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1 year ago

14

a delivery truck is carrying and 8713 lb load of pet food. At a weighing station, the loaded truck weighs 17200 lb. What is the

weight of the empty truck?

1 answer:

netineya [11]1 year ago

6 0

We know that the load is 8713 lbs.

The total weight (truck + load) is 17200 lb.

Then, we can calculate the weight of the empty truck as:

$\begin{gathered} L=8713 \\ W=L+T=17200 \\ \Rightarrow T=W-L \\ T=17200-L=17200-8713=8487 \\ \end{gathered}$

Answer: the empty truck's weight is 8487 lb.

T: empty truck's weight

W: total weight (loaded truck's weight)

L: Load

The equation is:

T = W - L

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Help with 30 please. thanks.

Svet_ta [14]

Answer:

See Below.

Step-by-step explanation:

We have the equation:

$\displaystyle y = \left(3e^{2x}-4x+1\right)^{{}^1\! / \! {}_2}$

And we want to show that:

$\displaystyle y \frac{d^2y }{dx^2} + \left(\frac{dy}{dx}\right) ^2 = 6e^{2x}$

Instead of differentiating directly, we can first square both sides:

$\displaystyle y^2 = 3e^{2x} -4x + 1$

We can find the first derivative through implicit differentiation:

$\displaystyle 2y \frac{dy}{dx} = 6e^{2x} -4$

Hence:

$\displaystyle \frac{dy}{dx} = \frac{3e^{2x} -2}{y}$

And we can find the second derivative by using the quotient rule:

$\displaystyle \begin{aligned}\frac{d^2y}{dx^2} & = \frac{(3e^{2x}-2)'(y)-(3e^{2x}-2)(y)'}{(y)^2}\\ \\ &= \frac{6ye^{2x}-\left(3e^{2x}-2\right)\left(\dfrac{dy}{dx}\right)}{y^2} \\ \\ &=\frac{6ye^{2x} -\left(3e^{2x} -2\right)\left(\dfrac{3e^{2x}-2}{y}\right)}{y^2}\\ \\ &=\frac{6y^2e^{2x}-\left(3e^{2x}-2\right)^2}{y^3}\end{aligned}$

Substitute:

$\displaystyle y\left(\frac{6y^2e^{2x}-\left(3e^{2x}-2\right)^2}{y^3}\right) + \left(\frac{3e^{2x}-2}{y}\right)^2 =6e^{2x}$

Simplify:

$\displaystyle \frac{6y^2e^{2x}- \left(3e^{2x} -2\right)^2}{y^2} + \frac{\left(3e^{2x}-2\right)^2}{y^2}= 6e^{2x}$

Combine fractions:

$\displaystyle \frac{\left(6y^2e^{2x}-\left(3e^{2x} - 2\right)^2\right) +\left(\left(3e^{2x}-2\right)^2\right)}{y^2} = 6e^{2x}$

Simplify:

$\displaystyle \frac{6y^2e^{2x}}{y^2} = 6e^{2x}$

Simplify:

$6e^{2x} \stackrel{\checkmark}{=} 6e^{2x}$

Q.E.D.

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2 years ago

Find the mass of the triangle with vertices (1; 0; 0), (0; 2; 0), (0; 1; 1) if the density function is given by (x; y; z)

Luda [366]

Answer:

$=\frac{17}{3}$

Step-by-step explanation:

Density of a function is $\rho(x,y)=x^{2} +y^{2}$

I have drawn the right angle triangle for visualization

equation for the line passing through (1,0) and (0,4) is

$\frac{y}{4} =\frac{x-1}{-1}$

$y=4-4x$

= $\int_{0}^1\int_{0}^{4-4x} (x^{2}+y^{2})dydx$

= $\int_{0}^{1}(x^{2}+\frac{y^{3} }{3})dx$

= $\int_{0}^{1}(x^{2}(4-4x)+\frac{1}{3}(4-4x)^{3} )dx$

= $\int_{0}^{1}(\frac{-76}{3}x^{3} +68x^{2}-64x^{}+\frac{64}{3} )dx$

= $=(\frac{-76}{3} \frac{x^{4} }{4})+\frac{68}{3}x^{3}-32x^{2}+\frac{64}{3}x^{})$

$=\frac{17}{3}$

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The 1971 Sylmar earthquake in Los Angeles had a Richter scale magnitude of 6.3. Suppose an architect has designed a building as

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Answer:

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Step-by-step explanation:

here's the solution in attached image

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Remo needs to buy a countertop for a bathroom. He calculated the area as 10 square feet. The actual area is 9.5 square feet. Wha

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Answer:

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3 years ago

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