Determine all possible angles θ for equilibrium, 0∘<θ<90∘.
Please need help as quick as you can . What is the slope of the line that passes through the points (16, –1) and (–4, 10)? A. -20/11 B. -11/20 C. 11/20 D. 20/11
Triangle ABC has two known angles. Angle A measures 55 degrees. Angle b measures 30 degrees.What is the measure of angle C?
A car manufacturer claims that, when driven at a speed of 50 miles per hour on a highway, the mileage of a certain model follows a normal distribution with mean μ = 30 miles per gallon and standard deviation σ= 4 miles per gallon.
the weight of an object on the moon is about .167 of its weight on Earth. How much does a 180 lb astronaut weigh on the moon?
Lilly has a bag of 140 colored marbles. The bag has an equal number of green and blue marbles and an equal number of red and yellow marbles. If Lilly arranged all of the green marbles in groups of 8 and all of the blue marbles in groups of 7, how many red marbles are in the bag?
The driver of a car traveling at 54ft/sec suddenly applies the brakes. The position of the car is s=54t-3t^2, t seconds afyer the driver applies the brakes.
How many seconds after the driver applies the brakes does the car come to a stop
After time [tex]t = 9[/tex] seconds the driver applies the brakes does the car come to a stop.
What is time?" Time is defined as the measurable slot of period in which required action is done."
Formula used
[tex]y = x^{n} \\\\\implies \frac{dy}{dx} = nx^{n-1}[/tex]
According to the question,
Position of the car [tex]'s' = 54t - 3t^{2}[/tex]
[tex]'s'[/tex] represents the distance
[tex]'t'[/tex] is the time in seconds
When driver applies break [tex]v= 0[/tex],
[tex]v = \frac{ds}{dt}[/tex]
Calculate the first derivative with respect to time we get,
[tex]'s' = 54t - 3t^{2}\\\\\implies \frac{ds}{dt} = 54- 6t[/tex]
As [tex]\frac{ds}{dt} =0[/tex] we get the required time as per given condition,
[tex]54-6t =0\\\\\implies 6t =54\\\\\implies t = 9[/tex]
Hence, after time [tex]t = 9[/tex] seconds the driver applies the brakes does the car come to a stop.
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If s = {r, u, d} is a set of linearly dependent vectors. if x = 5r + u + d, determine whether t = {r, u, x} is a linearly dependent set
Eric has 4 bags of 10 marbles and 6 single marbles . how many marbles does eric have
A polygon has vertices at (4, 1), (4, 7), (10, 7) and (10, 1). How does the perimeter of the polygon change if each coordinate is multiplied by 3?
There are 365,493 blue pens and 549,384 black pens how many more black pens are there then blue pens
By subtracting the number of blue pens from the number of black pens, we find that there are 183,891 more black pens than blue pens.
To find out how many more black pens there are than blue pens, we need to subtract the number of blue pens from the number of black pens. The student provided the numbers as 365,493 blue pens and 549,384 black pens.
Here is the calculation:
Number of black pens: 549,384Number of blue pens: 365,493Difference (black pens - blue pens): 549,384 - 365,493 = 183,891There are 183,891 more black pens than blue pens.
help me solve this, Pre-Calculus Question
I only need the last part
A pizzeria baked 12 pizza pies in 3 hours. At this rate, how many pizza pies can they bake in 7 hours?
Two small fires are spotted by a ranger from a fire tower 60 feet above ground. The angles of depressions re 11.6° and 9.4°. How far apart are the fires? (The fires are in the same general direction from the tower.)
How much do parents pay per day? If a childcare center charges $150 per week during the school year. In the summer, parents can pay a prorated amount based on the number of days of attendance.
For the x-values 1, 2, 3, and so on, the y-values of a function form a geometric sequence that increases in value. What type of function is it? A. Exponential growth B. Decreasing linear C. Increasing linear D. Exponential decay
Answer:
Option A: Exponential growth
Step-by-step explanation:
If for values of x values of y increases and forms a geometric sequence then it would be an exponential growth function because geometric sequence is an exponential function and since, it is increasing hence, an exponential growth.
Option B is incorrect because because y is not decreasing
Option C and D are incorrect because geometric sequence can never be linear since, it gives common ratio.
Final answer:
The function described, where y-values form an increasing geometric sequence as x-values increase, is characterized as Exponential growth. This is consistent with an exponential curve where the rate of growth is proportional to the current value, which aligns with the behavior of a geometric sequence.
Explanation:
For the given scenario where the y-values of a function form a geometric sequence that increases for the x-values 1, 2, 3, and so on, the type of function is described as Exponential growth. This is because in a geometric sequence each term after the first is found by multiplying the previous term by a constant called the common ratio, which is analogous to the exponential function where the growth rate of the value is proportional to its current value. The more the x-value increases, the higher and faster the y-value grows, following the pattern of an exponential growth curve.
Answer A. Exponential growth fits the description as it involves an increasing geometric sequence. Answer B. Decreasing linear refers to a linear function that decreases with each increment in x, which does not describe the function in question. Similarly, Answer C. Increasing linear describes a function that increases at a constant rate, not geometrically. Answer D. Exponential decay would imply the y-values decrease as x increases, which is also not the case described.
a construction crew Must build 4 miles of road in one week on Monday they build 1/2 mile of road in one week on Tuesday they build 1/3 mile of road how many more miles of road are left to build
Write the equation of a line, in general form , that has an slope of zero and a y-intercept of (0, -6).
Find the area of the specified region shared by the circles r = 4 and r = 8sin
Find the length and width of a rectangle that has the given perimeter and a maximum area. perimeter: 128 meters
I keep getting 13. It's supposed to be 3. Can you show me how it's done? 3(a-5) = -6
PLEASE HELP 15 POINTS WILL GIVE BRAINLIEST The following formula, F = ma, relates three quantities: Force (F), mass (m), and acceleration (a). A: Solve this equation, F = ma for a. B If F = -24 units and m = 10 units, what is the acceleration, a? Use the equation from Part (a) to answer the question. C: If F = 24 units and a = 12 units, what is the mass, m? Use the equation, F = ma, to plug in the known values and solve for m
Suppose 8 out of every 20 students are absent from school less than 5 days a year.Predict how many students would be absent less than 5 days a year out of 40,000 students.
What is the meaning of the term theorem
What percent of 9.2 is 43.7
The requried 475% of 9.2 is 43.7, as of the given percentage situation.
What is the percentage?The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.
Here,
In the question, we are asked to determine the 43.7 is what percent of 9.2.
So, let the percent be x,
x % of 9.2 = 43.7
x/100 × 9.2 = 43.7
x = 43.7/9.2 × 100%
x = 475%
Thus, the requried 475% of 9.2 is 43.7, as of the given percentage situation.
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five friends went to a local restaurant and all had the buffet at $6.75 each. the following is the restaurant bill. does it seem reasonable 5($6.75) =&67.50
Find the difference: 16.25 - 7.92
what is the least common denominator for 5/6 and 3/8
F(x, y) = x2 + y2 + 4x − 4y, x2 + y2 ≤ 81 find the extreme values of f on the region described by the inequality.
The extreme values of a function are the minimum and the maximum values of the function.
The extreme values are: -8 and 131.91
The given parameters are:
[tex]\mathbf{F(x,y) = x^2 + y^2 + 4x - 4y}[/tex]
[tex]\mathbf{x^2 + y^2 \le 81}[/tex]
Find the gradient of F(x,y)
[tex]\mathbf{f_x(x) = 2x + 4}[/tex]
[tex]\mathbf{f_y(y) = 2y - 4}[/tex]
Set to 0, to solve for x and y
[tex]\mathbf{2x + 4 = 0}[/tex]
[tex]\mathbf{2x = -4}[/tex]
[tex]\mathbf{x = -2}[/tex]
[tex]\mathbf{2y - 4 = 0}[/tex]
[tex]\mathbf{2y = 4}[/tex]
[tex]\mathbf{y = 2}[/tex]
So, the critical point is:
[tex]\mathbf{(x,y) = (-2,2)}[/tex]
Also, we have: [tex]\mathbf{x^2 + y^2 \le 81}[/tex]
Calculate the gradients
[tex]\mathbf{g_x = 2x}[/tex]
[tex]\mathbf{g_y = 2y}[/tex]
Equate the gradients as follows:
[tex]\mathbf{f_x = \lambda \cdot g_x}[/tex]
[tex]\mathbf{f_y = \lambda \cdot g_y}[/tex]
So, we have:
[tex]\mathbf{2x + 4 = \lambda \cdot 2x}[/tex]
[tex]\mathbf{2y - 4 = \lambda \cdot 2y}[/tex]
Make [tex]\mathbf{\lambda}[/tex] the subject, in the above equations
[tex]\mathbf{\lambda = \frac{x + 2}{x}}[/tex]
[tex]\mathbf{\lambda = \frac{y - 2}{y}}[/tex]
Equate the above equations, so we have:
[tex]\mathbf{\frac{x + 2}{x} = \frac{y - 2}{y} }[/tex]
Cross multiply
[tex]\mathbf{xy + 2y = xy - 2x}[/tex]
Subtract xy from both sides
[tex]\mathbf{2y =- 2x}[/tex]
Divide both sides by 2
[tex]\mathbf{y =- x}[/tex]
Substitute [tex]\mathbf{y =- x}[/tex] in [tex]\mathbf{x^2 + y^2 = 81}[/tex]
[tex]\mathbf{x^2 + (-x)^2 = 81}[/tex]
[tex]\mathbf{x^2 + x^2 = 81}[/tex]
[tex]\mathbf{2x^2 = 81}[/tex]
Divide both sides by 2
[tex]\mathbf{x^2 = \frac{81}{2}}[/tex]
Take square roots
[tex]\mathbf{x = \±\frac{9}{\sqrt2}}[/tex]
Rationalize
[tex]\mathbf{x = \±\frac{9\sqrt2}{2}}[/tex]
Recall that: [tex]\mathbf{y =- x}[/tex]
So, we have:
[tex]\mathbf{y = \±\frac{9\sqrt2}{2}}[/tex]
The ordered pairs are:
[tex]\mathbf{(x,y) = \{(\frac{9\sqrt2}{2},-\frac{9\sqrt2}{2}),(-\frac{9\sqrt2}{2},\frac{9\sqrt2}{2})\}}[/tex]
Hence, the points are:
[tex]\mathbf{(x,y) = \{(-2,2),(\frac{9\sqrt2}{2},-\frac{9\sqrt2}{2}),(-\frac{9\sqrt2}{2},\frac{9\sqrt2}{2})\}}[/tex]
Substitute these values in [tex]\mathbf{F(x,y) = x^2 + y^2 + 4x - 4y}[/tex]
[tex]\mathbf{F(2,2) = (-2)^2 + 2^2 + 4(-2) - 4(2) =-8}[/tex]
[tex]\mathbf{F(\frac{9\sqrt2}{2},-\frac{9\sqrt2}{2}) = (\frac{9\sqrt2}{2})^2 + (-\frac{9\sqrt2}{2})^2 + 4(\frac{9\sqrt2}{2}) - 4(-\frac{9\sqrt2}{2}) =131.91}[/tex]
[tex]\mathbf{F(-\frac{9\sqrt2}{2},\frac{9\sqrt2}{2}) = (-\frac{9\sqrt2}{2})^2 + (\frac{9\sqrt2}{2})^2 + 4(-\frac{9\sqrt2}{2}) - 4(\frac{9\sqrt2}{2}) =30.09}[/tex]
Hence, the extreme values of the function are: -8 and 131.91
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Find the rate of change of the area of a square with respect to the length z , the diagonal of the square. what is the rate when z=2?
The rate of change of Area, A with respect to the diagonal length, z and the rate of change when z = 2 is :
[tex]\frac{dA}{dz} = z [/tex][tex]\frac{dA}{dz} = 2 \: when \: z = 2 [/tex]The area of a square is rated to its diagonal thus :
Area of square = ALength of diagonal = zThe relationship between Area and diagonal of a square is : [tex]A \: = 0.5 {z}^{2} [/tex]
The rate of change of area with respect to the length, z of the square's diagonal ;
This the first differential of Area with respect to z
[tex] \frac{dA}{dz} = 2(0.5)z \: = z[/tex]
Therefore, the rate of change of area, A with respect to the length, z of the diagonal is [tex]\frac{dA}{dz} = z [/tex]
The rate of change [tex]\frac{dA}{dz} [/tex] when z = 2 can be calculated thus :
Substitute z = 2 in the relation [tex]\frac{dA}{dz} = z [/tex]
Therefore, [tex]\frac{dA}{dz} = 2 [/tex]
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