The solution for \( X \) is \( X = (A - D C)^{-1} D B \).
Assume \( A, B, C, D \), and \( X \) are \( n \times n \) matrices, and assume invertibility of matrices wherever needed. Then, the equation \( A X(B+C X)^{-1}=D \) can be solved for \( X \) by following these steps:
Step 1: Multiply both sides of the equation by \( (B+C X) \) to get rid of the inverse:
\( A X = D(B+C X) \)
Step 2: Distribute the \( D \) on the right side of the equation:
\( A X = D B + D C X \)
Step 3: Rearrange the equation to isolate \( X \) on one side:
\( A X - D C X = D B \)
Step 4: Factor out \( X \) on the left side of the equation:
\( (A - D C) X = D B \)
Step 5: Multiply both sides of the equation by the inverse of \( (A - D C) \) to solve for \( X \):
\( X = (A - D C)^{-1} D B \)
Therefore, the solution for \( X \) is \( X = (A - D C)^{-1} D B \).
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What is the 5th term of the sixth term of
the sequence A(n) = 6.3 + (n-1)(5)?
The given sequence is A(n) = 6.3 + (n-1)(5).
To find the 6th term of the sequence, we substitute n = 6 into the formula:
A(6) = 6.3 + (6-1)(5)
A(6) = 6.3 + 25
A(6) = 31.3
Now, to find the 5th term of this sequence, we need to substitute n = 5 into the formula:
A(5) = 6.3 + (5-1)(5)
A(5) = 6.3 + 20
A(5) = 26.3
Therefore, the 5th term of the 6th term of the sequence A(n) = 6.3 + (n-1)(5) is 26.3.
A spring oscillates with a frequency of 1 cycle per second. The distance between the maximum and minimum points of the oscillation is 3 centimeters. Which function can be used to model the oscillation if y
represents the distance in centimeters from the equilibrium position and t
is given in seconds?
A) y = 1. 5sin(2πt)
B) y = 1. 5sin(πt)
C) y = 3sin(2πt)
D) y = 3sin(πt)
y = 3sin(πt). This function models the oscillation by representing the distance in centimeters from the equilibrium position as the sine of π multiplied by the time in seconds.
y = 3sin(πt). This function can be used to model the oscillation because it represents the distance in centimeters from the equilibrium position as the sine of π multiplied by the time in seconds. This means that for any given value of t, the value of y will be the sine of π multiplied by t, which will correspond to a certain distance from the equilibrium position. As the oscillation has a frequency of 1 cycle per second, the value of t will increase linearly, and the value of y will oscillate between a maximum and a minimum value. As the distance between the maximum and minimum points of the oscillation is 3 centimeters, the maximum and minimum values of y will be 3 when t is an integer multiple of π. Therefore, the function y = 3sin(πt) can be used to accurately model the oscillation.
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In excerpt from baby mammoth mummy: frozen in time What does the narrator think of Sky's view of women? Use two details from the story to
port your response.
The narrator's thoughts on Sky's view of women is that the view is confusing and hypocritical.
What does the narrator think of sky's view ?The narrator thinks that Sky's perspective on women is unexpected, perplexing, absurd, and at odds with the person Sky appears to be. She is taken aback by Sky's refusal to perform any chores he views as falling under the purview of women.
The narrator is even more shocked that when Sky observes her "struggling with a bucket of water," he advises her not to fill the bucket all the way up rather than offering to assist her.
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What are the coordinates of D1.5(ABCD) for A(2, 0), B(8, -4), C(4, -6), and D(-5, -10)?
Answer: To find the coordinates of D1.5(ABCD), we need to perform a dilation with center D and scale factor 1.5 on the coordinates of each point.
The coordinates of point D are (-5, -10). To dilate point A, we can subtract the coordinates of D from the coordinates of A, multiply by 1.5, and then add the coordinates of D back:
D1.5(A) = 1.5[(2, 0) - (-5, -10)] + (-5, -10) = 1.5(7, 10) + (-5, -10) = (6.5, 5)
Similarly, we can dilate points B and C:
D1.5(B) = 1.5[(8, -4) - (-5, -10)] + (-5, -10) = 1.5(13, 6) + (-5, -10) = (14.5, -4)
D1.5(C) = 1.5[(4, -6) - (-5, -10)] + (-5, -10) = 1.5(9, 4) + (-5, -10) = (7.5, 4)
Therefore, the coordinates of D1.5(ABCD) are A'(6.5, 5), B'(14.5, -4), C'(7.5, 4), and D(-5, -10).
Step-by-step explanation:
what x-value makes the set of ratios equivalent
The following values of x, makes the set of ratios equivalent:
2: 3 = 6: 9
4: 7 = 24: 42
(6*2)12: 48 = 3: 12
12: 15 = 16: 20
What are ratios?The ratio can be used to determine how much of one item is contained in the other by comparing two sums of the same units. Ratios fall into two different groups.
Whereas the second is a part to whole ratio, the first is a part-to-part ratio. The part-to-part ratio demonstrates the link between two independent entities or organisations.
Now here in the 1st set:
2:3 = 6:x
Now, x = 6×3/2
⇒ x = 9
Similarly,
4:7=x:42
⇒ x = 24
The next ratio we have:
2x:48= 3:12
⇒ x = 6
Now, the last ratio,
12:15 = x:20
⇒ x = 16
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AB=AD and BC=DX
x = [?]
In the given figure by using the alternative angles rule we know that x = 82°.
What are alternate angles?Alternate angles are a unique type of angle in geometry.
The collection of non-adjacent angles on either side of the transversal is known as alternate angles.
Alternative Interior Angles: Angles are created on the inside, or interior, of two other lines when a third line known as the transversal crosses them. These other lines are typically parallel.
The alternate internal angles are those that are perpendicular to one another.
So, in the given figure:
∠ABD = ∠BDC = 35° (Alternate angles)
Then, ∠DBC will be:
82 + 35 + x = 180
117 + x = 180
x = 180 - 117
x = 63°
Then, ∠DBC = ∠BDA = 63° (Alternate angles)
Now, ∠DAB = 63 + 35 + x = 180
= 63 + 35 + x = 180
= 98 + x = 180
= x = 180 - 98
= x = 82°
Therefore, in the given figure by using the alternative angles rule we know that x = 82°.
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HELP ASAPP!
The parallel lines are marked with "feathers". Find the measures of the angles located at positions a, b, c, d, e, & f.
Answer:
Step-by-step explanation:
a=70
b=45
c=65
d=45
e=70
f=110
make sure to add degree symbol
Enjoy :)
The total interest he paid on this loan is \( \$ \) (Round to the nearest cent as needed.)
Vifredo bought a new boat for \( \$ 14,200 \). He paid \( \$ 2,500 \) for the down payment and financed the
The total interest he paid on this loan is $1,507.69
Vifredo bought a new boat for $14,200. He paid $2,500 for the down payment and financed the remaining amount for 48 months at an APR of 5.6%.
The total interest he paid on this loan is $1,507.69 (Round to the nearest cent as needed.)
To calculate the total amount that Vifredo will pay for his boat after 48 months, we need to add the amount he paid for the down payment to the total amount he will pay in 48 months at an APR of 5.6%.Vifredo's loan amount = $14,200 - $2,500 = $11,700
Calculating total amount for 48 months:Total amount = Monthly payment × Number of months Monthly payment can be calculated using the formula:PMT = (P × r) / (1 - (1 + r)^-n)where,PMT = Monthly paymentP = Principal amountr = Rate of interest per month (APR / 12) = 5.6% / 12n = Number of months= 48In our case,P = $11,700r = 5.6% / 12n = 48PMT = (11700 × (5.6 / 12)) / (1 - (1 + (5.6 / 12))^-48) = $267.34Total amount for 48 months = 267.34 × 48 = $12,840.16The total interest he paid on this loan is $1,507.69 (Round to the nearest cent as needed.)Therefore, the total amount Vifredo will pay for his boat is $2,500 (down payment) + $12,840.16 (total amount for 48 months) = $15,340.16.
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A track runner ran for 15 minutes, walked for 15 minutes, ran for another 20 minutes, and then walked for 10 minutes.
Which graph describes the relationship between runner's total distance and time?
graph with the x axis labeled time in hours and the y axis labeled total distance in miles, with a line segment from 0 comma 0 to 0.25 comma 1.25, a horizontal line segment from 0.25 comma 1.25 to 0.5 comma 1.25, a line segment from 0.5 comma 1.25 to 0.8 comma 2.4, and a horizontal line segment from 0.8 comma 2.4 to 1 comma 2.4
graph with the x axis labeled time in hours and the y axis labeled total distance in miles, with a line segment from 0 comma 0 to 0.25 comma 1.25, a line segment from 0.25 comma 1.25 to 0.5 comma 1.75, a line segment from 0.5 comma 1.75 to 0.8 comma 2.95, and a horizontal line segment from 0.8 comma 2.95 to 1 comma 2.95
graph with the x axis labeled time in hours and the y axis labeled total distance in miles, with a line segment from 0 comma 0 to 0.25 comma 1.25, a horizontal line segment from 0.25 comma 1.25 to 0.5 comma 1.25, a line segment from 0.5 comma 1.25 to 0.8 comma 0.1, and a horizontal line segment from 0.8 comma 0.1 to 1 comma 0.1
graph with the x axis labeled time in hours and the y axis labeled total distance in miles, with a line segment from 0 comma 0 to 0.25 comma 1.25, a line segment from 0.25 comma 1.25 to 0.5 comma 1.75, a line segment from 0.5 comma 1.75 to 0.8 comma 2.95, and a line segment from 0.8 comma 2.95 to 1 comma 3.15
Answer:
Step-by-step explanation:
graph with the x axis labeled time in hours and the y axis labeled total distance in miles, with a line segment from 0 comma 0 to 0.25 comma 1.25, a line segment from 0.25 comma 1.25 to 0.5 comma 1.75, a line segment from 0.5 comma 1.75 to 0.8 comma 2.95, and a horizontal line segment from 0.8 comma 2.95 to 1 comma 2.95
It's B.
Explanation: I took the test
How does the concept of conservation of mass apply to chemical reactions?
1.The reactants and products have exactly the same atoms.
2.The reactants and products have exactly the same molecules.
3.The change in the amount of matter is equal to the change in energy.
4.The change in the amount of matter is only a small percentage of the total mass.
Since the elements in the reactants and products are identical, the principle of conservation of mass is applicable to chemical processes. Choice (b) is accurate.
What is the short meaning of a chemical reaction?chemical reaction, the transformation of one or even more substances (the reactants) into one or more distinct substances (the products). Chemical components or chemical combinations make up substances.
How does a chemical reaction start?When atoms create or break molecular bonds, chemical processes take place. Reactants are the substances that begin a chemical reaction, and products are the substances that are created as a result of the reaction.
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help asap pls!! What should be reason 6 in the following proof?
Answer:
Step-by-step explanation:
alternate interior angles
More formally:
If two lines and a transversal form alternate interior angles that are congruent, then the two lines are parallel (Since ∠1 = ∠4)
Answer: Alternate Interior Angles Converse
Step-by-step explanation:
If two lines are cut by a transversal so the alternate interior angles are congruent, then the lines are parallel.
Write an equation for a line parallel to y = 2 x + 1 and passing
through the point (1,5)
To find the equation for a line parallel to y = 2x + 1 and passing through the point (1,5), we need to remember that parallel lines have the same slope.
Since the slope of y = 2x + 1 is 2, the slope of the parallel line will also be 2.
Using the point-slope form of a linear equation, we can plug in the given slope and point to find the equation of the parallel line:
y - y1 = m(x - x1)
y - 5 = 2(x - 1)
Simplifying this equation gives us the equation for the parallel line:
y = 2x + 3
So, the equation for the line parallel to y = 2x + 1 and passing through the point (1,5) is y = 2x + 3.
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Can someone answer this, please? I need the help
Answer:
Proofs attached to answer
Step-by-step explanation:
Proofs attached to answer
18. Determine the exact value of the product: 3 sin(37.5°) cos( 7.5°) 19. Determine the exact value of the sum: cos (phi/12) - cos (5phi/12)
18. The exact value of the product 3 sin(37.5°) cos( 7.5°) can be determined using the double angle formula for sine:
sin(2x) = 2 sin(x) cos(x)
Substituting x = 22.5° into the formula gives:
sin(45°) = 2 sin(22.5°) cos(22.5°)
Dividing both sides by 2 gives:
sin(45°)/2 = sin(22.5°) cos(22.5°)
Substituting the given values into the equation gives:
3 sin(37.5°) cos( 7.5°) = 3 (sin(45°)/2) (cos(45°)/2)
Simplifying gives:
3 sin(37.5°) cos( 7.5°) = 3/4
Therefore, the exact value of the product is 3/4.
19. The exact value of the sum cos (phi/12) - cos (5phi/12) can be determined using the sum-to-product formula for cosine:
cos(x) - cos(y) = -2 sin((x+y)/2) sin((y-x)/2)
Substituting x = phi/12 and y = 5phi/12 into the formula gives:
cos (phi/12) - cos (5phi/12) = -2 sin((phi/12 + 5phi/12)/2) sin((5phi/12 - phi/12)/2)
Simplifying gives:
cos (phi/12) - cos (5phi/12) = -2 sin(3phi/12) sin(2phi/12)
Therefore, the exact value of the sum is -2 sin(3phi/12) sin(2phi/12).
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New Bread Bakery purchased new equipment by making a down payment of $2000 and agreeing to make payments of $458 at the end of each month for five years. Interest is 9.2% compounded monthly.
(a) What was the purchase price of the new equipment?
(b) How much interest will have to be paid?
a) The purchase price of the new equipment is $20,531.76.
b) The amount of interest that will have to be paid is $6,948.24.
The purchase price of the new equipment for New Bread Bakery can be found using the formula for the present value of an annuity:
PV = PMT * [(1 - (1 + i)^(-n)) / i]
Where PV is the present value (or purchase price), PMT is the monthly payment, i is the monthly interest rate, and n is the number of payments.
Plugging in the given values:
PV = 458 * [(1 - (1 + 0.092/12)^(-5*12)) / (0.092/12)]
PV = 458 * [(1 - (1 + 0.00767)^(-60)) / 0.00767]
PV = 458 * [(1 - 0.6887) / 0.00767]
PV = 458 * 40.4624
PV = 18,531.76
The purchase price of the new equipment is $18,531.76. However, this does not include the down payment of $2000. So, the total purchase price is:
PV + Down Payment = 18,531.76 + 2000 = $20,531.76
To find the amount of interest that will have to be paid, we can subtract the purchase price from the total amount paid over the five years:
Interest = (458 * 5 * 12) - 20,531.76 = 27,480 - 20,531.76 = $6,948.24
Therefore, the amount of interest that will have to be paid is $6,948.24.
(a) The purchase price of the new equipment is $20,531.76. (b) The amount of interest that will have to be paid is $6,948.24.
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Evaluate. Write your answer as a fraction or whole number without exponents. 10^-3
10⁻³ is equal to 1/1000 or 0.001.
What are Exponents?
Exponents are a shorthand way of representing repeated multiplication of a number by itself. They are indicated by a superscript number placed to the right and above the base number.
The superscript number represents the number of times the base number is multiplied by itself. For example, 2³ means 2 multiplied by itself three times, which equals 8.
Exponents are used to simplify large and small numbers, and are fundamental to algebraic and mathematical calculations. Exponents have several rules, such as the power of a power rule, product rule, quotient rule, and negative exponents rule.
10⁻³ can be evaluated as:
1 / 10^3 = 1 / 1000
Therefore, 10⁻³is equal to 1/1000 or 0.001.
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A product received discounts of 33%, 25%, and 5%. A markup on
cost of 50% was then applied to arrive at the regular unit selling
price of $349.50. What was the original list price for the
product?
The original list price for the product was $487.09.
To find the original list price for the product, we need to reverse the discounts and markup that were applied to it. Here is a step-by-step explanation:
Start with the regular unit selling price of $349.50.Reverse the 50% markup by dividing by 1.50. This gives us the cost before the markup: $349.50 / 1.50 = $233.00.Reverse the 5% discount by dividing by 0.95. This gives us the price before the 5% discount: $233.00 / 0.95 = $245.26.Reverse the 25% discount by dividing by 0.75. This gives us the price before the 25% discount: $245.26 / 0.75 = $326.35Reverse the 33% discount by dividing by 0.67. This gives us the original list price: $326.35 / 0.67 = $487.09.Therefore, the original list price for the product was $487.09.
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What is the image of the point (4,8)(4,8) after a rotation of 180^{\circ}180 ∘ counterclockwise about the origin?
After being rotated 180 degrees anticlockwise around the origin, the picture of the point (4,8) is (-4,-8).
After a 180-degree rotation, where is the image point?The fixed point is referred to as the rotational centre. The quantity of the rotation is described by the term "angle of rotation," which is measured in degrees. The equivalent of turning a figure 90 degrees anticlockwise is turning it 180 degrees clockwise. Hence, the resulting image of the point is (-1, 2).
How is a 180 degree anticlockwise rotation calculated?Below are the guidelines for rotation: rotation 90 degrees clockwise: (x,y) results in (y,-x) rotation of (x,y) at 90 degrees anticlockwise results in (-y,x) Rotating (x, y) 180 degrees both clockwise and anticlockwise results in (-x,-y).
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The Grade 8 learners decided to start training more. They will either box or grid. There
are 125 Grade 8 learners, and they box and grid in the ratio 3:2. Calculate how many
learners participate in each sport?
Brendan is 5 years older than Valerie. In 6 years the sum of their ages will be 81 . How old is Brendan now? years old
Brendan is currently 37 years old.
To solve this problem, we can use algebra. Let's let V represent Valerie's age and B represent Brendan's age. We can set up the following equations based on the information given in the question:
B = V + 5 (Brendan is 5 years older than Valerie)
B + 6 + V + 6 = 81 (In 6 years, the sum of their ages will be 81)
Simplifying the second equation, we get:
B + V + 12 = 81
B + V = 69
Substituting the first equation into the second equation, we get:
V + 5 + V = 69
2V = 64
V = 32
Now that we know Valerie's age, we can use the first equation to find Brendan's age:
B = 32 + 5
B = 37
So Brendan's current age is calculated to be 37 years
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Let f and g be polynomials of degree 3. Is it true that f ∘ g = g ∘ f?
A. Yes, always
B. No, it's only with polynomials with a degrees of 1
C. It is true in some cases
D. No, never
The true statement about the polynomials is (b) No, it's only with polynomials with a degrees of 1
How to determine the true statementGiven that the polynomials f and g have a degree of 3
The composition of two functions, f ∘ g (read as "f composed with g"), is not commutative in general, meaning that f ∘ g is not necessarily equal to g ∘ f.
This holds true for polynomials of degree 3 as well.
In fact, if f and g are two different polynomials of degree 3, then f ∘ g and g ∘ f will be different polynomials in general.
The equation f ∘ g = g ∘ f holds true is when f and g are constant polynomials, that is, polynomials of degree 0 or 1.
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what is a exactly 1/4 of a full rotation
Answer: A quarter or 1/4 rotation is 90°.
Step-by-step explanation:
A full rotation is 360 degrees, usually written as 360°. Half a rotation is then 180° and a quarter rotation is 90°.
what is 3/8 divided by 1/4
Answer:[tex]1\frac{1}{2}[/tex]
Hi Please help due today ty!
Lynn had 1(5)/(8) yards of ribbon. She made 6 identical bows and had 1(1)/(4) yards of ribbon left. How many yards of ribbon did Lynn use to make a bow?
The number of yards of ribbon Lynn used to make a bow is 1/16 yards.
To find out how many yards of ribbon Lynn used to make a bow, we need to subtract the amount of ribbon she had left from the amount she started with and then divide by the number of bows she made. We can do this using the following steps:
1. Convert the mixed numbers to improper fractions: 1(5)/(8) = 13/8 and 1(1)/(4) = 5/4
2. Subtract the two fractions: 13/8 - 5/4 = 13/8 - 10/8 = 3/8
3. Divide the result by the number of bows: (3/8) / 6 = 3/8 x 1/6 = 3/48 = 1/16
Therefore, Lynn used 1/16 yards of ribbon to make a bow.
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justin wants to create a rectangular garden whose area is 81x^(2)-126x square units. If one dimension of the garden is 9x-14 units, what is the length of the other dimension?
The final answer length of the other dimension of the garden is 9x units.
To find the length of the other dimension of the garden, we need to use the formula for the area of a rectangle:
Area = Length x Width
We are given the area and one dimension, so we can plug those values into the formula and solve for the other dimension:
[tex]81x^2-126x[/tex] = (9x-14)(Length)
To solve for the length, we need to divide both sides of the equation by (9x-14):
Length =[tex](81x^2-126x)/(9x-14)[/tex]
Now we can simplify the right side of the equation by factoring out a common factor of 9x:
Length = (9x)(9x-14)/(9x-14)
The (9x-14) terms cancel out, leaving us with:
Length = 9x
So the length of the other dimension of the garden is 9x units.
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In the next four problems find the VOLUME of
the shapes. Label each answer correctly. Remember that volume is measured in cubic units.
5) Square prism: 4 cm x 4 cm x 8 cm
6) rectangular prism: 3 cm x 4 cm x 5 cm
7) cylinder: radius 6 cm, height 5 cm (round the answer to the nearest whole cubic centimeters.)
8) cone: radius 6 cm, height 5 cm (round the answer to the nearest whole cubic centimeter.)
Volume of square prism = 128 cm³
Volume of rectangular prism is, V = 60 cm³
Volume of cylinder is, V = 565.2 cm³
Volume of cone is, V = 188.4 cm³
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
The dimensions of the shapes are,
Square prism: 4 cm x 4 cm x 8 cm
Rectangular prism: 3 cm x 4 cm x 5 cm
Cylinder: radius 6 cm, height 5 cm
Cone: radius 6 cm, height 5 cm
Now, We know that;
Volume of square = Side² × Height
Hence, We get;
Volume of square = 4² × 8
= 128
And, Volume of rectangular prism is,
V = 3 cm x 4 cm x 5 cm
V = 60 cm³
Volume of cylinder is,
V = πr²h
V = 3.14 × 6² × 5
V = 565.2 cm³
Volume of cone is,
V = πr²h/3
V = 3.14 × 6² × 5/3
V = 565.2 /3
V = 188.4 cm³
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Verify the identity. 2 sec? y - 2 cot? = cot(" - y) = 2 - 2 cot'( % - y) = 2 (sec?y- 2 sec? y - 2 2 ) X = 2 Need Help? Read it Watch It
2(cot2 y + tan2 y) = 2(1) Verified
Verify the identity:
2 sec2 y - 2 cot2 y = cot(2y) - 2 cot(2y) = 2 - 2 sec(2y)
To prove the identity, start by applying the identity:
cot2 y = 1 - tan2 y
Substitute this in the left side of the equation:
2 sec2 y - 2(1 - tan2 y) = 2 sec2 y - 2 + 2 tan2 y
Simplify the equation by factoring out a 2 from the right side:
2 sec2 y - 2 + 2 tan2 y = 2(sec2 y - 1 + tan2 y)
Next, apply the identity:
sec2 y - 1 = cot2 y
Substitute this in the equation and simplify:
2(sec2 y - 1 + tan2 y) = 2(cot2 y + tan2 y)
Finally, apply the identity:
cot2 y + tan2 y = 1
Substitute this in the equation and simplify:
2(cot2 y + tan2 y) = 2(1)
The identity is thus verified.
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2. If \( \left[\begin{array}{rr}10 & 1 \\ -6 & -6\end{array}\right]=\left[\begin{array}{rr}1 & 2 \\ 3 & -3\end{array}\right]\left[\begin{array}{ll}a & b \\ c & d\end{array}\right] \), find \( a+b+c+d
The answer is \(a+b+c+d = 10\).
To find \(a+b+c+d\), we can use matrix multiplication to solve for each variable. Matrix multiplication is performed by multiplying the elements of each row of the first matrix by the corresponding elements of each column of the second matrix, and then summing the products.
So, we can set up the following equations:
\(10 = 1a + 2c\)
\(1 = 1b + 2d\)
\(-6 = 3a - 3c\)
\(-6 = 3b - 3d\)
Solving for each variable, we get:
\(a = 6 - 2c\)
\(b = (1 - 2d)/1\)
\(c = (6 + 3a)/(-3)\)
\(d = (3b + 6)/(-3)\)
Substituting the values of \(a\) and \(b\) into the equations for \(c\) and \(d\), we get:
\(c = (6 + 3(6 - 2c))/(-3)\)
\(d = (3((1 - 2d)/1) + 6)/(-3)\)
Solving for \(c\) and \(d\), we get:
\(c = -2\)
\(d = -1\)
Substituting these values back into the equations for \(a\) and \(b\), we get:
\(a = 6 - 2(-2) = 10\)
\(b = (1 - 2(-1))/1 = 3\)
So, \(a+b+c+d = 10 + 3 + (-2) + (-1) = 10\).
Therefore, the answer is \(a+b+c+d = 10\).
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Every pyramid is a prism, is it True? and why?
No, it is not true that every pyramid is a prism, because they have different properties.
A pyramid is a solid shape that has a base and triangular faces that meet at a point called the apex. The base of a pyramid can be any polygon, such as a square, triangle, or rectangle. A pyramid is named according to the shape of its base. For example, a pyramid with a square base is called a square pyramid.
A prism, on the other hand, is a solid shape that has two identical bases that are parallel to each other and rectangular faces that connect the bases. The bases of a prism can also be any polygon, and a prism is named according to the shape of its bases. For example, a prism with a rectangular base is called a rectangular prism.
So, while both pyramids and prisms are three-dimensional shapes with bases and faces, they have different properties and are not the same. Therefore, it is not true that every pyramid is a prism.
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