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8201.

In the kite, AC = 10 and BD = 6. What is the area of kite ABCD?

Answer» In the kite, AC = 10 and BD = 6. What is the area of kite ABCD?

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8202.

(iv) tan-1 (2 cos (2π/3) )

Answer» The value ofinverse tan ratios are (i) is π / 6, (ii) is - π / 6,(iii) is 0 and (iv) is- π / 4.

To find the values of the above inverse trigonometric ratios, we will use trigonometric identities.

8203.

(iii) tan-1 (cos (π/2) )

Answer» The value ofinverse tan ratios are (i) is π / 6, (ii) is - π / 6,(iii) is 0 and (iv) is- π / 4.

To find the values of the above inverse trigonometric ratios, we will use trigonometric identities.

8204.

(ii) tan-1 (-1/√3)

Answer» The value ofinverse tan ratios are (i) is π / 6, (ii) is - π / 6,(iii) is 0 and (iv) is- π / 4.

To find the values of the above inverse trigonometric ratios, we will use trigonometric identities.

8205.

(i) tan-1 (1/√3)

Answer» The value ofinverse tan ratios are (i) is π / 6, (ii) is - π / 6,(iii) is 0 and (iv) is- π / 4.

To find the values of the above inverse trigonometric ratios, we will use trigonometric identities.

8206.

Find the value of each of the following:

Answer» The value ofinverse tan ratios are (i) is π / 6, (ii) is - π / 6,(iii) is 0 and (iv) is- π / 4.

To find the values of the above inverse trigonometric ratios, we will use trigonometric identities.

8207.

Write an equation in slope-intercept form, given that the line passes through the point (2, 7) and has a slope of 2?

Answer» Write an equation in slope-intercept form, given that the line passes through the point (2, 7) and has a slope of 2?

Solution:

8208.

Which quadratic equation is equivalent to (x2- 1)2- 11(x2- 1) + 24 = 0?

Answer» Which quadratic equation is equivalent to (x2- 1)2- 11(x2- 1) + 24 = 0?

Solution:

8209.

Solve the equation 8 - 2x = - 8x + 14

Answer» Solve the equation8 - 2x = - 8x + 14

Solution:

8210.

How do you find the mode of a data set?

Answer» Mode is the value that appears most frequently in a data set. A set of data may have one mode, more than one mode, or no mode at all.

Themode is one of the most frequently used metrics in statistics.

8211.

Find the taylor polynomial t3(x) for the function f centered at the number: f (x) = 7 tan-1(x), a = 1, t3(x)

Answer» Find the taylor polynomial t3(x) for the function f centered at the number:
f (x) = 7 tan - 1(x), a = 1 t3(x)

Solution:

8212.

A polygon has an angle sum of 360° and each angle measures 90°. What is the polygon?

Answer» Rectangle andsquare are polygons that have an angle sum of 360° and each angle measures 90°.

A closed shape having sides and vertices is known as a polygon. If a polygon hasinterior angles and sides are equal, it is known as a regular polygon.

8213.

How many crores make 10 million?

Answer» 1 crore makes 10 million.

Crore is a place value that is used in the Indian place value chart, whereas, million is a place value that is used in the International place value chart.

8214.

Show that (sinθ -cosθ + 1) / ( sinθ + cosθ - 1) = 1 /(secθ - tanθ )

Answer» Answer : (sinθ -cosθ + 1) / ( sinθ + cosθ - 1) = 1 /(secθ - tanθ )

We can use the trigonometric identity (sec2θ = 1 + tan2θ)

8215.

Let f(x) = x2− 8x + 5. Find f(−1).

Answer» For f(x) = x2− 8x + 5, f(-1) = 14

We have the functionf(x) = x2− 8x + 5

8216.

Find the exact length of the curve. y = 2 + 8x3/2, 0 ≤ x ≤ 1?

Answer» The exact length of the curve is 7.995.

The length of a curve is a geometrical concept that addressed by integral calculus. It is a method for calculating the exact lengths of line segments.

8217.

Prove that: sin6x + cos6x = 1 - 3 sin2x cos2x.

Answer» sin6x + cos6x = 1 - 3 sin2x cos2x

Cosine and Sine are primary trigonometric functions. They are also known as complemetary functions

8218.

In Triangle ABC, ∠A is a Right Angle and ∠B = 45°. Find BC. If your answer is not an Integer, Leave it in Simplest Radical Form.

Answer» If∠A is a Right Angle and ∠B = 45°, then BC = AB√2

We will be using the Angle Sum Theorem and the Pythagorastheorem to solve this.

8219.

Explain the term Jacobian.

Answer» Explain the term Jacobian.

Solution:

8220.

Multiples that are shared by two or more numbers are called __________

Answer» Multiples that are shared by two or more numbers arecalled the common multiples of the two numbers.

A multiple is a product that we get when one number is multiplied by another number.

8221.

Using divisibility test, determine which of the following numbers are divisibly by 4, by 8 (a) 572 (b) 726352 (c) 5500 (d) 6000 (e) 12159 (f) 14560 (g) 21084 (h) 31795072 (i) 1700 (j) 2150

Answer» The numbers which are divisible by 4 are a), b), c), d), f), g), h) and i) while the numbers divisible by 8 are b),d),f) and h).

A divisibility rule is a kind of shortcut to figure out if a given integer is divisible by a divisor, without performing the whole division process but by examining its digits.

8222.

How to convert kilometers per hour to meters per second?

Answer» To convert kilometers per hour tometers per second, we multiply the given value by 5/18

Kilometers per hour can be easily converted intometers per second by using a conversion factor.

8223.

What is 15% of 20?

Answer» 15% of 20 is 3.

A percentis a ratio of a number expressed out of100.

8224.

Derive the equation of the parabola with a focus at (0, 1) and a directrix of y = -1.

Answer» Derive the equation of the parabola with a focus at (0, 1) and a directrix of y = -1.

Solution:

8225.

What is 7 to the power of 0?

Answer» 7 to the power of 0 is 1.

We will solve this question by using the zero property of exponents.

8226.

What is 33(1/3)%as a fraction?

Answer» 33(1/3)%as a fraction is 1/3

Percent means per hundred or for every hundred. We represent percentage with the symbol %.

8227.

Write an equation in slope-intercept form when the slope and a point are given.

Answer» Write an equation in slope-intercept form when the slope and a point are given.

Solution:

8228.

What is the difference between an outcome and an event?

Answer» Thedifference between an outcome and an event is - an event is the total number of outcomes whereas an outcome is the result of an event.

Outcome and Event are both terms of Probability that will be discussed here.

8229.

What number fills in the blank to complete the factorization of 3x + 24? _____(x + 8)

Answer» What number fills in the blank to complete the factorization of 3x + 24? _____(x + 8)

Solution:

8230.

Find the 12th partial sum of the summation of negative 2i minus 10, from i equals 1 to infinity.

Answer» The12th partial sum of the summation of negative 2i minus 10, from i equals 1 to infinity is -276.

A partial sum is basically the sum of part of a sequence. Sometimes partial sums are called "Finite Series".

8231.

What is 105% as a fraction?

Answer» 105% can be represented as 21/20in fraction form.

AFractioncan be a portion or section of any quantity out of a whole, where, the whole can be any number, a specific value, or a thing. All fractions consist ofa numerator and a denominator.

8232.

Find the volume of the cylinder in terms of pi?

Answer» Find the volume of the cylinder in terms of pi?

Solution:

8233.

If the diameter of circle c is 3 times the diameter of circle d, then what is the ratio of their areas?

Answer» The ratio of the area of circle 'c' to the area of circle 'd' is 9:1

The area of a circle is given by the formula: π/4 × (diameter)2

8234.

How many cubic centimeters cm3 are in a cubic meter m3?

Answer» 1 cubic meter = 106 cubic centimeter

We will use the concept of measuring systems in order to find the required answer. We will use the fact that 1 meter is equal to 100 centimeters.

8235.

How many faces edges and vertices does a cube have?

Answer» A cube has 6 faces,12edges, and 8 vertices

A cube is a 3-dimensional object with edges of equal length.

8236.

How to measure the height of a tree using trigonometry?

Answer» Basic trigonometric formulas for tangent functions can easily help us to find the height of the tree.

We can make use of the tangent function in trigonometry to find the height of the triangle.

8237.

If xy + 3ey = 3e, find the value of y'' at the point where x = 0.

Answer» If xy + 3ey = 3e, find the value of y'' at the point where x = 0.

Solution:

8238.

How to find the average of a set of numbers?

Answer» The average of a set of numbers is obtained by dividing the sum of the values by the number of values in the set.

The average of a set of values is equal to the sum of the values divided by the number of values.

8239.

What is the value of (-7 + 3i) - (2 - 6i)? -9 + 9i,-9 - 3i,-5 - 3i,- 5 + 9i

Answer» What is the value of (- 7 + 3i) - (2 - 6i)?

Solution:

8240.

What is 14/9 as a mixed number?

Answer» 14/9 as a mixed number is 1 5/9.

Animproper fractionis a typeof fractionwhere the numerator is greater than or equal to the denominator.

8241.

Find the derivative of the function using the definition of derivative. g(x) = 5 - x

Answer» Find the derivative of the function using the definition of derivative. g(x) = 5 - x

Solution:

8242.

What is the Equation of the Line that Passes through the Points (−3, 2) and (−5, 8)?

Answer» What is the equation of the line that passes through the points (-3, 2) and (-5, 8)?

Solution:

8243.

Determine if 25110 is divisible by 45 Hint: 5 and 9 are co-prime numbers. Test the divisibility of the number by 5 and 9.

Answer» Yes, 25110 is divisible by 45

We can check the divisibilityby using the numbers 5 and 9 which are co-prime numbers. The divisibility can be tested by using the prime factorization method.

8244.

Find an equation for the nth term of the arithmetic sequence. a18 = 97, a20 = 281.

Answer» Find an equation for the nth term of the arithmetic sequence. a18 = 97, a20 = 281.

Solution:

8245.

How do you verify the identity: cos2x− sin2x= 1 − 2sin2x

Answer» The identitycos2x− sin2x= 1 − 2sin2xis verified.

Trigonometric identities are equations that relate different trigonometric functions using different mathematical operations.

8246.

Find the limit: lim x➝0 sin | x | / 2x

Answer» The limit: lim x➝0 sin | x | / 2x does not exist.

We will use the concept of limits and function to find our required limit

8247.

What is 10% of 20?

Answer» 10% of 20 is 2.

A percentis a ratio of a number expressed out of100.

8248.

What is the solution set of {x | x < -5} ∩ {x | x > 5}?

Answer» What is the solution set of {x | x < -5} ∩ {x | x > 5}?

Solution:

8249.

If Sam has 6 different hats and 3 different scarves, how many different combinations could he wear?

Answer» If Sam has 6 different hats and 3 different scarves, how many different combinations could he wear?

Solution:

8250.

5,7,19,24,10,17,21,6,22,5,9

Answer» The mean, median, and mode for the given data set are 13.18, 10, 5 respectively.

Mean, median, and mode are important statistics parameters to analyze any data set.