the dump truck weighs 18 tons when filled. at the same time the dump truck is being filled, an identical truck filled to capacity is being emptied at a rate of 1/8 ton per minute. how much sad is in each dump truck when the trucks are the same weight

Answer:

61 is the Answer

Step-by-step explanation:

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The area of the surface is  [tex]\rm \dfrac{1}{54}(53\sqrt{53} -17\sqrt{17} )[/tex] and this can be determined by doing the integration.

Given :

The part of the surface [tex]\rm z = 9+5x+2y^2[/tex] that lies above the triangle with vertices (0, 0), (0, 1), (2, 1).

The formula of the surface area is given by:

[tex]\rm A(S) = \int \int_D\sqrt{1+\left(\dfrac{\delta z}{\delta x}\right)^2 +\left(\dfrac{\delta z}{\delta y}\right)^2 }[/tex]

Now, the values of D varies from:

D = {(x,y): 0 [tex]\leq[/tex] y [tex]\leq[/tex] 1 , 0 [tex]\leq[/tex] x [tex]\leq[/tex] 2y}

Now, the area of the surface is given by:

[tex]\rm A(S) = \int \int_D\sqrt{1+4^2+(6y)^2 }\;dA[/tex]

[tex]\rm A(S) = \int^1_0 \int^{2y}_0\sqrt{17+36y^2 }\;dx\;dy[/tex]

[tex]\rm A(S) = \int^1_02y\sqrt{17+36y^2 }\;dy[/tex]

Now, let [tex]u=17+36y^2[/tex]

[tex]du = 72y dy[/tex]

[tex]\rm \dfrac{du}{36}=2ydy[/tex]

Now, the integral becomes:

[tex]\rm A(S)= \dfrac{1}{36}\sqrt{u} \; du[/tex]

[tex]\rm A(S) = \dfrac{1}{54}\times u^{3/2}+C[/tex]

Now, substitute the value of u in the above expression.

[tex]\rm A(S) = \dfrac{1}{54}\times \left[\left[\sqrt{17+36y^2} \right]^{3/2}\right]^1_0[/tex]

Now, simplify the above expression.

[tex]\rm A(S) = \dfrac{1}{54}(53\sqrt{53} -17\sqrt{17} )[/tex]

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To calculate the surface area of the part of the surface z = 9 + 5x + 2y² lying over a triangle, the limits of the variables are determined by triangle vertices. Then, the double integral of the surface area formula, which integrates the square root of 1 plus the squares of the partial derivatives of the function over these limits, is computed.

The problem presented is leading us to calculate the surface area of a part of z = 9 + 5x + 2y² that lies above a right triangle whose vertices are (0, 0), (0, 1), (2, 1). The first step in resolving this is to recognize the given formula of the surface, it is a quadratic surface in three-dimensional space, also known as a paraboloid.

The vertices of the triangle give as a hint to define the limits of the variables. Given that this triangle is defined in the xy plane, owing to the vertices of the triangle provided, the limits for x would range from 0 to 2, the limits of y would range from 0 to 1 (since for x = 0, y = 1 and for x = 2, y = 1).

Finally, the area S of a part of the surface z = f(x, y) that lies above the region D in the xy plane is defined by the double integral: S = ∫∫D √(1 + (fx)² + (fy)²) dA where fx and fy are partial derivatives of the function f(x, y) with respect to x and y respectively. The integral needs to be computed over the region D which is defined by triangle vertices.

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In a mathematical proof, missing statements and reasons are usually concluded from the given statements and the relevant geometric postulates or theorems. They could include establishing the congruency of angles or declaring the parallelism of lines.

Without the concrete steps of the proof or the reasoning proposed, it is difficult to provide the exact missing statements and reasons. However, in a general mathematical proof, common reasons used include 'definition of congruent angles', 'definition of parallel lines', 'alternate interior angles theorem', etc.

For instance, if we have a proof that involves stating two angles are congruent, the missing statement might be 'Angle A is congruent to Angle B', and the missing reason could be 'Definition of Congruent Angles' or 'Angle Bisector Theorem', if an angle bisector comes into the picture.

Another missing statement might be 'Segment AB is parallel to Segment CD', with the reason being 'Corresponding Angles Postulate', or 'Alternate Interior Angles Theorem', if the proof involves parallel lines.

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Yes C is correct which would be

Use the distance formula to find QT, then multiply by 4.

The perimeter of the rhombus can be found by C. use the distance formula to find QT and then multiply by 4.

A rhombus is a two dimensional shape which consists of four equal sides with opposite side being parallel and opposite angles being equal.

Perimeter of a straight sided figures or objects is the total length of it's boundary.

Actual perimeter = QR + RS + ST + TQ

That is add all the sides.

Now since the polygon is rhombus, all the sides are of equal length.

So, it is enough to find any side length of the rhombus and then multiply by 4.

The length of a side can be found using the distance formula.

So the correct way is use the distance formula to find QT and then multiply by 4.

Hence the correct option is C.

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Your question is incomplete. The complete question is as given below.

Answer:

D)

Step-by-step explanation:

Percent means "per hundred" or "out of one hundred." While B) is out of one hundred, turn it into a percent, and the percentage would be .95%. A) and C) are not out of 100, so those answers are not applicable. The only answer left is D), which is correct, because 95/100 is equivalent to 95%.

5.483 gallons bought to cover 658 square feet.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

Each gallon of shingle stain covers 120 square feet.

We have to find gallons should be bought to cover 658 square feet.

We have to perform division

= 658/120

= 5.483 gallons

Hence, 5.483 gallons bought to cover 658 square feet.

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In the question it must be 10 instead of 101010, y instead of yyy and x instead of xxx.

Since, Enrique earns 10 points for each question that he answers correctly on a geography test.

We have to write an equation for the number of points, 'y' Enrique scores on the test when he answers 'x' questions correctly.

So, Number of points scored = Points scored for one question [tex] \times [/tex] Number of questions answered correctly.

So, Number of points scored = [tex] 10 \times x [/tex]

[tex] y=10 \times x [/tex]

y = 10x is the required equation.

Answer:

636

Step-by-step explanation:

trust

Answer:

x=3 y=3

Step-by-step explanation:

The sum of the squares of two numbers is 18, and the product of those two numbers is 9, you just need to create an equation:

So the sum of the squares is 18, the first number will be represented as X and the second as Y:

[tex]x^{2}+ y^{2} =18[/tex]

And the other one is that the product of the two numbers is 9:

[tex]xy=9[/tex]

We have a system of equations here, we clear X from the first one:

[tex]x=\frac{9}{y}[/tex]

And instert that value of x in the first one:

[tex]x^{2}+ y^{2} =18\\(\frac{9}{y} )^{2}+ y^{2} =18\\81=y^2(18-y^2)\\y^4-18y^2+81=0\\(y^2-9)(y^2-9)=0\\Y^2-9=0\\y^2=9\\y=3[/tex]

By solving this equation we get that the first number is 3.

The second number is solved by inserting the value of Y into one of the equations, in this case we will use the second:

[tex]xy=9\\x=\frac{9}{y} \\x=\frac{9}{3} \\x=3[/tex]

So we get that x and y are both 3.

A good guess for the real root of the polynomial [tex]f(x) = x^3 - 6x^2 + 11x - 6[/tex] that is neither 1, even, nor negative, would be a positive odd integer such as 3 or 5, considering the constraints and the Rational Root Theorem.

The real root of the cubic equation [tex]f(x) = x^3 - 6x^2 + 11x - 6[/tex] that is neither 1, even, nor negative would most likely be a positive odd number (since all positive even numbers are, by default, also excluded). Considering the smallest odd numbers greater than 1 are 3 and 5, and given that we're working with integers, a good guess for the real root would be either 3 or 5. However, one can apply the Rational Root Theorem which states that any rational root, expressed in its lowest form p/q, must have p as a factor of the constant term and q as a factor of the leading coefficient. In this case, the possible rational roots could be

divisors of 6 (constant term) over divisors of 1 (leading coefficient), which gives us only divisors of 6 itself

since the leading coefficient is 1. Among those divisors, the ones that fit the criteria of being neither 1, even, nor negative, would be 3 or positive odd integers.

Final answer:

The probability of rolling an even number or a prime number on a six-sided die is 5/6, considering the unique favorable outcomes of 2, 3, 4, 5, and 6 against the total possible outcomes.

Explanation:

The question asks, "What is the probability of rolling an even number or a prime number on a number cube?" To answer this, first identify the outcomes on a six-sided die which are even and those that are prime.

Even numbers on a die: 2, 4, 6. Prime numbers on a die: 2, 3, 5. Notice that 2 is both even and prime, and it only needs to be counted once. Therefore, the unique favorable outcomes are 2, 3, 4, 5, 6.

The die has a total of 6 sides, making the total number of possible outcomes 6. The probability of rolling an even number or a prime number is therefore the number of favorable outcomes (5) divided by the total number of outcomes (6), which simplifies to 5/6.

Answer:

14

Step-by-step explanation:

Let the legs of the triangle each have length $x$ (they are equal because it is an isosceles right triangle). Then

x^2 + x^2 = (14√2)^2 = 14^2 × (√2)^2 = 14^2 × 2, so x^2 = 14^2. Given that x must be positive, we have x = 14. So, the value of each leg is 14

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Answer:

AB and CD are intersecting lines but are not perpendicular.

See attached image.

Step-by-step explanation: