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3 years ago

7

A 400 foot rope is extended from the ground to the top of a building. The building is 35 ft tall. What is the angle made by the

rope with respect to the ground?

1 answer:

velikii [3]3 years ago

3 0

Answer:

The angle is $5.0^{0}$ .

Step-by-step explanation:

The building is 35 feet tall, and the rope is 400 feet long.Applying the trigonometric function, we have;

Sin θ = $\frac{opposite}{hypotenuse}$

The height of the building represents the opposite side, while the length of the rope represents the hypotenuse. Thus;

Sin θ = $\frac{35}{400}$

Sin θ = 0.0875

θ = $Sin^{-1}$ 0.0875

= $5.02^{0}$

The angle made by the rope with respect to the ground is approximately $5.0^{0}$ .

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A binary operation is defined on the set of real numbers ℝ by

zloy xaker [14]

Answer:

I. m = 2401

II. ((n+1) ∆ y)/n = 1/n[(n – y + 2)(n – y) + 1]

Step-by-step explanation:

I. Determination of m

x ∆ y = x² − 2xy + y²

2 ∆ − 5 = √m

2² − 2(2 × –5) + (–5)² = √m

4 – 2(–10) + 25 = √m

4 + 20 + 25 = √m

49 = √m

Take the square of both side

49² = m

2401 = m

m = 2401

II. Simplify ((n+1) ∆ y)/n

We'll begin by obtaining (n+1) ∆ y. This can be obtained as follow:

x ∆ y = x² − 2xy + y²

(n+1) ∆ y = (n+1)² – 2(n+1)y + y²

(n+1) ∆ y = n² + 2n + 1 – 2ny – 2y + y²

(n+1) ∆ y = n² + 2n – 2ny – 2y + y² + 1

(n+1) ∆ y = n² – 2ny + y² + 2n – 2y + 1

(n+1) ∆ y = n² – ny – ny + y² + 2n – 2y + 1

(n+1) ∆ y = n(n – y) – y(n – y) + 2(n – y) + 1

(n+1) ∆ y = (n – y + 2)(n – y) + 1

((n+1) ∆ y)/n = [(n – y + 2)(n – y) + 1] / n

((n+1) ∆ y)/n = 1/n[(n – y + 2)(n – y) + 1]

7 0

3 years ago

What is the domain of y=3^x-2 +1

mel-nik [20]

Answer:

x∈R

Step-by-step explanation:

4 0

3 years ago

A 10-yr-old competes in gymnastics. For several competitions, she received the following "All-Around" scores: 35.5, 36.3. 36.6,

Delicious77 [7]

Answer:

The child needs a score of 37.2 to move up to the next level of the competition.

Step-by-step explanation:

The mean is the sum of all scores divided by the number of competions. So

$M = \frac{S}{T}$

In which S is the sum of all her scores and T is the number of competitions.

The child has five competions:

Which means that $T = 5$

She has to get a mean of at least 36.5, so $M = 36.5$

Her scores are: 35.5, 36.3. 36.6, and 36.9. Her last score, i am going to call x. So

$S = 35.5 + 36.3 + 36.6 + 36.9 + x = 145.3 + x$

The child needs a score of _____ to move up to the next level of the competition.

This score is x. So

$M = \frac{S}{T}$

$36.5 = \frac{145.3 + x}{5}$

$145.3 + x = 36.5*5$

$x = 37.2$

3 0

3 years ago

A study of 25 graduates of 4-year public colleges revealed the mean amount owed by a student in student loans was $55,051. The s

Harman [31]

Answer:

Step 1

The data represent amount.

A 90% confidence interval for the population mean is,

First, compute t-critical value then find confidence interval.

The t critical value for the 90% confidence interval is,

The sample size is small and two-tailed test. Look in the column headed and the row headed in the t distribution table by using degree of freedom is,

The t critical value for the 90% confidence interval is 1.711.

A 90% confidence interval for the population mean is .

Step 2

It is reasonable to conclude that mean of the population is actually $55000 due to a 90% confidence intrerval for population mean is between $52461.23 and $57640.77 does include $55000.

The data represent amount.

A 90% confidence interval for the population mean is,

First, compute t-critical value then find confidence interval.

The t critical value for the 90% confidence interval is,

The sample size is small and two-tailed test. Look in the column headed and the row headed in the t distribution table by using degree of freedom is,

The t critical value for the 90% confidence interval is 1.711.

A 90% confidence interval for the population mean is .

It is reasonable to conclude that mean of the population is actually $55000 due to a 90% confidence intrerval for population mean is between $52461.23 and $57640.77 does include $55000.

5 0

2 years ago

What 2 numbers add to get 2 and multiply to 4

rusak2 [61]

Factor 4
4=1 times 4
2 times 2
they don't add to 2
set up equation
x+y=2
xy=4

first equation, subtract x from both sides
y=2-x
subsitute for y
x(2-x)=4
distribute
2x-x^2=4
add x^2
2x=x^2+4
subtract 2x
0=x^2-2x+4
use quadratic formula which is
if you have ax^2+bx+c=0 then
x= $\frac{ -b+/-\sqrt{b^{2}-4ac} }{2a}$ so

1x^2-2x+4=0
a=1
b=-2
c=4
x= $\frac{ -(-2)+/-\sqrt{(-2)^{2}-4(1)(4)} }{2(1)}$
x= $\frac{ 2+/-\sqrt{4-16} }{2}$
x= $\frac{ 2+/-\sqrt{-12} }{2}$
we have $\sqrt{-12}$ and that doesn't give a real solution
therefor there are no real solutions
but if you want to solve fully
x= $\frac{ 2+/-2\sqrt{-3} }{2}$
i= $\sqrt{-1}$
x= $\frac{ 2+/-2i\sqrt{3} }{2}$
x= $1+/-i\sqrt{3}$
x= $1-i\sqrt{3}$ or x= $1+i\sqrt{3}$ (those are the 2 numbers)

6 0

3 years ago