What is the equation of a vertical line passing through (−5, −2)? a: x = −5 b: x = −7 c: y = −3 d: y = −2

The following picture is a square pyramid where DE=8 cm and m∠ADE=60°.

Goryan [66]

Given:

The length of DE is 8 cm and the measure of ∠ADE is 60°.

We need to determine the surface area of the pyramid.

Length of AD:

The length of AD is given by

$cos 60^{\circ}=\frac{FD}{8}$

$4=FD$

Length of AD = 8 cm

Slant height:

The slant height EF can be determined using the trigonometric ratio.

Thus, we have;

$sin \ 60^{\circ}=\frac{EF}{8}$

$sin \ 60^{\circ} \times 8=EF$

$\frac{\sqrt{3}}{2} \times 8=EF$

$4\sqrt{3}=EF$

Thus, the slant height EF is 4√3

Surface area of the square pyramid:

The surface area of the square pyramid can be determined using the formula,

$SA=Area \ of \ square + \frac{1}{2} (Perimeter \ of \ base ) (slant \ height)$

Substituting the values, we have;

$SA=8^2+\frac{1}{2}(8+8+8+8)(4 \sqrt{3})$

$SA=64+\frac{1}{2}(32)(4 \sqrt{3})$

$SA=64+(16)(4 \sqrt{3})$

$SA=64+64 \sqrt{3}$

The exact form of the area of the square pyramid is $64+64 \sqrt{3}$

Substituting √3 = 1.732 in the above expression, we have;

$SA = 64 + 110.848$

$SA = 174.848$

Rounding off to one decimal place, we get;

$SA = 174.8$

Thus, the area of the square pyramid is 174.8 cm²

7 0

2 years ago

Read 2 more answers

Simplify this exponential expression: (-49) 2/5

ioda

Answer:

I think it is 12 4/5

Step-by-step explanation:

hope this helps if not let me now

4 0

1 year ago

I need help with this equation can someone please help me

Vanyuwa [196]

Answer:

d= 24

Step-by-step explanation:

-2= d/3 - 10

-6= d-30

-d=-30+6

-d= -24

d= 24

6 0

3 years ago

A bank manager is interested in the average length of time that customers are willing to wait in line before they give up and le

Fynjy0 [20]

Answer: The average length of time that the 25 customers waited before leaving the bank. e. Statistic

The list of times for the 25 customers who left the bank. f.Data

All of the bank's customers d. Population

The 25 customers that the manager observed leave. c. Sample

The length of time a customer waits before leaving the bank. a. Variable.

The average length of time that all customers will wait before leaving the bank a. Parameter

Step-by-step explanation:

A data is a list of observations.

In statistics, a variable is an attribute that defines a person, place, thing, or thought.

A large group that have similar individuals as per the researcher's point of view is known as population, where its subset is known as sample.

The measure of certain characteristic in population is known as parameter, where for sample it is known as statistic.

8 0

3 years ago

4x10^5 scientific notation

dmitriy555 [2]

This is already written in scientific notation, but if you are asking what the answer would be written out it is: 400000

8 0

3 years ago