Answer:
Length of the base = 15 cm
Volume = 1125√2 cm³ = 1590.99 cm³ (2 d.p.)
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{6.6cm}\underline{Lateral Surface Area of a square pyramid}\\\\$LSA=a \sqrt{a^2+4h^2}$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the base edge \\\phantom{ww}$\bullet$ $h$ is the height\\\end{minipage}}[/tex]
[tex]\boxed{\begin{minipage}{6.6cm}\underline{Base Area of a square pyramid}\\\\$BA=a^2$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the base edge \\\end{minipage}}[/tex]
If the lateral surface area (LSA) of the pyramid is three times the base area (BA):
[tex]\implies a \sqrt{a^2+4h^2}=3a^2[/tex]
Rearrange the equation to isolate h²:
[tex]\implies \sqrt{a^2+4h^2}=3a[/tex]
[tex]\implies (\sqrt{a^2+4h^2})^2=(3a)^2[/tex]
[tex]\implies a^2+4h^2=9a^2[/tex]
[tex]\implies 4h^2=8a^2[/tex]
[tex]\implies h^2=2a^2[/tex]
[tex]\boxed{\begin{minipage}{6.6cm}\underline{Total Surface Area of a square pyramid}\\\\$SA=a^2+a \sqrt{a^2+4h^2}$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the base edge \\\phantom{ww}$\bullet$ $h$ is the height\\\end{minipage}}[/tex]
Given:
SA = 900 cm²h² = 2a²Substitute these values into the formula for the total surface area and solve for a:
[tex]\implies a^2+a\sqrt{a^2+4(2a^2)}=900[/tex]
[tex]\implies a^2+a\sqrt{a^2+8a^2}=900[/tex]
[tex]\implies a^2+a\sqrt{9a^2}=900[/tex]
[tex]\implies a^2+a(3a)=900[/tex]
[tex]\implies a^2+3a^2=900[/tex]
[tex]\implies 4a^2=900[/tex]
[tex]\implies a^2=225[/tex]
[tex]\implies a=15[/tex]
Therefore, the length of the base of the square based pyramid is:
a = 15 cmTo find the height (h), substitute the found value of a into the formula for h² and solve for h:
[tex]\implies h^2=2(15)^2[/tex]
[tex]\implies \sqrt{h^2}=\sqrt{2(15)^2}[/tex]
[tex]\implies h=\sqrt{2}\sqrt{(15)^2}[/tex]
[tex]\implies h=15\sqrt{2}[/tex]
Therefore, the height of the square based pyramid is:
h = 15√2 cm[tex]\boxed{\begin{minipage}{5cm}\underline{Volume of a square pyramid}\\\\$V=\dfrac{1}{3}a^2h$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the base edge \\\phantom{ww}$\bullet$ $h$ is the height\\\end{minipage}}[/tex]
Given:
a = 15h = 15√2Substitute the values into the formula and solve for volume:
[tex]\implies V=\dfrac{1}{3}(15)^2 \cdot 15\sqrt{2}[/tex]
[tex]\implies V=\dfrac{225}{3} \cdot 15\sqrt{2}[/tex]
[tex]\implies V=75\cdot 15\sqrt{2}[/tex]
[tex]\implies V=1125\sqrt{2}[/tex]
[tex]\implies V=1590.99[/tex]
Therefore, the volume of the square based pyramid is:
1590.99 cm³ (2 d.p.)1
Which expression is equivalent to (5³)⁹?
A 53+9
B 53x9
©5³ +5⁹
5³ x 5⁹
Answer: (D) 5³ * 5⁹.
Step-by-step explanation:
The expression (5³)⁹ is the same as 5³ * 5³ * 5³ * 5³ * 5³ * 5³ * 5³ * 5³ * 5³, which can be simplified to 5^9 * 5^9 * 5^9 * 5^9 * 5^9 * 5^9 * 5^9 * 5^9 * 5^9. The only expression from the options above that is equivalent to this is 5³ * 5⁹, so the correct answer is (D) 5³ * 5⁹.
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answer: "approximately nine years
explanation : if an investment scheme promises an 8% annual compounded rate of return, it will take approximately nine years (72 / 8 = 9) to double the invested money.
hope this helps!!
Which property states that the sum of any two whole number is always a whole number?
The closure property of the whole number states that "Addition and multiplication of two whole numbers is always a whole number."
What is Property of Closure ?
A set has the closure property only under a particular operation which is if the result of the operation is always an element in the set. When a set has the closure property under a particular operation, then we say that the set is “closed under the operation.”
a)The set of integers is closed under the operation of addition because the sum of any two integers is always another integer and is therefore in the set of integers.
b) The set of integers is not closed under the operation of division because when you divide one integer by another, you don’t always get another integer as the answer. For example, 4 and 9 are both integers, but 4 ÷ 9 = 4/9. 4/9 is not an integer, so it is not in the set of integers!
Hence , the closure property of the whole number states that "Addition and multiplication of two whole numbers is always a whole number.
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Estimate fx and fy at point B. 70 50 30 y 4 - -30 2 С 10 B -10- 0 - 00 30 50 10 -10 A -70 -2 -20 -4 (Use decimal notation. Give your answer to one decimal place.)
It is difficult to accurately estimate the values of fx and fy at point B without more information. In order to estimate the values of the partial derivatives at a point, you typically need to have a contour map or some other representation of the function in the neighborhood of that point.
A contour map is a graphical representation of a function that shows the values of the function at different points in the xy plane. The lines on the map, called contour lines, represent the values of the function, and the spacing between the lines indicates the rate of change of the function.
To estimate the values of the partial derivatives at a point using a contour map, you can:
Identify the contour line that passes through the point of interest.Look for nearby points on the map that have coordinates that differ only in the x or y direction from the point of interest.Calculate the difference in the function values at these points and divide by the difference in the x or y coordinate, depending on which partial derivative you are estimating.For example, to estimate fx at point B, you could:
Identify the contour line that passes through point B.Look for nearby points on the map that have y-coordinates that are the same as point B but x-coordinates that are different.Calculate the difference in the function values at these points and divide by the difference in the x-coordinates to estimate fx at point B.Without a contour map or other representation of the function in the neighborhood of point B, it is not possible to accurately estimate the values of fx and fy.
Since the question is incomplete and there is no similar one found, the answer is general.
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What is the maximum value of this function f x )= − 16x2 32x 20?
On solving the provided question, we can say that - the maximum value or maxima of the given function is 36.
What is maxima?Maximum describes a high point (plural maxima). The term "minimum" refers to a low point (plural minima). Extremum is the Latin term used to describe the greatest or minimum (plural extrema). When greater points are possible elsewhere but not close by, we say local maximum (or minimum). The greatest and smallest values of a function in either a specified range or throughout the whole domain are referred to as a function's maxima and minima, generally known as extrema, in mathematical analysis.
The vertex is used to determine that the function's maximum value is 36.
Function is provided by:
f(x) = [tex]16x^2 + 32x + 20[/tex]
coefficients -
[tex]a = -16, b = 32 , c =20[/tex]
[tex]f_{max} = \frac{32^2 - 4(-16)(20)}{4(-16)}[/tex] = 36
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TEXT ANSWER Which ordered pair did you select? Explain why or why not it is a function. Answer in complete sentence.
i picked (3,5) as my ordered pair im giveing brainlist to whoever answers correct and in a complete sentence oh and fast
Answer:
* Can you please give us a photo of the problem you want help with? I have an idea of what the problem could be about, though. The answer I give is what I think the problem is about *
I picked (3,5) as my ordered pair. It is not a function because the coordinate (3,5) has the same x-value as the coordinate [put the coordinate with the same x-value here], and functions cannot have the same x-values for different y-values in order to pass the "vertical line test".
What is the mode of 12345?
If we answer yes, then 1, 2, 3, 4, and 5. No phrase is used more than once in this passage. Therefore, there is currently no most prevalent phrase. Thus, this data does not contain a mode.
How can I locate the mode?The mode calculation is a rather simple process. Organize the numbers in a set in whatever order—from lowest to highest as well as highest to lowest—and then tally the frequency with which each number appears in the group. The mode is the one that shows up most frequently.
The purpose of mode calculation?When the mean, as well as median, as well as median cannot be employed, the mode informs us of the most prevalent value in categorical data. The mode provides insight into the location of a dataset's "center".
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How many of these numbers are divisible by 3?
The numbers which are divisible by 3 are countless. We determine it by the divisibility rules.
What is divisible in mathematics?
A number is called divisible by others whenever it is divided properly and obtain a whole number as an outcome. As example 125 can be divided by 5 and we get the whole number 25 so 125 is said divisible by 5.
On the other hand, 225 cannot be divided by 10 and we get a decimal number. So, 225 is not divisible by 10.
How many numbers are divisible by 3?A number is said to be divisible by 3 if the sum of the digits is divided by 3. Suppose we are given two number 308 and 492.
At first, we will sum the digit of each number, 3+0+8 = 11
the sum of the digit of 492 = 4+9+2 = 15
we cannot divide 11 by 3 but 15 is divided by 3. Hence, 492 is divisible by 3.
So, there are countless number which are divisible by 3.
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Question 5
Ethan put $1,250 into a savings account. The account pays 4.5% simple interest on an annual basis. If he does not add or withdraw money
from the account, how much interest will he earn after 2 years? Round to the nearest cent.
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Answer:
To calculate the interest earned on a savings account, you first need to determine the interest rate per year and the time the money is invested. In this case, the interest rate is 4.5% and the time is 2 years.
The formula for simple interest is I=Prt, where I is the interest earned, P is the principal (the initial amount invested), r is the interest rate, and t is the time. Plugging in the values from the problem, we get I = 1250 * 0.045 * 2 = $112.50.
Therefore, Ethan will earn $112.50 in interest after 2 years if he does not add or withdraw any money from the account. Rounded to the nearest cent, this is $112.00.
Step-by-step explanation:
What is mean mode formula?
Mean mode formula - Mean = {Sum of Observation} ÷ {Total numbers of Observations}
What does the mode mean?
By summing all the numbers in a data collection and dividing by the total number of values in the set, the mean (average) of the data set can be determined.
A data collection is ordered from least to largest, and the median is the midpoint number. A data set's mode is the number that appears the most frequently.
What are the mean, median, and example?
The most frequent number, or the one that happens the most frequently, is known as the mode. Example: Since the number 2 appears three times, more than any other number, it is the mode of the numbers 4, 2, 4, 3, and 2.
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Eric rides his bike 4 1/3 hours during the week. His little brother rides his bike 1 3/4 hours during the week. How many more hours does Eric ride his bike during the week than his little brother? Enter your answer as a mixed number in simplest form by filling in the boxes.
A force of 343.8 N is used to push a car 38.5 m horizontally in 4.86 s. Calculate the power developed.
Important Formulas:
[tex]w=Fd[/tex]
[tex]p=\dfrac{w}{t}[/tex]
w = work (Measured in Joules)
F = Force (Measured in Newtons)
d = distance (Measured in meters)
p = power (Measured in watts)
t = time (measured in seconds)
______________________________
Given:
[tex]f=343.8N[/tex]
[tex]d=38.5m[/tex]
[tex]t=4.86s[/tex]
[tex]p=?[/tex]
______________________________
Finding Work:
[tex]w=Fd[/tex]
[tex]w=(343.8)(38.5)[/tex]
[tex]w=13236.3J[/tex]
______________________________
Finding Power:
[tex]p=\dfrac{w}{t}[/tex]
[tex]p=\dfrac{13236.3}{4.86}[/tex]
[tex]\fbox{p = 2723.52 watts}[/tex]
Can anyone please help me with this question?
Question: If α and β are the roots of 4x^2 + 3x + 7 = 0, find the value of 1/ α + 1/ β
The numeric value of the expression 1/α + 1/β is given as follows:
-3/7.
How to obtain the numeric value of the expression?The quadratic function in this problem is given as follows:
4x² + 3x + 7 = 0.
The coefficients of the quadratic function are given as follows:
a = 4, b = 3, c = 7.
The sum of the roots is given as follows:
α + β = -b/a.
Hence:
α + β = -3/4
The product of the roots is given as follows
αβ = c/a
Hence:
αβ =7/4.
These values are used to obtain the numeric value of the expression, as follows:
1/α + 1/β = (α + β)/αβ = (-3/4)/(7/4) = -3/7.
(the least common multiple of α and β is αβ, and then the least common factor is used to solve the expression).
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Guys, can you help me with my homework?
Using two column proof, we have been able to show that ΔABE is congruent to ΔCDE via SAS Congruency Postulate.
How to handle two column proof?We are given certain statements of the given triangle and we want to get a flowchart of a proof which is a two column proof. Thus;
Statement 1; CD = AB
Reason 1; Given
Statement 2; BE = DE
Reason 2; AC is the segment bisector of BD
Statement 3; ∠ABE = ∠CDE
Reason 3; Alternate angles theorem
Statement 4; ΔABE ≅ ΔCDE
Reason 4; SAS Congruency Postulate
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Two containers designed to hold water are side by side, both in the shape of a cylinder. Container A has a diameter of 12 feet and a height of 19 feet. Container B has a diameter of 14 feet and a height of 13 feet. Container A is full of water and the water is pumped into Container B until Conainter B is completely full.
After the pumping is complete, what is the volume of the empty space inside Container A, to the nearest tenth of a cubic foot?
After the pumping is complete, the volume of the empty space inside container [A] will be 1147.72 ft³.
What is volume of a cylinder? What is equation modelling? What is a mathematical equation and expression?The volume of the cylinder is equivalent to -v{c} = πr²h = π(d/2)²h
Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis of the given problem.A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical equation is used to equate two expressions.Given are two containers designed to hold water are side by side, both in the shape of a cylinder. Container A has a diameter of 12 feet and a height of 19 feet. Container B has a diameter of 14 feet and a height of 13 feet. Container A is full of water and the water is pumped into Container B until Container B is completely full.
Volume of container [A] -
V{A} = (22/7) x (12/2)² x 19
V{A} = (22/7) x 6 x 6 x 19
V{A} = 3149.72 ft³
Volume of container [B] -
V{A} = (22/7) x (14/2)² x 13
V{A} = (22/7) x 7 x 7 x 13
V{B} = 2002 ft³
V{A} - V{B} → Empty space = 3149.72 ft³ - 2002 ft³ = 1147.72 ft³
Therefore, the free space inside the container A will be 1147.72 ft³.
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What are 3 examples inequality?
Ruth ha 12 roll at her bakery. She receive an online order for 60 roll. Ruth bake roll in batche of 24. Select the equation that repreent the given ituation and find the number of batche Ruth need to make to complete the order
the equation that represents the given situation is 12x + 24 = 60 and the number of batches Ruth needs to make to complete the order is 2 batches
The issue can be approached from the reverse. She already has 12 rolls, so take that out of the total. 48 will result from this. The "x" would then indicate how many more batches of 24 she needs to make in order to reach that 48 because she manufactures rolls in batches of 24. She would bake two additional batches to get 60 because 48 divided by 24 is equal to 2. If you put this concept into an equation, you get 24x + 12 = 60; 2 batches
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The meaure of the exterior angle of a quadrilateral are x°x°, 2x°2x°, 4x°4x°, and 5x°5x°. Find the meaure of the mallet exterior angle
The meaure of the smallest exterior angle among the four exterior angles of a quadrilateral are x°,2x°, 4x°, and 5x° is x = 30° .
What is exterior angles?The angle formed between one side of a polygon and another line segment extending from the adjacent side is called the exterior angle of the polygon.
Exterior and interior angles form a straight line and form a linear pair. Therefore, if we know the interior angles of a quadrilateral, we can easily find the exterior angles.Exterior angle + interior angle = 180°A quadrilateral has 4 interior and 4 exterior angles.The sum of the exterior angle measurements of a polygon equals 360 degrees, regardless of the number of sides of the polygon..We have, quadrilateral with exterior angles x° , 2x° , 4x° and 5x° .
As we discuss, the sum of exterior angles of quadrilateral (polygon of four sides) = 360°
=> x° + 2x° + 4x° + 5x° = 360°
Adding all x values on left hand side,
=] 12x° = 360°
=> x = 360/12 = 30°
Now, the smallest exterior angle of quadrilateral is x° , so it's measure is 30°.
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find the part what is 120% of 10.9
Square Root of 120
In this mini-lesson, we will calculate the square root of 120 by the long division method along with solved examples and interactive questions. The square root of a number is the number that gets multiplied to itself to give the original number. 4 is a square root of 16 because 4 × 4 = 16 and the symbol square root is written as √ and is an integral part of mathematics.
Let us take a look at what the square root of 120 is.
Square Root of 120: √120 = 10.954
Square of 120: 1202 = 14400
Answer: 13.08
Step-by-step explanation:
i hope this helps
How do you solve inequality questions?
An inequality like the statement, x + 3 > 5, can be solved by finding the value of the variable, "x", which is x > 2.
How to Solve an Inequality Question?Inequalities are used to express relationships between quantities or values that are not equal. They can be used to describe constraints or limitations on a solution to a problem, or to represent a range of possible values.
Inequality can also be used to describe relationships between variables in algebraic expressions or equations.
To solve an inequality, we need to isolate the variable in the given statement to determine the value of the variable.
For example, given the inequality, x + 3 > 5, in order to solve this inequality, we need to find the value of x by subtracting 3 from both sides:
x + 3 - 3 > 5 - 3
x > 2.
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To decorate a cake, you make a shade of orange icing using 24 drops of red food coloring for every 8 drops of yellow. How many drops of yellow food coloring would you need if you use 9 drops of red food coloring?.
The solution of 3 drops of yellow food coloring needed to make a shade of orange icing with 9 drops of red food coloring is 72/24
The formula for calculating the number of drops of yellow food coloring required to make a shade of orange icing would be:
Yellow Food Coloring Drops = (Red Food Coloring Drops x 8) / 24
In this example, we are using 9 drops of red food coloring. To calculate the number of drops of yellow food coloring needed, we would plug in 9 for the number of drops of red food coloring, resulting in the following equation:
Yellow Food Coloring Drops = (9 x 8) / 24
We can solve this equation by multiplying both sides by 24 to get:
Yellow Food Coloring Drops x 24 = 9 x 8
We can further simplify the equation by multiplying the numbers on the right side of the equation to get:
Yellow Food Coloring Drops x 24 = 72
Finally, we can solve for the number of drops of yellow food coloring by dividing both sides of the equation by 24 to get:
Yellow Food Coloring Drops = 72/24
After simplification, we end up with the solution of 3 drops of yellow food coloring needed to make a shade of orange icing with 9 drops of red food coloring.
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How do you find the x-intercept of a linear equation in two variables?
To find the x-intercept of a linear equation in two variables we set y intercept to 0.
When we are given with a two variable linear equation, we plug 0 in place of y and solve the equation to get the x-intercept of that linear equation.
For example, let us consider the linear equation 2x + 3y = 4
To get the x-intercept of the equation 2x + 3y = 4 we would plug y = 0.
Therefore, 2x + 3(0) = 0
⇒ 2x + 0 = 4
⇒ x = 4/2 = 2
Thus, the x-intercept of the linear equation 2x + 3y = 4 is 2.
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your company makes game parts using 3-d printers. one customer wants a circular game coin that is 2.0 centimeters across and 0.5 centimeters thick, as shown below. you need to estimate the amount of plastic you will need for each batch of 50 coins. how many cubic centimeters is that, rounded up if necessary to be a multiple of 10 cubic centimeters?
The amount of plastic needed for each batch of 50 coins is equal to the volume of 50 coins that is 80 cu.cm.
The diameter of the coin is 2.0 cm.
As radius is half of the diameter, so its radius will be 1.0 cm.
It is given that the coin is circular in shape, so the area of the circular surface will be πr² = 3.14 × 1² = 3.14 sq. cm. (π = 3.14)
The thickness of the coin is 0.5 cm, which will be considered as the height of the coin.
So, the volume of each coin will be = 3.14 × 0.5 = 1.57 cu. cm.
Therefore, the plastic needed for the batch of 50 coins is,
1.57 × 50 = 78.5 cu.cm and in multiple of 10 it will be 80 cu.cm.
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How do you solve a 3x3 for beginners?
Choose an equation, multiply a row by a constant to make it equal to 1, use row operations to make all other elements in the same column equal to 0, repeat for all elements in the matrix, when all elements are equal to 1, the 3x3 matrix is solved
To solve a 3x3 matrix for beginners, start by writing the equation in the form of Ax = B. Then, choose a set of three equations from the matrix that are independent of each other and solve the first equation for one of the unknowns, substituting the known values for the other two unknowns. Substitute the value of the unknown from the first equation into the other two equations and solve for the remaining two unknowns. Finally, check the solution by substituting the values of all three unknowns into the original equation.
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What is the value of 5x25 − 3x32 2x − 12 at x 1?
The value of the given expression 5x²⁵ - 3x³² + 2x - 12 at x = 1 is -8.
Explain the term power of the number?How many times you should multiply a number depends on its power. Exponents and indices are other names for powers. For instance, 8^2 may also be referred to as "8 to the power 2," "8 to the second power," or just "8 squared."The given expression is:
5x²⁵ - 3x³² + 2x - 12
To evaluate the value at x=1.
Substitute x = 1 in the given expression.
= 5(1)²⁵ - 3(1)³² + 2(1) - 12
Simplify:
= 5 - 3 + 2 - 12
= -8
Therefore, the value of the given expression at x = 1 is -8.
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The correct question is-
What is the value of 5x²⁵ - 3x³² + 2x - 12 at x=1?
What is the relationship between the volume of rectangular prism and of a pyramid with the same height and base?
The volume of the pyramid is 1/3 of the volume of the prism.
The relationship between the volumes of pyramids and prisms is that when a prism and pyramid have the same base and height. The volume of the pyramid is 1/3 of the volume of the prism.
To see by the mathematically:
If a pyramid and a prism have the same base and height, their volumes are always in the ratio of
1:3.
As volume of prism is 108 cubic meters,
volume of pyramid is 1/3 × 108 = 36 cubic meters.
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Do the one you would like please show work
Step-by-step explanation:
I am not what the answer My teacher
What is the inverse function calculator?
The inverse of the function that is provided is calculated using the inverse function calculator. When a function, f(x), is given, its inverse, x=f(y), is calculated by switching the variables ( y ).
Given,
Inverse function;
An inverse in mathematics is a function that "undoes" another function. In other words, if f(x) produces y, then y entered into the inverse of f produces x. An invertible function is one that has an inverse, and the inverse is represented by the symbol f1.
Inverse function calculator;
The calculator for inverse functions determines the inverse of the supplied function. If a function, f(x), is supplied, then the inverse of the function, x=f(y), is determined by exchanging the variables ( y ).
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f(x) = 10 –
f(134) :
X
134
Answer: -1/34
Step-by-step explanation:
Answer:
f(134) = 9
Step-by-step explanation:
substitute x = 134 into f(x) and evaluate
f(x) = 10 - [tex]\frac{x}{134}[/tex] , then
f(134) = 10 - [tex]\frac{134}{134}[/tex] = 10 - 1 = 9
How do you find the maximum value of a parabola using calculus?
You can use calculus to find the maximum value of a parabola by these steps which are given in the solution part.
What is Parabola?A parabola is a U-shaped curve this is drawn for a quadratic function,
To find the maximum value of a parabola using calculus, you can follow these steps:
1. Identify the equation of the parabola in the form "y = ax² + bx + c," where "a," "b," and "c" are constants.
2. Take the derivative of the equation with respect to x.
3. Set the derivative equal to 0 and solve for x. This will give you the value of x at the vertex of the parabola.
Substitute the value of x that you found in step 3 back into the original equation to find the corresponding y-value. This y-value is the maximum or minimum value of the parabola, depending on the value of a. If a is positive, the parabola opens upwards and the y-value is the maximum. If a is negative, the parabola opens downwards and the y-value is the minimum.
For example, suppose you want to find the maximum value of the parabola y = 2x² - 4x + 3. First, take the derivative of the equation: y' = 4x - 4. Set this equal to 0 and solve for x: 0 = 4x - 4, x = 1.
Substituting this value back into the original equation gives us y = 2(1)² - 4(1) + 3 = 2 - 4 + 3 = 1.
Therefore, the maximum value of the parabola is 1.
Learn more about the parabola here:
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