Answers
Among the given options, V [tex]57^\circ[/tex] is the closest estimate for the measure of the other acute angle.
What is the measure of the other acute angle?To find the measure of the other acute angle, we can use the fact that the sum of the angles of a triangle is 180°. Let x be the measure of the other acute angle. Then we have:
[tex]x + 32.9^\circ + 90^\circ = 180^\circ[/tex]
Simplifying the equation, we get:
[tex]x = 180^\circ - 32.9^\circ - 90^\circ[/tex]
[tex]x = 57.1^\circ[/tex]
So the exact measure of the other acute angle is [tex]57.1^\circ.[/tex]
Therefore, Among the given options, V [tex]57.1^\circ.[/tex] is the closest estimate for the measure of the other acute angle.
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Related Questions
how do i use change of base formula with logorothims
Answers
To use the change of base formula, we first identify the base of the original logarithm and the desired base of the new logarithm.
The change of base formula is a useful tool in logarithmic functions that allows us to rewrite a logarithm with one base as an equivalent logarithm with a different base. The formula is as follows:
logᵦ a = logᵦ(x) / logₐ(x)
where a is the value being logged, β is the base of the original logarithm, and x is any positive number other than 1.
We then apply the formula by taking the logarithm of the value being logged with the desired base, and dividing it by the logarithm of the same value with the original base.
For example, let's say we want to rewrite the logarithm log₂ 8 in base 10. Using the change of base formula, we have:
log₂ 8 = log₁₀ 8 / log₁₀ 2
The value of log₁₀ 8 is simply 0.9031, and the value of log₁₀ 2 is 0.3010, so we have:
log₂ 8 = 0.9031 / 0.3010 ≈ 3
Therefore, log₂ 8 is equivalent to log₁₀ 8 ≈ 3. By using the change of base formula, we can simplify logarithmic expressions and evaluate them using common logarithms or natural logarithms.
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The total number of a particular chain store in the world can be modeled by the cubic function y = 10.4x^3- 403x^2 +5585x-8695,where X is the number of years after 2000 and Y is the total number of stores.
a)graph the function on the window[2,20,2]by [8000,23000,1000]
b)what does the model predict the number of stores will be in 2020.
c)does the number of stores ever decrease over this period of years, ending 2020, according to the model
Answers
The model predicts that the number of stores will be at a minimum of approximately 8,123 stores in the year 2009, and will increase from there without bound.
What do you mean by term cubic function ?A cubic function is a type of polynomial function with the highest degree term being 3. In other words, a cubic function is a function of the form[tex]f(x) = ax^3 + bx^2 + cx + d[/tex], where a, b, c, and d are constants. The graph of a cubic function is a curve that can take on various shapes depending on the values of the coefficients.
b) To find the predicted number of stores in 2020, we need to find the value of the function when x = 20 (since 2020 is 20 years after 2000). We can substitute x = 20 into the function and evaluate:
[tex]y = 10.4x^3 - 403x^2 + 5585x - 8695\\y = 10.4(20)^3 - 403(20)^2 + 5585(20) - 8695\\y = 140,385[/tex]
Therefore, the model predicts that the number of stores in 2020 will be 140,385.
c) To determine if the number of stores ever decreases over the period of years ending in 2020 according to the model, we can look at the behavior of the function. The function is a cubic function with a positive leading coefficient, which means it will have a global minimum (i.e., the lowest point on the graph) and then increase without bound as x approaches positive or negative infinity.
To find the global minimum, we can take the derivative of the function and set it equal to zero:
[tex]y' = 31.2x^2 - 806x + 5585\\0 = 31.2x^2 - 806x + 5585[/tex]
x ≈ 8.68 or x ≈ 22.12
The first solution, x ≈ 8.68, is within the range of interest (2000 to 2020), so we can use it to find the global minimum:
[tex]y = 10.4x^3 - 403x^2 + 5585x - 8695[/tex]
y ≈ 8,123
Therefore, the model predicts that the number of stores will be at a minimum of approximately 8,123 stores in the year 2009, and will increase from there without bound. So according to the model, the number of stores never decreases over the period of years ending in 2020.
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Select the correct answer. A parabola declines through (negative 2, 4), (negative 1 point 5, 2), (negative 1, 1), (0, 0) and rises through (1, 1), (1 point 5, 2) and (2, 4) on the x y coordinate plane. The function f(x) = x2 is graphed above. Which of the graphs below represents the function g(x) = (x + 1)2? A parabola declines through (negative 2, 5), (negative 1 point 5, 3), (negative 1, 2), (0, 1) and rises through (1, 2), (1 point 5, 3) and (2, 5) on the x y coordinate plane. W. A parabola declines through (negative 2, 3), (negative 1 point 5, 1), (1, 0), (0, negative 1) and rises through (1, 1), (1 point 5, 1) and (2, 2) on the x y coordinate plane. X. A parabola declines through (negative 3, 4), (negative 2 point 5, 2), (negative 2, 1), (negative 1, 0), (0, 1), (0 point 5, 2) and (1, 4) on the x y coordinate plane. Y. A parabola declines through (negative 1, 4), (negative 0 point 5, 2), (0, 1) and (1, 0) and rises through (2, 1), (2 point 5, 2) and (3, 4) on the x y coordinate plane. Z. A. W B. X C. Y D. Z Res
Answers
Thw correct option based on the information given about the parabola will be B. X.
How to explain the parabolaThe observed parabola has its vertex situated at (0, 0), declining until (0, 0) then again rising. Its equation falls in the form of f(x) = a(x - 0)² + 0, which simplifies to ax².
In order to detect the value of 'a' we can utilize any point on the parabola itself. Let's take (1, 1):
1 = a(1)²
1 = a
Therefore, the formula for the presented parabola is exsiting in the form of f(x) = x².
Now consider g(x) = (x + 1)² such that it's merely a horizontal movement of function f(x) = x². The vertex of g(x) stands at (-1, 0) and linearly declines until (-1, 1) prior to onching higher again. All this leaves us with option X as the only conceivable graph for g(x).
Therefore, the answer is B) X.
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Can someone answer these 4 trig questions fast and accurately ty
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The evaluation of the trigonometric identities to find the sine of the sum of angles A and B, using the values for cos(A) and sin(B) indicates;
15. sin(A + B) = -52/85
16. A + B is in Quadrant III
What are trigonometric identities?Trigonometric identities are equations involving trigonometric ratios that are true for the values of the input variables.
15. cos(A) = -15/17, sin(B) = 4/5
The trigonometric identity for the sine of the addition of two angles, the addition formula indicates that we get;
sin(A + B) = sin(A)·cos(B) + cos(A)·sin(B)
cos(B) = √(1 - (4/5)²) = √(1 - 16/25) = 3/5
sin(A) = √(1 - (-15/17)²) = 8/17
Therefore; sin(A + B) = (8/17) × (3/5) + (-15/17) × (4/5) = -52/85
sin(A + B) = -52/8516. π/2 < A < π, and 0 < B < π/2
Therefore; π/2 + 0 < A + B < π + π/2
The solution from the previous question indicates that we get;
sin(A + B) = -52/85
The sine of an angle is negative in the third and fourth quadrant
The fourth quadrant is; π + π/2 < θ < 2·π
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If Melisha can pay for her vehicle with a 4-year loan or with a lease with the same down payment and same interest rate, why will the loan have a higher monthly payment?
A. Because the lease is riskier to the financing company.
B. Because the loan is riskler to the financing company.
C. Because Melisha will own her vehicle at the end of the loan.
D. Because Melisha will own her vehicle at the end of the lease.
Answers
The loan have a higher monthly payment Because the lease is riskier to the financing company.
To Determine the costs of buying versus leasing a motor vehicle, we need to consider the total costs associated with each option. For buying, the total cost is the sum of the down payment, loan payments, and the estimated value at the end of the loan, minus the resale value of the car.
On the other hand, for leasing, the total cost can be calculated as the sum of the security deposit, lease payments, and end-of-lease charges. We also need to consider the opportunity cost of investing the down payment and the security deposit.
We know that Melisha can pay for her vehicle with a 4-year loan or with a lease with the same down payment and same interest rate.
Therefore, the loan have a higher monthly payment Because the lease is riskier to the financing company.
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the function g(x) = 12x^2-sinx is the first derivative of f(x). If f(0)=-2 what is the value of f(2pi
Answers
Answer:
[tex]f(2\pi) = 32\pi^3 - 2[/tex]
Step-by-step explanation:
Main steps:
Step 1: Use integration to find a general equation for f
Step 2: Find the value of the constant of integration
Step 3: Find the value of f for the given input
Step 1: Use integration to find a general equation for f
If [tex]f'(x) = g(x)[/tex], then [tex]f(x) = \int g(x) ~dx[/tex]
[tex]f(x) = \int [12x^2 - sin(x)] ~dx[/tex]
Integration of a difference is the difference of the integrals
[tex]f(x) = \int 12x^2 ~dx - \int sin(x) ~dx[/tex]
Scalar rule
[tex]f(x) = 12\int x^2 ~dx - \int sin(x) ~dx[/tex]
Apply the Power rule & integral relationship between sine and cosine:
Power Rule: [tex]\int x^n ~dx=\frac{1}{n+1}x^{n+1} +C[/tex]sine-cosine integral relationship: [tex]\int sin(x) ~dx=-cos(x)+C[/tex][tex]f(x) = 12*(\frac{1}{3}x^3+C_1) - (-cos(x) + C_2)[/tex]
Simplifying
[tex]f(x) = 12*\frac{1}{3}x^3+12*C_1 +cos(x) + -C_2[/tex]
[tex]f(x) = 4x^3+cos(x) +(12C_1 -C_2)[/tex]
Ultimately, all of the constant of integration terms at the end can combine into one single unknown constant of integration:
[tex]f(x) = 4x^3 + cos(x) + C[/tex]
Step 2: Find the value of the constant of integration
Now, according to the problem, [tex]f(0) = -2[/tex], so we can substitute those x,y values into the equation and solve for the value of the constant of integration:
[tex]-2 = 4(0)^3 + cos(0) + C[/tex]
[tex]-2 = 0 + 1 + C[/tex]
[tex]-2 = 1 + C[/tex]
[tex]-3 = C[/tex]
Knowing the constant of integration, we now know the full equation for the function f:
[tex]f(x) = 4x^3 + cos(x) -3[/tex]
Step 3: Find the value of f for the given input
So, to find [tex]f(2\pi)[/tex], use 2 pi as the input, and simplify:
[tex]f(2\pi) = 4(2\pi)^3 + cos(2\pi) -3[/tex]
[tex]f(2\pi) = 4*8\pi^3 + 1 -3[/tex]
[tex]f(2\pi) = 32\pi^3 - 2[/tex]
Answer:
[tex]f(2 \pi)=32\pi^3-2[/tex]
Step-by-step explanation:
Fundamental Theorem of Calculus[tex]\displaystyle \int \text{f}(x)\:\text{d}x=\text{F}(x)+\text{C} \iff \text{f}(x)=\dfrac{\text{d}}{\text{d}x}(\text{F}(x))[/tex]
If differentiating takes you from one function to another, then integrating the second function will take you back to the first with a constant of integration.
Given:
[tex]g(x)=12x^2-\sin x[/tex][tex]f(0)=-2[/tex]If g(x) is the first derivative of f(x), we can find f(x) by integrating g(x) and using f(0) = -2 to find the constant of integration.
[tex]\boxed{\begin{minipage}{4 cm}\underline{Integrating $x^n$}\\\\$\displaystyle \int x^n\:\text{d}x=\dfrac{x^{n+1}}{n+1}+\text{C}$\end{minipage}}[/tex] [tex]\boxed{\begin{minipage}{4 cm}\underline{Integrating $\sin x$}\\\\$\displaystyle \int \sin x\:\text{d}x=-\cos x+\text{C}$\end{minipage}}[/tex]
[tex]\begin{aligned} \displaystyle f(x)&=\int f'(x)\; \text{d}x\\\\&=\int g(x)\;\text{d}x\\\\&=\int (12x^2-\sin x)\;\text{d}x\\\\&=\int 12x^2\; \text{d}x-\int \sin x \; \text{d}x\\\\&=12\int x^2\; \text{d}x-\int \sin x \; \text{d}x\\\\&=12\cdot \dfrac{x^{(2+1)}}{2+1}-(-\cos x)+\text{C}\\\\&=4x^{3}+\cos x+\text{C}\end{aligned}[/tex]
To find the constant of integration, substitute f(0) = -2 and solve for C:
[tex]\begin{aligned}f(0)=4(0)^3+\cos (0) + \text{C}&=-2\\0+1+\text{C}&=-2\\\text{C}&=-3\end{aligned}[/tex]
Therefore, the equation of function f(x) is:
[tex]\boxed{f(x)=4x^3+ \cos x - 3}[/tex]
To find the value of f(2π), substitute x = 2π into function f(x):
[tex]\begin{aligned}f(2 \pi)&=4(2 \pi)^3+ \cos (2 \pi) - 3\\&=4\cdot 2^3 \cdot \pi^3+1 - 3\\&=32\pi^3-2\\\end{aligned}[/tex]
Therefore, the value of f(2π) is 32π³ - 2.
Need help solving this problem
Answers
# 27
2
G
A
1 2 3
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1,7
Johnny uses a wheelbarrow to move planting soil to a delivery truck. The
volume of planting soil that fits in the wheelbarrow measures 2 feet by 3 feet
by 1.5 feet. The delivery truck measures 11 feet by 8 feet and is 6 feet tall.
Johnny puts planting soil in the delivery truck until the truck is 70% full.
What is the minimum number of times Johnny needs to use the wheelbarrow
until the delivery truck is 70% full?
Answers
He will need to use the wheelbarrow at least 41 times to fill the delivery truck to 70% of its capacity.
Define volumeVolume is a measure of the amount of space that a substance or object occupies in three dimensions. It is typically measured in units such as cubic meters (m³), cubic centimeters (cm³), liters (L), or gallons (gal), depending on the system of measurement being used.
First, let's calculate the total volume of the delivery truck:
Volume of delivery truck = length x width x height
Volume of delivery truck = 11 ft x 8 ft x 6 ft
Volume of delivery truck = 528 cubic feet
To fill the delivery truck to 70% of its capacity, Johnny needs to put 0.7 x 528 = 369.6 cubic feet of planting soil in the truck.
Now, let's calculate the volume of planting soil that fits in the wheelbarrow:
Volume of wheelbarrow = length x width x height
Volume of wheelbarrow = 2 ft x 3 ft x 1.5 ft
Volume of wheelbarrow = 9 cubic feet
Number of loads = Total volume of planting soil needed / Volume of each load
Number of loads = 369.6 cubic feet / 9 cubic feet
Number of loads = 41.0666667
Since Johnny cannot use a fraction of a load, he will need to use the wheelbarrow at least 41 times to fill the delivery truck to 70% of its capacity.
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which fraction is greater than the fraction by the model if the fraction is 3/8
Answers
The calculated value of the fraction that is greater than the fraction by the model is 1/2
Which fraction is greater than the fraction by the modelFrom the question, we have the following parameters that can be used in our computation:
Model fraction = 3/8
A fraction that is greater than the fraction by the model is represented as
Fraction > Model fraction
Substitute the known values in the above equation, so, we have the following representation
Fraction > 3/8
Add 1 to the numerator
So, we have
Fraction = 4/8
Simplify
Fraction = 1/2
Hence, the fraction that is greater than the fraction by the model is 1/2
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PLEASE HELP!
For a group of objects made of the same material, the weight of an object varies directly with its volume. If an object that has a volume of 20 cubic inches weighs 28 ounces, what is the constant of variation?
20
5/7
7/5
28
Answers
The constant of variation that exists between the weight and the volume of the objects would be = 7/5. That is option C.
How to calculate the constant of variation?A measurement is said to vary directly with another when the increase in proportion of the object leads to a direct decrease to the other one.
That is for the given object;
Weight is directly proportional to Volume
Therefore, weight = k Volume
K = constant of variation
make k the subject of formula;
k= weight/volume
but weight = 28
volume = 20
k = 28/20
= 7/5
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please help me understand
Answers
when T = 0, L = 150 (the original number of pages to read) and when T = 6 hours (time to read the entire book), L = 0 (no pages left to read).
What is Graph ?A chart can be defined as a pictorial representation or diagram that presents data or values in an organized manner. Points on a graph often represent a relationship between two or more things.
We can use a linear equation of the form to describe a function that relates the number of pages read to the time elapsed since the start of reading:
L = mT + b
where L is the number of pages remaining, T is the elapsed time in hours, m is the page read rate in pages per hour, and b is the original number of pages remaining when T = 0.
In this case, we know that Ray is reading at a constant rate of 25 pages per hour, so m = -25 (since we are counting the remaining pages). We also know that when T = 0 (start of reading), 150 pages remain unread, so b = 150. Combining everything we get:
L = -25T + 150
This formula describes a function that combines the number of pages being read with the time elapsed since the start of reading. Note that when T = 0, L = 150 (the original number of pages to read) and when T = 6 hours (time to read the entire book), L = 0 (no pages left to read).
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What is the area of Rectangle A?
Answers
Answer:
30 square units
Step-by-step explanation:
The area of a rectangle is its length multiplied by its width.
We can see that the length of Rectangle A is 6 units, and its width is 5 units.
Multiplying these together to get the rectangle's area:
6 units × 5 units = 30 square units
The circle below is centered at the point (-3, 4) and has a radius of length 3.
What is its equation?
-10
-5
5
Answers
Answer:
C. (x + 3)² + (y - 4)² = 9
Step-by-step explanation:
The equation for a circle is r² = (x - a)² + (y - b)² where "r" is the radius and (a, b) is the center.
We are given that (-3, 4) is the center and the radius is 3, so that means a = -3, b = 4, and r = 3. Insert the values to their respective places in the equation:
3² = (x - (-3))² + (y - 4)²
9 = (x + 3)² + (y - 4)²
Answer:
equation of a circle: (x-a)²+(y-b)²=r²
(x-(-3))²+(y-4)²=3²
(x+3)²+(y-4)²= 9
(x+6x+9)+(y-8y+16) =9
x+6x+9+y-8y+16=9
x+y+6x-8y+9+16-9=0
x+y+6x-8y+16 =0
what does it mean the name of the numbers
help
Answers
Answer:
It is called as triangular numbers
Step-by-step explanation:
these numbers can be represented as a triangle of dots
Factor the polynomial, if possible. Check your answer using foil.
y² + 49
Answers
Answer:
its prime
Step-by-step explanation:
it can not be factored using foil
How do I solve this?
Answers
The 99% confidence interval estimate of the population standard deviation is [12.54, 54.62] mi/h.
What is a confidence interval?A confidence interval is the mean of your estimate plus and minus the variation in that estimate. This is the range of values you expect your estimate to fall between if you redo your test.
x = [64, 60, 56, 60, 52, 59, 58, 59, 70, 68]
s = 5.963
n = 10
CI = [(n-1)*s²/chi2_upper, (n-1)*s²/chi2 lower]
CI = [(9*5.963^m²)/19.022, (9*5.963²)/2.700]
CI = [12.54, 54.62]
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The Venn diagram below shows the 14 students in Ms. Cooper's class.
The diagram shows the memberships for the Chess Club and the Science Club. (ALL SHOWN IN PHOTO BELOW) **AM GIVING BRAINLIEST AND 30 POINTS!!!**
Answers
Answer:
Step-by-step explanation:
2. Ricky wants to make rice cream. Of 1 kilogram of rice, milk2/5 is rice and 1/6 is sugar. Find the quantity of rice and sugar needed for 1 kg of rice milk.
Answers
The quantities of rice, milk and sugar needed for 1 kg of rice milk are 0.4 kg, 0.4 kg and 0.167 kg respectively.
To solve the above problem, we can use the following equation:
Rice + Milk + Sugar = 1 kg
Rice = 2/5 (1 kg) = 0.4 kg
Milk = 2/5 (1 kg) = 0.4 kg
Sugar = 1/6 (1 kg) = 0.167 kg
Therefore, the quantities of rice, milk and sugar needed for 1 kg of rice milk are 0.4 kg, 0.4 kg and 0.167 kg respectively.
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Correct answer gets brainliest!!!!
Answers
Answer:
a) 5
Step-by-step explanation:
the question say how many zero-dimensional objects are labeled on the object. so, you would count how many blue dots you see on the object, as you can see their are four dots on the the bottom, and one dot at the top.
so, 4 dots + 1 dot = ?
5 blue dots
so your answer is 5.
hopefully this helps, let me know if it doesn't.
I am half as old as my sister. In 6 years’ times will be 22. How old am now?
Answers
Answer:15
Step-by-step explanation:
Abel cycled at an average speed of 10 km/h from his home to the neighbourhood park.
On reaching the park, he cycled back home along the same route at an average speed of
8 Km/h. He took 1 1/5 hours for the whole journey. How long did he take to cycle from the park
to his home?
Answers
Answer:
Time = Distance / Speed
Time is taken from home to park = d / 10
Abel cycled back from the park to his home at an average speed of 8 km/h. The time taken for this part of the journey can be calculated using the same formula:
Time = Distance / Speed
Time is taken from park to home = d / 8
According to the given information, the total time taken for the whole journey is 1 1/5 hours, which is equivalent to 6/5 hours.
Total time is taken = Time from home to park + Time from park to home
6/5 = d/10 + d/8
To simplify the equation, let's find the least common multiple (LCM) of 10 and 8, which is 40:
(6/5) * 40 = (d/10) * 40 + (d/8) * 40
48 = 4d + 5d
48 = 9d
d = 48/9
d = 16/3 km
Now, to find the time taken from the park to Abel's home, we substitute the distance value:
Time from park to home = (16/3) / 8
Time from park to home = (16/3) * (1/8)
Time from park to home = 16/24
Time from park to home = 2/3 hour
Since 2/3 of an hour is equal to 40 minutes, Abel took 40 minutes to cycle from the park to his home.
Therefore, Abel took 40 minutes (or 2/3 of an hour) to cycle from the park to his home.
< Question 6 of 6
Use the Shell Method to find the volume of a solid obtained by rotating the region B about the x-axis.
0
y=x²³ +b
Assume a = 2 and b = 2.
(Use symbolic notation and fractions where needed.)
volume:
Answers
Answer:
Step-by-step explanation: 5
Triangle P'Q'R' (shown below) is a dilation of Triangle PQR (not shown) using center point C and a scale factor of 1.5.
What is the length, in units, of segment PQ? Explain your thinking by writing or showing math work.
Answers
The length of segment PQ is equals to the length of segment P'Q' divided by 1.5, that is:
PQ = P'Q'/1.5
What is a dilation?A dilation can be defined as a transformation that multiplies the distance between every point in an object and a fixed point, called the center of dilation, by a constant factor called the scale factor.
The scale factor for this problem is given as follows:
k = 1.5.
Hence the equation relating the lengths PQ and P'Q' is given as follows:
P'Q' = 1.5PQ
PQ = P'Q'/1.5
(as the length on the dilated figure is the original length multiplied by the scale factor).
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Question 6(Multiple Choice Worth 1 points)
(06.01 MC)
P
The cross-sectional areas of a triangular prism and a right cylinder are congruent. The triangular prism has a height of 5 units, and the right cylinder has a height of 5 units. Which
conclusion can be made from the given information?
O The volume of the prism is half the volume of the cylinder.
O The volume of the prism is twice the volume of the cylinder.
The volume of the prism is equal to the volume of the cylinder.
O The volume of the prism is not equal to the volume of the cylinder.
N
Answers
we cannot conclude that the volume of the prism is half the volume of the cylinder, twice the volume of the cylinder, or not equal to the volume of the cylinder.
How to solve the problem ?
The given information states that the cross-sectional areas of a triangular prism and a right cylinder are congruent, and both have a height of 5 units. Based on this information, we can conclude that the volumes of the two shapes may be equal, but we cannot conclude that the volume of the prism is half or twice the volume of the cylinder.
To determine the volumes of the two shapes, we need to know their respective formulas. The volume of a triangular prism is given by V = (1/2)bh, where b is the length of the base of the triangular cross-section and h is the height of the prism. The volume of a right cylinder is given by V = πr²h, where r is the radius of the circular cross-section and h is the height of the cylinder.
Since the cross-sectional areas of the two shapes are congruent, we can assume that their bases are similar. Therefore, the base of the triangular prism must be a triangle with the same area as the circular base of the cylinder. However, without further information about the shape and size of the cross-section, we cannot determine the values of b and r.
Therefore, we cannot conclude that the volume of the prism is half the volume of the cylinder, twice the volume of the cylinder, or not equal to the volume of the cylinder. The only conclusion that can be made is that the volume of the prism is equal to the volume of the cylinder, assuming that the cross-sectional areas are congruent.
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Needdd help pleaseeeee
Answers
The value of the matrix 4G + 2F is [tex]4[G] + 2[F] = \begin{bmatrix}34 & -4 & 28 & -18 & 58 \\-42 & -8 & 16 & 30 & 8 \\24 & 34 & 4 & 34\end{bmatrix}[/tex]
Matrices are an essential tool in mathematics and can be used to solve a variety of problems. In this case, we are given two matrices G and F, and we are asked to find the value of 4G + 2F.
To understand how to calculate the value of 4G + 2F, we first need to understand what it means to multiply a matrix by a scalar. When we multiply a matrix by a scalar, we simply multiply every element in the matrix by that scalar.
Now that we understand scalar multiplication, we can use it to find the value of 4G + 2F. We simply need to multiply each matrix by its respective scalar and then add the results element-wise.
[tex]4G = 4\begin{bmatrix}8 &-5 &8 &-2 &10 \\-6& -7&1 & 9& 2\\4&6 &3 &7 &5 \\-4 & -3& 0& -10& -9\end{bmatrix}= \begin{bmatrix}32 & -20 & 32 & -8 & 40 \\-24 & -28 & 4 & 36 & 8 \\16 & 24 & 12 & 28 & 20 \\-16 & -12 & 0 & -40 & -36\end{bmatrix}[/tex]
Now we have to find the value of 2[F]. that can be calculated as follows
[tex]2F = 2\begin{bmatrix}1 &8 &-2 &-5 &9 \\-9& 10&6 &-3&0\\4&5 &-4 &3 &7 \\2 &-10&-6 & -1& -8\end{bmatrix}= \begin{bmatrix}2 & 16 & -4 & -10 & 18 \\-18 & 20 & 12 & -6 & 0 \\8 & 10 & -8 & 6 & 14 \\4 & -20 & -12 & -2 & -16\end{bmatrix}[/tex]
Now we can add the two matrices element-wise to get the final result:
[tex]4G + 2F = \begin{bmatrix}32 & -20 & 32 & -8 & 40 \\-24 & -28 & 4 & 36 & 8 \\16 & 24 & 12 & 28 & 20 \\-16 & -12 & 0 & -40 & -36\end{bmatrix} +\begin{bmatrix}2 & 16 & -4 & -10 & 18 \\-18 & 20 & 12 & -6 & 0 \\8 & 10 & -8 & 6 & 14 \\4 & -20 & -12 & -2 & -16\end{bmatrix}[/tex]
[tex]4[G] + 2[F] = \begin{bmatrix}34 & -4 & 28 & -18 & 58 \\-42 & -8 & 16 & 30 & 8 \\24 & 34 & 4 & 34\end{bmatrix}[/tex]
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What's the solution to the equation 2^x + 4 = 2^3x?
a) x = 1
b) x = 2
c) x = 3
d) x = -2
Answers
Answer:
Step-by-step explanation:
2x2x2 = 2^3
2^3 = 8
2^x + 4 = 8
so x= 2
NEED HELP ASAP! (10POINTS)
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The statement that is true on the linear relationship between the brochures and cost of printing is A. the printing fee is $ 2.50.
How to find the printing fee ?To find the printing fee, find the difference between the total cost of two different numbers of brochures printed.
The printing fee is:
= ( Total cost of 43 - total cost of 40 ) / ( Difference between 43 and 40 )
= ( 607.50 - 600 ) / ( 43 - 40 )
= 7. 50 / 3
= $ 2. 50
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Each ice cube measures 1.2in high and 1in in diameter. What is the volume of all 3 ice cubes
Answers
[tex]\sf V_{3 Cylinders} =2.8274(in^{3} ).[/tex]
Step-by-step explanation:1. Find a formula for the volume (assuming the shape of the ice cubes is cylindrical).From the provided information about the ice cubes (height and diameter), it's safe to assume that they are cylinder shaped ice cubes. They could be circular cone ice cubes, but the safest assumption is cylinders. Now, to find the volume of a cylinder we use the following formula:
[tex]\sf V_{Cylinder} =\pi r^{2} h[/tex] or [tex]\dfrac{\pi d^{2} h}{4}[/tex].
For the fist equation, "r" stands for radius, and "h" for height.
On the alternate equation, "d" stands for diameter.
2. Calculate.Since we're given the diameter and height, let's use the alternate equation:
[tex]\sf V_{Cylinder} =\dfrac{\pi (1(in))^{2} 1.2(in)}{4}=\dfrac{3}{10} \pi (in^{3} )=0.9425(in^{3} ).[/tex]
3. Calculate the volume of the 3 cubes.This can be done by just multiplying the volume of a single cube ([tex]\dfrac{3}{10} \pi (in^{2} )[/tex]) by 3.
[tex]\sf V_{3 Cylinders} =(3)\dfrac{3}{10} \pi (in^{3} )=\dfrac{9}{10} \pi (in^{3} )=\boxed{\sf 2.8274(in^{3} )}.[/tex]
4. Alternative answer (assuminng the ice cubes have a circular cone shape).Assuming the ice cubes have the shape of a circular cone, this is the process for calculating the volume of all 3 cubes:
[tex]\sf V_{Cone} =\dfrac{1}{3} \pi r^{2} h\\ \\\\ \\ V_{3Cones} =3*\dfrac{1}{3} \pi r^{2} h\\ \\ \\= \pi r^{2} h\\ \\ \\=\pi (\dfrac{1(in)}{2} )^{2} (1.2(in))\\ \\\\ =\dfrac{3}{10} \pi (in^{3} )=\boxed{\sf 0.9425(in^{3} )}[/tex]
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what is the answer for this question
Answers
Answer:
The yellow region is 13.73 cm squared
Step-by-step explanation:
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Area of square:
[tex]8 * 8 = 64 cm^2[/tex]
Area of the 4 quarter-circles:
[tex]4(\pi r^2)/4[/tex]
The fours cancel each other, we are left with:
[tex]\pi r^2[/tex]
r = 4, so substitute that, we get:
[tex]\pi 4^2 = 16 \pi cm^2[/tex]
Which can be approximated to 50.27 cm squared
Subtract the area of the circle from the square:
[tex]64 - 50.27 = 13.73 cm^2[/tex]
So the area of the yellow region is 13.73 cm squared
The weights of four similar packs of tomatoes are listed below.
Pack A: 2.456 pounds
Pack B: 2.457 pounds
Pack C: 2.454 pounds
Pack D: 2.459 pounds
Malcolm rounds the weights to the nearest hundredth pound. Which weight does
not round to 2.46 pounds?
A 2.456 pounds
B 2.457 pounds
C 2.454 pounds
D 2.459 pounds
Answers
Answer:
The weight that does not round to 2.46 pounds is C 2.454 pounds.
Step-by-step explanation:
Based on the given information, the weights of the four similar packs of tomatoes are as follows:
Pack A: 2.456 poundsPack B: 2.457 poundsPack C: 2.454 poundsPack D: 2.459 poundsMalcolm rounds the weights to the nearest hundredth pound. To round to the nearest hundredth pound, we look at the digit in the hundredths place. If it is 5 or greater, we round up the digit in the tenths place. If it is less than 5, we leave the digit in the tenths place as it is. Therefore, we can obtain the rounded weights as follows:
Pack A: 2.46 poundsPack B: 2.46 poundsPack C: 2.45 poundsPack D: 2.46 poundsFrom the above rounded weights, we see that Pack C rounds to 2.45 pounds and does not round to 2.46 pounds. Therefore, the weight that does not round to 2.46 pounds is C 2.454 pounds.
