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3 years ago

Is the number 1.0303 a rational number, whole number, or integer?

2 answers:

6 0

IT is an rational number because a whole number is a number with no decimal part, an integer is a natural number with no decimal part that could be either negative or positive. Since the number does not have a decimal part, it is rational.

DENIUS [597]3 years ago

4 0

It would be a rational number cause the number is a decimal.
I hope that helped.

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The angle of elevation of the top of a pole as seen from a point 13 ft away from the base is double its angle of elevation as se

spayn [35]

The height of the pole above the level of the observer's eyes is 31.42 ft

Let the angle of elevation of the top of the pole from a point 47 ft away be α.

Let the angle of elevation of the top of the pole from the point 13 ft away be β.

Since the angle of elevation of a point 13 feet away is twice that from 47 ft away, we have that β = 2α.

If the height of the pole above the level of the observer's eye is h, we have that

tanβ = tan2α = h/13 and tanα = h/47

From trigonometric identities tan2α = 2tanα/(1 - tan²α)

Substituting the values of the variables into the equation, we have

tan2α = 2tanα/(1 - tan²α)

h/13 = 2h/47 ÷ [1 - (h/47)²]

Dividing through by h, we have

1/13 = 2/47 ÷ [1 - (h/47)²]

Cross-multiplying, we have

1/13 = 2/47 ÷ [1 - (h/47)²]

1 - (h/47)² = 2/47 × 13

1 - (h/47)² = 26/47

(h/47)² = 1 - 26/47

(h/47)² = (47 - 26)/47

(h/47)² = 21/47

Taking square-root of both sides, we have

h/47 = √(21/47)

Cross-multiplyng, we have

h = √(21/47) × 47

h = √(21 × 47)

h = √987

h = 31.42 ft

The height of the pole above the level of the observer's eyes is 31.42 ft

Learn more about height of a pole here:

brainly.com/question/10375496

4 0

2 years ago

Suppose you'd like to save enough money to pay cash for your next car. The goal is to save an extra $28,000 over the next 6 year

Anna35 [415]

Given:

• Amount to save, A = $28,000

• Time, t = 6 years

• Interest rate, r = 5.3% ==> 0.053

• Number of times compounded = quarterly = 4 times

Let's find the amount that must be deposited into the account quarterly.

Apply the formula:

$FV=P(\frac{(1+\frac{r}{n})^{nt}-1}{\frac{r}{n}})$

Where:

FV is the future value = $28,000

r = 0.053

n = 4

t = 6 years

Thus, we have:

$28000=P(\frac{(1+\frac{0.053}{4})^{4\times6}-1)}{\frac{0.053}{4}}$

Let's solve for P.

We have:

$\begin{gathered} 28000=P(\frac{(1+0.01325)^{24}-1}{0.01325}) \\ \\ 28000=P(\frac{(1.01325)^{24}-1)^{}}{0.01325}) \\ \\ 28000=P(\frac{1.371509114-1}{0.01325}) \\ \\ 28000=P(\frac{0.371509114}{0.01325}) \end{gathered}$

Solving further: