The required surface area of the prism is 378 square meters.
How to find the area of Prism?To find the surface area of the prism, we need to know the dimensions of the prism. Let's call the length, width, and height of the prism l, w, and h, respectively.
Since the prism has right angles between its faces, we know that it is a right rectangular prism.
The formula for the volume of a right rectangular prism is V = lwh, and we know that the volume of the prism is 490m^3. Therefore,
lwh = 490
We are not given any specific values for l, w, or h, so we need to use another piece of information to solve for one of these variables.
The surface area of a right rectangular prism is given by the formula
SA = 2lw + 2lh + 2wh
If we can find the value of one of these dimensions, we can use it to calculate the surface area of the prism
lwh = 490
Since we know that the prism has right angles between its faces, we can assume that its dimensions are integers. We can start by testing integer values for l and w, and see if we can find an integer value for h that satisfies the equation.
For example, if we let l = 7 and w = 10, we get
7 * 10 * h = 490
Simplifying, we get
70h = 490
Dividing both sides by 70, we get
h = 7
Therefore, the dimensions of the prism are l = 7, w = 10, and h = 7.
To find the surface area, we can substitute these values into the formula for SA:
SA = 2lw + 2lh + 2wh
= 2(7)(10) + 2(7)(7) + 2(10)(7)
= 140 + 98 + 140
= 378
Therefore, the surface area of the prism is 378 square meters.
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Evaluate the given expression and show the steps, please.
To find:-
[tex]\displaystyle \sum_{n=1}^{4} 2(3^{n - 1})[/tex]Answer:-
We need to evaluate,
[tex]\implies s_4=\displaystyle \sum_{n=1}^{4} 2(3^{n - 1})[/tex]
Substituting n = 1 , 2 , 3 and 4 in [tex] 2(3^{n - 1})[/tex] and then adding them , we have;
[tex]\implies s_4 = 2(3^{1-1}) + 2( 3^{2-1})+2(3^{3-1})+2(3^{4-1}) \\[/tex]
Take out 2 as common,
[tex]\implies s_4 = 2 [ 3^0 + 3^1 + 3^2 + 3^3]\\[/tex]
[tex]\implies s_4 = 2 [ 1 + 3 + 9 + 27 ] \\[/tex]
[tex]\implies s_4 = 2 ( 40) \\[/tex]
[tex]\implies \underline{\underline{ s_4 = 80}} \\[/tex]
Hence the required answer is 80 .
and we are done!
Work out the circumstances of this circle. take π to be 3.142 and give your answer to 1 decimal place. Radius is 4cm
Answer:
Step-by-step explanation:
The formula for the circumference of a circle is:
C = 2πr
where C is the circumference, π is pi, and r is the radius.
Substituting the given value of π = 3.142 and r = 4 cm, we get:
C = 2 x 3.142 x 4
C = 25.136 cm
Therefore, the circumference of the circle is 25.1 cm (rounded to 1 decimal place).
Find the median of these numbers: 2.9, 9.1, 5.2, 2.9, 8.7, 7.4
Answer: 6.3
Step-by-step explanation:
Answer:
4.45
Step-by-step explanation:
5.2 + 7.4 ÷ 2 = 8.9 ÷ 2 = 4.45
Correct me if im wrong! Thank you!UwU
The area of the parallelogram is 60 square millimeters.
What is the parallelogram's base, b?
The base of the parallelogram is 60.
How to find?
To find the base of a parallelogram, we need to know its area and height. The area of a parallelogram is given by the formula:
A = b × h
where A is the area, b is the base, and h is the height.
In this case, we are given that the area of the parallelogram is 60 square millimeters. We do not know the height of the parallelogram, so we cannot solve for the base directly.
However, we do know that the area of a parallelogram is equal to the product of its base and height. So, if we can find the height of the parallelogram, we can then use the formula to solve for the base.
To find the height, we can use the formula:
h = A / b
where A is the area and b is the base.
Substituting the given values, we get:
h = 60 / b
Now, we still do not know the value of the base, but we can use this expression for the height to set up an equation that relates the base and height of the parallelogram.
We know that the opposite sides of a parallelogram are parallel and have the same length, so the height of the parallelogram is perpendicular to the base. Therefore, we can draw a perpendicular line from the height to the base, dividing the parallelogram into two congruent triangles.
Each triangle has an area of A/2, and its base and height are b and h, respectively. Therefore, we can set up the following equation:
A/2 = bh/2
Substituting the expression for the height, we get:
A/2 = b(60/b)/2
Simplifying, we get:
A/2 = 30
Multiplying both sides by 2, we get:
A = 60 = bh
Now we have an equation that relates the base and area of the parallelogram. Substituting the given value for the area, we get:
60 = b × h
Substituting the expression for the height, we get:
60 = b × (60 / b)
Simplifying, we get:
60 = 60
This equation is always true, which means that any value of b that satisfies the condition for a parallelogram (i.e., opposite sides are parallel and have the same length) will work. Therefore, we cannot determine the value of the base without additional information.
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Compute the voltage drop if the source voltage is 240V and the load voltage is 237V.
The voltage drop is the difference between the source voltage and the load voltage, which is 3V.
What is voltage drop?Voltage drop is the decrease of electric potential along the path of a current flowing in a circuit. Voltage drops in the internal resistance of the source, across conductors, across contacts, and across connectors are undesirable because some of the energy supplied is dissipated.
Voltage drop of the circuit conductors can be determined by multiplying the current of the circuit by the total resistance of the circuit conductors: VD = I x R.
The voltage drop can be calculated by subtracting the load voltage from the source voltage. In this case, the voltage drop is:
240V - 237V = 3V
Thus, the voltage drop is 3V.
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Help me on this one please.
Number 6 only.
Answer:
x=1.5
Step-by-step explanation:
g(x)=4x-(3x+7x/3) Find the slope and y=intercept. Express the intercept as an ordered pair. Simplify your answer.
Answer:
Slope: -(4/3)
Y-intercept: 0
Determine the product. Write your answer in scientific notation. (15.4 × 102) · (2.8 × 10–4) = ?
Answer:
Step-by-step explanation:
(15.4*102)*(2.8*10-4)
(1,570.8)*(28-4)
(1,570.8)*(24)
37,699.2
Among all rectangles that have a perimeter of 172
, find the dimensions of the one whose area is largest. Write your answers as fractions reduced to lowest terms.
Answer: 43x43 units 1849 units^2
By applying SAS congruence rule, you want to establish that triangle PQR =~ triangle KLM. It is given that PQ = KL and RP = MK. What additional information is needed to establish the congruence?
Answer:
Step-by-step explanation:
To establish the congruence of two triangles using the SAS (Side-Angle-Side) congruence rule, we need to know that two corresponding sides and the included angle are congruent.
In the given information, PQ = KL and RP = MK, but we do not know the measure of any included angle between the corresponding sides. Therefore, we need to know at least one angle that is congruent in both triangles to apply the SAS congruence rule.
Without additional information about an included angle, we cannot establish the congruence of triangle PQR and triangle KLM using the SAS congruence rule.