# 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...