Solve sin2x + 2sinx = 0 for 0 ≤ x < 2π. ...?

The cost of one candle can be found by dividing the total cost ($91.00) by the total number of candles sold (70), resulting in $1.30 per candle.

To find the cost of 1 candle, first calculate the total cost of all the candles sold. Fourteen boxes were sold for $91.00 in total. Since each box contains 5 candles, you can find the total number of candles by multiplying 14 boxes by 5 candles per box.

14 boxes × 5 candles per box = 70 candles total.

Now, to find the cost of one candle, divide the total cost by the total number of candles.
$91.00 / 70 candles = $1.30 per candle

Therefore, the cost of one candle is $1.30.

Answer:

True

Step-by-step explanation:

[tex]x = - 30 + 16 \\ \\ or \: \: x = - 14[/tex]

4.953 is larger than 4.951 because when comparing the digits from left to right, the thousandths place is different, where 3 is greater than 1.

To determine which number is larger, we compare them digit by digit starting from the left:

Both numbers have the same digit in the units place: 4.

Both numbers have the same digit in the tenths place: 9.

Both numbers have the same digit in the hundredths place: 5.

In the thousandths place, 4.953 has a 3, and 4.951 has a 1.

Since 3 is greater than 1, 4.953 is larger than 4.951.

Answer: The correct option is f(x) has three real roots and two imaginary roots.

Explanation:

It is given that the roots of fifth degree polynomial function are -2, 2 and 4+i.

Since he degree of f(x) is 5, therefore there are 5 roots of the function either real or imaginary.

According to the complex conjugate root theorem, if a+ib is a root of a polynomial function f(x), then a-ib is also a root of the polynomial f(x).

Since 4+i is a root of f(x), so by complex conjugate rot theorem 4-i is also a root of f(x).

From the the given data the number of real roots is 2 and the number of 2. The number of complex roots is always an even number, so the last root must be a real number.

Therefore, the correct option is f(x) has three real roots and two imaginary roots.

in mathematics, the common difference or we can call it the rate of change is the amount that we are constantly changing by either adding or subtracting to get to our next term. In other words, it’s consecutive terms increasing or decreasing.

To add the fractions 3/4 and 7/10, you need to find a common denominator, which in this case is 20. Both fractions are then converted to have this common denominator and added together to get the result 29/20.

The subject of your question is fraction addition. To add 3/4 and 7/10, first we need to find a common denominator. In this case, the common denominator is 20. Change 3/4 into a fraction with 20 as a denominator, you get 15/20. Change 7/10 to a fraction with denominator 20, you get 14/20. Add these two fractions together, we get (15+14)/20, which simplifies to 29/20.

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Two lines that intersect and form four right angles are perpendicular to each other. This is because they cross at a single point creating four 90 degree angles. Therefore, the lines are not parallel, the angles are not complementary, and their coplanar status is irrelevant.

If two lines intersect and form four right angles, it means that the lines are perpendicular to each other. In geometry, when two lines are perpendicular, they intersect at one point forming four right angles. A right angle is an angle of 90 degrees, which is the total division of a straight angle. Therefore, the two lines are not parallel because parallel lines do not intersect. The angles would not be complementary because complementary angles are two angles that add up to 90 degrees. Lastly, the lines being coplanar or not has no bearing on the angles they form when they intersect.

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Two lines intersecting to form four right angles are perpendicular, which is reflected in B. the lines are perpendicular. Parallel lines don't intersect, complementary angles are about their sum, and not coplanar doesn't relate to angles formed by intersection.

When two lines intersect and form 4 right angles, they possess a special relationship known as perpendicularity. These perpendicular lines meet to form 90-degree angles, also referred to as right angles. This fact is grounded in basic geometric principles.

The correct answer to the question is B. the lines are perpendicular. Choosing any of the other options would not accurately describe the relationship between the lines. Parallel lines do not intersect, complementary angles sum up to 90 degrees but do not describe the relationship between lines, and being not coplanar implies the lines do not lie in the same plane which is irrelevant to the intersection forming right angles.

It is important to recognize that according to Theorem 1, two straight lines cannot intersect in more than one point and Theorem 2 states that vertical angles, which are the angles opposite each other when two lines intersect, are equal. All this supports the fact that if the lines intersect in such a way to form 4 right angles, they are indeed perpendicular.

Answer:

Step-by-step explanation:

It is 2x by the third power because i dont know lol

To find a line parallel to y = -3/2x+3 through the point (-2,4), we use the point-slope form of a line using the given slope and coordinates.

To find a line parallel to a given line, we need to note that parallel lines have the same slope. The given equation is in the form y = mx + b, where m is the slope. In this case, the slope of the given line is -3/2. So, our parallel line will also have a slope of -3/2. Using the point-slope form of a line, we can substitute the slope and the coordinates of the given point (-2,4) to find the equation of the parallel line: y - y1 = m(x - x1). This gives us: y - 4 = -3/2(x - (-2)), which simplifies to y - 4 = -3/2(x + 2).

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Answer:  1000 ft³.

Step-by-step explanation:

Since, The volume of a cube = ( side )³

⇒ 1000 = (side)³ ⇒ side = 10

Hence, the side of the given cube = 10 feet

Since, the base of a cube = square having side 10 feet.

When we tilted the cube by 2 units,

Then, the base of the new solid = Rhombus having height 10 meters and base 10 feet,

Since, the square and rhombus are lying in the same base ( Shown in diagram)

Area of rhombus (Base of new solid) = Area of square having side 10 feet = 100 ft²

Since, the height of new solid is also 10 feet. the volume of new solid = Area of its base × height

=  10 × 100

= 1000 ft

Answer:

[tex]\displaystyle \frac{dy}{dx} = \frac{-\pi}{4} \sin \bigg( \frac{\pi t}{4} \bigg)[/tex]

General Formulas and Concepts:

Calculus

Differentiation

Derivative Property [Multiplied Constant]:                                                           [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]

Basic Power Rule:

Derivative Rule [Chain Rule]:                                                                                 [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle y = \cos \bigg( \frac{\pi t}{4} \bigg)[/tex]

Step 2: Differentiate

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

To find the width of a rectangular garden with a total perimeter of 120 feet and a known length of 40 feet, use the perimeter formula. Solving the equation, the width is determined to be 20 feet.

To find the width of a rectangular garden when you know the total fencing needed and the length of the garden, you can use the perimeter formula for a rectangle. The formula for the perimeter P of a rectangle is P = 2l + 2w, where l is the length and w is the width. In your case, the total perimeter is 120 feet and the length l is 40 feet. Setting up the equation using the given perimeter:

120 = 2(40) + 2w

Solving for w, the width:

120 = 80 + 2w

120 - 80 = 2w

40 = 2w

w = 20 feet

So, the width of the garden is 20 feet.