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Any trigonometry expert here to help, please?

In the below figure, the measures of the sides of the Trapazoid ABCD are given. If the nonparallel sides of the Trapazoid are perpendicular then #AC^2 + BD^2 = # ?

Find the value of #int_0^1tan^1((2x1)/(1+xx^2))dx#?

A thin rope 200 inches length is going to be cut into three pieces to form one circle and two equal squares. Which of the following represents the #r# of the circle, if the rope was finally cut in such a way that the total area of the shapes is minimized?

It's a calculus problem?

The function #f(x)=sin(3x)+cos(3x)# is the result of series of transformations with the first one being a horizontal translation of the function #sin(x)#. Which of this describes the first transformation?

Can #tan(x)=cot(x)#? If yes, list all possible values of #x#?

Compute the exact value of #{tan220^\circsin220^\circ}/{tan220^\circsin220^\circ}# without a calcuator?

If #f# is continuous on #[a,b]#, then #d/dx(int_a^bf(x)dx)=f(x)#?
True or False?

Geometry question, please help?

Does the sequence defined by #a_1=2#, #a_(n+1)=72/(1+a_n)# converge? What does it converge to?

If #log_b5=z# , then the value of #log_{b^2}5# is given by?
(a). #z/2# (b). #z^2# (c). #z# (d). None of these

A straight line through #p# and #q# is drawn perpendicular to a line through points #p(x,y)# and #r(x,(y+10))#. The possible coordinates of the point #q# are?
(a). #(17,y)# (b). #(1,y)# (c). #(0,y)# (d). All of these choices

If #A# and #B# are two events such that #P(A)+P(B)P(AandB)=P(A)# , then ?

According to the fundamental theorem of algebra, how many roots does the polynomial #f(x)=x^4+3x^2+7# have over the complex numbers, and counting roots with multiplicity greater than one as distinct? (i.e #f(x)=x^2# has two roots, both are zero).

Which of the following represents the area of the region bounded by the graph of the function #f(x)=sqrt{x}# , the xaxis, the yaxis and the tangent to the graph of #f(x)# at point #(4, 2)#..?

Statement is lengthy, so I have attached the picture of it?

The product of a number and negative fiveninths decreased by fortythree is the same as twentyfive increased by fiveninths times the number. What is the number?

Bank A pays #1%# interest per year, compounded yearly. Bank B pays #5%# interest per year, compounded monthly. How long does it take before an investment in Bank B has grown to twice as much as the same investment in Bank A?

Winter began harshly and the land is slippery. "Even guys can't take it as of late."
Can you please explain the meaning of the second sentence?

I'm confused to comprehend the meaning of this sentence. "Now you've completely lost the tack on being a whacko/wacko in what you are writing". Please correct and explain?

Would anybody please explain the meaning of this? "If it takes a hen and a half, a day and a half, to lay an egg and a half, how long does it take a one legged grasshoper to kick the seeds out of the dill pickle?"

In a cirlce #H#, if #angleDHG=(11x36)^\circ# and #angleGHF=(x+12)^\circ#, find #hat{DG}#? I've found #x=17# and the #angleDHG=151^\circ#. Would you please help me on the next step to find the arc length?

A particle travels at #2 units per# second along the curve #y=x^33x^2+2#. How long does it take to travel from the local maximum to the local minimum?

Prove #cos(x)+sin(x)tan(x)=sec(x)#?

The four forces, taken together, act as a single resulting force. What is the magnitude of this resulting force? The forces are acting on a point and the magnitude of each force is show in the diagram.

The correlation coefficient of a linear fit between two variables #X# and #Y# is #1#. I want to know, does the line containing the points for the strong negative correlation always have a slope of negative one? Thanks :)

Use the table to calculate the probability that it is a Thursday, given that Jemma has travelled to work either by a train or a bus? The table show the relative frequencies with which Jemma uses each type of transport on her two travel day.

A room has relative humidity of #20%# at #20# degrees Celsius with dimensions #3m \times 3m \times 2.7m#. Determine the amount of water vapour in grams and liters that must be added to the air of the room in order to raise the relative humidity to #60%#?

A #10# #kg# block is hanging from #2# ropes. One exerts a #50# #N# force at a #15^{\circ}# angle. The other exerts a #95# #N# force at a #60^{\circ}# angle. Find the direction and the magnitude of the force that will bring the block into equilibrium?

How can I put inline spaces in my explanations here on Socratic?

Evaluate the limit #\lim_{x\rightarrow 0^+}(1/tan(x))^{1/ln(x)}#?

Given a triangle whose sides are #24# #cm#, #30# #cm#, and #36# #cm#. Find the radius of a circle which is tangent to the shortest and longest side of the triangle and whose center lies on the third side?

If #cos(t)=4/7# and #t# is in the 4th quadrant, find #sin(t)#?

The line #y=3x+c# crosses the hyperbola #xy=12# twice. Find the range of possible values for c?

Suppose scores in a certain school test follows a normal probability distribution, with #\mu=70# and #sigma=10#. Grade A is awarded to the highest #2.5%# students. What is the dividing point between grade A & grade B?

The cost of fuel per km for a truck travelling at a speed v[km/h] is given by #C(v)=v/100+25/v#. (a) What speed result in the lowest fuel cost per km
(b) Assume the driver is paid #$40/h#. What speed would give the lowest cost, including wage for 1000Km?

A polynomial function #f(x)# with integer coefficients has a leading coefficient of #24# and a constant term of 1. State the possible roots of #f(x)#? Please include details. Thanks!

Find the coordinates of the epicenter? Given values are attached as a picture!

Find the upper and lower estimates for the temperature? The given values are attached as a picture! Thanks.

How to crack this SAT Geometry problem? Thanks :)

How to crack this SAT problem? Seem's more like physics to me than mathematics. Thanks :)

It's a geometry question stating to find the area of quadrilateral ABCD?

What is electric potential across a resistor if a resistance of #20# #ohms# draws a current of #6# #amperes#?

A pair of fair sixsided dice is thrown eight times. Find the probability that a score greater than #7# is scored no more than five times?

Given that, #\overline{AD}=45# and #\overline{DG}=60#, find the lengths of other line segments in this right triangle #\triangle ABC# given that the #DEFG# is a square?

Determine which of the following definite integral equals #lim_{n\to infty} \Sigma_{i=1}^n 1/nsqrt{i/n}#?

In #\triangle DEF#, #M# is the centroid. (i). Find #\overline{MK}# and #\overline{DK}# #" "# (ii). Find #\overline{LM}# and #\overline{LE}# #" "# (iii). Write an expression for #FJ#?

How much current is being supplied by the current source? What is the power absorbed by the conductor?

#AB=BC=10\ cm# , #AC=12\ cm# #\Rightarrow r=?#

Let, #f(x)=3/2x# and #g(x)=(1/2)^x1#. #" "# What are the solutions to the equation #f(x)=g(x)#? #" "#Also graph the functions on the same coordinate plane!

Find the perimeter of the triangle #ABC#?

How to but put multiple line spacing between paragraphs? By default, no matter how many multiple line spacing you add, the display gives single line space.

This problem includes factorial. Can anybody solve this?

Find all the critical points for this function?

#\lim _{n\to \infty }\sum _{i=1}^n\frac{3}{n}[(\frac{i}{n})^2+1]#.........??

I am confused on this transformation problem. Can anybody help?

I know that it will be of the form #2C(x)=C(x/2)#, but I am still stuck to write the transformed function. Can anybody help?

A bookshelf holds #24# mysteries, #12# nonfiction books, and #4# biographies. What is the probability of selecting a mystery book and then without replacing it, selecting a nonfiction book?

Find the exact value of #tan(\theta)# if #csc(\theta)=4/3# and the terminal side of the #\theta# lies in the third quadrant?

If #x# is nearly equal to one, then find the approximate value of #{mx^mnx^n}/{mn}#?

For Geometry lovers, help me solve this?

Find the coordinates of all points whose distance from #(0,3)# is #\sqrt{5}# and whose distance from #(3,4)# is #\sqrt{5}#?

Find the equation of the circle which passes through the origin and #(4, −8)#? #\ \ \ \ # Why do we use midpoint of two points to calculate the equation of circle? The points might make a chord rather than a diameter! Give me some insight?

If #" "##((n), (k))=((n!), (k!(nk)!))# #" "# show that #" "##((n), (k))=((n), (nk))#...?

How to solve for #x# using proportion?

Trigonometry bearings confuses me. I only solved right and obtuse triangles using pythagorean, sines and cosines laws?

What is Pragmatism? Explain with a simple real world example!

I just learnt the whiskerplot (boxplot) and will go with the option #C# and #D#. I just want you to make me correct if I am wrong or provide the explanation if my choices are right?

Why squaring both sides of a radical equation is an irreversible operation?

A set of cards has 5 red cards and 5 black cards. If 3 cards are selected at random, what is the probability to select at least 1 black card?

Find a quadratic function with zeros at #a+4# and #2a# where #a# is a constant. Write the function in standard form #f(x)=ax^2+bx+c#, and give the values of #a#, #b# and #c#. Assume the leading coefficient is 1?

An item costing #$125# was marked up by #30%# of the selling price. During a sale, the item was reduced to #$120#. What was the rate of markdown during the sale?

Factorials and Combinations is always an intimidating topic for me. Help?

In the expansion of #(a+x)(1x/4)^n#, the first three terms are #4+bx+5/4x^2#, where #n# is a positive integer greater than #2#. Find the values of #n#, of #a# and of #b#?

This question belongs to logic category? Picture attached!

Probaility Question?

Please provide a detailed explanation to this problem?

Basic English Grammar MCQ's. Any native american here, Help?

The skill you can use is center, spread, and shape of distributions... Explanation?

The text in white is question's statement. I'm stuck on second part of this problem. I am unable to write down any expression out of question's requirement?

I ended up applying all the circle theorem's I knew. Can you help me figure this out?

Calculate the most appropriate measure of central tendency and dispersion for the given dataset? You must show your work!
# #
#0, 0, 3, 2, 5, 7, 1, 8, 10, 2, 2, 1, 4, 6, 0, 7, 5, 7, 7, 4#

Calculate the most appropriate measures of central tendency and dispersion for the given dataset? You must show your work!

Calculate the most appropriate measure of central tendency and dispersion for the given dataset?

Probability?

What point is the author making when he talks about ways to prevent pollution?

Electrostatics?

Answer Part (b)?

Geometry: Similarities?

Theoretical Process. #" "# Can you explain the part #b)#...?

Probabilities?

If I want to create a solution with #\text{Fe}^{+3}=0.2\ \text{M}# using #5\ g# of #"Fe"_2"O"_3#, how many #"mL"# of water must I add?

After reacting all of the #FeS# in a #1.5\ L# of a reaction solution that had #[FeS]=0.2\ M#, how many grams of #Fe_2O_3# were formed? #" "# # # #4FeS+7O_2\rightarrow 2Fe_2O_3+4SO_2#

Redox half reaction problem?

How many grams of #HCL# must you dissolve in #1400\ mL# to make a solution with #pH=2.7##\ \ #?

Can you help?

Which compound has the highest melting point? State the reason!

Calculate the change in molar entropy and change in Gibbs' free energy when 1 mol of liquid butanol vaporizes at 25ºC to a gas that is at 0.001 atm?

Calculate the change in Gibbs' free energy and entropy for the freezing of liquid water at 5º C, if the vapor pressure above the ice is 3.012 mmHg and that above the water is 3.163 mmHg? #DeltabarH_"fus" = "5.85 kJ/mol"# at this temperature.

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