Answers
Answer:
Figure 1: 623.2 in²
Figure 2: 679.8 in²
Step-by-step explanation:
For a pyramid total surface area
= Base Area + Lateral Surface Area
Figure 1 is a triangular prism
It's base is an equilateral triangle with side = 20 in
Area of an equilateral triangle = \(\dfrac{\sqrt{3}}{4} a^2\) where \(a\) is the length of the base
So in figure 1, base area = area of equilateral triangle with side a = 20 in
\(\text{Base Area =} \dfrac{\sqrt{3}}{4} \cdot 20^2 \approx 173.2 \;in^2\)
Each lateral side is an isosceles triangle with base = 20 and height = 15
Area of each triangle
\(= \dfrac{1}{2} \cdot base \cdot height\)
\(= \dfrac{1}{2} \cdot 20 \cdot 15 \\\\= 150 \; in^2\)
There are three such lateral sides so total lateral area = 150 x 3 = 450 in²
Total surface area = 173.21 + 450 = 623.2 in²
Figure 2
This is a regular hexagonal pyramid
The base is a regular hexagon of side 10
Base area = Area of hexagon of side 10
Area of a regular hexagon with side a
\(= \dfrac{3\sqrt{3}}{4} a^2\)
Base area of Figure 2
\(= \dfrac{3\sqrt{3}}{4} 10^2\\\\\approx 259.8 \;in^2\)
The lateral surface consists of 6 isosceles triangles each with a base = 10 in and height = 14 in
Area of each isosceles triangle
\(= \dfrac{1}{2} \cdot 10 \cdot 14 \\\\= 70 \;in^2\)
Since there are 6 such lateral triangles, total lateral surface area
= 70 x 6 = 420 in²
So total surface area = base area + total lateral surface area
= 259.8 + 420 = 679.8 in²
Related Questions
Your starting annual salary of $35,000 increases by 4% each year. Write a function that represents the situation.
(marked brainliest if u explain in depth pls)
Answers
This is because you are multiplying 35,000 by 1.04 every year
What this means is that there will be a 4% increase on the value for the previous year.
An example of this would be:
35,000 x 1.04= 36,400 - for first year
36,400 x 1.04= 37,856 - for second year
37,856 x 1.04= 39,370.24 - for third year
And this can go on for however long you want it to.
The “t” represents how many years you want the money to compound(build up).
For example I did 3 years of increasing on my calculator down below.
If you input this into your calculator it should look like this:
A triangle has side lengths of 13, 9, and 5. Is the triangle a right triangle? Explain.
2Points
Use complete sentences in your explanation.
Hint: Pythagorean Theorem: a^2+ b^2 = c^2
Answers
Answer: This triangle is not a right triangle
Step-by-step explanation:
In a right triangle, the hypotenuse(c) is always the longest side and a and b are the shorter sides. Thus, 5^2+9^2=13^2. Simplify this to get 25+81=169, then 106=169. Because 106 does not equal 169, it is not a right triangle.
Hope it helps <3
What about this one
Answers
Answer:
3/20
Step-by-step explanation:
Answer:
3/20
Step-by-step explanation:
The circle is a whole, or 1
1 - 1/4 - 3/5 = area shaded
1 - 5/20 - 12/20 = area shaded
1 - 17/20 = area shaded
3/20 = area shaded
Another method:
1 - 0.25 - 0.6
1 - 0.85 = 0.15
0.15 = 3/20
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
how fo I do this? please, need help
Answers
Answer:
Round off to the two decimal places then plot on your Cartesian Plane
Write the equation in slope-intercept form.
8y - 3x = 16
Answers
This is the answer because in the equation 8y-3x+16 you would re-write it as 8y=3x+16 but to write it in slope-intercept form, you need to get the 8 away from the y. To do this you divide y by everything; creating y=3/8x+2 ( slope intercept form).
Jess has $43 in her bank account. Destiny is negative 21. What's the difference between Jess and Destiny's account?
Answers
Answer:
$64
Step-by-step explanation:
This would be the answer because if we figure out what needs to be added to -21 to reach 43 we get 64.
(-21+64 - $43.)
Have a blessed day! Also brainliest would be appreciated :)
Please help me. Which one is it?
Answers
Answer:
commutative property of multiplication
associative property of multiplication
Answer:
(1 + 1 + 1 + 1)u is distributive property. It contains multiplication and addition both. I hope it is correct. pls give me brainliest if possible. appreciated
Spencer, Jaclyn, and Ayden go shrimping in
Louisiana. Spencer catches 2 pounds,
Jaclyn collects 3.25 pounds, and Ayden nets
4.375 pounds. How many pounds of shrimp
did they catch?
Answers
The total pounds of shrimp they catch is 9.625 pounds
Sum of values and decimalsDecimal number are numbers that has decimal points. Given the following information;
The total shrimp Spencer catch = 2 pounds
The total shrimp Jaclyn catch = 3.25 pounds
The total shrimp Ayden catch = 4.375 pounds
Determine the total pounds of shrimp they catch
Total shrimp = 2 + 3.25 + 4.375
Total shrimp = 9.625 pounds
Hence the total pounds of shrimp they catch is 9.625 pounds
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What's 65.247 rounded to the nearest tenth
Answers
Answer:
65.2
Step-by-step explanation:
the two is the tenth and your not adding any thing because the 4 is less than five
find the height of a tree whose shadow is 42m long when the shadow of a man 1.8m tall is 2.4m long
Answers
Answer:
The ratio 1.8 : 2.4 can be rewritten as 3 : 4. We have to solve:
3 : 4 = x : 42
3 * 42 = 4x
x = 3 * 42 / 4 = 31.5
Calculate the distance between the points =G−9, 6 and =Q−2, 1 in the coordinate plane.
Answers
The distance between the points G(-9, 6) and Q(-2, 1) in the coordinate plane is approximately 8.6.
To calculate the distance between two points in a coordinate plane, we can use the distance formula. The distance formula is derived from the Pythagorean theorem and can be stated as follows:
Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
In this case, the given points are G(-9, 6) and Q(-2, 1).
Step 1: Identify the coordinates of the two points.
G has coordinates (-9, 6) and Q has coordinates (-2, 1).
Step 2: Substitute the coordinates into the distance formula.
Using the distance formula, we can plug in the values as follows:
Distance = sqrt((-2 - (-9))^2 + (1 - 6)^2)
Simplifying the formula:
Distance = sqrt((7)^2 + (-5)^2)
Distance = sqrt(49 + 25)
Distance = sqrt(74)
Step 3: Calculate the square root.
Taking the square root of 74, we get:
Distance ≈ 8.6
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5. A theater wants to take in at least $2000 for the matinee. Children's
tickets cost $5 each and adult tickets cost $10 each. The theater can seat
up to 350 people. Select all the combinations of children and adult tickets
that will make the $2000 goal.
There are several possible answers.
A- (80, 150)
B- (40, 200)
C- (60, 150)
D- (70, 160)
E- (90, 200)
F- (200, 100)
Answers
The required number of children and adults for sitting in the theater are 300 and 50 respectively.
Explain linear equation of two variable.A equation is supposed to be linear equation in two factors in the event that it is written as hatchet + by + c=0, where a, b and c are genuine numbers and the coefficients of x and y, i.e an a and b separately, are not equivalent to nothing. For instance, 10x+4y = 3 and - x+5y = 2 are straight equation in two factors.
According to question:Let be consider number of children be x and that of adults is y.
We have,
x + y = 350-------(1)
y = 350 - x
And 5x + 10y = 2000------------------(2)
Put value of y in equation (2)
5x + 10( 350 - x) = 2000
5x + 3500 - 10x = 2000
-5x = -1500
x = 300
Then
y = 350 - x = 350 - 300 = 50
Thus, There will be 300 children and 50 adults in the theater .
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The population density of a cow pasture at Evergreen Farm is 56 cows per acre, and the population of cows in the pasture is 126. Whay is the area, in acres, of the pasture?
Answers
The area of the cow pasture at Evergreen Farm is 2.25 acres.
Finding the Area of a Cow Pasture at Evergreen FarmGiven:
Population density of the cow pasture at Evergreen Farm = 56 cows per acrePopulation of cows in the pasture = 126To find:
Area of the cow pasture in acres
Let A be the area of the cow pasture in acres.
According to the given information, the population density of the cow pasture is 56 cows per acre.
Therefore, the number of cows in the pasture is:
56 cows/acre × A acres = 126 cows
Simplifying the above equation, we get:
A = 126 cows / (56 cows/acre)
A = 2.25 acres
Therefore, the area of the cow pasture at Evergreen Farm is 2.25 acres.
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True or False Animal-like protists get nutrients by creating them inside themselves.
Answers
someone please help.........
Answers
Answer:
i think its 1/16
Step-by-step explanation:
a) estimate the area under the graph of f(x) = 5 cos(x) from x = 0 to x = /2 using four approximating rectangles and right endpoints. (round your answers to four decimal places.)
Answers
The estimated area under the graph of f(x) = 5 cos(x) from x = 0 to x = π/2 using four approximating rectangles and right endpoints is approximately 0.8916.
To estimate the area under the graph of f(x) = 5 cos(x) from x = 0 to x = π/2 using four approximating rectangles and right endpoints, we can use the right Riemann sum method.
The width of each rectangle, Δx, is given by the interval width divided by the number of rectangles.
In this case, Δx = (π/2 - 0)/4 = π/8.
To calculate the right endpoint values, we evaluate f(x) at the right endpoint of each rectangle.
For the first rectangle, the right endpoint is x = π/8.
For the second rectangle, the right endpoint is x = π/4.
For the third rectangle, the right endpoint is x = 3π/8.
And for the fourth rectangle, the right endpoint is x = π/2.
Now, let's calculate the area for each rectangle by multiplying the width (Δx) by the corresponding height (f(x)):
Rectangle 1: Area = f(π/8) * Δx = 5cos(π/8) * π/8
Rectangle 2: Area = f(π/4) * Δx = 5cos(π/4) * π/8
Rectangle 3: Area = f(3π/8) * Δx = 5cos(3π/8) * π/8
Rectangle 4: Area = f(π/2) * Δx = 5cos(π/2) * π/8
Now, let's calculate the values:
Rectangle 1: Area = 5cos(π/8) * π/8 ≈ 0.2887
Rectangle 2: Area = 5cos(π/4) * π/8 ≈ 0.3142
Rectangle 3: Area = 5cos(3π/8) * π/8 ≈ 0.2887
Rectangle 4: Area = 5cos(π/2) * π/8 ≈ 0
Finally, to estimate the total area, we sum up the areas of all four rectangles:
Total Area ≈ 0.2887 + 0.3142 + 0.2887 + 0 ≈ 0.8916
Therefore, the estimated area under the graph of f(x) = 5 cos(x) from x = 0 to x = π/2 using four approximating rectangles and right endpoints is approximately 0.8916.
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when using the least-squares line for prediction, are results more reliable for extrapolation or interpolation?
Answers
When using the least-squares line for prediction, the results are generally more reliable for interpolation rather than extrapolation. Interpolation refers to predicting values within the range of the data used to create the least-squares line, while extrapolation involves predicting values beyond that range. The reliability of extrapolation decreases because it assumes that the relationship between the variables continues outside the observed data, which may not always be accurate due to potential unforeseen factors or changes in the underlying relationship.
The least-squares line is a method used to find the best-fit line that minimizes the sum of the squared residuals between the observed data points and the predicted values on the line. It is commonly used for linear regression analysis to make predictions based on the relationship between two variables.
When using the least-squares line for interpolation, the predicted values are within the range of the data used to create the line. In this scenario, the least-squares line provides a reliable estimate because it is based on observed data points and their relationship. Interpolation assumes that the underlying relationship between the variables remains relatively consistent within the observed range.
However, when it comes to extrapolation, the reliability of the results decreases. Extrapolation involves predicting values beyond the observed range of the data. While it is possible to extend the least-squares line to make predictions, it assumes that the relationship between the variables continues in the same manner outside the observed range. This assumption may not always hold true due to potential unforeseen factors or changes in the relationship between the variables.
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what is this answer?
7k-3k+11
Answers
Answer:
4k+11 is the answer
Step-by-step explanation:
7k-3k =4k
4k+11!
At a baseball game, a vender sold a combined total of sodas and hot dogs. the number of sodas sold was three times the number of hot dogs sold. find the number of sodas and the number of hot dogs sold.
Answers
The number of sodas sold is 168
The number of hot dogs sold is 56
Total of sodas and hot dogs=224
Let the number of sodas sold be s, and the number of hot dogs sold be s
So we have the following:
s=3h.................i
s+h=224..........ii
we solve the two equation to find the value of s and h,
From equation ii, s=224-h, replacing this in equation i, we have:
224-h=3h
224=4h
h=56
Now, s=3*56
=168
s=168
Number of sodas=168
Number of hot dog sold=56
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The complete question is given below;
A vender sold a combined total of 224 sodas and hot dogs. The number of sodas sold was three times the number of hot dogs sold. Find the number of sodas and the number of hot dogs sold.
helppppp
Question 9 (Essay Worth 10 points)
(08.01 HC)
Use the function f(x) to answer the questions:
f(x) = 4x² +8x-5
Part A: What are the x-intercepts of the graph of f(x)? Show your work. (2 points)
Part B: Is the vertex of the graph of f(x) going to be a maximum or a minimum? What are the coordinates of the vertex? Justify your answers and show your work. (3 points)
Part C: What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part A and Part B to draw the graph. (5 points)
Answers
To find the x-intercepts of the graph of f(x), we need to set f(x) = 0 and solve for x:
4x² + 8x - 5 = 0
We can use the quadratic formula to solve for x:
x = (-b ± sqrt(b² - 4ac)) / 2a
where a = 4, b = 8, and c = -5.
x = (-8 ± sqrt(8² - 4(4)(-5))) / 2(4)
x = (-8 ± sqrt(144)) / 8
x = (-8 ± 12) / 8
x = -1/2 or x = 5/2
Therefore, the x-intercepts of the graph of f(x) are -1/2 and 5/2.
Part B:
The vertex of the graph of f(x) can be found using the formula:
x = -b / 2a
y = f(x)
where a = 4, b = 8, and c = -5.
x = -8 / 2(4)
x = -1
y = f(-1)
y = 4(-1)² + 8(-1) - 5
y = -1
Therefore, the vertex of the graph of f(x) is (-1, -1). Since the coefficient of the x² term is positive, the parabola opens upwards, so the vertex is a minimum.
Part C:
To graph f(x), we can use the information obtained in Part A and Part B. The x-intercepts are -1/2 and 5/2, and the vertex is (-1, -1). We can also find the y-intercept by setting x = 0:
f(0) = 4(0)² + 8(0) - 5
f(0) = -5
Therefore, the y-intercept is (0, -5).
We can also find the axis of symmetry by using the x-coordinate of the vertex:
x = -1
Therefore, the axis of symmetry is x = -1.
To draw the graph, we can plot the x-intercepts, y-intercept, and vertex, and then sketch a smooth curve passing through these points. Since the vertex is a minimum, the curve will open upwards. We can also use the axis of symmetry to help us draw the curve symmetrically.
Therefore, the steps to graph f(x) are:
1. Find the x-intercepts by solving 4x² + 8x - 5 = 0.
2. Find the y-intercept by setting x = 0.
3. Find the vertex by using x = -b / 2a and y = f(x).
4. Find the axis of symmetry by using the x-coordinate of the vertex.
5. Plot the x-intercepts, y-intercept, and vertex.
6. Sketch a smooth curve passing through these points, opening upwards and symmetrically about the axis of symmetry.
how much total urine volume is excreted during this time period? (b) develop equations for the velocity of urine as it exits the body. assume that the urethra is 5.6 mm in diameter
Answers
(a) Total urine volume is excreted during this time period is 442.34 mL.
(b) Equations for the velocity of urine is v = (-3 x \(V_t\) + 7.35) / 2.46 x \(10^{-5}\)
(a) To determine the total urine volume excreted during this time period, we need to integrate the flow rate function over the given time period. However, we are given two different equations for the flow rate for different ranges of time:
For t < 12 seconds, V = -0.306 x \((t-7)^2\) + 15
For 12 ≤ t < 26.7 seconds, V = -3 x \(V_t\) + 7.35
To find the total urine volume, we need to first determine the time at which the flow rate changes from the first equation to the second.
We can do this by setting the two equations equal to each other and solving for t:
-0.306 x \((t-7)^2\) + 15 = -3 x \(V_t\) + 7.35
0.306 x \((t-7)^2\) + 3 x \(V_t\) = 7.65
0.306 x \((t-7)^2\) = 7.65 - 3 x \(V_t\)
\((t-7)^2\) = (7.65 - 3 x \(V_t\) ) / 0.306
t = 7 +/- \(\sqrt{((7.65 - 3 \times Vt) / 0.306)}\)
Since t < 12 for the first equation, we can ignore the negative root and use the positive root to find the time at which the flow rate changes:
t = 7 + \(\sqrt{((7.65 - 3 \times 12) / 0.306)}\)= 10.76 seconds
Now we can integrate each equation separately over their respective time ranges:
For 0 ≤ t < 10.76 seconds:
∫ V dt = ∫ (-0.306 x \((t-7)^2\) + 15) dt
= [-0.102 x \((t-7)^3\) + 15t] from t=0 to t=10.76
= 121.86 mL
For 10.76 ≤ t < 26.7 seconds:
∫ V dt = ∫ (-3 x \(V_t\) + 7.35) dt
= [-1.5 x \(V_t^2\) + 7.35t] from t=10.76 to t=26.7
= 320.48 mL
Therefore, the total urine volume excreted during this time period is:
121.86 mL + 320.48 mL = 442.34 mL
(b) To develop equations for the velocity of urine as it exits the body, we need to use the continuity equation, which states that the flow rate (V) is equal to the cross-sectional area (A) multiplied by the velocity (v):
V = A x v
We are given that the urethra has a diameter of 5.6 mm, which means the radius is 2.8 mm (or 0.0028 m).
The cross-sectional area can be calculated using the formula for the area of a circle:
A = π x \(r^2\)
A = 3.14 x \((0.0028)^2\)
A = 2.46 x \(10^{-5}\) \(m^2\)
Now we can rearrange the continuity equation to solve for the velocity:
v = V / A
Substituting the given equations for V, we get:
For t < 12 seconds:
v = (-0.306 x \((t-7)^2\) + 15) / 2.46 x \(10^{-5}\)
For 12 ≤ t < 26.7 seconds:
v = (-3 x \(V_t\) + 7.35) / 2.46 x \(10^{-5}\)
Note that the velocity will be in units
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Question:-
The flow of urine from the bladder, through the urethra, and out of the body, is induced by increased pressure in the bladder resulting from muscle contractions around the bladder with simultaneous relaxation of the muscles in the urethra. The mean pressure in the bladder can be estimated using the velocity of urine as it exits the body. Assume that the bladder is about 5 cm above the external urethral orifice. (This height is different for males and females.) The flow rate of urine from the bladder can be approximately described with the following equations, where t is time in seconds, and V is flow rate in mL/s:
V = -0.306 X (t – 7)2 + 15 Osts 12
V = -3 X Vt 12 + 7.35 12 st < 26.7
(a) How much total urine volume is excreted during this time period?
(b) Develop equations for the velocity of as it exits the body. Assume that the urethra is 5.6 mm in diameter.
What is the most common error when entering a formula is to reference the wrong cell in the formula?
Answers
The most common error when entering a formula is to reference the wrong cell in the formula.
This error occurs when the cell references within a formula do not match the intended cells. It can lead to incorrect calculations and produce unexpected results. For example, if a formula is supposed to use data from cell A1 but mistakenly refers to cell B1, the calculation will be based on the wrong data. It is important to double-check and ensure that the cell references in a formula accurately reflect the intended data sources to avoid this common mistake.
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Im not sure how to do this one
Answers
Answer:
B
Step-by-step explanation:
6x - 8x - 4 = - 2x - 2 , that is
- 2x - 4 = - 2x - 2 ( add 4 to both sides )
- 2x = - 2x + 2 ( add 2x to both sides )
0 = 2 ← not possible
this indicates the equation has no solution
Answer:
6x-8x-4=-2x-2 (group the like terms)
6x-8x+2x= 4-2 (-8x+2x= -6x and 6x-6x=0) (4-2=2)
answer= 0=2
,therefore: it has no solution
Step-by-step explanation:
the answer is 0=2 which mean there is nothing that 2 is equivalent to because when you group the like terms and work out the answer the x in the equation will be canceled.
What is an equivalent expression for 4-2x+5x
Answers
Answer:
that would be 2x+5x
Step-by-step explanation:
because 4 -2 = 2x+5x
just ad the rest to the answer , hope this helps :).
Answer
\(\boldsymbol{4+3x}\)
Step-by-step explanation
In order to simplify this expression, we add like terms:
4 - 2x + 5x
4 + 3x
These two aren't like terms so we can't add them.
∴ answer : 4 + 3x
find the measure kyc pls its urgent
Answers
The measure of angle KYC, considering the concept of vertical angles, is given as follows:
m < KYC = 69º.
What are vertical angles?Vertical angles are angles that are opposite by the same vertex on crossing segments, hence they share a common vertex, thus being congruent, meaning that they end up having the same angle measure.
The vertical angles for this problem are given as follows:
<KYC and 69º.
As they are opposite by the vertex at the crossing of the two diagonal segments for this problem.
Hence the measure of angle KYC is given as follows:
m < KYC = 69º.
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PLSSS HELLPPPPP ASAPPP
Answers
Answer:
y = 80 degrees, and x = 100 degrees
Step-by-step explanation:
what form is y=mx +b
Answers
Answer:
This is the slope intercept form of a line.
Step-by-step explanation:
Answer:
Step-by-step explanation:
slope intercept form
Which expression could be represented by this model?
Guys please help me no one will help me!:(
Answers
Answer:
8 x 9 maybe?
Step-by-step explanation:
Find the area of the rectangle to the right. 9 inches for width and 5y inches for the length
Answers
Answer:
The area is 45 inches
Step-by-step explanation:
L×W=A
I am confused about ii) help please
Answers
Step-by-step explanation:
i)=
m=2/3
x=-3
y = 5
now
y=mx+c
or, 5 = 2/3× -3 + c
or, 5 = -2+c
c =7
now,
y= mx + c
or, y = 2/3×x+7
or, y = 2x/3+7
or, 3y = 2x+21
so, 3y-2x=21
equation would be 3y-2x=21.
now
ii)=
if slope of 3y-2x=21 and 2x-3y = 0 are same, they are parallel.
2x-3y = 0
2x = 3y
lets suppose x is 9
now
2x=3y
2×9 = 3y
or, 18 = 3y
so, y = 6
one coordinate would be (9,6) now
lets again suppose x is 3
2x=3y
2×3 = 3y
or, 6 = 3y
so, y = 2
another coordinate is (3,2)
now lets find slope
x1=9,y1=6
x2=3,y2=2
slope = (y2-y1)/(x2-x1)
= (2-6)/(3-9)
= -4/-6
= 2/3
Since, slope of 3y-2x=21 and 2x-3y has same slope 2/3, they are parallel.