced by a scale factor to give ∆WXY. The scale factor should be a fraction, suggesting, the original size of the ∆ was reduced upon transformation.

Thus, the ratio of their corresponding sides = the scale factor.

This is: [tex] \frac{8}{12} = \frac{16}{24} = \frac{12}{18} = \frac{2}{3} [/tex]

If you multiply the side length of ∆TUV by ⅔, you'd get side length of ∆WXY.

So, Theodore is wrong.

Answer: -2

Step-by-step explanation:

-2 - 7 = -9

Answer:

[tex]\Huge \boxed{c=-2}[/tex]

Step-by-step explanation:

[tex]c-7=-9[/tex]

We need to isolate the [tex]c[/tex] variable on one side of the equation.

Adding 7 to both sides of the equation.

[tex]c-7+7=-9+7[/tex]

Simplifying the equation.

[tex]c=-2[/tex]

Answer: Find answer in the attached file

Answer:

the probability that a randomly chosen test-taker will score 142 or lower = 0.8643

Step-by-step explanation:

We are given;

Data point; x = 142

Mean; μ = 153

Standard deviation; σ = 10

So,let's find the z-score using;

z = (x - μ)/σ

z = (142 - 153)/10

z = -1.1

From the z-distribution table attached, the probability is;

P(z < -1.1) = 1 - 0.13567 ≈ 0.8643

Answer:

The answer is

Step-by-step explanation:

To find an equation of a line given a point and slope we use the formula

y - y1 = m(x - x1)

where

m is the slope

(x1 , y1) is the point

From the question

slope = 4

point = ( 3 , - 2)

Substitute the values into the above formula

We have

Hope this helps you

Answer:

y+

Step-by-step explanation:

Point-Slope form- (y − y 1) = m ⋅ (x − x 1)

Slope: m = 4

Point: (x1, y1) = (3, -2)

Answer: y + 2 = 4 ⋅ (x - 3)

Answer:

The  value  is   [tex]\left 35 } \atop }} \right. P_3 = 39270[/tex]

Step-by-step explanation:

From the question we are told that

    The  total number of cars is  [tex]n = 35[/tex]

     The  number cars considered is  [tex]r = 3[/tex]

Generally the number of different top three finishes possible for this race of 35 cars  is mathematically represented as

       [tex]\left n } \atop }} \right. P_r = \frac{n!}{(n - r) !}[/tex]

       [tex]\left 35 } \atop }} \right. P_3 = \frac{35! }{(35 - 3) !}[/tex]

       [tex]\left 35 } \atop }} \right. P_3 = \frac{35 * 34 * 33 * 32! }{32 !}[/tex]

       [tex]\left 35 } \atop }} \right. P_3 = 39270[/tex]

Answer:

tan (thita) = 35/13

Step-by-step explanation:

Tan( angle) = opposite/ adjacent

Tan( angle) = 35/13

Angle = arc tan 35/13

Angle = 69.624 degrees

Round the answer as needed.

Step-by-step explanation:

a variable is a quantity that may change within the context of a mathematical problem or experiment

I hope this was helpful

Answer:

3.04

Step-by-step explanation:

Given the prediction equation:

y_hat = 145.5 -5.5*x

- - - - x - - - - - - - - - у

1 - - 10.36 - - - - 87.87

2 - - 9.96 - - - - 89.83

3 - - 12.50 - - - - 71.61

1) y_hat = 145.5 -5.5*(10.36)

y_hat = 145.5 - 56.98 = 88.58

2) y_hat = 145.5 -5.5*(9.96)

y_hat = 145.5 - 54.78 = 90.72

3) y_hat = 145.5 -5.5*(12.50)

y_hat = 145.5 - 68.75 = 76.75

Root mean squared error (RMSE) :

Number of observations (n) = 3

√(Σ(y_hat - y)^2) / n

y_hat = predicted value

y = actual value

Σ[(88.58-87.87)^2+(90.72-89.83)^2+(76.75-71.61)]

Σ(0.71^2) + (0.89^2) + (5.14^2)

27.7158 / 3 = 9.2386

√9.2386

= 3.0395065

= 3.04

Answer:

2

Step-by-step explanation:

-7 - (-8) = 1

1 + (-3) = -2

-2 + 6 = 4

4 - 2 = 2

Answer:

2

Step-by-step explanation:

Start by removing the parentheses appropriately:

-(-8) = +8, and

+(-3) = -3

Then

-7 - (-8) + (-3) + 6 - 2  =  -7 + 8 - 3 + 6 - 2

Now, working from left to right, we perform the indicated operations:

-7 + 8 comes out to 1, and so we have 1 - 3 + 6 - 2.

Continuing, we get -2 + 6 - 2, or 4 - 2, or 2

Answer:

24,300

Step-by-step explanation:

So on Thursday you have 300 next day it's 900 bc 300x3=900

Friday: 900x3=2,700

Saturday: 2,700x3=8,100

Sunday: 8,100x3=24,300

Answer:

b = [tex]\frac{ln190}{ln200}[/tex]

Step-by-step explanation:

Using the rule of logarithms

log [tex]x^{n}[/tex] ⇔ nlogx

Given

190 = [tex]200^{b}[/tex] ( take the natural log ln of both sides )

ln190 = ln[tex]200^{b}[/tex] = bln200 ( divide both sides by ln200 )

[tex]\frac{ln190}{ln200}[/tex] = b

Answer to part (a) is: 33 degrees

Answer to part (b) is: 5 meters

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

Explanation:

Check out the diagram below.

For now, focus only on triangle ABC. The ladder is segment AC = 10. We first need to find the length of [tex]AB = h_1[/tex] which is the initial height of the ladder.

sin(angle) = opposite/hypotenuse

sin(70) = h/10

h = 10*sin(70)

h = 9.396926 approximately

Subtract off 4 since the ladder slips 4 meters down the wall

h-4 = 9.396926-4

h-4 = 5.396926

which is the new height the ladder reaches. The hypotenuse stays the same

sin(angle) = opposite/hypotenuse

sin(theta) = 5.396926/10

theta = arcsin(5.396926/10)

theta = 32.662715

theta = 33 degrees when rounding to 2 significant figures

This is the value of [tex]\theta_2[/tex] in the diagram below.

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

We'll use the cosine rule with the old theta value [tex]\theta_1[/tex]

cos(angle) = adjacent/hypotenuse

cos(70) = x/10

x = 10*cos(70)

x = 3.420201 is the approximate distance the foot of the ladder is from the wall. This is before the ladder slips.

After the ladder slips, we use the new angle value [tex]\theta_2[/tex]

cos(angle) = adjacent/hypotenuse

cos(32.662715) = x/10

x = 10*cos(32.662715)

x = 8.418622

Subtract the two x values

8.418622-3.420201 =  4.998421

which gives the approximate distance the foot of the ladder moved (the distance from point C to point E in the diagram)

This rounds to 5.0 or simply 5 when rounding to 2 significant figures.

Answer:

[tex] {\sqrt[ 3 ]{x^{2} } }•{ \sqrt[4] {{y}^{3}} }[/tex]

Explanation-

As,

[tex]a^{\frac{1}{n} } = \sqrt[n]{a} [/tex]

and

[tex]a^{-n}=1/a^n[/tex]

Answer:

C

Step-by-step explanation:

Note that the right triangle has two tick marks.

This means that the sides are equivalent.

Therefore, this is a 45-45-90 triangle.

In a 45-45-90 triangle, the side lengths are n, and the hypotenuse is n√2

Since n is 5√2, then the hypotenuse x is n√2. Thus:

[tex]x=n\sqrt2\\x=(5\sqrt2)\sqrt2[/tex]

Simplify:

[tex]x=5(2)=10[/tex]

The answer is C :)

Answer:

RU = 9

ST = 3

Step-by-step explanation:

RT = 6

RS = ST = (1/2)RT = (1/2)(6) = 3

ST = 3

RU = 3ST = 3 * 3 = 9

Answer:

B. 0.58 + 1.48h

Step-by-step explanation:

h+0.48h+0.58

=(1h+0.48h)+0.58

=1.48h +0.58

Answer:

c. 48 packages

d. Possibilities:

1 x 28 = 28

2 x 14 = 28

4 x 7 = 28

7 x 4 = 28

14 x 2 = 28

28 x 1 = 28

Possible combinations:

17, 1, 28

17, 2, 14

17, 4, 7

17, 7, 4

17, 14, 2

17, 28, 1

Step-by-step explanation:

c. 127 employees get 3 uniforms each, meaning a total of 127 * 3 = 381 uniforms

The uniforms come in packs of 8, so dividing 381 by 8, we get:

381/8 = 47.625

However, you probably can't order a portion of a package, so you must round up to 48 packages. There will be 3 uniforms left over.

d. The divisors of 28 are 1, 2, 4, 7, 14, and 28. All I did was enumerate the six possibilities.

Answer:

Option D.

Step-by-step explanation:

We need to find the circumstances that would likely make factoring the best method for solving a quadratic equation.

A quadratic equation is prime if its factors can not possible. So, option A is incorrect.

In a quadratic equation leading coefficient can not be zero. So, option B is incorrect.

For large numbers (coefficient or constant), quadratic formula is best method. So, option C is incorrect.

The difference of 2 perfect squares is:

[tex]x^2-a^2=(x-a)(x+a)[/tex]

In this case factoring is the best method.

Therefore, the correct option is D.

Answer:

14.74%

Step-by-step explanation:

The formula for ANNUAL PERCENTAGE YIELD (APY) for an account that is COMPOUNDED CONTINUOUSLY is given as

APY = Pe^rt - 1

Where P = Principal

e = exponential

r = rate

t = time

Since Principal and Time was not given in the question,

APY = e^r - 1

r = 13.75% = 0.1375

APY = e^0.1375 - 1

APY = 1.147401706 - 1

APY = 0.147401706

Converting to percentage

= 0.147401706 × 100

= 14.7401706%

Approximately to 2 decimal places: 14.74%

Therefore, the annual percentage yield is 14.74%

Answer: y = 3x + 7

Step-by-step explanation:

Since we are given the slope and y intercept we could write the equation in slope intercept form as y=mx +b .Only m and b are needed to write the equation.M is the slope and B is the y intercept.

Answer:

y=3x+7

Step-by-step explanation:

The equation of a line in slope-intercept form is:

y=mx+b

where m is the slope and b is the y-intercept.

We know the slope is 3, so we can substitute 3 in for m.

y=3x+b

We also know the y-intercept is (0,7). When writing the equation of a line in this form, we can ignore the x-coordinate of 0. Therefore, the y-intercept is also just 7. Substitute 7 in for b.

y=3x+7

The equation of a line with a slope of 3 and a y-intercept of (0,7) is y=3x+7

Answer:

7

Step-by-step explanation:

Given the following data:

Average speed : 60.5, 63.2, 54.7, 51.6, 72.3, 70.7, 67.2, and 65.4

To construct a one-sample t - statistic, the value of the degree of freedom will be ;

In a one sample test of known mean, if the number of observations are 4, one can choose to vary at most three of the observations and still obtain the mean, that is the 4th observation must remain fixed.

Degree of freedom = Number of observations (n) - 1. This is the maximum number of independent variables which can be varied.

Nunber of observations or sample size in the data above is 8

Hence,

Degree of freedom = (8 - 1) = 7

Answer:the anwser is 7

Step-by-step explanation:

Answer:

6:8 and 9:12

Step-by-step explanation:

The equivalent ratios of the given quantity of silver parts of paint to green which is 3:4 are: 6:8 and 9:12.

When compared to one another, equivalent ratios are defined as having the same values.

For example, 8/16, 4/8 and 1/2 re equivalent ratios because:

Given:

The table that shows the ratio of the number of parts silver to number of parts green as 3 parts silver to 4 parts green, then

ratio = 3:4.

This means that for 3 parts of silver paint, we would require 4 parts of green paint to give the shade of paint that is needed.

so,

6/8 = 3/4

9/12 = 3/4

Thus, 6/8 = 9/12 = 3/4, which is equivalent.

Hence, the ratios that are equivalent to 3 parts silver paint to 4 parts green paint are: 6:8 and 9:12.

Learn more about equivalent ratios here:

brainly.com/question/13513438

#SPJ2

Answer:

That's my slovings for your question

Answer:

x = 100

Step-by-step explanation:

All you need is contained in the sheet attached

Answer:

x = 100

Step-by-step explanation:

3 log2(x) - 2 log2(5x) = 2

We know that a log(c) = log c^a

log2(x)^3 - log2(5x)^2 = 2

log2(x^3) - log2(25x^2) = 2

We know that log a - log b = log a/b

log2(x^3 /25x^2) = 2

Simplify

log2(x /25) = 2

Raise each side to  base 2

2^log2(x /25) = 2^2

x/25 = 4

Multiply each side by 25

x = 4*25

x = 100

Answer:

y= -207

Step-by-step explanation:

61 = 268 + y

Collect like terms

y= 61 - 268

Simplify

= -207

y= -207

Alternatively,

61 = 268 + y

Subtract 268 from both sides

61 - 268 = 268 + y - 268

-207 = y

Therefore,

y= -207