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4 years ago

Help i also need reasons for my calculations

Mathematics

1 answer:

lorasvet [3.4K]4 years ago

8 0

A=49 if you add up the two angles in that triangle you get 139 subtract that from 180 and there you go
B=15 if you calculate the other angle which are 95 and 70 you get 165 subtract that from 180 and bingo

Hope I helped

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Which of the following lists of orders pairs is a funtion

nordsb [41]

Answer:

Step-by-step explanation:

For it to be a function, every x value must have 1 unique y value ONLY.

In option A, you can see that the x value of 1 has 2 y values, 1 & 5. So it's not a function.

In option B, you can see that the x value of 0 has 2 y values, 0 & -4. Moreover, the x value of 4 also has 2 y values, 2 & -2. So it's not a function.

In option C, you can see that the x value of -2 has 2 y values, 4 & -4. This is not a function as well.

In option D, each x value has a unique y value that are different. So this is a function.

Answer is option D.

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3 years ago

Need help with this stuck on another problem

Cerrena [4.2K]

just remove perenthesis

5 0

3 years ago

1.) Find the length of the arc of the graph x^4 = y^6 from x = 1 to x = 8.

xxTIMURxx [149]

First, rewrite the equation so that y is a function of x :

$x^4 = y^6 \implies \left(x^4\right)^{1/6} = \left(y^6\right)^{1/6} \implies x^{4/6} = y^{6/6} \implies y = x^{2/3}$

(If you were to plot the actual curve, you would have both $y=x^{2/3}$ and $y=-x^{2/3}$ , but one curve is a reflection of the other, so the arc length for 1 ≤ x ≤ 8 would be the same on both curves. It doesn't matter which "half-curve" you choose to work with.)

The arc length is then given by the definite integral,

$\displaystyle \int_1^8 \sqrt{1 + \left(\frac{\mathrm dy}{\mathrm dx}\right)^2}\,\mathrm dx$

We have

$y = x^{2/3} \implies \dfrac{\mathrm dy}{\mathrm dx} = \dfrac23x^{-1/3} \implies \left(\dfrac{\mathrm dy}{\mathrm dx}\right)^2 = \dfrac49x^{-2/3}$

Then in the integral,

$\displaystyle \int_1^8 \sqrt{1 + \frac49x^{-2/3}}\,\mathrm dx = \int_1^8 \sqrt{\frac49x^{-2/3}}\sqrt{\frac94x^{2/3}+1}\,\mathrm dx = \int_1^8 \frac23x^{-1/3} \sqrt{\frac94x^{2/3}+1}\,\mathrm dx$

Substitute

$u = \dfrac94x^{2/3}+1 \text{ and } \mathrm du = \dfrac{18}{12}x^{-1/3}\,\mathrm dx = \dfrac32x^{-1/3}\,\mathrm dx$

This transforms the integral to

$\displaystyle \frac49 \int_{13/4}^{10} \sqrt{u}\,\mathrm du$

and computing it is trivial:

$\displaystyle \frac49 \int_{13/4}^{10} u^{1/2} \,\mathrm du = \frac49\cdot\frac23 u^{3/2}\bigg|_{13/4}^{10} = \frac8{27} \left(10^{3/2} - \left(\frac{13}4\right)^{3/2}\right)$

We can simplify this further to

$\displaystyle \frac8{27} \left(10\sqrt{10} - \frac{13\sqrt{13}}8\right) = \boxed{\frac{80\sqrt{10}-13\sqrt{13}}{27}}$

7 0

3 years ago

The points (1,2),(1,-3),and (5,-3) form a triangle on the coordinate plane. b. What is the perimeter of the triangle?

Alexeev081 [22]

The perimeter of the triangle is 13.56 units.

The perimeter of a shape on a coordinate plane is found by finding the distance between all points, and then adding them together. It's easier to write it out than to type so I'll attach a photo of my work.

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3 years ago

Find the density of a 40 gram pyramid with rectangular base 5 x 6 cm and height 8 cm.

e-lub [12.9K]

Density is mass
volume
With those dimensions, the volume of the pyramid is;
V = lw(h/3)
V = (5)(6)(8/3)
V = 80 cm^3

D = 40 g = 1 g/cm^3
80 cm^3

3 0

3 years ago

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