Answer:
The area of a horizontal cross section at a height is [tex]\pi\times(2-\dfrac{y}{7})^2[/tex]
Step-by-step explanation:
Given that,
Height = 14 m
Radius = 2 m
Let V be the volume of a right circular cone
We need to calculate the value of R
Using given data
[tex]\dfrac{h}{r}=\dfrac{h-y}{R}[/tex]
Put the value into the formula
[tex]\dfrac{14}{2}=\dfrac{14-y}{R}[/tex]
[tex]7R=14-y[/tex]
[tex]R=2-\dfrac{y}{7}[/tex]
We need to calculate the area of a horizontal cross section at a height y
Using formula of area
[tex]A=\pi R^2[/tex]
Put the value into the formula
[tex]A=\pi\times(2-\dfrac{y}{7})^2[/tex]
Hence, The area of a horizontal cross section at a height is [tex]\pi\times(2-\dfrac{y}{7})^2[/tex]
The area of the circular cone at height y can be derived as a function, A,
having y as the input variable.
Correct response:
[tex]Area \ of \ horizontal \ cross \ section \ at \ height \ y \ is \ \underline{ A = \pi \times \dfrac{\left(14 - y\right)^2}{7} }[/tex]
Method used for deriving the areaThe given parameters are;
Shape of figure = Right circular cone
Height of the cone, h = 14
Base radius, R = 2
Required:
The area of a cross section at a height y using similar triangles
Solution:
We have using similar triangles;
[tex]\mathbf{\dfrac{h}{h - y} }= \dfrac{R}{r} [/tex]
Which gives;
[tex]\mathbf{\dfrac{14}{14 - y}} = \dfrac{2}{r} [/tex]
Therefore;
2·(14 - y) = 14·r
28 - 2·y = 14·r
[tex]r = \dfrac{28 - 2 \cdot y}{14} = 2 - \dfrac{y}{7} [/tex]
The horizontal cross sectional area, A = π × r²
Therefore;
[tex]Area \ of \ the \ cross \ sectional \ area,\ A = \pi \times \left(2 - \dfrac{y}{7} \right) = \underline{ \pi \times \dfrac{\left(14 - y \right)^2}{7} }[/tex]
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If the area of a triangle is 100 in^2, and the height is 10in, find the length of the base in inches.
Round to the nearest inch if applicable.
Answer:
Area of a triangle is 100 in²
Height of triangle is 10 in .
we have been asked to find the length of its base .
Formula Used to Find length of its base
☯[tex] \bf\: Area \: of \: triangle \: = \dfrac{1}{2} \times base \: \times height \: [/tex]
Put the given value we obtain
[tex] \rm \implies \: 100 = \dfrac{1}{2} \times base \: \times 10 \\ \\ \rm \implies \: 100 = \dfrac{1}{ \cancel2} \times base \: \times \cancel{10} \\ \\ \rm \implies \: 100 = base \: \times 5 \\ \\ \rm \implies \: base \: = \dfrac{100}{5} \\ \\ \rm \implies \: base \: = \cancel\dfrac{100}{5} \\ \\ \rm \implies \: base \: = 20 \: inch[/tex]
So, the length of its base is 20 inch .
The base length of the triangle with the given values of area and length of height to the nearest inch 20in.
What is a triangle?
A triangle is a two-dimensional shape with three edges and three vertices.
The area of a triangle is expressed as;
A = (1/2) × base × height
Given the data in the question;
Area of the triangle A = 100in²Length of Height = 10inLength of Base = ?We substitute our given values into the expression above.
A = (1/2) × base × height
100in² = (1/2) × Base × 10in
100in² = 0.5 × 10in × Base
100in² = 5in × Base
Base = 100in² / 5in
Base = 20in
Therefore, the base length of the triangle with the given values of area and length of height to the nearest inch 20in.
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hello help me with this question thanks in advance
• Can you list down similarities of your experience with your circle of friends?
A recent study published in Nature Communications says the reason for this likeness is that best friends actually have similar — or sometimes identical — brain activity.. Yup , your closest friends "get you" because it's like their basically looking in the mirror.. Friends and tend to have certain characteristics in common , Such as Age, Education and even intelligence — and yet , Research has long suggested that personality isn't one of these commonalities.. Some scientific research has shown how you're likely to be attracted to people who share similar facial characteristics as you. One theory for this is that we associate people who look like us with our parents, and thus have more positive feelings towards their features. Similarities are also important for friendships.A sequence is given by the equation a, = an 1-2. If a1 =12, what is the
value of the term of A4 ?
Answer:
a= 11 to the power of 2. check the formula dude.
Someone plz help me quickkkk
Answer:
40 because I had the same exact problem and I got an A+
If the sum of a number and nine is tripled. The result is eight less than twice the number
Answer:
-35
Step-by-step explanation:
[tex]3(x+9)=2x-8[/tex]
[tex]3x+27=2x-8[/tex]
[tex]x+35=0[/tex]
[tex]x=-35[/tex]
Answer:
The number is -35.
Step-by-step explanation:
3(n + 9) = 2n - 8
3n + 27 = 2n - 8
n = -35
The perimeter of rectangle is 36 the length is 3 more than two times the width
Answer:
The width of the rectangle is equal to 5 and the length is equal to 13
Step-by-step explanation:
Perimeter of rectangle = (Length + Width) ×2
Perimeter of rectangle = (13 + 5) ×2
Perimeter of rectangle = 36
The length of the rectangle is 13, which is 3 more than two times the width, if the width is 5
5 (Width) ×2 = 10
10 +3 = 13 (Length)
Which of these whole aumbers are even
7,987
936
13,483
15
Answer:
936
Step-by-step explanation:
Femi's last 5 bowling scores were 68, 75, 72, 90, and 80.
What was Femi's mean score?
Answer:
77
Step-by-step explanation:
Please answer my question fast.
Answer: 19
Step-by-step explanation: Take 1836 and divide by 23 because 23 is the amount of boxes James needs to fill. Then after you divide you have 19 left over. :)
An advertising executive wants to determine if a new billboard placed in a city caused sales of her product to increase. To do this, she selects random stores that sell the product on the billboard and compares the amount sold in one business cycle before the billboard was placed to the sales of one business cycle after. Suppose that data were collected for a random sample of 10 stores, where each difference is calculated by subtracting the number of units sold in thousands before the billboard was placed from the number of units sold in thousands after the billboard was placed. Assume that the numbers are normally distributed. The executive uses the alternative hypothesis Ha:μd>0. Using a test statistic of t≈6.537, which has 9 degrees of freedom, determine the range that contains the p-value.
Complete Question
The complete question is shown on the first and second uploaded image
Answer:
The correct option is the first and the last option
Step-by-step explanation:
From the question we are told that
The sample size is n = 10
The null hypothesis is [tex]H_o : \mu_d = 0[/tex]
The alternative hypothesis is [tex]H_a : \mu_d > 0[/tex]
The test statistics is [tex]t \approx 6.537[/tex]
The level of significance is [tex]\alpha = 0.05[/tex]
Generally the p-value is mathematically represented as
[tex]p-value = P(t > 6.537 )[/tex]
From z-table [tex]P(t > 6.537 ) = 0[/tex]
So
[tex]p-value = 0[/tex]
From the value obtained we see that [tex]p-value < \alpha[/tex] hence we reject the null hypothesis that the true mean difference between the number of units sold after the billboard was placed and the number of units sold before the billboard was placed is equal to zero
Thus we conclude that
Based on the results of the hypothesis test, there is not enough evidence at the level of significance(0.05) to suggest that the true mean difference between the number of units sold after the billboard was placed and the number of units sold before the billboard was placed is greater than zero
A rectangular frame has width 7 in. longer than its length. What is the width of the painting if its area is 18 in?
A)6 inches
B)2 inches
C)3 inches
D)9inches
Answer:
9inches
Step-by-step explanation:
i think i hope its right..
. Solve the system of equations using the Elimination Method.
X+3y - 2z=2
3x+2y+z=13
-2x+3y - 3z= -5
Answer:
{x,y,z}={1,3,4}
Step-by-step explanation:
System of Linear Equations given :
[1] x + 3y - 2z = 2
[2] 3x + 2y + z = 13
[3] -2x + 3y - 3z = -5
Solve by Substitution :
// Solve equation [2] for the variable z
[2] z = -3x - 2y + 13
// Plug this in for variable z in equation [1]
[1] x + 3y - 2•(-3x-2y+13) = 2
[1] 7x + 7y = 28
// Plug this in for variable z in equation [3]
[3] -2x + 3y - 3•(-3x-2y+13) = -5
[3] 7x + 9y = 34
// Solve equation [3] for the variable y
[3] 9y = -7x + 34
[3] y = -7x/9 + 34/9
// Plug this in for variable y in equation [1]
[1] 7x + 7•(-7x/9+34/9) = 28
[1] 14x/9 = 14/9
[1] 14x = 14
// Solve equation [1] for the variable x
[1] 14x = 14
[1] x = 1
// By now we know this much :
x = 1
y = -7x/9+34/9
z = -3x-2y+13
// Use the x value to solve for y
y = -(7/9)(1)+34/9 = 3
// Use the x and y values to solve for z
z = -3(1)-2(3)+13 = 4
Solution :
{x,y,z} = {1,3,4}
2 less than or equal to x less than or equal to 6 1 less than or equal to y less than or equal to 5 x plus y less than or equal to 8 maximum for P = 3x + 2y
Answer: A) -10 ≤ x ≤ 10 , -10 ≤ y ≤ 10
Step-by-step explanation:
What is the measure of the unknown angle? 7 50° n
Answer:
310°
Step-by-step explanation:
360 - 50 = 310
A full circle is 360, therefore you just need to take away the degree they gave you from it in order to find the remaining angle.
Which graph represents the inequality y≥1−3x?
Answer:
first one
Step-by-step explanation:
The line must pass through the coordinates (1/3, 0) and (0, 1). Hence the correct graph will be Graph A
Inequality graphInequality is are expressions not separated by an equal sign
The correct graph must have a solid line and shaded above the graph. The correct inequality sign will be a greater than or equal
Given the inequality y≥1−3x
The line must pass through the coordinates (1/3, 0) and (0, 1). Hence the correct graph will be Graph A
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Multiplying an integer by a negative number word problem example
Answer:
7 * (-4)
Step-by-step explanation:
Firstly, 7 is an integer(meaning there is nothing special about it, its not a decimal, its just an integer). -4 being the negative number in the example
hope i helped
:D
what is the probability and odd for 7/16
Answer:
What is the probability and odd for 7/16
There is a 30.43 percent of a particular outcome and 69.57 percent of another outcome.
GIVING BRAINLEST TO WHOEVER ANSWERS FIRST!!!!!!!!!!!!
Which two methods can be used to solve the equation 5/7 n = 8 3/5 ?
Group of answer choices
Multiply both sides by 5/7 or divide both sides by 7/5.
Divide both sides by 5/7 or multiply both sides by 7/5.
Add 5/7 to both sides or subtract 7/5 from both sides.
Subtract 5/7 to both sides or add 7/5 to both sides.
Answer:
b. divide both sides by 5/7 or multiply both sides by 7/5
Explain and Prove that the sides of the triangles below are a right triangle.
1.) 5, 10,12
2.) 6,5,3
3.) 3, 4, 5
4.) 6, 8,10
*Pls explain all ill give you brainliest or w.e its called*
If the function f(x) = 4* is translated up 6 and left 2, write the new function
Answer:
f(x+2)+6 = 4^(x+2)+6
Step-by-step explanation:
(The power is to the x+2) Hope this helps!:)
(9x + 4) (2x2 – 17x - 9) = 0
-
Answer:
I literally just did this one. you get 3 solutions x=9, -1/2, -4/9. factor the 2nd group.
Simplify the expression.
(5+6i)+(-2+4i)
Answer: 3 + 10i
Step-by-step explanation:
Complex numbers follow the same rules that real numbers do when it comes to addition and subtraction. Removing the parenthesis we have:
[tex]5+6i-2+4i[/tex]
Combine the real parts, then combine the complex parts:
[tex]3+10i[/tex]
Samantha has saved $40 towards buying a $125 electronic book reader. Starting this week, she plans to save an additional $15 each week.
Write and solve an inequality that can be used to find the minimum number of weeks, w, it will take Samantha to save for the book reader
125 = 40 + 15w
W = number of weeks
6 weeks is 125 = 40 + 15(16)
15(16) is 90 so 90 + 40 = 130
So the inequality would be w >= 6
To be more precise because 6 weeks is $130 and not $125, divide 85 (money still needed) by 15 to get the decimal 5.66…, so it would be w >= 5.66…
A population of five families is to be sampled. The incomes of the five families (in thousands of dollars) are: Family Income ($000) A 12 B 23 C 18 D 7 E 16 a. Find the population mean income of the five families. 2 point
The population mean income of the five families is their average income
The population mean income of the five families is #15.2
How to determine the population mean?The income of the five families in a thousand dollars is given as:
A 12 B 23 C 18 D 7 E 16
The population mean is then calculated as:
[tex]\mu = \frac{\sum x}n[/tex]
So, we have:
[tex]\mu = \frac{12 + 23 + 18 + 7 + 16}5[/tex]
Evaluate the sum
[tex]\mu = \frac{76}5[/tex]
Evaluate the quotient
[tex]\mu = 15.2[/tex]
Hence, the population mean income of the five families is #15.2 thousand
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What is 2/3 - (-2/3)?
OA) -4/3
OB) 4/3
C) 0
OD) 2/3
Answer:
OB
-2 multiply by a -2 is a - 4 which is a numerator then
3 doesn't change cause it is a denomenator
thus your final answer is a -4/3
Which is a better deal: five packs of gums for $3.00 , seven packs of gum for $4.00
Answer:
I believe the better deal would be,
Seven packs of gum for $4.00.
The map shows the location of the houses of Dan, Joe, Lee, and Roy:
The coordinates of the community center are (−5, −1). Who has a house in the same quadrant as the community center?
a Dan
b Joe
c Lee
d Roy
Answer:
c Lee
Step-by-step explanation:
The coordinates of the community center are both negative. They place it 2 units left and 3 units up from Lee's house in the 3rd quadrant.
please help
calculate each unknown side length.
Answer:
x = 6.6 inchesy ≈ 12.0 inchesStep-by-step explanation:
The Pythagorean theorem relates side lengths in right triangles. It tells you the square of the hypotenuse is equal to the sum of the squares of the sides.
__
Left triangle8.8² + x² = 11²
x² = 121 -77.44 = 43.56
x = √43.56 = 6.6 . . . inches
__
Right triangle6.6² +10² = y²
43.56 +100 = y² = 143.56
y = √143.56 ≈ 11.982
y ≈ 12.0 . . . inches
let f(x)=3-3x+5x^2.calculate the following.
f(a)=
f(a+h)=
f(a+h)-f(a)/h= for h≠0
Answer & step-by-step explanation:
[tex]f(a)[/tex] is simply calculating by replacing a in lieu of x
[tex]f(a) = 3-3a+5a^2[/tex]
Same difference for [tex]f(a+h)[/tex], just be careful with products and squares:
[tex]f(a+h) = 3-3(a+h)+5(a+h)^2 = 3-3a-3h+5a^2+10ah+5h^2 = 3-3a+5a^2 -3h+10ah+5h^2[/tex]
In the last step i just reorganized terms so that everything containing h was at the end.
Finally, for the incremental ratio, writing it as 1/h for the sake of font sizes:[tex]\frac{f(a+h)-f(a)}h = \frac1h[(3-3a+5a^2-3h+10ah+5h^2)-(3-3a+5a^2)]=\\\frac1h(-3h+10ah+5h^2) = 10a-3 +5h[/tex]
Establish a relationship to determine the equivalent resistance R of a combination of three resistors having resistances R1, R2 and R3 connected in series. Calculate the equivalent resistance of the combination of three resistors of 2 Ω, 3 Ω and 6 Ω joined in parallel.
Answer:
Step-by-step explanation:
the resistors which connected in series
equivalent resistance = R1 +R2 + R
is the relationship between the resistors connected in series.
For parallel connection
R1 = 2ohm
R2 = 3ohm
R3 = 6ohm
for equivalent resistance (Rt)
1/Rt = 1/R1 + 1/R2 + 1/R3
1/Rt = 1/2 + 1/3 + 1/6
1/Rt = (3 + 2 + 1)/6 = 6/6 =1/1
Rt = 1 ohm
equivalent resistance = 1 ohm