The total volume of the dill spears is approximately 160 cm³.
To find the total volume of the dill spears, we'll need to determine the volume of the pickling liquid and subtract it from the total volume of the jar.
Given information:
Base area of the jar = 45 cm²
Height of the jar = 13 cm
Pickle juice drained = 160 cm³
First, let's calculate the volume of the jar:
The volume of a cylinder can be found using the formula V = πr²h, where r is the radius of the base and h is the height of the cylinder.
The base area of the jar is given as 45 cm², which means πr² = 45.
So, we can find the radius (r) of the base using the formula r = √(45/π).
Let's calculate the value of r:
r = √(45/π) ≈ 3.79 cm
Now we can find the volume of the jar:
V_jar = πr²h
= π(3.79)²(13)
≈ 1818.73 cm³
Next, let's calculate the volume of the pickling liquid:
Given that 160 cm³ of pickle juice was drained, the volume of the pickling liquid is equal to the volume of the jar minus the volume of the drained pickle juice.
V_pickling_liquid = V_jar - 160
≈ 1818.73 cm³ - 160 cm³
≈ 1658.73 cm³
Finally, to find the total volume of the dill spears, we need to subtract the volume of the pickling liquid from the volume of the jar:
Total volume of dill spears = V_jar - V_pickling_liquid
≈ 1818.73 cm³ - 1658.73 cm³
≈ 160 cm³
Therefore, the total volume of the dill spears is approximately 160 cm³.
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point slope form (0,12), (-6,0)
This is the equation of the line in point-slope form, where the slope is 2 and the given point is (0, 12).
To find the equation of a line in point-slope form, we need a point on the line and the slope of the line.
Given the points (0, 12) and (-6, 0), we can calculate the slope using the formula:
slope = (y2 - y1) / (x2 - x1)
Using the coordinates (0, 12) as (x1, y1) and (-6, 0) as (x2, y2):
slope = (0 - 12) / (-6 - 0)
slope = -12 / -6
slope = 2
Now that we have the slope, we can use the point-slope form of the equation:
y - y1 = m(x - x1)
Using the point (0, 12) as (x1, y1) and the slope (m) as 2:
y - 12 = 2(x - 0)
Simplifying the equation:
y - 12 = 2x
This is the equation of the line in point-slope form, where the slope is 2 and the given point is (0, 12).
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graph the equation y = 2x + 2
Answer:
Step-by-step explanation:
When the equation is in the slope intercept form of y = mx + b, you know that the m is the slope and the b is the y-intercept (0, b)
By looking at the equation y=2x + 2, you can determine that the y-intercept will be at the point (0, 2) and the slope is 2.
To graph, start with the point of (0, 2) then go up 2 units and to the right 1 unit. So the next point will be at (1, 4)
You can also, substitute and number in for the x and calculate the y value. For example, if x is 3, then y=2(3)+2; y = 8 so the point (3, 8) is on the line.
Write a linear equation for the following table.
x = number
y = cost
0
15
35
55
75
95
y =
4
8
12
16
X +
Answer:
[tex]m = \frac{35 - 15}{4 - 0} = \frac{20}{4} = 5[/tex]
[tex]y = 5x + 15[/tex]
elsa hikes up a mountain. she hikes back down at a constant rate the table shows elsas elevation at each hour after she begins her descent
The linear equation from the given table is expressed as:
y = -1500x + 8350
How to find the equation from the table?The general form for the equation of a line in slope intercept form is:
y = mx + c
where:
m is slope
c is y-intercept
The formula for the equation of a line through two coordinates is:
(y - y₁)/(x - x₁) = (y₂ - y₁)/(x₂ - x₁)
We will take the two coordinates (1, 6850) and (2, 5350)
Thus:
(y - 6850)/(x - 1) = (5350 - 6850)/(2 - 1)
(y - 6850)/(x - 1) = -1500
y - 6850 = -1500x + 1500
y = -1500x + 1500 + 6850
y = -1500x + 8350
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√7
7. Given that the sin(E)= 4 and TE = 4, determine the
remaining sides of A THE. Give exact answers.
E
Answer:
Step-by-step explanation:
To determine the remaining sides of triangle THE given that sin(E) = 4 and TE = 4, we can use the sine ratio.
The sine ratio is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse in a right triangle.
In this case, sin(E) = 4/TE, which means the side opposite angle E is 4 and the hypotenuse TE is 4.
Using the Pythagorean theorem, we can find the length of the remaining side TH:
TH^2 = TE^2 - HE^2
TH^2 = 4^2 - 4^2
TH^2 = 16 - 16
TH^2 = 0
TH = 0
Therefore, the length of side TH is 0.
number 33!!!! this is a test !!!
33.) The volume of the given triangular prism would be= 36. That is option E.(NOTA)
How to calculate the volume of a triangular prism?To calculate the volume of a triangular prism, the formula that should be used is given as follows;
Volume= BH
where;
B= area of base = 1/2 × base×height
= 1/2×4×3
= 6
H= 6
Volume= 6×6= 36.
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given f(x) = x^3 - 10x + k, and the remainder when f(x) is divided by x + 3 is 6, then what is the value of K?
Answer:
Step-by-step explanation:
(x^3 - 10x + K)/(X+3) = 6 GIVEN
for different values of x there are many possible values of k some i will show
when we substitute x=1
we get k=33
at x=2
weget k=42
so many values are possible for k
because there is no intervel in question which restrics us from taking different values of x or k so you take any value of x you will get different values of k
Which type of conic section is defined by the equation:... 100pts
Answer:
This is an equation of a parabola.
[tex](y+6)^2=4(x+1)[/tex]
Step-by-step explanation:
A conic section is a curve obtained by the intersection of a plane and a cone. The three major conic sections are parabola, hyperbola and ellipse (the circle is a special type of ellipse).
The standard equations for hyperbolas and ellipses all include x² and y² terms. The standard equation for a parabola includes the square of only one of the two variables.
Therefore, the equation y² - 4x + 12y + 32 = 0 represents a parabola, as there is no x² term.
As the y-variable is squared, the parabola is horizontal (sideways), and has an axis of symmetry parallel to the x-axis.
The conic form of a sideways parabola is:
[tex]\boxed{(y-k)^2=4p(x-h)}[/tex]
where:
(h, k) is the vertex.(h+p, k) is the focus.x = h-p is the directrix.To write the given equation in conic form, we need to complete the square for the y-variable.
Rearrange the equation so that the y-terms are on the left side:
[tex]y^2 + 12y = 4x - 32[/tex]
Add the square of half the coefficient of the y-term to both sides of the equation:
[tex]y^2 + 12y+\left(\dfrac{-12}{2}\right)^2 = 4x - 32+\left(\dfrac{-12}{2}\right)^2[/tex]
[tex]y^2 + 12y+\left(-6\right)^2 = 4x - 32+\left(-6\right)^2[/tex]
[tex]y^2 + 12y+36 = 4x - 32+36[/tex]
[tex]y^2 + 12y+36 = 4x +4[/tex]
Factor the perfect square trinomial on the left side of the equation:
[tex](y+6)^2=4x+4[/tex]
Factor out the coefficient of the x-term from the right side of the equation:
[tex](y+6)^2=4(x+1)[/tex]
Therefore, the equation of the given conic section in conic form is:
[tex]\boxed{(y+6)^2=4(x+1)}[/tex]
where:
(-1, -6) is the vertex.(0, -6) is the focus.x = -2 is the directrix.The conic section of the equation y² - 9x + 12y + 32 = 0 is a parabola
Selecting the conic section of the equationThe given equation is
y² - 9x + 12y + 32 = 0
The above equation is an illustration of a parabola equation
The standard form of a parabola is
(x - h)² = 4a(y - k)²
Where
(h, k) is the center
While the general form of the equation is
Ax² + Dx + Ey + F = 0
In this case, the equation y² - 9x + 12y + 32 = 0 takes the general form
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Find the value of x.
WHOEVER CAN ANSWER 50 POINTS IF U CAN SOLVE IT PLEASE IM DESPERATE
Answer:
First, the graph is overall decreasing with two local maximums and two local minimums.
Second, it has 5 zeros, since there is one intersection and two touching points with the x-axis.
Considering the above observations we can state that:
The degree of f(x) is odd;The leading coefficient is negative;There are 5 distinct zeros;There are 2 relative maximum values.3. Determine whether the triangles are similar. If they are, write a similarity statement.
Look at picture for reference
Please show work
The triangles DEF and SRQ are not similar triangles
Identifying the similar triangles in the figure.From the question, we have the following parameters that can be used in our computation:
The triangles in this figure are
DEF and SRQ
These triangles are not similar
This is because:
The corresponding angles in the triangles are not equal
For DEF, the angles are
50, 90 and 40
For SRQ, the angles are
51, 90 and 39
This means that they are not similar by any similarity statement
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En un punto de un cuerpo rigido se aplica una fuerza F = (4.501 - 3.25) N. Determine el torque que
experimenta dicho cuerpo si el radio vector trazado desde el punto de aplicación de la fuerza al punto de
giro es r = (1.801 + 2.50j) m
The torque experienced by the rigid body is -17.10375 k N·m.
To determine the torque experienced by a rigid body when a force is applied, we need to calculate the cross product between the force vector and the radius vector from the point of application of the force to the point of rotation.
Since a force F = (4.501 - 3.25) N is applied and the radius vector is r = (1.801 + 2.50j) m, where j is the imaginary unit, we can calculate the cross product using the formula:
Torque = r x F
The cross product between two vectors is calculated as follows:
Torque = (r_x * F_y - r_y * F_x)k
Where r_x and r_y are the components of the radius vector and F_x and F_y are the components of the force vector. Furthermore, k is a unit vector in the direction of the axis of rotation.
Substituting the given values, we have:
Torque = ((1.801 * -3.25) - (2.50 * 4.501))k
Calculating the cross product:
Torque = (-5.85125 - 11.2525)k
Simplifying:
Torque = -17.10375k
Therefore, the torque experienced by the rigid body is -17.10375 k N·m.
The negative sign indicates that the torque is in the opposite direction to the axis of rotation. The magnitude of the torque is measured in newtons per meter (N·m) and represents the capacity of a force to produce a rotation in a rigid body around a specific axis.
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One more question thank you
Answer:
Step-by-step explanation:
n=30
r=12
Plug into formula
you get:
1.7 in²
Determine the measure of the interior angle at vertex F.
A. 54
B. 108
C. 36
D. 72
The measure of the interior angle at vertex F is 72 degrees.
How to find the interior angle at vertex FA hexagon is a polygon with six sides. The sum of the interior angles of a hexagon is equal to 720 degrees.
The angle of the hexagon is given in terms of x,
The sum of the angle is equal to 720 degrees
[tex]4\text{x}+4\text{x}+4\text{x}+4\text{x}+2\text{x}+2\text{x} = 720[/tex]
[tex]20\text{x} = 720[/tex]
[tex]\text{x} = 36[/tex]
[tex]\bold{2x = 72^\circ}[/tex]
Therefore, the measure of interior angle at vertex F is equal to 72 degrees.
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50 Points! Multiple choice geometry question. Photo attached. Thank you!
Answer: D
Step-by-step explanation:
Similar means that if you multiplied all of the sides by the same number it would proportionally be that much larger.
D) 4x2=8
12x2=24
15x2=30 All sides were multiplied by 2 so D is similar
Answer:
D)
Step-by-step explanation:
Figure D is similar in all mesurements .
...
The crew from Disneyland Entertainment launches fireworks at an angle. The height of the firework can be modeled by h(t) = -2t^2+ 8t + 300 where height, h, is measured in feet and the
time, t, in seconds. What is the greatest height the fireworks reach?
Answer:
The function given here is a quadratic function of the form f(t) = at^2 + bt + c, where a is -2, b is 8, and c is 300. The maximum value of a quadratic function occurs at its vertex. For a function in the form f(t) = at^2 + bt + c, the t-coordinate of the vertex is given by -b/(2a). We can use this to find the time at which the firework reaches its maximum height.
Given a = -2 and b = 8, we can calculate t = -b/(2a):
t = -8/(2*-2) = 2
We can then substitute this value back into the height equation to find the maximum height:
h(2) = -2(2)^2 + 8*2 + 300
h(2) = -8 + 16 + 300
h(2) = 308
So, the greatest height the fireworks reach is 308 feet.
Help excel college student
EOP511
The total petty cash expenditures would be =$130.84
How to calculate the petty cash expenditures?To calculate the petty cash expenditures, the following is added up as follows;
The cost for stamp = $12.50
The cost for coffee supplies = $25.19
The cost for pizza delivery = $15.50
The cost for white board markers = $20.00
The cost for sympathy greeting card= $5.78
The cost of flowers for Jean's retirement farewell = $39.87
The cost of courier = $12.00
Therefore the total petty cash expenditures would be= 12.50+25.19+15.50+20+5.78+39.87+12= $130.84
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priya and han each wrote an equation of a line with slope 1/3 that passes through the point (1,2). priyas equation is y - 2 = 1/3 (x-1) and hans equation is 3y-x=5. do you agree with either of them? explain or show your reasoning
I agree with both Priya's and Han's equations.
To determine if either Priya or Han equation is correct, we can substitute the coordinates of the given point (1,2) into each equation and check if the equation holds true.
For Priya's equation, y - 2 = (1/3)(x - 1), substituting x = 1 and y = 2:
2 - 2 = (1/3)(1 - 1)
0 = 0
The equation holds true, so Priya's equation is correct.
For Han's equation, 3y - x = 5, substituting x = 1 and y = 2:
3(2) - 1 = 5
6 - 1 = 5
5 = 5
The equation also holds true, so Han's equation is correct.
Both Priya's and Han's equations are valid equations of the line with a slope of 1/3 passing through the point (1,2). The equations have different forms, but they are algebraically equivalent and represent the same line. Therefore, I agree with both Priya's and Han's equations.
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Determine the equation of the midline of the following graph.
Answer:
y = -3
Step-by-step explanation:
The midline of a sinusoidal function is the horizontal center line about which the function oscillates periodically.
The midline is positioned halfway between the maximum (peaks) and minimum (troughs) values of the graph. It serves as a baseline that helps visualize the oscillations of the function.
To find the equation of the midline, we need to determine the average y-value between the maximum and minimum y-values.
In this case, the maximum y-value is -1, and the minimum y-value is -5. To find the equation of the midline, sum the maximum and minimum y-values, and divide by 2:
[tex]y=\dfrac{-1 + (-5)}{2} = \dfrac{-6}{2}=-3[/tex]
Therefore, the equation of the midline for the graphed sinusoidal function is y = -3.
Michelle had 5 paperback books and 3 hardcover books on the shelf by her bed. Write a ratio to represent the ratio of paperback books to hardcover books.
3:5
five over three
3 to 8
5:8
Answer: The correct ratio to represent the ratio of paperback books to hardcover books is 5:3.
how to find surfes area
Remember to use the appropriate units for measurements when calculating surface area.
To find the surface area of an object, you need to calculate the total area of all its exposed surfaces. The method for finding the surface area will vary depending on the shape of the object. Here are some common shapes and their respective formulas:
1. Cube: The surface area of a cube can be found by multiplying the length of one side by itself and then multiplying by 6 since a cube has six equal faces. The formula is: SA = 6s^2, where s is the length of a side.
2. Rectangular Prism: A rectangular prism has six faces, each of which is a rectangle. To find the surface area, calculate the area of each face and add them up. The formula is: SA = 2lw + 2lh + 2wh, where l, w, and h represent the length, width, and height of the prism.
3. Cylinder: The surface area of a cylinder includes the area of two circular bases and the area of the curved side. The formula is: SA = 2πr^2 + 2πrh, where r is the radius and h is the height.
4. Sphere: The surface area of a sphere can be found using the formula: SA = 4πr^2, where r is the radius.
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I can’t figure this out. Please help
Answer:
Relative maximum at x=0; Relative minimum at x=8/3
Step-by-step explanation:
To find the relative maximums and the relative minimums, you must first find the first derivative of the function. The first derivative of this function is 6x^2-16x. Simply it and you get 2x(3x-8). X would be equal to 0 and 8/3. Next, make a number line where you put 0 and 8/3 have a value of zero.
+ - +
-------------------0----------------------------8/3-----------------------
Plug in a value of x<0 to get the region left of 0. Say we use -1, we get -2(-3-8), which is positive, meaning that it is increasing there. From 0 to 8/3, if we use 1, we get 2(3-8), which is decreasing. If we use 3, we get 6(9-8), which is increasing. From this, we can see that when x=0, the graph has a relative maximum. When x=8/3, the graph has a relative minimum.
9.
Find the volume of the cylinder. All measurements are in
centimeters. Keep your answer exact.
5
Answer:
The volume of the cylinder is 628.318530718
Step-by-step explanation:
The formula used to find the volume of a cylinder (v) is [tex]v = \pi r^2h[/tex], where r = radius and h = height. As the question says to keep the answer exact, we will be using pi as opposed to 3.14.
The radius is 5, and the height is 8. Plug these values into the equation and solve:
[tex]v =\pi *5^2*8[/tex]
[tex]v = 628.318530718[/tex]
So, the exact volume of the cylinder is 628.318530718. Rounded is 628.32
Answer:
200π or 628
Step-by-step explanation:
Note: your picture is not clear so I am assuming the height to be 8.
r = 5
h = 8
Volume = πr²h
= π * 5² * 8
= (25*8) π
= 200π
= 200*3.14
= 628
find x using the trigonometric function
The value of x in the diagram given in the question is 6
How do i determine the value of x?From the question given above, the following data were obtained:
Angle (θ) = 60Adjacent = 3Hypotenuse = x =?The value of x can be obtained using cos ratio.
Cos θ = Adjacent / Hypotenuse
Cos 60 = 3 / x
Cross multiply
x × Cos 60 = 3
Divide both sides by Cos 60
x = 3 / Cos 60
= 3 / 0.5
= 6
Thus, the value of x is 6
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The points A, B and C have position vectors a, b, c, referred to an origin O. i. Given that the point X lies on AB produced so that AB : BX = 2 : 1, find x, the position vector of X, in terms of a and b. ii. If Y lies on BC, between B and C so that BY : Y C = 1 : 3, find y, the position vector of Y, in terms of a and b iii. Given that Z is the midpoint of AC, Calculate the ratio XY : Y Z.
i. The position vector of X is 2b - a.
ii. The position vector of Y is (3b + c)/4.
iii. The ratio XY : Y Z is [tex]|(2b - a) - ((3b + c)/4)|/|((3b + c)/4) - (a + c)/2|[/tex]. Simplifying this expression will give us the final ratio.
i. To find the position vector x of point X, we can use the concept of vector addition. Since AB : BX = 2 : 1, we can express AB as a vector from A to B, which is given by (b - a). To find BX, we can use the fact that BX is twice as long as AB, so BX = 2 * (b - a). Adding this to the vector AB will give us the position vector of X: x = a + 2 * (b - a) = 2b - a.
ii. Similar to the previous part, we can express BC as a vector from B to C, which is given by (c - b). Since BY : YC = 1 : 3, we can find BY by dividing the vector BC into four equal parts and taking one part, so BY = (1/4) * (c - b). Adding this to the vector BY will give us the position vector of Y: y = b + (1/4) * (c - b) = (3b + c)/4.
iii. Z is the midpoint of AC, so we can find Z by taking the average of the vectors a and c: z = (a + c)/2. The ratio XY : YZ can be calculated by finding the lengths of the vectors XY and YZ and taking their ratio. Since XY = |x - y| and YZ = |y - z|, we have XY : YZ = |x - y|/|y - z|. Plugging in the values of x, y, and z we found earlier, we get XY : YZ =[tex]|(2b - a) - ((3b + c)/4)|/|((3b + c)/4) - (a + c)/2|[/tex].
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A rectangular tin measure 20cm by 10cm by 10cm. What's it's capacity in litres
Answer:
2 Litres
Step-by-step explanation:
A rectangular tin measure 20cm by 10cm by 10cm. What's it's capacity in litres
find Volume ( Volume = L x W x h)20 * 10 * 10 = 2000cm^3
Convert cubic centimeters to litres1000 cm^3 = 1 Litres
2000 cm^3 = 2 Litres
the peterson family and the stewart family each used their sprinklers last summer. the water output rate for the peterson family’s sprinkler was 35 L per hour. the water output rate for the stewart family’s sprinkler was 40 L per hour. the families used their sprinklers for a combined total of 45 hours, resulting in a total water output of 1,650 L. how long was each sprinkler used?
The Peterson family used their sprinkler for 30 hours, while the Stewart family used theirs for 15 hours.
Let's assume that the Peterson family used their sprinkler for a certain number of hours, which we'll denote as x, and the Stewart family used their sprinkler for the remaining hours, which would be 45 - x.
The water output rate for the Peterson family's sprinkler is given as 35 L per hour. Therefore, the total water output for the Peterson family can be calculated by multiplying the water output rate (35 L/h) by the number of hours they used the sprinkler (x): 35x.
Similarly, for the Stewart family, with a water output rate of 40 L per hour, the total water output for their sprinkler is given by 40(45 - x).
According to the problem, the combined total water output for both families is 1,650 L. Therefore, we can write the equation:
35x + 40(45 - x) = 1,650.
Simplifying the equation, we get:
35x + 1,800 - 40x = 1,650,
-5x = 1,650 - 1,800,
-5x = -150.
Dividing both sides of the equation by -5, we find:
x = -150 / -5 = 30.
So, the Peterson family used their sprinkler for 30 hours, and the Stewart family used theirs for 45 - 30 = 15 hours.
Therefore, the Peterson family used their sprinkler for 30 hours, while the Stewart family used theirs for 15 hours.
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In a class of 34, girls 21 play tennis and 18 play netball. If all the girl play at least one of the Games, how many of them play both games.
Solution:
Formula: Total = Group 1 + Group 2 - Both + Neither
where:
- Total = total number of girls in the class (34)
- Group 1 = number of girls playing tennis (21)
- Group 2 = number of girls playing netball (18)
- Both = number of girls playing both games (what we want to find)
- Neither = number of girls playing neither game (0, since all the girls play at least one game)
Plugging in the values, we get:
34 = 21 + 18 - Both + 0
Simplifying:
34 = 39 - Both
Both = 39 - 34
Both = 5
Find the midpoint of WZ of WXYZ with the vertices W(0, 0), X(h, 0), Y(h,b), and Z(0, b).
(0, h/2)
(h/2, b/2)
(0, b/2)
(h/2, 0)
Third option is correct.The midpoint of WZ of WXYZ with the vertices W(0, 0), X(h, 0), Y(h,b), and Z(0, b) is (0, b/2).
To find the midpoint of segment WZ, we need to average the x-coordinates and the y-coordinates of the endpoints.
The coordinates of point W are (0, 0), and the coordinates of point Z are (0, b).
To find the x-coordinate of the midpoint, we average the x-coordinates of W and Z:
(x-coordinate of W + x-coordinate of Z) / 2 = (0 + 0) / 2 = 0 / 2 = 0
To find the y-coordinate of the midpoint, we average the y-coordinates of W and Z:
(y-coordinate of W + y-coordinate of Z) / 2 = (0 + b) / 2 = b / 2
Therefore, the midpoint of segment WZ is (0, b/2).
So, the correct answer is (0, b/2).
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Calc II Question
Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by the given curves about the x axis
x = 4y^2 - y^3
x = 0