evaluate

1. Evaluate and interpreting

Can someone assist me with this please.
2. Inverse trig Functions: Evaluate quantities that are defined without a calculator.

Problem: Inverse of Sin(root3/2) For starters, I know that the range for inverse trigfunctions for tan and sin are -pi/2 to pi/2. and for cosine the range is 0 to pi. I am not understanding what this problem wants me to do? I realize that sin(root3/2) is 60 degrees or pi/3, is that all they...
3. Evaluate and simplify f(2a/b+3)

Assume that f(x)=x+10/x^2+9 for every real number x. Evaluate and simplify f(2a/b+3).
4. Evaluate and simplify f(b/3)

assume that f(x)= x+7/x^2+4 for every real number x. evaluate and simplify f(b/3).
5. How to evaluate -5*sqrt(5) - (5)*sqrt(15) rectangular/polar form

Hi kind people, I am working on converting between rectangular and polar forms. We are given z1 = -5*sqrt(5) - (5)*sqrt(15)*i thus, a = -5*sqrt(5) b = -5*sqrt(15) I know to get r we squared from the formula r^2 = a^2 + b^2 (gives you 10*sqrt(5) ) Then I get to arctan = b/a to get the...
6. Evaluate the difference quotient for each function f(x)

Hi so I need help on this problem: f(x)=4x^2-6 I know the formula is f(x+h)-f(x) over h I just keep trying it and I keep getting the wrong answer. THE ANSWER IS : 8x+4h I did: 4(x+h)^2-6 -(4x^2-6) <-- So I basically just plugged in the formula all over h, then I got 4x^2+2xh+h^2 -6...
7. Evaluate the Improper Integral

Evaluate the improper integral. Am i starting this problem off right? I checked the integral calculator website and it said the answer is 1/2 or 0.5
8. Evaluate Series with the Comparison Test

Does \sum_{k=1}^\infty \sqrt \frac{k^4}{4k^6+7} converge? Correct answer, no by comparison with series \sum \frac{1}{2k}. \frac{k^4}{4k^6+7} \leq \frac{k^4}{4k^6} = \frac{1}{4k^2}. \sqrt \frac{k^4}{4k^6+7} \leq \sqrt \frac{1}{4k^2} = \frac{1}{2k}. The series \sum_{k=1}^\infty \frac{1}{2k} =...
9. Using Riemann Sums to evaluate an integral?

We're not using anti-derivatives yet to solve integrals. Instead, we are using the definition of a definite integral involving Riemann Sums. My problem is evaluating the integral where a=-2, b=2, and f(x)=√(4-x) using the definition. I think I have the right set up by solving for the change in...
10. Using substitution to evaluate the integrals involving trigonometric functions

How did they get 1/4? I find it confusing when dealing with trig functions. I've showed my workt, I hope someone catches my error. Thanks!
11. Substitution formula to evaluate the integral

Who can spot my mistake? Please click on the image.
12. Using area to evaluate the definite integral

I didn't want to finish this problem because I have a hunch that I am already doing it incorrectly. I went on wolfram alpha and looked at their explanation but it was too complicated. The answer is highlighted in yellow btw. Can anyone help me finish this? Thanks.
13. Evaluate triple integral

$$\displaystyle\int_{0}^{1}\int_{0}^{x}\int_{0}^{ \sqrt{x^2+y^2}} {(x^2+y^2)^{3/2}\over x^2+y^2+z^2}\,dz\,dy\,dx$$ Need to find these either with spherical or cylindrical coordinates. I think. I presume I could use spherical coordinates here, but I am not completely sure how to set this all up...
14. How to evaluate surface area & volume of a uniform tetradecahedron

A uniform tetradecahedron has 2 congruent regular hexagonal faces each with side a=20 cm & 12 congruent trapezoidal faces. All its 18 vertices eventually & exactly lie on a spherical surface with a certain radius. How to evaluate the surface area & volume of solid. any help is greatly...
15. Evaluate face angle of a decahedron with 10 congruent faces each as a right kite

A decahedron has 10 congruent faces each as a right kite having two pairs of unequal sides a & b (a<b). It has 12 vertices which lie on a spherical surface. I have to calculate the correct value of theta angle (as shown in the diagram). Any help is highly appreciated. thanks...
16. How to evaluate solid angle subtended by a finite plane bounded by straight lines

How to calculate solid angle (in Ste-radian) subtended by a plane bounded by the straight lines x=-8, x=12, y=-6 & y=20 in XY-plane at the point (8, -10, -6). Any help is highly appreciated. thanks ................... (Flower)(Flower)(Flower)
17. Difficult to evaluate area of a spherical triangle than that of a plane tritangle

Difficult to evaluate area of a spherical triangle than that of a plane triangle How to evaluate the area covered by a spherical triangle, having one of its interior angles 150 degree included by two adjacent sides (each as a great circle arc) of lengths 26 & 39 units, on the spherical...
18. Difficult to evaluate area of a spherical rectangle than that of a plane rectangle

How to evaluate the area covered by a spherical rectangle, having length & width (each as a great circle arc) of 18 & 6 units respectively, on a spherical surface with a radius 50 units? any help is highly appreciated. thanks in advance.......(Flower)(Flower)
19. How to evaluate total numbers lying between two in a set of linear permutations

I am trying to evaluate the total numbers which are lying between 20450757870 & 87500752074 when all the 11-digit significant numbers, formed by permuting the digits 0, 0, 0, 2, 4, 5, 5, 7, 7, 7, 8 together, are arranged in decreasing order. your help is highly appreciated. thanks...
20. Evaluate volume of decahedron with 10 congruent faces each as a right kite

I am trying to evaluate the volume of this decahedron which has 10 congruent faces each as a right kite (i.e. a cyclic quadrilateral consisting of two congruent right triangles with common hypotenuse) having two pairs of unequal sides a=12 cm & b=20 cm. But not sure how to start. Any help or...