At the coordinates (X, Y, Z) = (3, -2, 0), L(x, y, z) = C+35 + x - 12Cz is the linear approximation to the function f(Dy, Z) = Ce^2yz+32.
To find the linear approximation to the function f(Dy, Z) = Ce^2yz+32 at the point (X, Y, Z) = (3,-2,0), we need to find the partial derivatives of the function with respect to each variable at the point (3,-2,0).
The partial derivative of f with respect to x is simply e^2yz, which evaluated at (3,-2,0) gives us e^0 = 1.
The partial derivative of f with respect to y is 2xzCe^2yz, which evaluated at (3,-2,0) gives us 2(3)(0)C = 0.
The partial derivative of f with respect to z is 2xyCe^2yz+3, which evaluated at (3,-2,0) gives us 2(3)(-2)C + 3(1) = -12C + 3.
Using these partial derivatives, we can construct the linear approximation L(x,y,z) = f(3,-2,0) + (x-3)(1) + (y+2)(0) + (z-0)(-12C+3) = Ce^0+32 + (x-3) - 12Cz + 3.
Simplifying this expression, we get L(x,y,z) = C+35 + x - 12Cz.
Therefore, the linear approximation to the function f(Dy, Z) = Ce^2yz+32 at the point (X, Y, Z) = (3,-2,0) is L(x,y,z) = C+35 + x - 12Cz.
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Caleb has
coins (nickels, dimes, and quarters) in a jar, totaling. He has three more nickels than dimes. How many quarters does Caleb have?
Caleb has 30 quarters.
What is arithmetic?
Mathematical arithmetic is the study of the properties of the standard operations on numbers, such as addition, subtraction, multiplication, division, exponentiation, and root extraction.
Here, we have
Given: Caleb has 51 coins (nickels, dimes, and quarters) in a jar, totaling $9. He has three more nickels than dimes.
We have to find out how many quarters Caleb has.
Let x be nickel,
y be dimes and
z be quarters
x + y + z = 51.....(1)
1 quartes = 25 cents
1 dimes = 10 cents
1 nickel = 5 cents
Now, the total dollar is $9,
5x/100 + 10y/100 + 25z/100 = 9
5x + 10y + 25z = 900
x + 2y + 5z = 180....(2)
and
y + 3 = x...(3)
Solving equation(1) and (2), we get
From (1)
x + x-3 + z = 51
2x + z = 54....(4)
From (2)
x + 2(x -3) + 5z = 180
3x + 5z = 186...(5)
Now, by solving equations (4) and (5), we get
x = 12
z = 30
Now,
y + 3 = x
y + 3 = 12
y = 9
Hence, Caleb has 30 quarters.
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Which equation represents a line that is perpendicular to the line
represented by 2x - y = 7?
(1) y = -x + 6
(2) y = x + 6
(3) y = -2x + 6
(4) y = 2x + 6
A hot water pipe needs to be insulated to prevent heat loss. The outer pipe has a diameter D = 48.7 cm (correct to 3 significant figures). The inner pipe has a diameter d = 19.25 cm (correct to 2 decimal places). Work out the upper and lower bound of the cross-sectional area of the insulation, A (the shaded area between the inner and outer pipes) in cm2 to the nearest whole number. Give your answer in interval form, using A as the variable.
The upper and lower bound of the cross-sectional area of the insulation, would be A = [ 3129, 3137 ] cm².
How to find the upper and lower bond ?The upper and lower bound of A would be found by the formula :
A = π x ( R ² - r ² )
The upper bound is therefore:
= π x (( 48. 75 / 2) ² - ( 19.2 45 / 2) ²)
= π x ( 1183. 0625 - 184. 857025 )
= π x 998. 205475
= 3, 137 cm²
The lower bound will then be:
= π x ( ( 48. 65 / 2 ) ²- (19. 255 / 2) ²)
= π x ( 1180. 9225 - 184. 963025)
= π x 995. 959475
= 3, 129 cm²
The interval form is therefore A = [ 3129, 3137 ] cm²
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What is 0.50 divided by 0.25
Answer:
2
Step-by-step explanation:
0.50/0.25 = 50/25
= 2
Dividing 0.50/0.25 no. is same as 50/25 when we multultiply by 100/ 100 so it is 2
ans. = 2
0.50 / 0.25
5/10 x 100/5
=2
Urgenttttt what is true about the series given: 25+5+1+...
the series converges to 31.25 the series diverges .
the series converges to 125
the series does not converge or diverge .
The statement "the series converges to 31.25" is true about the given series.
Given series is 25 + 5 + 1 + ....
We can clearly see that given series is infinite geometric series.
First term is a=25
common ratio is r = 5/25
= 1/5
We know that the formula of sum of an infinite geometric series is
S = a / (1 - r)
S = 25 / (1 - 1/5)
S = 25/(4/5)
S = (25*5)/4
S = 125/4
S = 31.5
Therefore, the sum of the infinite geometric series is 31.25.
Since, the sum of the series is a finite number, we can say that the series converges.
Therefore, the statement "the series converges to 31.25" is true about the given series.
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Davis spent 25 minutes working on math problems. Carl worked on math problems for m fewer minutes.
Drag a number and symbols to represent the amount of time Carl worked on problems.
X
M
25
The amount of time Carl represent is 25-m on the problems.
The statement "Davis spent 25 minutes working on math problems. Carl worked on math problems for m fewer minutes" means that Carl spent some amount of time working on math problems, but that amount is m minutes less than what Davis spent.
To represent the amount of time Carl worked on math problems, we can use the variable X. We know that X is equal to the amount of time Carl worked on math problems, and that X is equal to 25 minus m.
This is because Davis spent 25 minutes on math problems, and Carl worked on them for m fewer minutes. So if we subtract m from 25, we get the amount of time Carl worked on math problems.
Therefore, the equation X = 25 - m represents the amount of time Carl worked on math problems, where X is the amount of time in minutes and m is the number of minutes Carl worked less than Davis.
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Pls help i really need help on this
Where the function f(x) = x² + 2x - 3 is given, note that the x-intercepts of the function f(x) are -3 and 1, and the minimum value of the function is -4. See the attached graph.
What is the explanation for the above response?
To find the minimum and maximum points of the function f(x), we can complete the square:
f(x) = x^2 + 2x - 3
= (x + 1)^2 - 4
We can see that the function is in the vertex form f(x) = a(x - h)^2 + k, where the vertex is (-1, -4).
Since the coefficient of the x^2 term is positive, the parabola opens upwards, and the vertex is the minimum point. Therefore, the minimum value of the function f(x) is -4.
To find the x-intercepts, we can set f(x) = 0:
(x + 1)^2 - 4 = 0
(x + 1)^2 = 4
Taking the square root of both sides, we get:
x + 1 = ±2
x = -1 ± 2
Therefore, the x-intercepts of the function f(x) are x = -3 and x = 1.
In summary, the x-intercepts of the function f(x) are -3 and 1, and the minimum value of the function is -4, which occurs at the vertex (-1, -4).
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Hello! Help please thank you
Answer:
2(2(3) + 2(5) + 3(5)) = 2(6 + 10 + 15) = 2(31)
= 62
D is the correct answer.
Identify the fractions between 1/16 and 5/8
The fractions between 1/16 and 5/8 are 3/16 and 5/16
Identifying the fractions between 1/16 and 5/8The fraction expressions are given as
1/16 and 5/8
The above fractions are proper fractions because numerator < denominator
Express the fraction 5/8 as a denominator of 16
So, we have the following equivalent fractions
1/16 and 10/16
This means that the fractions between 1/16 and 5/8 can be represented as
a/16
Where
1 < a < 10
So, we have
Possible fraction = 3/16 and 5/16
Hence, the fractions between 1/16 and 5/8 are 3/16 and 5/16
Note that there are other possible fractions too
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A basic pattern of 1 blue bead and 1 green bead is used to make a bracelet that is 37cm long. The bracelet is made by repeating the basic pattern 10 times. The length of a blue bead is Bcm. The length of a green bead is 1. 2cm. Complete the question to represent the length of the bracelet
Answer: Therefore, the length of a blue bead is 2.5 cm, and the length of a green bead is 1.2 cm. And the length of the bracelet is:
10 × (2.5 + 1.2) = 37 cm.
Step-by-step explanation:
To represent the length of the bracelet, we need to determine the length of each repetition of the basic pattern and then multiply it by the number of times the pattern is repeated.
The length of each repetition of the basic pattern is the sum of the length of one blue bead and one green bead, which is:
B + 1.2 cm
Since the basic pattern is repeated 10 times, the total length of the bracelet is:
10 × (B + 1.2) cm
And we know that the total length of the bracelet is 37 cm, so we can set up an equation:
10 × (B + 1.2) = 37
Simplifying the equation, we can divide both sides by 10:
B + 1.2 = 3.7
Subtracting 1.2 from both sides, we get:
B = 2.5
Therefore, the length of a blue bead is 2.5 cm, and the length of a green bead is 1.2 cm. And the length of the bracelet is:
10 × (2.5 + 1.2) = 37 cm.
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The mean of a sample is a. always equal to the mean of the population. b. always smaller than the mean of the population c. computed by summing the data values and dividing the sum by (n - 1) d. computed by summing all the data values and dividing the sum by the number of items
The mean of a sample is computed by summing all the data values and dividing the sum by the number of items in the sample. Thus, the correct answer is d.
Option a is incorrect because the mean of a sample is not always equal to the mean of the population, unless the sample is a complete representation of the population (which is often not the case).
Option b is incorrect because the mean of a sample can be greater than, equal to, or smaller than the mean of the population, depending on the sampling method and the characteristics of the population.
Option c is incorrect because the sample mean is computed by summing the data values and dividing the sum by the number of items in the sample minus one only if the sample is taken from a normally distributed population and the standard deviation of the population is unknown. Otherwise, the sample mean is computed by dividing the sum of the data values by the number of items in the sample.
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3. Compute the integral JSS, udv, where U is the part of the ball of radius 3, centered at 0,0,0), that lies in the 1st octant. Recall that the first octant is the part of the 3d space where all three coordinates I, y, z are nonnegative. (Hint: You may use cylindrical or spherical coordinates for this computation, but note that the computation with cylindrical coordinates will involve a trigonometric substitution - 30 spherical cooridnates should be preferable.)
To compute the integral JSS, udv, where U is the part of the ball of radius 3, centered at 0,0,0), that lies in the 1st octant, we can use spherical coordinates. Since the region is defined as having all three coordinates nonnegative, we can set our limits of integration as follows: 0 ≤ ρ ≤ 3, 0 ≤ θ ≤ π/2, and 0 ≤ φ ≤ π/2.
Using the Jacobian transformation, we have:
JSS, udv = ∫∫∫U ρ²sinφ dρdθdφ
Substituting in our limits of integration, we get:
JSS, udv = ∫0^π/2 ∫0^π/2 ∫0³ ρ²sinφ dρdθdφ
Evaluating the integral, we get:
JSS, udv = (3³/3) [(sin(π/2) - sin(0))] [(1/2) (π/2 - 0)]
JSS, udv = 9/2 π
Therefore, the value of the integral JSS, udv, over the part of the ball of radius 3 that lies in the 1st octant is 9/2π.
To compute the integral JSS, udv, over the region U, which is the part of the ball of radius 3 centered at (0,0,0) and lies in the first octant, we will use spherical coordinates for this computation as it's more preferable.
In spherical coordinates, the volume element is given by dv = ρ² * sin(φ) * dρ * dφ * dθ, where ρ is the radial distance, φ is the polar angle (between 0 and π/2 for the first octant), and θ is the azimuthal angle (between 0 and π/2 for the first octant).
Now, we need to set up the integral for the volume of the region U:
JSS, udv = ∫∫∫ (ρ² * sin(φ) * dρ * dφ * dθ), with limits of integration as follows:
ρ: 0 to 3 (radius of the ball),
φ: 0 to π/2 (for the first octant),
θ: 0 to π/2 (for the first octant).
So, the integral becomes:
JSS, udv = ∫(0 to π/2) ∫(0 to π/2) ∫(0 to 3) (ρ² * sin(φ) * dρ * dφ * dθ)
By evaluating this integral, we will obtain the volume of the region U in the first octant.
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Which expression is equivalent to: (5²)⁴ ?
(Exponent Form Only, please)
.....................
7*. All lengths are in cm. Find the area of the right angled
triangle.
x-14( shortest side)
2x+5( hypotenuse)
2x+3( remaining side)
Answer:
504 cm^2.
Step-by-step explanation:
By Pythagoras:
(2x + 5)^2 = (2x + 3)^2 + (x - 14)^2
4x^2 + 20x + 25 = 4x^2 + 12x + 9 + x^2 - 28x + 196
20x - 12x + 28x + 25 - 9 - 196 = x^2
x^2 - 36x + 180 = 0
(x - 6)(x - 30) = 0
x = 6, 30.
As one of the sides is x - 14, x mst be 30 as its length has to be positive.
So the area of the triangle
= 1/2 * (x - 14) 8 (2x + 3)
= 1/2 * (30-14)(60 + 3)
= 1/2 * 16 * 63
= 504 cm^2.
Write two numbers that multiply to the value on top and add to the value on bottom.
Answer:
-17 and -5
Step-by-step explanation:
-5 x -17 = 85
-5 + -17 = -22
Please answer the question correctly and neatly. Please find the
exact answer. Will upvote if correct.
Find the volume of the solid obtailed by rotating the region bounded by the given curves about the specified axis. y= x, y = 1 about y = 3
The region bounded by the given curves is a triangle with vertices at (0,0), (1,1), and (1,0). When this region is revolved around the line y=3, we obtain a solid with a hole in the middle.
To find the volume of this solid, we can use the method of cylindrical shells. Imagine slicing the solid into thin cylindrical shells with radius r and height Δy. The volume of each shell is approximately 2πrΔy times the thickness of the shell.
The distance between the axis of rotation (y=3) and the line y=1 is 2 units. Therefore, the radius of each cylindrical shell is r = 3 - y. The height of each shell is Δy = dx, where x is the distance from the y-axis.
To set up the integral, we need to express x in terms of y. Since the region is bounded by y=x and y=1, we have x=y for 0<=y<=1. Therefore, the integral for the volume of the solid is:
V = ∫[0,1] 2π(3-y)x dx
= 2π ∫[0,1] (3-y)y dx
Evaluating this integral, we get:
V = 2π [3y^2/2 - y^3/3] from 0 to 1
= 2π (3/2 - 1/3)
= 2π/3
Therefore, the volume of the solid obtained by rotating the region bounded by y=x, y=1 about y=3 is (2/3)π cubic units.
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Find the radius of gyration of a plate covering the region
bounded by y=x2, x=6, and the x-axis with
respect to the x-axis
(Type exact answer)
The radius of gyration of the plate about the x-axis is [tex]6 \sqrt{6} / 5[/tex] units.
How to find the radius of gyration of a plate covering the region?To find the radius of gyration of a plate covering the region bounded by [tex]y = x^2[/tex], x = 6, and the x-axis with respect to the x-axis, we need to use the formula:
[tex]k_x = \sqrt{(I_x / A)}[/tex]
where [tex]k_x[/tex] is the radius of gyration, [tex]I_x[/tex] is the moment of inertia of the plate about the x-axis, and A is the area of the plate.
We can calculate the area A of the plate as follows:
[tex]A = \int\limits^6_0 { x^2}\, dx\\= [x^3/3]\ from\ 0\ to\ 6\\= 72[/tex]
To find the moment of inertia [tex]I_x[/tex], we can use the formula:
[tex]I_x = \int\ {y^2} \, dA[/tex]
where y is the perpendicular distance of an element of area [tex]dA[/tex] from the x-axis. We can express y in terms of x as y = x². Therefore, we have:
[tex]dA = y dx = x^2 dx\\I_x = \int\limits^6_0 { x^2 (x^2)} dx\\= \int\limits^6_0 {x^4}\, dx\\= [x^5/5]\ from\ 0\ to\ 6\\= 6^5/5[/tex]
Substituting these values into the formula for [tex]k_x[/tex], we get:
[tex]k_x = \sqrt{(I_x / A)}\\= \sqrt{((6^5/5) / 72)}\\= \sqrt{(6^3 / 5)}\\= 6 \sqrt{6} / 5[/tex]
Therefore, the radius of gyration of the plate about the x-axis is [tex]6 \sqrt{6}/ 5[/tex] units.
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I need help finding the decimal for these equations.
Answer:
Carlos=1.5041
Mykala=2.6991
William=4.1350
Emily=4.1773
Find the volume of this cone.
Round to the nearest tenth.
10ft
6ft
The volume of the given cone is 402.1 cubic feet if the slant height is 10ft and the length is 6ft.
To calculate the volume of a cone, the formula used is :
V = (1/3) * π * [tex]r^2[/tex] * h
Here, the radius is the unknown term. we need to calculate the radius of the cone. We can use the Pythagorean theorem to find the radius of the cone.
[tex]l^2 = r^2 + h^2[/tex]
[tex]10^2 = r^2 + 6^2[/tex]
[tex]r = \sqrt{(10^2 - 6^2)}[/tex]
radius = 8 ft
V = (1/3) * π * [tex]r^2[/tex] * h
V = (1/3) * π *[tex]8^2[/tex] * 6
V = (1/3) * π * 384
V = 402.1 cubic feet
Therefore we can infer that the volume of the given cone is 402.1 cubic feet.
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The complete question is:
'Find the volume of this cone. Round to the nearest tenth.
slant height = 10ft
length = 6ft
put the measuraments from greatest to least
The measurements from greatest to least would be ordered as follows:
6 yards 2 1/2 feet 45 inchesHow to order the measurements ?First, we need to convert all the units to the same unit. Let's convert everything to inches, since that is the smallest unit.
6 yards = 6 x 3 = 18 feet
18 feet = 18 x 12 = 216 inches
2 1/2 feet = 2 x 12 + 6 = 30 inches
So now we have:
6 yards = 216 inches
2 1/2 feet = 30 inches
45 inches = 45 inches
Putting these in order from greatest to least, we have:
216 inches, 45 inches, 30 inches
Therefore, the measurements from greatest to least would be ordered as follows:
6 yards, 45 inches, 2 1/2 feet
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The full question is:
Put the measurements from greatest to least. 45 inches, 6 yards, and 2 1/2 feet
In 3 minutes, a conveyor belt moves 200 pounds of recyclable aluminum from the delivery truck to a storage area. A smaller belt moves the same quantity of cans the same distance in 9 minutes. If both belts are used, find how long it takes to move the cans to the storage area
If both belts are used, it will take 2.25 minutes to move the cans to the storage area
To solve this problem, we need to use the concept of rate of work. We know that the larger belt can move 200 pounds of aluminum in 3 minutes, which means its rate of work is 200/3 = 66.67 pounds per minute. Similarly, the smaller belt can move the same quantity of cans in 9 minutes, which means its rate of work is 200/9 = 22.22 pounds per minute.
When both belts are used together, their rates of work add up, so the total rate of work is 66.67 + 22.22 = 88.89 pounds per minute. We can use this rate of work to find how long it will take to move the cans to the storage area.
Let's assume that it takes x minutes to move the cans using both belts. Then, we can set up the following equation:
88.89x = 200
Solving for x, we get:
x = 2.25 minutes
Therefore, it will take 2.25 minutes to move the cans to the storage area using both belts.
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Find the coordinates of point P along the directed line segment cap A cap b$AB$AB so that cap A cap p$AP$AP to cap p cap b$PB$PB is the given ratio.
cap A times open paren negative 7 comma negative 5 close paren
The coordinates of point P along the directed line segment AB with a ratio of 1:4 are (-5, -2).
Since the ratio of AP to PB is 1:4, we can use the midpoint formula to find the coordinates of point A. The midpoint formula is
((x₁ + x₂)/2, (y₁ + y₂)/2)
Plugging in the coordinates of points P and B, we get:
((4(-7) - 2)/5, (4(-5) + 0)/5) = (-30/5, -20/5) = (-6, -4)
we can use the point-slope formula to find the equation of the line segment AB:
(y - (-4)) = (1/5)(x - (-6))
Simplifying this equation, we get:
y = (1/5)x + 2
Finally, we can use the given ratio of 1:4 to find the coordinates of point P. Since the ratio of AP to PB is 1:4, we can use the ratio formula to find the coordinates of point P:
(x, y) = (4(-5) + (-2))/5, (4(-2) - (-4))/5) = (-30/5, 12/5) = (-6, 2.4)
Rounding off to one decimal place, we get the coordinates of point P as (-5, -2).
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If arc wvx=(13x+9) and angle wxz=(5x+36) find angle wxy
Angle WXY is vertical to angle WXZ, they are equal, therefore, angle WXY is also 141 degrees.
How to find the angle WXY using information about the arc WVX and angle WXZ in a circle?To find the angle WXY, we need to use the properties of angles formed by intersecting chords in a circle. The angles formed by intersecting chords are related to the arcs intercepted by those chords.
Given that the arc WVX is equal to (13x + 9) and the angle WXZ is equal to (5x + 36), we can set up an equation:
Angle WXZ = [tex]\frac{1}{2}[/tex] * Arc WVX
(5x + 36) = [tex]\frac{1}{2}[/tex] * (13x + 9)
To solve for x, we'll multiply both sides of the equation by 2 to eliminate the fraction:
2(5x + 36) = 13x + 9
10x + 72 = 13x + 9
Subtracting 10x and 9 from both sides, we get:
72 - 9 = 13x - 10x
63 = 3x
Dividing both sides by 3, we find:
x = 21
Now that we have the value of x, we can substitute it back into the equation for the angle WXZ to find its value:
Angle WXZ = 5x + 36 = 5(21) + 36 = 105 + 36 = 141 degrees
Since angle WXY is vertical to angle WXZ, they are equal. Therefore, the angle WXY is also 141 degrees.
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The cost after the coupon is $21. 25 she decides to add a 20% tip. How much is she adding for a tip
If the cost after the coupon is $21.25 and she decides to add a 20% tip, she will be adding $4.25 for the tip.
Find out how much a 20% tip would be on a cost of $21.25 after applying a coupon.
Identify the total cost after the coupon.
In this case, the cost is $21.25.
Determine the percentage for the tip.
The tip percentage is given as 20%.
Convert the percentage to a decimal.
To do this, divide the percentage by 100. So, 20% divided by 100 is equal to 0.2.
Multiply the total cost by the tip percentage in decimal form.
Now, multiply $21.25 (total cost) by 0.2 (tip percentage as a decimal).
$21.25 x 0.2 = $4.25
Calculate the tip amount.
The tip amount is $4.25.
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Skyler has 4 1/3 hours until she needs to go to bed she watches a movie for 2 2/9 hours how much time does she have left
Step-by-step explanation:
just convert the 1/3 and times 3 to both it's numerator and denominator.
once you have the same denominator as the other mixed number, you can start to minus.
Answer:
2 1/9 hrs
Step-by-step explanation:
4 1/3 = 13/3 = 39/9
2 2/9 = 20/9
39/9 - 20/9 = 19/9 = 2 1/9 hrs
or,
(4 - 2) + (3/9 - 2/9) = 2 1/9 hrs
WHATS THE AREA PLEASE HELP DUE in 5 minutes
Answer:
The answer to your problem is, 201.06 or 201.1
Step-by-step explanation:
To find the area you use the formula:
A = π [tex]r^2[/tex]
R = Radius
A = Area
We know the radius of the circle is 8
So replace A = π [tex]r^2[/tex]
= π × 8 ≈ 201.06193
Or 201.06 or 201.1
Thus the answer to your problem is, 201.06 or 201.1
Add. Hint: Use the place value blocks to help solve
8
+
7
8+78, plus, 7. 8
+
7
=
8+7=start color #0c7f99, 8, end color #0c7f99, plus, start color #ca337c, 7, end color #ca337c, equals
The answer of addition is 94.
What is addition?The phrase "the addition" refers to combining two or more numbers. Adding two numbers is indicated by the plus sign (+), therefore adding three is written as three plus three.
To add 8 and 78, we can start by adding the ones place digits, which are 8 and 7.
8 + 7 = 15
Since 15 is greater than 10, we need to regroup 10 ones as 1 ten and carry it over to the tens place. We can represent this with place value blocks by moving a rod of 10 ones from the ones place to the tens place.
So we have:
8
+78
---
```
8
+78
---
16 (write 6 in the ones place and carry 1 to the tens place)
```
Now we can add the tens place digits, which are 1 (carried over) and 8:
1 + 8 = 9
So the final result is:
8
+78
-----
86
Therefore, 8 plus 78, plus 7 is:
```
8
+78
+ 7
---
94
```
So the answer of addition is 94.
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The faces of a rectangular prism have areas of 9, 9, 25, 25, 49, and 49 square meters. Find the volume of the rectangular prism, in cubic meters
The volume of the rectangular prism is 105 cubic meters.
To find the volume of the rectangular prism, we can use the formula V = lwh, where V is the volume, l is the length, w is the width, and h is the height.
Since there are three pairs of congruent faces, we can deduce that the areas of the three pairs of faces represent the three dimensions of the rectangular prism. The areas are 9, 25, and 49 square meters, which are the squares of the sides' lengths.
Take the square root of each area to find the corresponding side lengths:
√9 = 3 meters
√25 = 5 meters
√49 = 7 meters
Now, apply the formula to find the volume:
V = lwh = 3 × 5 × 7 = 105 cubic meters.
The volume of the rectangular prism is 105 cubic meters.
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tomas earns 0.5% commision on the sale price of a new car. On wednesday, he sells a new car for $24,500. How much commison does tomas earn on this sale
Tomas earns a commission of $122.50 on the sale of the new car.
Tomas earns a 0.5% commission on the sale price of a new car. On Wednesday, he sells a new car for $24,500. To determine the commission Tomas earns, we need to multiply the sale price by the commission rate. The commission rate is given as 0.5%, which can be expressed as a decimal by dividing by 100. So, 0.5% is equal to 0.005 as a decimal.
Now, we can calculate Tomas's commission by multiplying the sale price by the commission rate. In this case, we multiply $24,500 by 0.005:
$24,500 x 0.005 = $122.50
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6. Yu is considering two different banks for his $3,000 savings account: OPTION A 4% FOR 20 YEARS SIMPLE INTEREST OPTION B 2% FOR 10 YEARS COMPOUND INTEREST 8 What is the interest earned on option A? O What is the total value on option A? What is the interest earned on option B? O What is the total value on option B? 10 Which is the better option?
The interest earned on Option A is $2400 and Option B is $666.18. Option A is the better option as Option A has a higher total value of $5400 compared to Option B's total value of $3666.18.
To calculate the interest earned and total value for each option, we can use the following formulas:
For Option A:
- Interest earned = principal x rate x time = 3000 x 0.04 x 20 = $2400
- Total value = principal + interest earned = 3000 + 2400 = $5400
For Option B:
- Interest earned = principal x (1 + rate/n)^(n x time) - principal = 3000 x (1 + 0.02/1)^(1 x 10) - 3000 = $666.18
- Total value = principal + interest earned = 3000 + 666.18 = $3666.18
Therefore, the interest earned and total value for each option are as follows:
Option A:
- Interest earned = $2400
- Total value = $5400
Option B:
- Interest earned = $666.18
- Total value = $3666.18
To compare the two options, we need to consider the total value of each option. Option A has a higher total value of $5400 compared to Option B's total value of $3666.18. Therefore, Option A is the better option.
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