1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Pani-rosa [81]
2 years ago
13

Vignesh owns a cottage in the shape of a cube with each edge of length 26 feet. The roof is in the shape of a square pyramid and

it extends two feet over the edge of the cottage on each side. The lateral sides of the roof are 17 feet long. What is the total surface area of the roof?

Mathematics
2 answers:
Zina [86]2 years ago
4 0

Answer:

56√93 ≈ 540 ft²

Step-by-step explanation:

The roof is made up of 4 congruent isosceles triangles. Since the roof extends 2 ft over the edge of the cottage on each side, then the base of each triangle is 26 + 2 = 28 ft.

Let's calculate the area of one of the triangles and then just multiply by 4. See attachment. Drop a perpendicular from the vertex of a triangle to its base. We now have the triangle broken up into two right triangles. The hypotenuse is 17 ft and one of the legs of the right triangle is 28 / 2 = 14 ft. Then the height / other leg is:

\sqrt{17^2-14^2} =\sqrt{289-196} =\sqrt{93}

We now have the dimensions of each triangle: the height is √93 and the base is 28. The area of a triangle is: A = (1/2) * b * h, so we have the following.

A = (1/2) * b * h

A = (1/2) * 28 * √93 = 14√93

Multiply this by 4:

14√93 * 4 = 56√93

The total surface area is 56√93 ≈ 540 ft².

Novay_Z [31]2 years ago
3 0

Answer:

1,244 ft²

Step-by-step explanation:

Lateral surface area of the roof:

4(½ × (26+4) × 17)

1020

Part of the base:

(26+4)² - 26²

30² - 26²

224

Total surface area:

1020 + 224

1244

You might be interested in
Can someone please help me
Salsk061 [2.6K]

Answer:

B

Step-by-step explanation:

Area of pool = l × b

l = 6x and b = 3x - 5

Area = 6x(3x - 5)

Area = 18x² - 30x

4 0
3 years ago
Find the slope of the line that passes through the following points. (-8,-1) (-4,-2)
lana [24]

Answer:

-1/4

Step-by-step explanation:

We can find the slope of a line given two points by using

m = (y2-y1)/(x2-x1)

    = (-2- -1)/( -4 - -8)

    = (-2+1)/(-4+8)

     = -1/4

8 0
3 years ago
Read 2 more answers
A rectangle has a length at most two more than seven times the width. If the perimeter is less than or equal to 52 units, find t
ella [17]

7x + 2 \leqslant 52
7 0
2 years ago
8
wolverine [178]
Answer:c
explanation: its 90 degrees

good luck!
3 0
2 years ago
Read 2 more answers
In a study of government financial aid for college​ students, it becomes necessary to estimate the percentage of​ full-time coll
ICE Princess25 [194]

Answer:

a) n = 1037.

b) n = 1026.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \pi, and a confidence level of 1-\alpha, we have the following confidence interval of proportions.

\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}

In which

z is the zscore that has a pvalue of 1 - \frac{\alpha}{2}

The margin of error is:

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

99% confidence level

So \alpha = 0.01, z is the value of Z that has a pvalue of 1 - \frac{0.01}{2} = 0.995, so Z = 2.575.

​(a) Assume that nothing is known about the percentage to be estimated.

We need to find n when M = 0.04.

We dont know the percentage to be estimated, so we use \pi = 0.5, which is when we are going to need the largest sample size.

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

0.04 = 2.575\sqrt{\frac{0.5*0.5}{n}}

0.04\sqrt{n} = 2.575*0.5

(\sqrt{n}) = \frac{2.575*0.5}{0.04}

(\sqrt{n})^{2} = (\frac{2.575*0.5}{0.04})^{2}

n = 1036.03

Rounding up

n = 1037.

(b) Assume prior studies have shown that about 55​% of​ full-time students earn​ bachelor's degrees in four years or less.

\pi = 0.55

So

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

0.04 = 2.575\sqrt{\frac{0.55*0.45}{n}}

0.04\sqrt{n} = 2.575*\sqrt{0.55*0.45}

(\sqrt{n}) = \frac{2.575*\sqrt{0.55*0.45}}{0.04}

(\sqrt{n})^{2} = (\frac{2.575*\sqrt{0.55*0.45}}{0.04})^{2}

n = 1025.7

Rounding up

n = 1026.

6 0
3 years ago
Other questions:
  • The gear ratio describes the ratio of one gear's diameter to another gear in the same chain. The gear ratio between two specific
    14·1 answer
  • Please help one of my last questions.....
    7·1 answer
  • mr. williams physical education class lasts 7/8 hour. how many minutes are spent warming up and cooling down if they spent 3/10?
    12·1 answer
  • Compare and order the numbers below.
    9·1 answer
  • Scott is reading two books at the same time to prepare for a report he is writing. So far, he has read 407 of the total number o
    15·1 answer
  • NEED HELP ASAP <3
    5·1 answer
  • What is the area of the trapezoid?
    13·1 answer
  • What are the coordinates of the x-intercept of the line -3x-5y=12?
    10·2 answers
  • A square has a perimeter of 12x 52 units. which expression represents the side length of the square in units? x 4 x 40 3x 13 3x
    12·1 answer
  • Draw a histogram and a box-and-whisker plot to represent the combined data, and answer the questions. Be sure to include the new
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!