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3 years ago

Can you give me the work and the answers for these please.

Mathematics

1 answer:

n200080 [17]3 years ago

7 0

1. The diagonal is the hypotenuse so,
√[12² + 12²] = 16.97

2. The same process is done
51.96

3. Again, use the Pythagorean theorem
35.78

4. The perimeter is 44, so the length of a side is 11, the diagonal is
15.57

5. The diagonal is 20, the formula is
d =s√2
where d is the diagonal and s is the side
s = 14.14

You might be interested in

What best describes the distance between two points with coordinates (2,-3) and (-4,2)

Fed [463]

Answer:

Option c (7.8) is the correct alternative.

Step-by-step explanation:

The given points are:

(x₁, y₁) = (2, -3)

(x₂, y₂) = (-4, 2)

As we know,

The distance between two points will be:

= $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

On substituting the values, we get

= $\sqrt{(-4-2)^2+(2-(-3))^2}$

= $\sqrt{(-4-2)^2+(2+3)^2}$

= $\sqrt{(6)^2+(5)^2}$

= $\sqrt{36+25}$

= $\sqrt{61}$

= $7.8 \ units$

6 0

3 years ago

The function f(x) = (10)–x is reflected across the x-axis to create the function g(x). Which ordered pair is on g(x)? (–2, 75) (

IRINA_888 [86]

Neither point is on either function.
f(x) reflected over the x-axis is
y=-10 + x

7 0

2 years ago

The sum of the measures of the angles of a triangle is 180. The sum of the measures of the second and third angles is five times

erastova [34]

Answer:

1st ∡ = 15.5°

2nd ∡ = 77.25°

3rd ∡ = 87.25°

Step-by-step explanation:

1st ∡: x

2nd ∡: y

3rd ∡: z

Equations we can create from data given in problem:

y + z = 5x

z = 5x + 10

We have enough expressions to create an equation:

x + 5x + 5x + 10 = 180

11x = 170

x = 15.5

y = 5(15.5) = 77.25

z = y + 10 = 87.25

8 0

3 years ago

Evaluate the integral Integral ∫ from (1,2,3 ) to (5, 7,-2 ) y dx + x dy + 4 dz by finding parametric equations for the line seg

n200080 [17]

$\vec F(x,y,z)=y\,\vec\imath+x\,\vec\jmath+3\,\vec k$

is conservative if there is a scalar function $f(x,y,z)$ such that $\nabla f=\vec F$ . This would require

$\dfrac{\partial f}{\partial x}=y$

$\dfrac{\partial f}{\partial y}=x$

$\dfrac{\partial f}{\partial z}=3$

(or perhaps the last partial derivative should be 4 to match up with the integral?)

From these equations we find

$f(x,y,z)=xy+g(y,z)$

$\dfrac{\partial f}{\partial y}=x=x+\dfrac{\partial g}{\partial y}\implies\dfrac{\partial g}{\partial y}=0\implies g(y,z)=h(z)$

$f(x,y,z)=xy+h(z)$

$\dfrac{\partial f}{\partial z}=3=\dfrac{\mathrm dh}{\mathrm dz}\implies h(z)=3z+C$

$f(x,y,z)=xy+3z+C$

so $\vec F$ is indeed conservative, and the gradient theorem (a.k.a. fundamental theorem of calculus for line integrals) applies. The value of the line integral depends only the endpoints: