the base of a right pyramid with a square is a square ABCD of side 10 cm the length of its slant Edge is 15 cm calculate the height of the pyramid the surface area of the pyramid the area of the pyramid​

Answers

Answer 1

Answer:

Solution

verified

Verified by Toppr

Correct option is A)

We first calculate slant height L of the pyramid with base s=10 cm and height 12 cm:

L 2 =H 2 +( 2s )

2

=12

2

+(

2

10

)

2

=12

2

+5

2

=144+25=169

⇒L=

169

=13

The perimeter of the base is P=4s, since it is a square, therefore,

P=4×10=40 cm

The general formula for the lateral surface area of a regular pyramid is LSA=

2

1

Pl where P represents the perimeter of the base and l is the slant height.

Since the perimeter of the pyramid is P=40 cm and the slant height is l=13 cm, therefore, the lateral surface area is:

LSA=

2

1

Pl=

2

1

×40×13=260 cm

2

Now, the area of the base B=s

2

with s=10 cm is:

B=s

2

=10

2

=100 cm

2

The general formula for the total surface area of a regular pyramid is TSA=

2

1

Pl+B where P represents the perimeter of the base, l is the slant height and B is the area of the base.

Since LSA=

2

1

Pl=260 cm

2

and area of the base is B=100 cm

2

, therefore, the total surface area is:

TSA=

2

1

Pl+B=260+100=360 cm

2

Hence, total surface area of the pyramid is 360 cm

2

.


Related Questions

Neftali is filling up a pool with water. The depth of water in the pool can be represented by the function d(t)=0.25t+30, where t is the time in minutes and d(t) is the depth, in inches, of water in the pool.

How deep is the water in the pool when Neftali starts filling the pool with water?

Answers

Answer: The answer is 0.25 inches every minute

Step-by-step explanation: The equation tells you that the pool started at 30 inches (0.25t+30). It says that the pool's depth rises 0.25 inches every minute. So the answer is that the pool started out as 30 inches (which is the y-intercept) and rose 0.25 inches every minute.

Hope this helped

FIND X PLEASE PLEASE PLEASE HELP IM BEGGING YOU

FIND X PLEASE PLEASE PLEASE HELP IM BEGGING YOU

Answers

Answer:

A

Step-by-step explanation:

Which best describes the rate of change?

Which best describes the rate of change?

Answers

Answer:

167

Step-by-step explanation:

2500÷15=166.666667

Round it up to 167

*I used 2500 and 15 because that's a point (15,2500) that you can see very clearly on the graph*

I need the answers to B and C please and thank you! :)

I need the answers to B and C please and thank you! :)

Answers

Answer:

2/9 and 4/9

Step-by-step explanation:

There are 3 * 3 = 9 possible outcomes of spinning the spinners. Out of those, there are only 2 ways to achieve a product of 6 (2 and 3 or 6 and 1) so the answer to B is 2/9. For C, there are 4 ways for the total to be greater than 10 (12, 18, 20, 30) so the answer is 4/9.

Answer:

b=2/9

c=4/9

Step-by-step explanation:

b: 2/3(there are two options you can land on that have a pair that multiplies to six)*1/3(each only has one pair)= 2/9

c: 2/3(6 or 4)*2/3(3 or 5) =4/9

Leroy made a scale drawing of a neighborhood park. The scale of the drawing was 1 centimeter: 4 meters. In the drawing, the volleyball court is 4 centimeters long. What is the length of the actual volleyball court?

Answers

Answer: 16 meters

Step-by-step explanation:

1 cm         4cm

--------    =  ---------

4m             16m

Amrit’s income is
32
%
more than Bethan’s income.
Amrit and Bethan’s combined income is
£
54

868
.

Calculate Amrit's income.

Answers

Amrit's income is £27434.16.

What is the arithmetic operation?

The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or more quantities. Included in them is the study of numbers, especially the order of operations, which is important for all other areas of mathematics, including algebra, data management, and geometry. The rules of arithmetic operations are required in order to answer the problem.

Let the Bethan's income be x

Amrit's income is 32% more than Bethan's income.

So, Amrit's income=x+32%

Amrit and Bethan's combined income is £54868.

According to given question we have

x+x+32%=£54868

2x+32/100=£54868

2x=54868-0.32

2x=54867.68

x=27433.84

Bethan's income=£ 27433.84

Amrit's income

=x+32%

=£ 27433.84+0.32

=£27434.16

Therefore,  Amrit's income is £27434.16.

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How do you do long division step by step?

Answers

Long division is a method of dividing large numbers by hand. It can be done using several different methods, but the standard algorithm is the most common.

The steps for the standard algorithm are as follows:

1. Begin by writing the dividend (the number to be divided) above the division bar and the divisor (the number that the dividend is being divided by) below the division bar.

2. Divide the leftmost digit of the dividend by the divisor. Write the result of this division to the left of the division bar.

3. Multiply the divisor by the quotient from the previous step, and write the result of this multiplication below the dividend.

4. Subtract the product from the dividend and write the result below the dividend.

5. Bring down the next digit of the dividend to the remainder and repeat steps 2-4 until the remainder is 0.

6. The result of the division is the quotient written to the left of the division bar.

Long division is a method of dividing large numbers by hand.

It involves dividing the leftmost digit of the dividend by the divisor, multiplying the divisor by the quotient, subtracting the product from the dividend, and repeating these steps until the remainder is 0. The result is the quotient written to the left of the division bar.

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Which is a counter example to: If the month is not January it must be June. *

Answers

Answer:

if the month is June it is not January

Step-by-step explanation:

you just flip the question

Ms. Nguyen needs to separate $385 into three parts to pay some debts. The second part must be five times as large as the first part. The third part must be $35 more than the first part. How much money must be in each part?

Answers

Answer:

1st: $50 2nd: $250 3rd: $85

What's 6 to the 10th power??

Answers

Answer:

Hey there

It is 60466176

Answer:

60,466,176

Step-by-step explanation:

6 * 6 * 6 * 6 * 6 * 6 * 6 * 6 * 6 * 6

A delivery person uses a service elevator to bring boxes of books up to an office. The delivery person weighs 150 lb and each box of books weighs 60 lb. The maximum capacity of the elevator is 1280lb. How many boxes of books can the delivery person bring up at one​ time?

Answers

18 boxes of books is the amount he can bring up

I am not irrational, I am not a whole number, I am not an integer, I am not positive. What number am I?

Answers

Answer:

YOU ARE ONE OF THESE NUMBERS 1,3,5,7,9 etc i hope this helps if it didnt im sorry

Step-by-step explanation:

the answer is 0 probably

the length and width of a rectangle are measured as 52 cm and 47 cm, respectively, with an error in measurement of at most 0.1 cm in each. use differentials to estimate the maximum error in the calculated area of the rectangle. step 1 if the length and width are given by x and y, then the area is given by a

Answers

According to the question the maximum error in the calculated area of the rectangle is \(\(4.7 \, \text{cm}^2\).\)

Step 1: The area of the rectangle is given by the formula:

\(\[A = xy\]\)

To estimate the maximum error in the calculated area, we can use differentials. Let's denote the length and width measurements as \(\(x\) and \(y\)\), respectively, and the corresponding maximum errors as \(\(\Delta x\) and \(\Delta y\).\)

Step 2: Express the area as a function of \(\(x\) and \(y\):\)

\(\[A = xy\]\)

Step 3: Take the differential of the area with respect to \(\(x\):\)

\(\[dA = \frac{\partial A}{\partial x} dx + \frac{\partial A}{\partial y} dy\]\)

Since \(\(\frac{\partial A}{\partial y}\)\) is 0 because the area does not directly depend on \(\(y\)\), the equation simplifies to:

\(\[dA = \frac{\partial A}{\partial x} dx\]\)

Step 4: Find \(\(\frac{\partial A}{\partial x}\)\) by differentiating the area function:

\(\[\frac{\partial A}{\partial x} = y\]\)

Step 5: Substitute the given values into the equation:

\(\[\Delta A = \frac{\partial A}{\partial x} \Delta x\]\)

\(\[\Delta A = y \Delta x\]\)

Step 6: Substitute the measured values for \(\(y\) and \(\Delta x\):\)

\(\[\Delta A = (47 \, \text{cm})(0.1 \, \text{cm})\]\)

Step 7: Calculate the maximum error in the area:

\(\[\Delta A = 4.7 \, \text{cm}^2\]\)

Therefore, the maximum error in the calculated area of the rectangle is \(\(4.7 \, \text{cm}^2\).\)

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-9x+3y=-30 in slope intercept form

Answers

Answer:

y = 3x - 10

Step-by-step explanation:

Answer:

y = 3x -10

Step-by-step explanation:

Slope intercept form is y = mx+b  where m is the slope and b is the y intercept

-9x +3y =-30

Add 9x from each side

-9x+9x +3y =9x-30

3y = 9x-30

Divide each side by 3

3y/3 = 9x/3 -30/3

y = 3x -10

There are 5 positions available in the new school. Of the applicant, 12 are men and 8 are women. In how many ways can 3 men and 2 women be chosen if they are equally considered?

Answers

There are 3080 ways 3 men and 2 women can be chosen if they are equally considered, using the multiplication principle of counting

What is the multiplication principle of counting

The multiplication principle states that if there are m ways to perform one task and n ways to perform another task, then there are m x n ways to perform both tasks together.

To find the number of ways to choose 3 men from the 12 men, we can use the formula for combination, which is: ⁿCᵣ = n! / (r! (n-r)!).

where n is the total number of men and r is the number of men chosen

so, the number of ways to choose 3 men from the 12 men = ¹²C₃ = 1.

Similarly, we evaluate the number of ways to choose 2 women from the 8 women

as = ⁸C₂ = 14

Now, using the multiplication principle, we can find the total number of ways 3 men and 2 women be chosen if they are equally considered.

220 x 14 = 3080

Therefore, there are 3080 ways 3 men and 2 women can be chosen if they are equally considered, using the multiplication principle of counting

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Write -3/20 as a decimal

Answers

Answer:

-.15

Step-by-step explanation:

Answer:

-0.15

Step-by-step explanation:

PLEASE HELP 5 of 5
A, B & C form a triangle where Z BAC = 90°,
AB = 2.6 mm and CA = 14.2 mm
Find the length of BC, giving your answer rounded to 1 DP.
BC =
mm
PLEASE HELP

Answers

Answer:

BC ≈ 14.4 mm

Step-by-step explanation:

Using Pythagoras' identity in the right triangle

BC² = AB² + AC² = 2.6² + 14.2² = 6.76 + 201.64 = 208.4

Take the square root of both sides

BC = \(\sqrt{208.4}\) ≈14.4 mm ( to 1 dec. place )








Consider an activity with these estimates for optimistic, most likely, and pessimistic time: 11, 21, 35 . Find the mean value of the activity time. (Please provide answer accurate to two decimal place

Answers

the main answer is that the mean value of the activity time is 21.67. This is calculated using the formula (optimistic + 4 * most likely + pessimistic) / 6.

To find the mean value of the activity time, we can use the three estimates provided: optimistic, most likely, and pessimistic time.

1. The optimistic time is the shortest possible time for completing the activity, which is 11 units.
2. The most likely time is the time that is most likely to be taken to complete the activity, which is 21 units.
3. The pessimistic time is the longest possible time for completing the activity, which is 35 units.

To calculate the mean value, we can use the following formula:
Mean value = (optimistic + 4 * most likely + pessimistic) / 6

Substituting the given values, we get:
Mean value = (11 + 4 * 21 + 35) / 6

Calculating the numerator first:
11 + 4 * 21 + 35 = 11 + 84 + 35 = 130

Now, we can calculate the mean value:
Mean value = 130 / 6

Dividing 130 by 6, we get:
Mean value = 21.67 (rounded to two decimal places)

Therefore, the mean value of the activity time is 21.67.

the main answer is that the mean value of the activity time is 21.67. This is calculated using the formula (optimistic + 4 * most likely + pessimistic) / 6.

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What i the equation of a line that i parallel to the line y =2x 7 and pae through the point -2,4

Answers

The equation of a line y=2x+8.

The equation of a straight line can be represented in the slope-intercept form, y = mx + c

Where c = intercept

Slope, m =change in the value of y on the vertical axis/change in the value of x on the horizontal axis

Looking at the given line,

y = 2x + 7

Compared with the slope-intercept equation,

Slope, m = 2

If a line is parallel to another line, it means that both lines have equal or the same slope. This means that the slope of the line passing through the point (-2, 4) is 2

Substituting m= 2, y = 4 and x = -2 into the equation, y = mx + c , it becomes

4 = 2 × - 2 + c

4 = - 4 + c

c = 4 + 4 = 8

The equation becomes y=2x+8.

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Which function has a range of all real numbers greater than or equal to -4?​

A. f(x) = x-4
B. f(x) = -4x
C. f(x) = (x+1)^2 - 4
D. f(x) = -|x-3|-4​

Answers

Answer:

C.  \(f(x)=(x+1)^2-4\)

Step-by-step explanation:

A. the graph is a straight line with slope 1.  It goes up/down infinitely far so the range is all real numbers.  Not A!

B. The graph is a straight line with slope -4, so, like the function in A, the range is all real numbers.  Not B!

D. The graph is an absolute value function  y = |x|, reflected over the x-axis, shifted right 3 units, then shifted down 4 units.  So the graph starts witha "vee" shape opening up, becomes a vee opening down, then ultimately gets shifted down 4 units.  The range is all real numbers less than or equal to -4.

See the attached graphs.  image2 is the function in answer choice D.

Which function has a range of all real numbers greater than or equal to -4?A. f(x) = x-4B. f(x) = -4xC.
Which function has a range of all real numbers greater than or equal to -4?A. f(x) = x-4B. f(x) = -4xC.

an open box is to be made from a two-foot by three-foot rectangular piece of metal by cutting equal squares from the corners and turning up the sides. find the volume of the largest box that can be made in this manner. round your final answer to the nearest hundredth.

Answers

The volume for the largest box will be 1.056 foot³. This can find out by application of differentiation.

What is AOD?

AOD is nothing but application of differentiation. It implies scopes where we can use differentiation to make our calculations easy.

Here, given

Length and breadth = 2,3 foot

Let us consider length of side of square = x

So, after cutting squares left sides of rectangular sheet = 2-2x , 3-2x

So, volume = (2-2x)*(3-2x)*x

                v = 4x³ - 10x² + 6x

To find largest volume , \(\frac{dv}{dx}\) = 0

                 \(\frac{dv}{dx}\) = 12x² - 20x + 6

                12x² - 20x + 6 = 0

                x = 0.4 , 1.3

But, for 1.3 volume will be negative i.e. not possible.

So, volume = 2.2*1.2*0.4

                   = 1.056 foot³

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when a 12.8 g sample of kcl dissolves in 75 g of water in a calorimeter the temperature drops from 31 degrees celsius to 21.6 degrees celsius

Answers

The heat released per gram of KCl is -238.1 J/g.

How to find out the temperature drops from 31 degrees celsius to 21.6 degrees celsius?

To calculate the heat absorbed by the water and the calorimeter, we can use the formula:

q = m * c * ΔT

where q is the heat absorbed or released, m is the mass of the substance, c is the specific heat capacity of the substance, and ΔT is the change in temperature.

First, we need to calculate the heat absorbed by the water:

q_water = m_water * c_water * ΔT_water

m_water = 75 g (mass of water)

c_water = 4.184 J/g°C (specific heat capacity of water)

ΔT_water = 31°C - 21.6°C = 9.4°C

q_water = 75 g * 4.184 J/g°C * 9.4°C = 2811.9 J

Next, we need to calculate the heat absorbed by the calorimeter:

q_calorimeter = c_calorimeter * ΔT_calorimeter

We assume the calorimeter has negligible mass, and its specific heat capacity is known. Therefore, we can use this simplified formula.

c_calorimeter = 25 J/°C (specific heat capacity of the calorimeter)

ΔT_calorimeter = 9.4°C

q_calorimeter = 25 J/°C * 9.4°C = 235 J

Finally, we can calculate the heat released by the KCl:

q_KCl = -q_water - q_calorimeter

q_KCl = -(2811.9 J + 235 J) = -3046.9 J

The negative sign indicates that heat is released by the KCl.

Now, we can calculate the heat released per gram of KCl:

heat_per_gram_KCl = q_KCl / m_KCl

m_KCl = 12.8 g (mass of KCl)

heat_per_gram_KCl = -3046.9 J / 12.8 g = -238.1 J/g

The heat released per gram of KCl is -238.1 J/g.

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a book contains 270 pages. A boy reads x pages everyday. If he still has some pages left after reading for 9 days, find the range of values for x​

Answers

Answer:

Step-by-step explanation:2x-24--4=2-42s-s2

2s2=4-=e=2e2e2e2e donate it hehe

the raw score on a certain standarized test is determined by subtracting1/4 of the number of incorrect answers

Answers

The number of incorrect answers is 8.

What is a linear equation?

linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept. Occasionally, the above is called a "linear equation of two variables," where y and x are the variables.

Let,

number correct of answer = x

number of incorrect answer = y

Given that,

Total number of answer  x+y = 30 ......(1)

Total score = x-\(\frac{1}{4}\)y = 20  .......(2)

In equation (2) multiply by -1 on both side.

-x+\(\frac{1}{4}\)y = -20   .......(3)

Now,

Adding both the equation (1) and (3)

x+y-x+\(\frac{1}{4}\)y = 30-20

\(\frac{5}{4} y\) = 10

y = 8

Hence, The number of incorrect answers is 8.

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the raw score on a certain standarized test is determined by subtracting1/4 of the number of incorrect

Solvex + 3 = −6.
A. x= -3 and x = 9
B. x = 3 and x = -9
C. X=-3 and x = -9
D. No solution

Solvex + 3 = 6.A. x= -3 and x = 9B. x = 3 and x = -9C. X=-3 and x = -9D. No solution

Answers

Step-by-step explanation:

please mark me as brainlest

Solvex + 3 = 6.A. x= -3 and x = 9B. x = 3 and x = -9C. X=-3 and x = -9D. No solution

Which of the attributes below are shared by both trapezoid
and parallelograms? Select all that apply.
A) 4 sides
B) 4 right angles
C) All sides are straight lines
D) 2 sets of parallel sides

Answers

The attributes shared by both trapezoids and parallelograms are:

A) 4 sides

C) All sides are straight lines

D) 2 sets of parallel sides

So the correct options are A), C), and D).

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\textcolor{red}{\underline{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

Can someone help please?

Can someone help please?

Answers

Answer:

A

Step-by-step explanation:

From left to right of the graph, we can observe that the generally the points are going down. This means that the trend line drawn will have a negative slope.

In the slope-intercept form, which is the form the given equations are in, we have y= mx +c, where m is the slope and c is the y-intercept.

We are only interested in the slope in this case, since no actual values are given. Thus, let's focus on the coefficients of x to determine whether the slope is positive or negative.

Option A: Slope= -⅔ (negative)

Option B: Slope= 3 (positive)

Since we have a negative slope, option A would be the best answer.

The attached image shows 2 graphs. The graph in blue shows the shape of a graph with negative slope, while the graph in red has a positive slope.

Can someone help please?

A drawing of a basketball backboard was made using semicircle and rectangle
What is the area of the drawing of the backboard
A: 126 in
B: 253.17in
C:380.34in
D:122.5 in

A drawing of a basketball backboard was made using semicircle and rectangle What is the area of the drawing

Answers

Answer:B 253.17
100% sure

4) One-square foot floor tiles come 26 to a package. Find how many packages are needed to
cover a rectangular floor 17 feet by 26 feet.

Answers

A total of 11492 packages are needed to cover a rectangular floor.

What is a rectangle?

Rectangles are four-sided polygons with all internal angles equal to 90 degrees. At each corner or vertex, two sides meet at right angles. The rectangle differs from a square in that its opposite sides are equal in length.

Given, One-square foot floor tiles come in 26 packages.

dimension of rectangular floor = 17 feet by 26 feet

Then, total area = 17*26 = 442 square foot

So, total packages needed = 442*26 = 11492

Hence, a total of 11492 packages is needed to cover a rectangular floor.

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help appreciated thanks

help appreciated thanks

Answers

Answer:

No

Step-by-step explanation:

x=(b-5)/c≠(5-b)/c

supposedly

b=6

c=1

x=6-5/1=1

x=5-6/1= -1

1≠ -1

Answer:

No

Step-by-step explanation:

x = b - 5 / L equal to - (5 - b) / L

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