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jeyben [28]
3 years ago
13

A boat is 104 feet from the base of cliff. If the distance from the top of the cliff to the boat is 26 less than twice the heigh

t of the cliff to the water. Find the height of the cliff. Round to the nearest tenth of a foot if necessary. ​
Mathematics
1 answer:
bearhunter [10]3 years ago
6 0

Answer: h = 68.5, 51.2

Step-by-step explanation:

Draw a right angle triangle. The base is the sea and the line perpendicular to it is the cliff  

The base is the distance of from boat to the cliff is 104

Let the height of the cliff be h.

The hypotenuse, the distance from the top of the cliff to the boat is therefore 2h-26

Pythagoras tells us that  

(2h−26)^2  = 104^2 + h^2

4h^2 − 52h + 289 = 10816 + h^2

3h^2 − 52h − 10527 = 0

h=68.5, 51.2

The other result is negative and therefore not relevant.

If you cannot factorize then solve using the formula.

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Which statements accurately describe the function f(x) = 3(16)^3/4? Check all that apply.
uysha [10]

Answers:

These are the statements that apply:

The initial value is 3.

The range is y >0.

The simplified base is 8.

Explanation:

1) Given expression:

f(x)=3(16)^{\frac{3}{4} x

2) Check every statement:

a) The initial value is 3?

initial value ⇒ x = 0 ⇒

f(0)=3(16)^{0}=3(1)=3

∴ The statement is right.

b) The initial value is 48?

Not, as it was already proved that it is 3.

c) The domain is x > 0?

No, because the domain of the exponential functions is all the Real numbers.

d) The range is y > 0?

That is correct, the exponential function is continuous, and monotonon increasing.

The limit when x → - ∞ is zero, but y never reaches zero, and the limit when x → ∞ is + ∞, meaning that the range is y > 0.

e) The simplified base is 12?

This is how you simplify the base:

3(16)^{\frac{3}{4} x}=3{{(16}^{(3/4)})}^x=3(16^{3/4}})^{x}=3((2^4)^{3/4})^x=3(2^3)^x=3(8)^x

Which shows that the simplified base is 8 (not 12).

f) The simplified base is 8?

Yes; this was just proved.

6 0
3 years ago
Read 2 more answers
Which expression represents the perimeter of the
Svetllana [295]
Answer: 15x + 6
5x + 2x+3 = 7x+3
6x+4 + 7x+3 = 13x + 7
13x+7 + 2x-1 = 15x+ 6
5 0
3 years ago
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Shalnov [3]
Have fun but I think it is b and e
5 0
3 years ago
Read 2 more answers
Please help
dsp73

Answer:

$147,848.5

Step-by-step explanation:

Fixed rate =7.35%

Mortgage Loan= $685,000

Selling price=$782,000

Property tax paid= $14,578.15

Therefore,

Prorated Amount Owed= Outstanding balance on the house + Interest paid on the loan for the year

Prorated Amount Owed=(782500-685000)+7.35% of 685000

=97500+50347.5

=$147,847.5

3 0
3 years ago
on saturday you bowl at mar vista bowl where renting shoes costs $2 and each game bowled is $3.50.on sunday you bowl at pinz whe
Vlad1618 [11]

Answer:

Let x= number of games bowled.

Amount spent at Vista Bowl=2+3.5x

Amount spent at Pinz Bowl=5+3.25x

Setting these two equations equal to each other and solving for x will give you the number of games you can bowl to make the cost the same:

                             2+3.5x=5+3.25x             setting equations equal

                             3.5x-3.25x=5-2               combining like terms

                             0.25x=3                          simplify

                             (1/4)x=3                         changing decimal into a fraction

                             x=(3)(4)                         multiply both sides by 4 to isolate the x

                             x=12                              answer

Step-by-step explanation:

3 0
3 years ago
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