The volume of the solid generated by rotating triangle ABC around AB is 24π cubic units.
To find the volume of the solid generated by rotating triangle ABC around side AB, you can use the method of cylindrical shells. The volume of the solid generated by rotating a region bounded by a curve around an axis is given by the formula:
[tex]\[ V = \int_{a}^{b} 2\pi x \cdot h(x) \, dx \][/tex]
Where:
[tex]\( a \) and \( b \) are the limits of integration along the x-axis (in this case, from 0 to the length of side AB),[/tex]
[tex]\( h(x) \) is the height of the curve at the position x, and[/tex]
[tex]\( 2\pi x \) represents the circumference of the cylindrical shell with radius x and height \( h(x) \).[/tex]
In this case, triangle ABC is a right triangle, so rotating it around AB will generate a cone with height AB and base radius AC.
Given that AB = 2 and AC = 6, the radius of the base of the cone formed by rotating the triangle will be [tex]\( r = AC = 6 \)[/tex]. The height of the cone will be the same as the length of side AB, so [tex]\( h = AB = 2 \).[/tex]
Now, we can calculate the volume:
[tex]\[ V = \int_{0}^{2} 2\pi x \cdot 6 \, dx \][/tex]
[tex]\[ = 12\pi \int_{0}^{2} x \, dx \][/tex]
[tex]\[ = 12\pi \left[\frac{x^2}{2}\right]_{0}^{2} \][/tex]
[tex]\[ = 12\pi \left(\frac{2^2}{2} - \frac{0^2}{2}\right) \][/tex]
[tex]\[ = 12\pi \left(\frac{4}{2}\right) \][/tex]
[tex]\[ = 12\pi \cdot 2 \][/tex]
[tex]\[ = 24\pi \][/tex]
So, the volume of the solid generated by rotating triangle ABC around side AB is [tex]\( 24\pi \)[/tex] cubic units.
The solid formed by rotating triangle ABC around side AB is a cone. The volume of this cone is calculated using the formula V = (1/3)πr^2h where r is the radius of the base and h is the height, resulting in approximately 57.91 cubic units.
The question asks for the volume of the solid generated by rotating a triangle around one of its sides. In this case, rotating triangle ABC with AB = 2, BC = 5, and AC = 6 around side AB will generate a conical surface. Since side AB will be the axis of rotation, the other two sides will act as generating lines of the cone, where side AC becomes the slant height (l) and side BC becomes the base's radius (r).
To calculate the volume of the cone, we use the formula V = (1/3)\u03c0r^2h, where r is the radius of the base, and h is the height of the cone. Here the height (h) of the cone is not directly provided, but with the Pythagorean theorem, we can find it since we know the slant height and radius: h = \\/(l^2 - r^2) = \\/(6^2 - 5^2) = \\/(36 - 25) = \\/11. Finally, the volume can be calculated: V = (1/3)\\(3.1415)\(5)^2\\/11\approx 57.91 cubic units.
The theorem of Pappus is a useful approach to solving this problem, but it requires knowing the centroid's distance from the axis of rotation, which is not provided, so we are not using that method here.
I need help with algebra 2a
Answer:
31
Step-by-step explanation:
[tex]\bf \displaystyle\sum\limits_{j=1}^{10}~2j+7\implies \displaystyle\sum\limits_{j=1}^{10}~2j+\displaystyle\sum\limits_{j=1}^{10}~7\implies 2\displaystyle\sum\limits_{j=1}^{10}~j+\displaystyle\sum\limits_{j=1}^{10}~7 \\\\\\ 2\cdot \cfrac{10(10+1)}{2}~~+~~(10)(7)\implies 2\cdot 55+70\implies 110+70\implies 180[/tex]
.The sum of the digits of a two-digit number is one-fifth the value of the
number. The tens digits is one less than the ones digit. What is the two-digit
number? (Hint: Assign a different variable to the value of each digit.)
Here's how I'm assigning a different variable to the value of each digit:
10x + y, where x is the first digit, and y is the second digit (you can test if this equation works)
The sum of the digits is 1/5 the value of the number. Using the information, we can form the equation:
x + y = (1/5)(10x + y)
Simplify
x + y = 2x + (1/5)y
The tens digit is one less than the ones digit. Using this information, we can form the equation:
x = y - 1
Adding both sides by 1 gives
x + 1 = y
Substituting this into the y's the first equation gives:
x + x + 1 = 2x + (1/5)(x + 1)
Distribute and simplify
2x + 1 = 2x + (1/5)x + 1/5
Subtract both sides by 2x
1 = (1/5)x + 1/5
Subtract 1/5 from both sides
4/5 = (1/5)x
Multiply both sides by 5
4 = x
x = 4
Use this to solve for y
x + 1 = y
4 + 1 = y
y = 5
Thus, x = 4 and y = 5. The 2 digit number is XY, which is 45.
Let me know if you need any clarifications; this was a very interesting math problem to solve!
Plz help me this isn’t that hard but I’m struggling so plz I don’t want another detention
Answer:
The length of the total 8 pieces in 0.8 meters = 6.4 meters
How many pieces there are in the remaining 0.4 meter = 6.5
Step-by-step explanation:
0.8 x 8 = 6.4
9 meters - 6.4 meters = the remaining 2.6 meters
2.6 x 0.4 = 6 1/2 pieces of ribbon in 0.4 meters.
What did Tarzan like to play?
Answer:
Step-by-step explanation:
Write the quadratic equation whose roots are 3 and 4, and whose leading coefficient is 2.
(Use the letter x to represent the variable.)
Step-by-step explanation:
equation-
(x-3) (x-4) =
[tex] {x }^{2} - 3x - 4x + 12 = {x}^{2} - 7x + 12[/tex]
Given the roots 3 and 4 of a quadratic equation, and the leading coefficient 2, the quadratic equation can be derived as 2x^2 - 14x + 24.
Explanation:To find a quadratic equation given its roots and leading coefficient, you use the factored form of a quadratic equation, x = (x - root1)(x - root2).
Given that the roots are 3 and 4, the equation takes the form of x = (x - 3)(x - 4). When you multiply this out, you get x^2 - 7x + 12.
The problem also states that the leading coefficient is 2, so we multiply our obtained equation by 2 to get: 2x^2 - 14x + 24.
So, the requested quadratic equation is 2x^2 - 14x + 24.
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Write the equation of the line that passes through (-1, 8) and is parallel to the line that passes through (5, -1) and (2, -5).
Answer:
[tex]\large\boxed{y=-\dfrac{3}{4}x+\dfrac{29}{4}}[/tex]
Step-by-step explanation:
[tex]\text{Let}\\\\k:y=m_1x+b_1,\ l:y=m_2x+b_2\\\\k\ ||\ l\iff m_1=m_2\\\\k\ \perp\ l\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\=================================[/tex]
[tex]\text{The formula of a slope:}\\\\m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\text{Calculate the slops:}\\\\(5,\ -1),\ (2,\ -5)\\\\m_1=\dfrac{-5-(-1)}{2-5}=\dfrac{-5+1}{-3}=\dfrac{-4}{-3}=\dfrac{4}{3}\\\\\text{Therefore}\\\\m_2=-\dfrac{1}{\frac{4}{3}}=-1\left(\dfrac{3}{4}\right)=-\dfrac{3}{4}\\\\\text{Put the value of slope and coordinates of the given point (-1, 8) }\\\text{to the equation of a line:}\\\\8=-\dfrac{3}{4}(-1)+b\\\\8=\dfrac{3}{4}+b\qquad\text{subtract}\ \dfrac{3}{4}\ \text{from both sides}\\\\7\dfrac{1}{4}=b\to b=\dfrac{29}{4}\\\\\text{Finally:}\\\\y=-\dfrac{3}{4}x+\dfrac{29}{4}[/tex]
A movie theater sells out 7 times per month. How many times will it sell out in the next 2 years?
1 year = 12 months.
2 years = 12 x 2 = 24 months.
Multiply the number of times it sells out per month by the number of months:
7 x 24 months = 168 times.
To the nearest tenth, what is the distance between the point (10, -11) and (-1, -5)
Answer:
≈ 12.5 units
Step-by-step explanation:
Calculate the distance d using the distance formula
d = √ (x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = (10, - 11) and (x₂, y₂ ) = (- 1, - 5)
d = [tex]\sqrt{(-1-10)^2+(-5+11)^2}[/tex]
= [tex]\sqrt{(-11)^2+6^2}[/tex]
= [tex]\sqrt{121+36}[/tex]
= [tex]\sqrt{157}[/tex] ≈ 12.5 ( to the nearest tenth )
The probability of drawing 2 defective pieces one after the other on the first and second samples, without replacement, from a lot of 50 pieces containing 5 defective pieces is approximately
Answer: The required probability is 0.004.
Step-by-step explanation:
Since we have given that
Number of pieces = 50
Number of defective pieces = 5
So, we need to draw 2 defective pieces.
So, the probability of drawing 2 defective pieces one after the other on the first and second samples would be
[tex]\dfrac{5}{50}\times \dfrac{4}{49}\\\\=\dfrac{20}{2450}\\\\=0.004[/tex]
Hence, the required probability is 0.004.
Final answer:
Calculating the probability of drawing two defective pieces sequentially from a set of 50 pieces with 5 defectives.
Explanation:
The probability of drawing 2 defective pieces one after the other without replacement:
Find the probability of drawing the first defective piece: 5/50 = 1/10.
Since the pieces are drawn without replacement, the probability of drawing the second defective piece after the first is: 4/49.
Multiply the probabilities: (1/10) * (4/49) = 4/245.
Given the following diagram, if m ∠ COF = 150°, then m ∠ BOC = AD ⊥ BF
150 °
90 °
45 °
30 °
Answer:
[tex]m\angle BOC=30^o[/tex]
Step-by-step explanation:
step 1
Find the measure of angle COD
we know that
[tex]m\angle COF=m\angle COD+m\angle DOF[/tex] ---> by addition angle postulate
we have
[tex]m\angle COF=150^o[/tex] ----> given problem
[tex]m\angle DOF=90^o[/tex] ----> because AD is perpendicular to BF
substitute the given values
[tex]150^o=m\angle COD+90^o[/tex]
[tex]m\angle COD=150^o-90^o[/tex]
[tex]m\angle COD=60^o[/tex]
step 2
Find the measure of angle BOC
we know that
[tex]m\angle BOC+m\angle COD=90^o[/tex] ---> by complementary angles
we have
[tex]m\angle COD=60^o[/tex]
substitute
[tex]m\angle BOC+60^o=90^o[/tex]
[tex]m\angle BOC=90^o-60^o[/tex]
[tex]m\angle BOC=30^o[/tex]
short answer: 30 degrees :)
what is the answer to the pic
Answer:
[tex]7[/tex]
Step-by-step explanation:
[tex]\frac{7^{-1}}{7^{-2}}[/tex]
[tex]7^{-1-(-2)}[/tex]
[tex]7^{-1+2}[/tex]
[tex]7^{1}[/tex]
[tex]7[/tex]
I used the following rules:
[tex]\frac{a^m}{a^n}=a^{m-n}[/tex]
[tex]a^1=a[/tex]
[tex]a \neq 0[/tex]
If James borrows $4,200 to pay his college tuition. He signs a 5 year simple interest loan. If monthly payments are $78.40, what is the interest rate on the loan?
Answer:
The rate of interest applied on the loan is 2.4%
Step-by-step explanation:
Given as :
The principal amount borrows as loan = p = $4200
The time period of loan = t = 5 years = 5 × 12 = 60 months
The monthly payment for loan = $78.40
So, The payment for 60 months = $78.40 × 60 = $4704
i.e Amount after 60 months = $4704
Let The rate of interest = r at simple interest
Now, From Simple Interest method
Simple interest = [tex]\dfrac{\textrm principal\times \textrm rate\times \textrm time}{100}[/tex]
Or, s.i = [tex]\dfrac{\textrm p\times \textrm r\times \textrm t}{100}[/tex]
Or, (Amount - principal) = [tex]\dfrac{\textrm p\times \textrm r\times \textrm t}{100}[/tex]
Or, $4704 - $4200 = [tex]\dfrac{\textrm 4200\times \textrm r\times \textrm 5}{100}[/tex]
Or,504 × 100 = 21,000 × r
∴, r = [tex]\dfrac{50400}{21000}[/tex]
i.e r = 2.4
So, The rate of interest = r = 2.4%
Hence, The rate of interest applied on the loan is 2.4% Answer
Karli and her friend can paint 6/7 of a picture in 3/14 of an hour. How many pictures can they paint in a full hour?
Find the product
(-3)(8)
Answer:
-24
Step-by-step explanation:
This is a simple multiplication problem. 8 times 3 is 24, and since one of the numbers is negative, the product (answer in multiplication) will be negative.
In multiplication and division of integers (positive and negative numbers), if the numbers have the same signs, the answer is ALWAYS positive, and if the numbers have different signs, the answer is ALWAYS negative.
Answer: -24
Step-by-step explanation: To multiply (-3)(8), it is important to understand that a negative times a positive is a negative so (-3)(8) is -24.
A student spends 2200 dollars during one semester of college. They spend 325 on books. What percentage was spent on books
Answer:
Step-by-step explanation:
percentage spent on books = (325/2200) * 100
= 325/22 = 14.77%
A cat is running away from a dog. After 5 seconds it is 16 feet away from the dog and after 11 seconds
it is 28 feet away from the dog. Let x represent the time in seconds that have passed and y represent the
distance in feet that the cat is away from the dog.
Answer:
18 feet
Step-by-step explanation:
Given:
A cat is running away from a dog.
After 5 seconds it is 16 feet away from the dog
After 11 seconds it is 28 feet away from the dog.
Let x represent the time in seconds that have passed and y represent the
distance in feet, so there are two points are formed such as (5, 16) and (11,28).
We will find the distance between dog and cat. by using distance formula of the two points.
[tex]d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2} }[/tex]
Now we substitute the given value in above equation.
[tex]d=\sqrt{(11-5)^{2}+(28-11)^{2} }[/tex]
[tex]d=\sqrt{(6)^{2}+(17)^{2} }[/tex]
[tex]d=\sqrt{36+289}[/tex]
[tex]d=\sqrt{325}[/tex]
[tex]d=18.08\ feet[/tex]
18.08 ≅ 18
So [tex]d=18\ feet[/tex]
Therefore the distance between dog and cat is 18 feet.
To find the linear equation for the distance between the cat and the dog, we calculate the slope with the given points and use it with one of the points to establish the equation y = 2x + 6. A graph can be drawn with the points (5, 16) and (11, 28) to visualize the cat's path.
The linear equation describing the distance the cat is from the dog in relation to time can be determined using the two given points: (5, 16) and (11, 28), where 'x' is the time in seconds and 'y' is the distance in feet.
We first find the slope (m) of the line using the formula:
m = (y2 - y1) / (x2 - x1)
Plugging in the values we get:
m = (28 - 16) / (11 - 5) = 12 / 6 = 2
This means for each second that passes, the cat is 2 feet further away from the dog. Next, we use one of the points and the slope to write the equation in point-slope form. Using the point (5, 16) we have:
y - 16 = 2(x - 5)
Expanding and simplifying this equation gives us:
y = 2x + 6
This is the linear equation that describes the distance of the cat from the dog over time. To draw a graph, we plot the two points given and draw the line that passes through them, which will represent the cat's path. The slope of 2 indicates that for every 1 second, the distance increases by 2 feet.
a concert venue can hold 200 people. student tickets are 50% less than adult tickets. Adult tickets at $50.00. The venue was sold out and made a revenue of $9125 for one event. How many adults vs. student tickets were sold?
The number of adult tickets sold is 165 and number of students tickets sold were 35
Solution:
Let "a" be the number of adult tickets sold
Let "s" be the number of student tickets sold
Cost of 1 adult ticket = $ 50.00
Student tickets are 50% less than adult tickets
Cost of 1 student ticket = Cost of 1 adult ticket - 50 % of Cost of 1 adult ticket
[tex]\rightarrow 50.00 - 50 \% \text{ of } 50.00\\\\\rightarrow 50 - \frac{50}{100} \times 50\\\\\rightarrow 50 - 25 = 25[/tex]
Thus Cost of 1 student ticket = $ 25
Given that a concert venue can hold 200 people
So we get,
number of adult tickets sold + number of student tickets sold = 200
a + s = 200 ----- eqn 1
The venue was sold out and made a revenue of $9125 for one event
So we can frame a equation as:
number of adult tickets sold x Cost of 1 adult ticket + number of student tickets sold x Cost of 1 student ticket = $ 9125
[tex]a \times 50.00 + s \times 25 = 9125[/tex]
50a + 25s = 9125 ---- eqn 2
Let us solve eqn 1 and eqn 2 to find values of "a" and "s"
From eqn 1,
a = 200 - s --- eqn 3
Substitute eqn 3 in eqn 2
50(200 - s) + 25s = 9125
10000 - 50s + 25s = 9125
-25s = 9125 - 10000
-25s = -875
s = 35Substitute s = 35 in eqn 3
a = 200 - 35
a = 165Thus the number of adult tickets sold is 165 and number of students tickets sold were 35
Solve the system of equations using any method.
6x + 4y = −8
4x − 2y = 2
A) (11/7, 2/7)
B) (2/7, 11/7)
C) (-2/7, 11/7)
D) (-2/7, -11/7)
PLEASE HELP!!!!
Answer:
My answer what I came up with is B And B
Tatiana wants to give friendship bracelets for 32 classmates. She already has 5 bracelets, and she can buy more bracelets in packages of 4. Will Tatiana have enough bracelets if she buy 5 packages? A. Yes, she will have enough for all 32 classmates if she orders 5 more packages of bracelets. Or b. No she will not have enough bracelets for all 32 classmates if she orders 5 more packages of bracelets
Answer:
b. No she will not have enough bracelets for all 32 classmates if she orders 5 more packages of bracelets
Step-by-step explanation:
write out the equation
p=the number of packages she needs to buy
32=5+4p
subtract five from both sides
32-5=5-5+4p
27=4p
dived both side by 4
27/4=4p/4
6.75=p round to 7
Check your answer:
4 x 7 = 28
add the number of bracelets she already has
28 + 5 = 33 bracelets
33>32
So 7 packages is the minimum number of packages she needs to buy
a certain triangle has two 45 degree angles what type of triangle is it
Answer:
most likely isosceles
Step-by-step explanation:
due to the fact that two angles are congruent and the other angle is probably not it would make it all isosceles triangle
A triangle with two 45-degree angles is a special type of triangle known as an isosceles triangle.
In a triangle, if two angles are congruent, then the opposite sides of those angles are also congruent. In an isosceles triangle, two sides are equal in length, and the angles opposite those sides are congruent. Since two angles of the triangle are 45 degrees each, their opposite sides are also equal in length, making it an isosceles triangle.
Evaluate f(1) using substitution:
f(x) =2x^3 -3x^2-18x+8
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Substitute 1 in everywhere you see 'x'
2(1)^3 - 3(1)^2 - 18(1) + 8
Solve:
f(1) = -11
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Final answer:
To evaluate the function f [tex](x) = 2x^3 - 3x^2 - 18x + 8[/tex] at x=1, substitute 1 for every instance of x in the function and simplify to get f(1) = -11.
Explanation:
The question appears to be a math problem where the student is asked to evaluate a function at a specific input. Specifically, the function given is [tex]f(x) = 2x^3 - 3x^2 - 18x + 8[/tex] and the student has been asked to evaluate this function when x is equal to 1. To find f(1), we replace every instance of x in the function with 1.
So, f(1) = [tex]2(1)^3 - 3(1)^2 - 18(1) + 8[/tex]= 2(1) - 3(1) - 18 + 8 = 2 - 3 - 18 + 8 = -11.
Thus, f(1) evaluates to -11.
The number of students enrolled at a college is 12,000 and grows 4% each year. Complete parts (a) through (e).
a) The initial amount a is
.
Answer:
48000
Step-by-step explanation:
12000 students
4%
1 =annually
12×4×1= 48000
Answer:12,000
Step-by-step explanation:can’t give you one cuz I’m doing this in mathxl :p
Select the correct answer from each drop-down menu.
A 4
7
15
B 15
4
7
C 15
7
4
Answer: The correct answer is: [C]: " [tex]15^{(7/4)}[/tex] " .
____________________________________
Step-by-step explanation:
____________________________________
Note the property for square roots in exponential form:
_____________________________________
→ [tex]\sqrt[a]{(b)^ c}[/tex] ; ↔ b[tex]b^{(c/a)}[/tex] ;
{ [tex]a\neq 0[/tex] ; [tex][a^{(b/c)}]\neq 0[/tex] ; [tex]c\neq 0[/tex] .}.
_____________________________________
As such, given:
→ [tex]\sqrt[4]{(15^7)}[/tex] ;
a = 15, b = 7, c = 4 .
→ [tex]\sqrt[4]{(15^7)}[/tex] ; ↔ [tex]15^{(7/4)}[/tex] ;
→ which corresponds to:
_____________________________________
Answer choice: [C]: " [tex]15^{(7/4)}[/tex] " .
_____________________________________
Hope this helps!
Wishing you well in your academic endeavors!
_____________________________________
Prove that ABCD is a square if a A(1,3) B(2,0) C(5,1) and D(4,4)
[tex]AB=BC=CD=AD = \sqrt{10}[/tex]
As all the sides have same length, ABCD is a square
Step-by-step explanation:
To prove ABCD a square we have to find the lengths of each side
So,
the distance formula will be used to find the lengths
The distance formula is:
[tex]d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Now,
[tex]AB = \sqrt{(2-1)^2+(0-3)^2}\\= \sqrt{(1)^2+(-3)^2}\\=\sqrt{1+9}\\=\sqrt{10}[/tex]
[tex]BC = \sqrt{(5-2)^2+(1-0)^2}\\= \sqrt{(3)^2+(1)^2}\\=\sqrt{9+1}\\=\sqrt{10}[/tex]
[tex]CD = \sqrt{(4-5)^2+(4-1)^2}\\= \sqrt{(-1)^2+(3)^2}\\=\sqrt{1+9}\\=\sqrt{10}[/tex]
[tex]AD = \sqrt{(4-1)^2+(4-3)^2}\\= \sqrt{(3)^2+(1)^2}\\=\sqrt{9+1}\\=\sqrt{10}[/tex]
we can see that
[tex]AB=BC=CD=AD = \sqrt{10}[/tex]
As all the sides have same length, ABCD is a square
Keywords: Distance formula, square
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Which equation has both -3 and 3 as possible values of y?
A
y^2=6
B
y^2=8
C
y^2=9
D
y^2=64
Answer:
C. [tex]y^2=9[/tex]
Step-by-step explanation:
1. [tex]y^2 = 9[/tex]
2. [tex]y = \frac{+}{}\sqrt{9}[/tex]
3. Equation solutions:
[tex]y_{1} = 3\\y_{2} = -3[/tex]
The following proof shows an equivalent system of equations created from another system of equations. Fill in the missing reason in the proof.
Statements Reasons
2x + 2y = 14
−x + y = 5 Given
2x + 2y = 14
y = x + 5 ?
Answer:
As addition property of equality clearly states that if we add the same number to both sides of an equation, the sides remain equal.
Step-by-step explanation:
[tex]2x + 2y = 14[/tex]
[tex]-x + y = 5[/tex] Add x in both sides (Addition Property of Equality)
[tex]2x + 2y = 14[/tex]
[tex]y = x + 5[/tex] Multiply both sides by 2
[tex]2x + 2y = 14[/tex]
[tex]2y = 2x + 10[/tex] Subtract 2x in both sides
[tex]+\left \{ {{2x + 2y=14} \atop {-2x + 2y=10}} \right.[/tex] ∵adding both equation
[tex]4y = 24[/tex] divide both sides by 4
[tex]y = 6[/tex]
Put the value of y = 6 to the equation [tex]-x + y = 5[/tex]
[tex]-x + 6 = 5[/tex] Subtract 6 from both sides
[tex]-x = -1[/tex] Change the sign
[tex]x = 1[/tex]
Keywords: Addition property of equality, reason, proof
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evaluate 81/36 x^2 - y^2/25
Answer:
Step-by-step explanation:
Final answer:
To simplify the given expression involving fractions and variables, multiply, divide, and subtract accordingly to obtain the simplified form. Therefore, the simplified expression is [tex](9/4)x^2 - (1/25)y^2.[/tex]
Explanation:
The given expression is:
[tex]81/36 * x^2 - y^2/25[/tex]
To simplify this expression:
Multiply 81/36 which equals 9/4.
Then, divide [tex]x^2[/tex] by 4, and subtract [tex]y^2[/tex] divided by 25.
Therefore, the simplified expression is [tex](9/4)x^2 - (1/25)y^2.[/tex]
what number is 10 times as great as 7962
To find a number that is 10 times greater than 7962, we can multiply.
7,962 * 10 = 79,620
79,620 is 10 times greater than 7,962.
Best of Luck!
Answer:
79,620
Step-by-step explanation:
7,962 (10) = 79,620
how can you use functions to solve real world problems ??
Answer:ioj;i;
hStep-by-step explanation:
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A gasoline generator provides the power to
light a construction project at night. The generator uses 5.5 gallons of gasoline for every 3 1/3 hours of operation.
Is of operation. How much
gasoline is used in 11 hours?
Answer:
The quantity of gasoline used for 11 hours is 18.37 gallons .
Step-by-step explanation:
Given as :
The quantity of gasoline use by generator = 5.5 gallons
The generator use 5.5 gallons of gasoline for duration = 3 [tex]\dfrac{1}{3}[/tex] hours
I.e The generator use 5.5 gallons of gasoline for duration = [tex]\dfrac{10}{3}[/tex] hours
Let The quantity of gasoline use by generator for 11 hours = x gallons
Now, According to question
Applying unitary method
∵For [tex]\dfrac{10}{3}[/tex] hours of power generate ,The quantity of gasoline use = 5.5 gallons
So For 1 hour of power generate ,The quantity of gasoline use = [tex]\frac{5.5}{\frac{10}{3}}[/tex] gallons
∴ For 11 hours of power generate ,The quantity of gasoline use = [tex]\frac{5.5}{\frac{10}{3}}[/tex] × 11 gallons
i.e For 11 hours of power generate ,The quantity of gasoline use = 1.67 × 11
Or, For 11 hours of power generate ,The quantity of gasoline use = 18.37 gallons
Hence,The quantity of gasoline used for 11 hours is 18.37 gallons . Answer