Applying Pythagorean Identity, the original equation sin² theta +cos theta = 2 can be altered by substituting sin² theta with 1 - cos² theta. This forms a quadratic equation: cos² theta - cos theta - 1 = 0, which can be solved using the quadratic formula to find the possible values of cos theta.
Explanation:To solve the equation sin² theta +cos theta = 2 by using the Pythagorean identity sin² theta +cos² theta =1, we can substitute sin² theta in the original equation with 1 - cos² theta.
Step-by-step solution:
We start by replacing sin² theta in the equation with 1 - cos² theta. So, the equation becomes 1 - cos² theta + cos theta - 2 = 0.This can be rearranged to form a quadratic equation as cos² theta - cos theta - 1 = 0.We can solve this quadratic equation using the quadratic formula cos theta = [- (-1) ± √{(-1)²-4(1)(-1)} ] /2(1).Computing the values, we get the two possible values of cos theta.Learn more about Pythagorean Identity here:https://brainly.com/question/24287773
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A ladder leans against a building. The angle of elevation of the ladder is 70°. The top of the ladder is 25 ft from the ground.
To the nearest tenth of a foot, how far from the building is the base of the ladder?
20.5 ft
30.5 ft
32.3 ft
39.5 ft
The distance from the building to the base of the ladder, when the ladder makes an angle of 70 degrees with the ground and the ladder is 25 feet long, can be calculated using the cosine function. The calculated distance is approximately 8.6 feet.
Explanation:To calculate the distance from the building to the base of the ladder, we have to use the trigonometric function cosine given the information in the problem. The cosine of an angle in a right triangle is defined as the adjacent (which is the distance we wish to find) over the hypotenuse (which is given as 25 feet).
Therefore, we write the equation as follows:
cos(70) = Adjacent/25
To find the 'Adjacent', we rearrange the equation:
Adjacent = 25*cos(70)
When you perform the calculation, you get Approximately 8.6 feet as the distance from the building to the base of the ladder.
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The base of the ladder is approximately 8.5 feet from the building. This is determined using trigonometry and the cosine of the ladder's angle of elevation.
Explanation:This is a trigonometry problem where we have to find the base of the triangle formed by the ladder, the ground, and the distance from the building. The question gives us the length of the ladder (hypotenuse in the right triangle) and the angle of elevation. We can thus use cosine of the angle (base/hypotenuse) to find the base.
We know that Cosine of 70° is equal to the (base / Hypotenuse). And in the present case, the hypotenuse is given to be 25 ft.
Therefore, calculation will be as follow:
Base = Cosine (70°) * Hypotenuse.
Base = Cosine (70°) * 25 ft.
After calculating, this gives a base length of approximately 8.5 feet. So, the base of the ladder is approximately 8.5 feet from the building.
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turn 11/40 into a decimal
Answer: 0.275
To get 11/40 converted to decimal, you simply divide 11 by 40. Then you get 0.275
Which of these ordered pairs is a solution to the linear inequality?
A lab worker monitors the growth of a bacteria colony starting at 9:00 a.m. At that time, there are 100 bacteria. According to the exponential function f(x) = 100(4)x, the bacteria quadruple every hour. Which equation could you use to determine the number of bacteria in the colony after 6 hours?
The equation to determine the number of bacteria in the colony after 6 hours is [tex]f(x) = 100(4)^x[/tex] and after 6 hours, there will be 409,600 bacteria in the colony.
To find the number of bacteria after 6 hours, one would substitute x with 6 in the exponential function [tex]f(x) = 100(4)^x[/tex].
This function models the growth of the bacteria colony, where the initial number of bacteria is 100 and they quadruple every hour.
The variable x represents the number of hours that have passed since the initial measurement at 9:00 a.m.
By substituting x = 6 into the function, we get:
[tex]f(6) = 100(4)^6[/tex]
Now, calculate the value of [tex](4)^6[/tex]:
[tex](4)^6 = 4 \times 4 \times 4 \times 4 \times 4 \times 4 = 4096[/tex]
Then, multiply this by the initial number of bacteria, which is 100:
f(6) = 100 [tex]\times[/tex] 4096
Finally, calculate the total number of bacteria after 6 hours:
f(6) = 409600
The radius of the base of a cone is 4 inches. the slant height of the cone is 6 inches. which is closest to the surface area of the cone?
Which number replaces the box to make this a true sentence? 3 × (6 – 2) = (? × 6) – (3 × 2)
3
Applying Distribution Law, we multiply 3 with 6 and 2.
So, 3 * ( 6 -2 ) = ( 3* 6 ) - ( 3 * 2)
so, '?' = 3
which of these is an example of discrete data?
A) distance
B) temperature
C) area of a room
D) pages in a book
Due tomorrow please help
The point, (-4, 1) is located in which quadrant?
Answer:
B its is B that is the most ansewrablea .
Step-by-step explanation:
the right rectangular prism will be sliced perpendicular to its base along the dashed line. Select from the drop-down menus to correctly describe the cross section formed by the slice.
Length of side AB???
your recipe calls for 1/2 a pound of potatoes. You use 1/6 of the bag of potatoes. whats the number of pounds per bag
Find the product.
y 4 · y 6
The volume of a cuboid is 1404cm3. The length is 9cm and the width is 130mm. Work out the height of the cuboid in cm.
To calculate the height of the cuboid, we convert the width to centimeters and use the volume formula. After conversion, we find the height by dividing the volume (1404cm³) by the product of the length (9cm) and width (13cm), resulting in a height of 12cm.
To find the height of the cuboid, we can use the formula for calculating volume, which is volume = length x width x height. The question gives us the volume of the cuboid as 1404cm³, the length as 9cm, and the width as 130mm. However, we need to ensure all units are the same, so let's convert the width from millimeters to centimeters: 130mm = 13cm (since 1cm = 10mm).
Now, using the formula for volume:
Volume = length x width x height1404cm³ = 9cm x 13cm x heightTo find the height, we divide the volume by the product of the length and width:
height = Volume / (length x width)height = 1404cm³ / (9cm x 13cm)height = 1404cm³ / 117cm²height = 12cmTherefore, the height of the cuboid is 12cm.
For f(x) = 2x + 1 and g(x) = x2 – 7, find (f – g)(x).
A. –x^2 + 2x – 6
B. –x^2 + 2x + 8
C. x^2 – 2x – 8
D. 2x^2 – 15
Susan has a rectangular garden that measures 20 feet by 10 feet. what is the least amount of fencing that she needs to buy in order to enclose the garden?
There are 80 marbles in a bag. You randomly choose 20 marbles from the bag. The results are shown in the table. Predict the total number of yellow marbles.
Color
Blue 6
Red 9
Yellow 5
There are about ___ yellow marbles.
What is an equation for a sine curve with amplitude 2, and period 4pi symbolradians?
The U-Drive Rent-A-Truck company plans to spend $15 million on 310 new vehicles. Each commercial van will cost $35 comma 000 , each small truck $70 comma 000 , and each large truck
$60 comma 000 . Past experience shows that they need twice as many vans as small trucks. How many of each type of vehicle can they buy?
Set the situation up as a system of linear equations based on the information provided in the problem. Then, solve the system to get the number of each type of vehicle that the company can buy.
Explanation:To solve this problem, let's set it up as a system of linear equations. This is a mathematics problem involving problem-solving and linear equations.
Let's denote v as the number of vans, s as the number of small trucks, and l as the number of large trucks.
We know that the total money spent should equal $15 million, and we can express this as:
(35,000v) + (70,000s) + (60,000l) = 15,000,000
We also know that the number of vans is twice the number of small trucks, so we can express this as:
v = 2s
We know also that the total number of vehicles is 310, so we have:
"v + s + l = 310"
Solving these three equations will give us the number of vans, small trucks, and large trucks that the company can buy.
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A set of data has 12 pieces of data. Which of the following statements is NOT TRUE?
A.) There are 3 pieces of data in the first quartile.
B.) There are 6 pieces of data between the first quartile and the third quartile.
C.) There are 9 pieces of data that are greater than the median.
D.) There are 3 pieces of data in the upper quartile.
Please help!!
The correct answer is C.) There are 9 pieces of data that are greater than the median. The statement that is NOT TRUE is C.) There are 9 pieces of data that are greater than the median.
To understand why option C is not true, let's review some basic concepts about quartiles and the median in a set of data:
- 3 pieces of data are less than Q1.
- 3 pieces of data are in the first quartile (Q1).
- 6 pieces of data are between Q1 and Q3 (the interquartile range, IQR).
- 3 pieces of data are in the third quartile (Q3).
- Including the median itself, 4 pieces of data are greater than or equal to the median.
This breakdown correctly accounts for all 12 pieces of data. As a result, the statement that is NOT TRUE is indeed option C:
C.) There are 9 pieces of data that are greater than the median.
Since there are 4 pieces of data that are greater than or equal to the median, option C, which asserts there are 9 such pieces, is false. The correct understanding aligns with your analysis of quartiles and the median in this dataset.
a___ is a solid consisting of a polygon, a point not in the same plane as the polygon, and all points between them.
A pyramid is the correct answer
The width of a rectangle is half the length. the perimeter of the rectangle is 54 in. what is the length of the rectangle?
If a circle has a radius of 18 feet what's the closest approximation for circumference
explain one of the theorems that you would use to find the zero of higher degree polynomial
Rational Root Theorem:
If the rational number [tex]x=\frac{b}{c}[/tex] is a zero of a higher degree polynomial:
[tex]P(x)=kx^{n}+...+m[/tex]
where all the coefficients are integers. Then [tex]b[/tex] will be a factor of [tex]m[/tex] and [tex]c[/tex] will be a factor of [tex]k[/tex]
1. Use the rational root theorem to enumerate all possible rational zeroes of the polynomial [tex]P(x)[/tex]
2. Evaluate the polynomial from the first step until you can find a zero. Let’s suppose the zero is [tex]x=r[/tex]. It will be a zero if [tex]P(r)=0[/tex]. Then if this is true, write the polynomial as:
[tex]P(x)=(x-r)Q(x)[/tex]
3. Repeat this process using [tex]Q(x)[/tex] this time rather than [tex]P(x)[/tex]. The process finishes until we reach a second degree polynomial, then solve as it is widely known for a quadratic equation.
A dilation produces a smaller figure. Which is a possible scale factor?
–2
1/3
1
4
Answer:
B
Step-by-step explanation:
Im assuming.
15 Points!
Find f(x) and g(x) so that the function can be described as y = f(g(x)).
roger gets $40 per day as wages and $4.50 as commission for every pair of shoes he sells in a day. His daily earnings goal is $112.
Write an equation to determine how many pairs of shoes, ppp, Roger must sell in a day to meet his daily earnings goal.
Find the number of pairs of shoes he must sell to meet his daily earnings goal.
Answer:
112=4.5p+40
16
Step-by-step explanation:
It would take an hour for plane A to meet plane B which is flying towards it. If the distance between them will be 200 miles after 45 minutes, how far apart are they now?
Answer:
800 miles apart
Step-by-step explanation:
0.75a+0.75b=200
0.25(a+b)=200
a+b=800 miles apart
i need help!!!!!!!!!!!!!!?!!!
When p is divided by 12, the quotient is q with a remainder of 5, where p and q are positive integers. what is the remainder when p is divided by 6?