Please help me solve 4 inequalities and show work. Will get brainiest!!

A block of glass has a mass of 22.5g and a volume of 9cm cubed.

melisa1 [442]

Answer:

density, mass of a unit volume of a material substance. The formula for density is d = M/V, where d is density, M is mass, and V is volume. Density is commonly expressed in units of grams per cubic centimetre.

Step-by-step explanation:

3 0

2 years ago

Use the Fundamental Theorem for Line Integrals to find Z C y cos(xy)dx + (x cos(xy) − zeyz)dy − yeyzdz, where C is the curve giv

Harrizon [31]

Answer:

The Line integral is π/2.

Step-by-step explanation:

We have to find a funtion f such that its gradient is (ycos(xy), x(cos(xy)-ze^(yz), -ye^(yz)). In other words:

$f_x = ycos(xy)$

$f_y = xcos(xy) - ze^{yz}$

$f_z = -ye^{yz}$

we can find the value of f using integration over each separate, variable. For example, if we integrate ycos(x,y) over the x variable (assuming y and z as constants), we should obtain any function like f plus a function h(y,z). We will use the substitution method. We call u(x) = xy. The derivate of u (in respect to x) is y, hence

$\int{ycos(xy)} \, dx = \int cos(u) \, du = sen(u) + C = sen(xy) + C(y,z)$

(Remember that c is treated like a constant just for the x-variable).

This means that f(x,y,z) = sen(x,y)+C(y,z). The derivate of f respect to the y-variable is xcos(xy) + d/dy (C(y,z)) = xcos(x,y) - ye^{yz}. Then, the derivate of C respect to y is -ze^{yz}. To obtain C, we can integrate that expression over the y-variable using again the substitution method, this time calling u(y) = yz, and du = zdy.

$\int {-ye^{yz}} \, dy = \int {-e^{u} \, dy} = -e^u +K = -e^{yz} + K(z)$

Where, again, the constant of integration depends on Z.

As a result,

$f(x,y,z) = cos(xy) - e^{yz} + K(z)$

if we derivate f over z, we obtain

$f_z(x,y,z) = -ye^{yz} + d/dz K(z)$

That should be equal to -ye^(yz), hence the derivate of K(z) is 0 and, as a consecuence, K can be any constant. We can take K = 0. We obtain, therefore, that f(x,y,z) = cos(xy) - e^(yz)

The endpoints of the curve are r(0) = (0,0,1) and r(1) = (1,π/2,0). FOr the Fundamental Theorem for Line integrals, the integral of the gradient of f over C is f(c(1)) - f(c(0)) = f((0,0,1)) - f((1,π/2,0)) = (cos(0)-0e^(0))-(cos(π/2)-π/2e⁰) = 0-(-π/2) = π/2.

3 0

3 years ago

There are 1295 students attending a small university there are 714 woman in rolled what percentage of students are woman

MatroZZZ [7]

Answer:

Approximately 55% of enrolled students are women.

Step-by-step explanation:

To find the percentage of a given set of data, you need to divide the number of actual students by the total number of students. In this case, they are wanting the percentage of just women students at the university:

$\frac{women students}{total students} =\frac{714}{1295}$ x 100 = 55%