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3 years ago

6

Angle of 74° with the ground if the foot of the latter 6.5 feet from the wall, how high on the wall is the ladder?

1 answer:

Pie3 years ago

7 0

Tanα=h/x

h=xtanα, we are told that x=6.5ft and α=74° so

h=6.5tan74 ft

h≈22.67 ft (to nearest hundredth of a foot)

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zloy xaker [14]

Answer:

15 degrees

Step-by-step explanation:

90-75= 15

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6 0

3 years ago

A space telescope on a mountaintop is housed inside of a cylindrical building with a hemispheric dome. If the circumference of t

Vlad1618 [11]

Answer:

$185553.7\text{ feet}^3$

Step-by-step explanation:

GIVEN: A space telescope on a mountaintop is housed inside of a cylindrical building with a hemispheric dome. If the circumference of the dome is $84\text{ feet}$ , and the total height of the building up to the top of the dome is $91\text{ feet}$ .

TO FIND: what is the approximate total volume of the building.

SOLUTION:

let the height of the mountaintop be $h\text{ feet}$

As the dome hemispherical.

circumference of a hemisphere $=\frac{1}{2}\times2\pi\times radius$

$=\pi\times radius$

$\frac{22}{7}\times radius=84$

$radius=26.75\text{ feet}$

total height of the building up to the top of the dome $=\text{radius of hemisphere}+\text{height of mountaintop}$

$=26.75+h=91$

$h=64.25\text{ feet}$

Volume of building $=\text{volume of cylindrical mountaintop}+\text{volume of dome}$

$=\pi(radius)^2h+\frac{2}{3}\pi(radius)^3$

as radius of mountain top is same as dome

putting values

$=3.14(26.75)^264.75+\frac{2}{3}3.14(26.75)^3$

$=145484.6+40069.1$

$185553.7\text{ feet}^3$

Hence the total volume of the building is $185553.7\text{ feet}^3$

5 0

3 years ago

Pls help fast 10 points instead of 5

Elodia [21]

Stop capping its 5 points

4 0

2 years ago

For what values of x does 25 Superscript x Baseline = 5 Superscript x squared minus 3?

umka2103 [35]

For this case we have the following equation:

$25^{x} = 5^{ x^2-3}$

Rewriting we have:

$5^{2 (x)} = 5^{ x^ 2-3}\\5^{ 2x} = 5^{ x^ 2-3}$

For expressions to be equal, exponents must be equal. So:

$2x = x ^ 2-3\\x ^ 2-2x-3 = 0$

To factor, we look for two numbers that, when multiplied, result in -3 and when added, result in -2. These numbers are -3 and 1.

$(x-3) (x + 1) = 0$

Thus, the roots are:

$x_ {1} = 3\\x_ {2} = - 1$

Answer:

$x_ {1} = 3\\x_ {2} = - 1$

8 0

3 years ago

What is the solution of the equation 4[x + 2(3x – 7)] = 22x – 65?

Arisa [49]

Answer: x=-3/2

Step-by-step explanation:

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3 years ago