[tex]\bf \textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=\stackrel{altitude}{height}\\ \cline{1-1} r=3\\ h=9 \end{cases}\implies V=\cfrac{\pi (3)^2(9)}{3}\implies V=27\pi \implies V\approx 84.8[/tex]
From the top of a tree a bird looks down on a field mouse at an angle of depression of 50°. If the field mouse is 40 meters from the base of the tree, find the vertical distance from the ground to the bird's eyes.
Answer:
The vertical distance from the ground to the bird's eyes is 47.67 m
Step-by-step explanation:
* Lets explain the situation of the problem
- There is a bird on the top of a tree
- The bird looks down on a field mouse at an angle of depression of 50°
- The field mouse is 40 meters from the base of the tree
* Consider that the vertical distance from the ground to the bird's eyes,
the distance from the field mouse to the base of the tree distance
from the bird eyes to the field mouse formed a right triangle
- The hypotenuse is the distance from the bird eyes to the field mouse
- The horizontal side is the distance from the field mouse to the base
of the tree
- The angle between the hypotenuse and the horizontal side is the
angle of depression which = 50°
- The opposite side to the angle of measure 50° is the vertical distance
from the ground to the bird's eyes
* Lets use trigonometry functions to find the vertical distance
∵ The length of the adjacent side to the angle of measure 50° is 40 m
∵ The length of the opposite side to the angle of measure 50° is h m
∵ tan Ф = opposite side to Ф ÷ adjacent side to Ф
∵ Ф = 50°
∴ tan 50° = h/40 ⇒ by using cross multiplication
∴ 40 tan 50° = h
∴ h = 47.67 m
* The vertical distance from the ground to the bird's eyes is 47.67 m
The graph of f(x) was vertically translated down by a value of k to get the function g(x) = 5x + k. What is the value of k? A -7 B -6 C 5 D 7
Answer:
[tex]{\boxed{\text{A. }\math{k = -7}}[/tex]
Step-by-step explanation:
The general rule for vertical translation of a function ƒ(x) ⟶ ƒ(x) + k .
A positive value of k means that the graph is shifted up by k units.
The graph of ƒ(x) was shifted from (0, 1) to (0, -6).
[tex]\text{The graph was shifted down by seven units, so }{\boxed{\mathbf{k = -7}}[/tex]
The value of k is -7.
What is vertical translation of a function?Vertical translation refers to the up or down movement of the graph of a function.
Here, the shape of the function remains the same.
It is also known as the movement/shifting of the graph along the y-axis.
In vertical translation, each point on the graph moves k units vertically and the graph is said to translated k units vertically.
The general rule for vertical translation of a function,
f(x)= g(x) + k .
here, the graph is shifted up by k units.
As, seen from the graph of g(x) is shifted from point (0, 1) to (0, -6).
Hence, the graph is shifted by -7 units.
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Find the area of the polygon.
Look at the picture please
A : 24.6 square units
B : 25.8 square units
C: 26.3 square units
D: 27.5 square units
Answer:
option D: 27.5 square units
Step-by-step explanation:
Divide the polygon in 6 figures
see the attached figure
Area of figure 1 (right triangle)
A1=(1/2)(3)(3)=4.5 units²
Area of figure 2 (rectangle)
A2=(1)(3)=3 units²
Area of figure 3 (rectangle)
A3=(1)(3)=3 units²
Area of figure 4 (right triangle)
A4=(1/2)(3)(3)=4.5 units²
Area of figure 5 (right triangle)
A5=(1/2)(4)(5)=10 units²
Area of figure 6 (right triangle)
A6=(1/2)(1)(5)=2.5 units²
The total area is equal to
At=A1+A2+A3+A4+A5+A6
At=4.5+3+3+4.5+10+2.5=27.5 units²
Answer:
Option D.
Step-by-step explanation:
As we know area of a triangle = [tex]\frac{1}{2}\times Base\times Height[/tex]
1. Area of ΔJKL = [tex]\frac{1}{2}\times(\text{Distance of L from base JK})\times (JK)[/tex]
= [tex]\frac{1}{2}\times (3)\times (5)[/tex]
=7.5 square units
2. Area of ΔIJL = [tex]\frac{1}{2}\times(\text{Distance of J from base IL})\times (IL)[/tex]
= [tex]\frac{1}{2}\times (3)\times (5)[/tex]
= 7.5 square units
3. Area of triangle IKL = [tex]\frac{1}{2}\times(\text{Distance of H from base IL})\times (IL)[/tex]
= [tex]\frac{1}{2}\times (5)\times (5)[/tex]
= [tex]\frac{25}{2}=12.5[/tex] square units
Now area of ΔJKL + ΔIJL + ΔIKL = 7.5 + 7.5 + 12.5
= 27.5 square units
Option D. is the answer.
What is the constant of proportionality in the equation y = 2 x?
Answer:
2
Step-by-step explanation:
2 is the constant of proportionality in the equation y = 2x . When two variables are directly proportional to each others . Where k is called the constant of proportionality . Thus in the question x and y are proportional variables
fiona ,an avid food blogger posted a total 216 recipes in 36 weeks. If she posted
Them at a constant rate, how many recipes did she upload in 15 weeks' time?
Answer:
90 recipes
Step-by-step explanation:
we know that
Fiona posted a total 216 recipes in 36 weeks
using proportion
Find out how many recipes did she upload in 15 weeks'
Let
x -----> the number of recipes
[tex]\frac{216}{36}\frac{recipes}{weeks}=\frac{x}{15}\frac{recipes}{weeks} \\\\x=216*15/36\\\\x= 90\ recipes[/tex]
Classify the triangle.
obtuse
equiangular
right
acute
Answer:
Acute
Step-by-step explanation:
Note the definitions:
Obtuse: At least one of the angles are greater than 90°
Equilateral: All angles are congruent & equal to 60°
Acute: All angles are less than 90°
Right: At least one angle is equal to 90°
In this case, the triangle is a D) acute, for it fits the requirement for being an acute... all angles are less than 90°.
~
Hello There!
The triangle shown in the image would be an acute triangle
An acute triangle is a triangle where all three sides are less than 90°
In the image, none of the angles shown are greater than 90° so this
is an example of an acute triangle
What is variability?
Answer:
Variability is when there is no consistency.
Step-by-step explanation:
Variation in data can be due to various factors. Variability can also be called the spread of data.
Standard deviation is a measure of variability as standard deviation measures the spread of data.
!!
Which of the following would not be the result of a substitution in the following system?
2x + y = 7
y - x= 1
A. 7 - 2x- x = 1
B. 2x + x + 1 = 7
C. 2(y + 1) + y = 7
The correct option is:
C. [tex]2(y+1)+y=7[/tex]
Why?To find which of the given options are not the result of a substitution in the given system, we need to isolate the variable in function of the other variable, and then substitute it.
So, substituting and discarding, we have:
- First equation:
[tex]2x+y=7[/tex]
Isolating "y", we have:
[tex]y=7-2x[/tex]
Then, substituting it into the second equation, we have:
[tex]y-x=1[/tex]
[tex]7-2x-x=1[/tex]
We have that it's a result of a substitutiong in the following system (option A)
- Second equation:
[tex]y-x=1[/tex]
Isolating "y", we have:
[tex]y=x+1[/tex]
Then, substituting it into the first equation, we have:
[tex]2x+y=7[/tex]
[tex]2x+(x+1)=7[/tex
[tex]2x+x+=7[/tex
We have that it's a result of a substitution in the following system (option B)
Hence, we have that the option C is not a result of a substitution in the given system of equations since there is not a possible value of the variable "x" that is equal "y+1".
So, the correct option is:
C. [tex]2(y+1)+y=7[/tex]
Have a nice day!
Answer:
C. 2(y + 1) + y = 7
Step-by-step explanation:
Where do I find the “solution” do a quadratic equation on a graph? How many possible real solutions are there when you solve a quadratic equation?
Answer:
Q1. The solution for the quadratic equation on a graph is same as the value of x-intercept(zeros)
Q2. discriminant(b^2-4ac) when y=ax^2 + bx + c
there are 3 situations:
1. discriminant > 0 → 2 real solutions(2 x-intercepts/zeros)
2. discriminant = 0 → 1 real solution(1 x-intercept/zero)
3. discriminant < 0 → 0 real solution(0 x-intercept/zero) → also 2 imaginary solution
Hope it helped!
Step-by-step explanation:
Answer:
1) You find the solution by identifying the x-intercepts.
2) Possible real solutions:
- One real solution.
- Two distinct real solutions.
Step-by-step explanation:
1) The graph of a quadratic equation is a parabola.
By definition, the x-intercepts (Where [tex]y=0[/tex]) are the solutions of the quadratic equation .
2) Given a quadratic equation [tex]ax^2+bx+c=0[/tex], you can know the number of real solutions by using this formula to find the Discriminant :
[tex]D=b^2-4ac[/tex]
If [tex]D=0[/tex], then there is one real solution with multiplicity two.
If [tex]D>0[/tex], then there are two distinct real solutions.
On a graph:
-If the graph has two x-intercepts, then the quadratic equation has two real solutions.
-If the graph has one x-intercept , then the quadratic equation has one real solution.
What is the measure of X in degrees
Answer:
C. 40°
Step-by-step explanation:
From the diagram, in triangle XYZ, XY=XZ=6 units. This means triangle XYZ is isosceles triangle with base YZ.
In isoscels triangle angles adjacent to the base are congruent, so
∠ZYX=∠YZX=70°
The sum of all interior angles in triangle is always 180°, so
∠ZYX+∠YZX+∠ZXY=180°
∠ZXY=180°-70°-70°
∠ZXY=40°
∠ZXY is ∠X, so ∠X=40°
if g(x) = x^2 - 4 find g (5) A. 6 B. 14 C. 21 D. 29
Answer:
C. 21
Step-by-step explanation:
g(x) = x² - 4
Give: x = 5
Plug in 5 for x in the equation:
g(5) = 5² - 4
Simplify. Remember to follow PEMDAS. First, solve the exponent, then subtract:
g(5) = (5 * 5) - 4
g(5) = 25 - 4
g(5) = 21
C. 21 is your answer.
~
What is the slope of the line that passes through the pair of points? (–6, 8), (2, 3)
Answer:
Step-by-step explanation:
Slope = y/x
y1-y2/x1-x2=slope of 2 points
8-3/-6-2 = 5/-8 which equals -5/8 or -.625.
The slope of line for the points is -5/8.
What is Slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx where, m is the slope
given:
We have the Points (–6, 8), (2, 3).
So, the slope is
m = (3- 8)/ (2- (-6))
m = -5 / (2+6)
m = -5 / 8
Thus, the Slope is -5/8.
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What is the measure of the angle formed by Main Street and Park Street?
35°
45°
90°
55°
Answer:
90-35=55
Hope this helps! <3
Use the given property to complete the statement.
Addition Property of Equality
If x = 5, then x + 3 =
The Addition Property of Equality allows us to add the same amount to both sides of an equation, so if x = 5, by adding 3 to both sides, x + 3 would be 8.
Explanation:The Addition Property of Equality is a principle of mathematics that states: if you add the same amount to both sides of an equation, the equation remains balanced. So, if we take the equation x = 5, according to the Addition Property of Equality, we can add 3 to both sides of the equation. This will give us: x + 3 = 5 + 3. Therefore, x + 3 = 8.
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A hotel is in the shape of a square pyramid. Each side of the base is 183 meters long and the height is 110 meters. What is the hotel's volume?
Check the picture below.
[tex]\bf \textit{volume of a pyramid}\\\\ V=\cfrac{1}{3}Bh~~ \begin{cases} B=area~of\\ \qquad its~base\\ h=height\\ \cline{1-1} B=\stackrel{183\times 183}{33489}\\ h=110 \end{cases}\implies V=\cfrac{1}{3}(33489)(110)\implies V=1227930[/tex]
Answer:
V =1127930 m^3
Step-by-step explanation:
The volume is
V = 1/3 B h
where B is the area of the base
B = area of the square
B = 183*183 since it is a square
B = 33489
V = 1/3 *(33489) * 110
V =1127930 m^3
Donna Dieter is trying to keep her lunches under 600 calories. Today, she had a peanut butter sandwich, one cup of vegetable soup, an apple, and a glass of milk. Did she stay under her goal?
Answer:
yes! total calories= 535
Step-by-step explanation:
answer:
Donna Dieter is trying to keep her lunches under 600 calories. Today she had a peanut butter sandwich, one cup of vegetable soup, an apple, and a glass of milk. Did she stay under her goal?
YES
x + 4y − z = −14
5x + 6y + 3z = 4
−2x + 7y + 2z = −17
A = -120
AX = -240
X = 2
Step-by-step explanation:
∵ x + 4y - z = -14
∵ 5x + 6y + 3z = 4
∵ -2x + 7y + 2z = -17
\left[\begin{array}{ccc}1&4&-1\\5&6&3\\-2&7&2\end{array}\right]=\left[\begin{array}{ccc}-14\\4\\-17\end{array}\right]
∴ A = 1(6×2 - 3×7) + (-4)(2×5 - 3×-2) + (-1)(5×7 - 6×-2)
∴ A = 1(12 - 21) + (-4)(10 - -6) + (-1)(35 - -12)
∴ A = -9 + (-4)(16) + (-1)(47) = -9 - 64 - 47 = -120
To find X replace the column of X by the column of the answer
\left[\begin{array}{ccc}-14&4&-1\\4&6&3\\-17&7&2\end{array}\right]
∴ AX = -14(6×2 - 3×7) + (-4)(4×2 - 3×-17) + (-1)(4×7 - 6×-17)
∴ AX = -14(12 - 21) + (-4)(8 - -51) + (-1)(28 - -102)
∴ AX = 126 + (-4)(59) + (-1)(130) = 126 - 236 - 130 = -240
∴ X = AX/A = -240/-120 = 2
Answer:
A -120
Ax -240
Ay 360
Az -480
x 2
y -3
z 4
Step-by-step explanation:
Which of the following is the solution set of the given equation? 14 + 8m = 14 - 3m - 5m ∅ {0} {all reals}
Answer:
{0}
Step-by-step explanation:
14 + 8m = 14 - 3m - 5m
Combine like terms
14 + 8m = 14 - 8m
Add 8m to each side
14 +8m +8m = 14 -8m +8m
14 +16m = 14
Subtract 14 from each side
14-14 +16m = 14-14
16m = 0
Divide by 16
16m/16 = 0/16
m = 0
Answer:
{0}
Step-by-step explanation:
The given equation is
[tex]14+8m=14-3m-5m[/tex]
We need to find the solution set of given equation.
Combine like terms on the right side of the given equation.
[tex]14+8m=14+(-3m-5m)[/tex]
[tex]14+8m=14+(-8m)[/tex]
[tex]14+8m=14-8m[/tex]
Add 8m on both sides.
[tex]14+8m+8m=14-8m+8m[/tex]
[tex]14+16m=14[/tex]
Subtract 14 from both sides.
[tex]14+16m-14=14-14[/tex]
[tex]16m=0[/tex]
Divide both sides by 16.
[tex]m=\frac{0}{16}[/tex]
[tex]m=0[/tex]
Therefore, the solution set is {0}.
What is the value of (3/10)^3
Answer:
27/1000
Step-by-step explanation:
To solve this, you would distribute the power 3 to the numerator and denomerator. 3^3 is 27 and 10^3 is 1000. So you get 27/1000
Answer:
the value is 27/1000 in other words the answer to your question is B
I want to say it’s 18in.. but I just wanna make sure
Answer:
you are correct
Step-by-step explanation:
area = 6 × 3 = 18 in²
Answer:
Yes!You got it correct!
Step-by-step explanation:
Good job!
A line passes through the point (-6,2) and has a slope of -5/2 ,Write an equation in pint slope form for this line
Answer:
see explanation
Step-by-step explanation:
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
here m = - [tex]\frac{5}{2}[/tex] and (a, b) = (- 6, 2), so
y - 2 = - [tex]\frac{5}{2}[/tex] (x - (- 6)), that is
y - 2 = - [tex]\frac{5}{2}[/tex] (x + 6) ← in point- slope form
An equation in point slope form for this line y - 2 = -5/2 (x + 6) .
What is slope?The point slope form of a straight line in geometry is used to represent the equation of a straight line using its slope 'm' and a point(x, y) that lies on the given line.
equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
Now, m = - 5/2
and (a, b) = (- 6, 2)
So, the equation of line be
y-2= -5/2 (x+6)
Hence,
y - 2 = -5/2 (x + 6) in point- slope form.
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PLEASE HELP PLEASE
How many nickels and dimes are in $2.40 if there are two times more nickels than dimes?
A) 12 nickels and 6 dimes
B) 6 nickels and 12 dimes
C) 24 nickels and 12 dimes
D) 12 nickels and 24 dimes
The problem is solved by calculating that there are 24 nickels and 12 dimes to make a total of $2.40, given that there are twice as many nickels as dimes.
Explanation:The subject of this question is Mathematics, specifically dealing with simple money-based equations. In the problem you're presented with, you've been asked to figure out the number of nickels and dimes that make up $2.40, given that there are twice as many nickels as there are dimes.
First, we can start by understanding the value of each coin. A nickel is worth $0.05, and a dime is worth $0.10. With the condition expressed in the problem, let's express the number of dimes as x, thus the number of nickels would then be 2x.
Because of their respective values, the total value of the dimes would be 0.10x and the total value of the nickels would be 0.05 × 2x or 0.10x. Adding both together, we'd have 0.10x + 0.10x = 0.20x, which we know equals $2.40 from the problem. Solving the equation 0.20x = 2.40 gives us x = 12. That's your number of dimes. The nickels would be 2 × 12 = 24. So, the answer to your problem would be 24 nickels and 12 dimes.
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A triangle has an area of 369.25 square inches. The height of the triangle is 42.2 inches. What is the length of the base of the triangle?
Step-by-step explanation:
[tex]1 \div 2 \times base \times height = area[/tex]
[tex]1 \div 2 \times x \times 42.2 = \ 369.25 \[/tex]
[tex]x = 369.25 \div 21.1[/tex]
[tex] = 17.5[/tex]
Answer:
Base = 17.5 inches.
Step-by-step explanation:
Given : A triangle has an area of 369.25 square inches. The height of the triangle is 42.2 inches.
To find : What is the length of the base of the triangle.
Solution : We have given
Area of triangle = 369.25 square inches.
Height = 42.2 inches.
Area of triangle = [tex]\frac{1}{2}*base*height[/tex].
Plugging the values.
369.25 = [tex]\frac{1}{2}*base*42.2[/tex].
On multiplying both sides by 2
369.25 * 2 = base * 42.2
738.5 = base * 42.2
On dividing both sides by 42.2
Base = 17.5 inches.
Therefore, Base = 17.5 inches.
The Starbuck cinnamon chip scone has 480 calories-more calories than a 440 calorie McDonald's double cheeseburger. a. One cinnamon chip scone provides what percent of the daily recommended calorie intake of 2000 calories for an adult woman?
Answer:
46%
Step-by-step explanation:
440 + 480 = 920
2000 / 920 =46%
Answer:
One cinnamon chip scone provides 46% of the daily recommended calorie intake of 2000 calories for an adult woman.
Step-by-step explanation:
Consider the provided information.
The Starbucks cinnamon chip scone has 480 calories-more calories than a 440 calorie McDonald's double cheeseburger.
First calculate the calories in Starbucks cinnamon chip scone .
Starbucks cinnamon has 480 calories-more than a 440 calorie cheeseburger.
The calories in Starbucks cinnamon = 480+440 = 920
Now we need to find the One cinnamon chip scone provides what percent of the daily recommended calorie intake of 2000 calories for an adult woman.
Find what percentage of 2000 is 920 as shown.
[tex]\frac{920}{2000}\times 100[/tex]
[tex]\frac{920}{20}[/tex]
[tex]46\%[/tex]
Hence, One cinnamon chip scone provides 46% of the daily recommended calorie intake of 2000 calories for an adult woman.
x-1/x^2-x-20 give the equivalent numerator if the denominator is (x-5)(x+4)(x+3)
Answer:
Step-by-step explanation:
First, factor the denominator: (x-5)(x+4)
Since the denominator already has the two values, you only need to multiply it by (x+3), which means you need to multiply the numerator by (x+3):
(x-1)(x+3)/(x-5)(x+4)(x+3)
(x-1)(x+3) then simplifies to [tex]x^2+2x-3[/tex]
Which point could be on the line that is parallel to line KL and passes through point M?
(-10,0)
(-6,2)
(0,-6)
(8,-10)
Answer:
(8,-10)
Step-by-step explanation:
step 1
Find the slope of line KL
K(-6,8),L(6,0)
m=(0-8)/(6+6)
m=-8/12=-2/3
step 2
Find the slope of the line that is parallel to KL
we know that
If two lines are parallel , then their slopes are the same
therefore
The slope of the parallel line to KL is m=-2/3
step 3
Find the equation of the line parallel to KL that pass through the point M
M(-4,-2)
The equation of the line into point slope form is equal to
y-y1=m(x-x1)
substitute
y+2=-(2/3)(x+4)
step 4
Verify the points
we know that
If the point lie on the line, then the point must satisfy the equation of the line
case a) (-10,0)
substitute the value of x and the value of y in the equation and then compare the result
-10+2=-(2/3)(0+4)
-8=-8/3 -----> is not true
therefore
The point is not on the line
case b) (-6,2)
substitute the value of x and the value of y in the equation and then compare the result
2+2=-(2/3)(-6+4)
4=4/3 -----> is not true
therefore
The point is not on the line
case c) (0,-6)
substitute the value of x and the value of y in the equation and then compare the result
-6+2=-(2/3)(0+4)
-4=-8/3 -----> is not true
therefore
The point is not on the line
case d) (8,-10)
substitute the value of x and the value of y in the equation and then compare the result
-10+2=-(2/3)(8+4)
-8=-8 -----> is true
therefore
The point is on the line
What is the solution to the equation 1/4x+2=-5/8x-5
Answer:
x=8 ?
Step-by-step explanation:
Which expression is equivalent to (2^3)^-5
Answer:
1/32768
Step-by-step explanation:
First, solve the parenthesis:
2^3 = 2 * 2 * 2 = (2 * 2) * 2 = (4) * 2 = 8
Next, solve the outer power. Note that it has a negative sign, which means that after you solve for the power sign, you have to put the number under 1.
(8)^-5 = 1/(8 * 8 * 8 * 8 * 8) = 1/32768
1/32768 is your answer.
~
Answer:
A) 1/2^15
Step-by-step explanation:
edge2021
If the unit selling price is $2.50 and the unit cost is
$1.00, what action is needed to maintain the gross
margin percentage when unit cost increases $0.25?
Lower the selling price.
Increase the selling price more than $0.25.
Maintain the same selling price.
Increase the selling price $0.25.
Answer:
D.
Increase by more than 0.25 dollars.
Step-by-step explanation:
What is the gross margin %?
Margin % = (2.50/1.00) * 100 = 250%
If the cost goes up 0.25 what will the selling price have to do to maintain a markup of 250%?
250% =(x/1.25) * 100%
Divide by 100%
250 / 100 = x / 1.25
2.5 = x / 1.25
Multiply both sides by 1.25
2.5 * 1.25 = x
3.125 = x
But that is really not the question. The question is, how much higher is that now than it used to be?
3.125 - 2.50 = 0.625 cents.
So you would have to increase the selling price by more than 0.25
A solid right pyramid has a square base. The length of the base edge is4 cm and the height of the pyramid is 3 cm period what is the volume of the pyramid?
Answer:
The volume of this pyramid is 16 cm³.
Step-by-step explanation:
The volume [tex]V[/tex] of a solid pyramid can be given as:
[tex]\displaystyle V = \frac{1}{3} \cdot b \cdot h[/tex],
where
[tex]b[/tex] is the area of the base of the pyramid, and[tex]h[/tex] is the height of the pyramid.Here's how to solve this problem with calculus without using the previous formula.
Imaging cutting the square-base pyramid in half, horizontally. Each horizontal cross-section will be a square. The lengths of these squares' sides range from 0 cm to 3 cm. This length will be also be proportional to the vertical distance from the vertice of the pyramid.
Refer to the sketch attached. Let the vertical distance from the vertice be [tex]x[/tex] cm.
At the vertice of this pyramid, [tex]x = 0[/tex] and the length of a side of the square is also [tex]0[/tex].At the base of this pyramid, [tex]x = 3[/tex] and the length of a side of the square is [tex]4[/tex] cm.As a result, the length of a side of the square will be
[tex]\displaystyle \frac{x}{3}\times 4 = \frac{4}{3}x[/tex].
The area of the square will be
[tex]\displaystyle \left(\frac{4}{3}x\right)^{2} = \frac{16}{9}x^{2}[/tex].
Integrate the area of the horizontal cross-section with respect to [tex]x[/tex]
from the top of the pyramid, where [tex]x = 0[/tex],to the base, where [tex]x = 3[/tex].[tex]\displaystyle \begin{aligned}\int_{0}^{3}{\frac{16}{9}x^{2}\cdot dx} &= \frac{16}{9}\int_{0}^{3}{x^{2}\cdot dx}\\ &= \frac{16}{9}\cdot \left(\frac{1}{3}\int_{0}^{3}{3x^{2}\cdot dx}\right) & \text{Set up the integrand for power rule}\\ &= \left.\frac{16}{9}\times \frac{1}{3}\cdot x^{3}\right|^{3}_{0}\\ &= \frac{16}{27}\times 3^{3} \\ &= 16\end{aligned}[/tex].
In other words, the volume of this pyramid is 16 cubic centimeters.
Answer:
16cm3
Step-by-step explanation: