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3 years ago

True or false & why? please help.

Mathematics

2 answers:

MrMuchimi3 years ago

4 0

False.
We know that $\sqrt{36} = 6$ , so $\sqrt{35}$ must be less than 6.
6 - (something less than 6) > 0

Lilit [14]3 years ago

3 0

Well, the answer to the first part of the equation is 0.08392022, then you just have to decipher if 0.08392022 < 0 is true or false. For why, you could put how rounding affected the answer. Hopefully this all makes sense. :)

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Anyone know this Geometry problem?

Yuliya22 [10]

Answer:

ST = 20

Step-by-step explanation:

RT is the sum of RS and ST

Replacing with length you get:

17 + x + 6 = 3x - 56

17 + 6 + 5 = 3x - x

28 = 2x

14 = x

ST = x + 6 = 14 + 6 = 20

6 0

3 years ago

Distribute and simplify these radicals. 23-(V+ 3) O 2V5 + 6 02/15 O 30 O 6/2+6

zhannawk [14.2K]

Answer:

Step-by-step explanation:

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3 years ago

What is the height of this relation: <br> h= -0.3d² + 1.2d + 1.5

marshall27 [118]

Answer:

h = -0.3d^2 + 1.2d + 1.5

Step-by-step explanation:

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3 years ago

Rewrite the following integral in spherical coordinates.

lora16 [44]

In cylindrical coordinates, we have $r^2=x^2+y^2$ , so that

$z = \pm \sqrt{2-r^2} = \pm \sqrt{2-x^2-y^2}$

correspond to the upper and lower halves of a sphere with radius $\sqrt2$ . In spherical coordinates, this sphere is $\rho=\sqrt2$ .

$1 \le r \le \sqrt2$ means our region is between two cylinders with radius 1 and $\sqrt2$ . In spherical coordinates, the inner cylinder has equation

$x^2+y^2 = 1 \implies \rho^2\cos^2(\theta) \sin^2(\phi) + \rho^2\sin^2(\theta) \sin^2(\phi) = \rho^2 \sin^2(\phi) = 1 \\\\ \implies \rho^2 = \csc^2(\phi) \\\\ \implies \rho = \csc(\phi)$

This cylinder meets the sphere when

$x^2 + y^2 + z^2 = 1 + z^2 = 2 \implies z^2 = 1 \\\\ \implies \rho^2 \cos^2(\phi) = 1 \\\\ \implies \rho^2 = \sec^2(\phi) \\\\ \implies \rho = \sec(\phi)$

which occurs at

$\csc(\phi) = \sec(\phi) \implies \tan(\phi) = 1 \implies \phi = \dfrac\pi4+n\pi$

where $n\in\Bbb Z$ . Then $\frac\pi4\le\phi\le\frac{3\pi}4$ .

The volume element transforms to

$dx\,dy\,dz = r\,dr\,d\theta\,dz = \rho^2 \sin(\phi) \, d\rho \, d\theta \, d\phi$

Putting everything together, we have

$\displaystyle \int_0^{2\pi} \int_1^{\sqrt2} \int_{-\sqrt{2-r^2}}^{\sqrt{2-r^2}} r \, dz \, dr \, d\theta = \boxed{\int_0^{2\pi} \int_{\pi/4}^{3\pi/4} \int_{\csc(\phi)}^{\sqrt2} \rho^2 \sin(\phi) \, d\rho \, d\phi \, d\theta} = \frac{4\pi}3$

4 0

2 years ago

When the angle of elevation of the sun is 78 degrees, a tree casts a 13 foot shadow. How tall is the tree?

oksian1 [2.3K]

Answer: 61.16 ft

Step-by-step explanation:

We can think in this situation as a triangle rectangle.

where:

The height of the tree is one cathetus

The shadow of the tree is the other cathetus.

We know that the angle of elevation of the sun is 78°, an angle of elevation is measured from the ground, then the adjacent cathetus to this angle is the shadow of the tree. And the opposite cathetus will be the height of the tree.

Now we can remember the relationship:

Tg(A) = (opposite cathetus)/(adjacent cathetus)

Where:

A = 78°

Adjacent cathetus = 13ft

opposite cathetus = height of the tree = H

Then we have the equation:

Tg(78°) = H/13ft

Tg(78°)*13ft = H = 61.16 ft

4 0

3 years ago