Work Shown:
tan(angle) = opposite/adjacent
tan(x) = 13/101
x = arctan(13/101)
x = 7.334379 approximately
x = 7.33
How many meters are equal to 18 kilometers?
Answer:
18000
Step-by-step explanation:
The number of meters in 18 kilometers is 18,000 meters(m)
How to convert meters to kilometers1900 meter(m) = 1 kilometer(km)x meters = 18 kilometers
x meters = 18 kilometers × 1000
x = 18,000 meters
Therefore, 18 kilometers is equivalent to 18,000 meters
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A curve has equation y=4x^3 -3x+3. Find the coordinates of the two stationary points. Determine whether each of the stationary points is a maximum or a minimum.
Answer:
There are two stationary points
Local max = (-0.5, 4)Local min = (0.5, 2)Note that 1/2 = 0.5
==========================================================
How to get those answers:
Stationary points occur when the derivative is zero, when the graph is neither increasing nor decreasing (i.e. it's staying still at that snapshot in time).
Apply the derivative to get:
f(x) = 4x^3 - 3x + 3
f ' (x) = 12x^2 - 3
Then set it equal to zero and solve for x.
f ' (x) = 0
12x^2 - 3 = 0
12x^2 = 3
x^2 = 3/12
x^2 = 1/4
x = sqrt(1/4) or x = -sqrt(1/4)
x = 1/2 or x = -1/2
x = 0.5 or x = -0.5
----------------------
Let's do the first derivative test to help determine if we have local mins, local maxes, or neither.
Set up a sign chart as shown below. Note the three distinct regions A,B,C
A = numbers to the left of -0.5B = numbers between -0.5 and 0.5; excluding both endpointsC = numbers to the right of 0.5The values -0.5 and 0.5 are not in any of the three regions. They are the boundaries.
The reason why I split things into regions like this is to test each region individually. We'll plug in a representative x value into the f ' (x) function.
To start off, we'll check region A. Let's try something like x = -2
f ' (x) = 12x^2 - 3
f ' (-2) = 12(-2)^2 - 3
f ' (-2) = 45
The actual result doesn't matter. All we care about is whether if its positive or negative. In this case, f ' (x) > 0 when we're in region A. This tells us f(x) is increasing on the interval [tex]-\infty < x < -0.5[/tex]
Let's check region B. I'll try x = 0.
f ' (x) = 12x^2 - 3
f ' (0) = 12(0) - 3
f ' (0) = -3
The result is negative, so f ' (x) < 0 when [tex]-0.5 < x < 0.5[/tex]. The f(x) curve is decreasing on this interval.
The change from increasing to decreasing as we pass through x = -0.5 indicates that we have a local max here.
Plug x = -0.5 into the original function to find its paired y coordinate.
f(x) = 4x^3 - 3x + 3
f(-0.5) = 4(-0.5)^3 - 3(-0.5) + 3
f(-0.5) = 4
The point (-0.5, 4) is a stationary point. More specifically, it's a local max.
Side note: This is the same as the point (-1/2, 4) when written in fraction form.
----------------------
Let's check region C
I'll try x = 2
f ' (x) = 12x^2 - 3
f ' (2) = 12(2)^2 - 3
f ' (2) = 45
The positive outcome tells us that any number from region C does the same, and f ' (x) > 0 when [tex]0.5 < x < \infty[/tex]. The function f(x) is increasing on this interval.
Region B decreases while C increases. The change from decreasing to increasing indicates we have a local min when x = 0.5
Plug this x value into the original equation
f(x) = 4x^3 - 3x + 3
f(0.5) = 4(0.5)^3 - 3(0.5) + 3
f(0.5) = 2
The local min is located at (0.5, 2) which is the other stationary point.
The graph and sign chart are shown below.
The local min is located at (0.5, 2) which is the other stationary point.
How to Determine whether each of the stationary points is a maximum or a minimum?Stationary points occur when the derivative is zero, when the graph is neither increasing nor decreasing.
Apply the derivative to get:
f(x) = 4x^3 - 3x + 3
f ' (x) = 12x^2 - 3
Then set it equal to zero and solve for x.
f ' (x) = 0
12x^2 - 3 = 0
12x^2 = 3
x^2 = 3/12
x^2 = 1/4
x = 1/2 or x = -1/2
x = 0.5 or x = -0.5
The first derivative test to help determine if we have local mins, local maxes, or neither.
A = numbers to the left of -0.5
B = numbers between -0.5 and 0.5 excluding both endpoints
C = numbers to the right of 0.5
Thus, The values -0.5 and 0.5 are not in any of the three regions. They are the boundaries.
Let's try something like x = -2
f ' (x) = 12x^2 - 3
f ' (-2) = 12(-2)^2 - 3
f ' (-2) = 45
In this case, f ' (x) > 0 when we're in region A.
Let's check region B x = 0.
f ' (x) = 12x^2 - 3
f ' (0) = 12(0) - 3
f ' (0) = -3
The result is negative, so f ' (x) < 0 when f(x) curve is decreasing on this interval.
The change from increasing to decreasing as we pass through x = -0.5 indicates that we have a local max here.
Substitute x = -0.5 into the original function to find its paired y coordinate.
f(x) = 4x^3 - 3x + 3
f(-0.5) = 4(-0.5)^3 - 3(-0.5) + 3
f(-0.5) = 4
The point (-0.5, 4) is a stationary point, it's a local max.
Let's check region C x = 2
f ' (x) = 12x^2 - 3
f ' (2) = 12(2)^2 - 3
f ' (2) = 45
The positive outcome tells us that any number from region C does the same, and f ' (x) > 0 when The function f(x) is increasing on this interval.
Susbtitute this x value into the original equation
f(x) = 4x^3 - 3x + 3
f(0.5) = 4(0.5)^3 - 3(0.5) + 3
f(0.5) = 2
Hence, The local min is located at (0.5, 2) which is the other stationary point.
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A marketing research company is estimating which of two soft drinks college students prefer. A random sample of n college students produced the following 95% confidence interval for the proportion of college students who prefer drink A: (.262. .622). Identify the point estimate for estimating the true proportion of college students who prefer that drink.
A) .18
B) .622
C) .262
D) .442
===================================================
Explanation:
To get the point estimate, we average the endpoints of the given confidence interval. Add up the endpoints and divide by 2
(low+high)/2 = (0.262+0.622)/2 = 0.442
The value 0.442 is right in the middle of the confidence interval, so it's a natural point estimate for the population proportion.
--------------
Alternative Method:
Subtract the endpoints to find the confidence interval width
width = high - low = 0.622 - 0.262 = 0.36
Cut this in half to get the margin of error (MoE)
MoE = width/2 = 0.36/2 = 0.18
Then we can either add on the MoE to the low endpoint, or subtract it from the high endpoint, to land on the center
center = low + MoE = 0.262 + 0.18 = 0.442center = high - MoE = 0.622 - 0.18 = 0.442Solve for the value of X
Check the picture below.
Please help i rlly need itttt
Answer:
The value of x is the value where the line crosses the x-axis!
________________________________________________________
Hope this helps!!
Please tell me if I have made a mistake!!
I enjoy learning from them:)
Answer:
x = y - b/m (with the obvious restriction m ≠ 0 )
Step-by-step explanation:
If
y = mx + b
subtracting b from both sides
y - b = mx
dividing both sides by m
y - b/m = x
flipping the sides (to make it look more normal)
x = y - b/m
patsy can decorate 3 1/2 cupcakes in 1/4 hour at this rate how many cupcakes can patsy decorate in 1 hour
Answer:
14
Step-by-step explanation:
3.5 cupcakes can be done by 15 mn
X cupcakes can be done by 1 hour
35 ×60mn =15X
210 /15=X
X= 14
so 14 cupcakes will be done by an hour
g(-2) mathematics what’s the answer I’m on a time limit this is due tomorrow omggggg
Answer:
-2g
Step-by-step explanation:
Distribute G to -2
In simple words multiply G and -2
A shed has dimensions of 12m in length and 5 m in width. Both the length and
width are increased by the same amount in order to increase the floor area by
more than double the original area. What is the amount of the increase in length?
Answer:
Length = 24
Step-by-step explanation:
It says, " Both the length and width are increased by the same amount..." this means that both 12m and 5m were increased. So 12 + 12 = 24 and 5 + 5 = 10.
lol Looks like someone has the same math assignment as me
To increase the volume of a sphere, you
must in crease the radius
decrease the radius
None of the answer choices is correct
decrease the circumference
The volume of a sphere is directly proportional to the radius cube thus with an increase in the radius it will increase so option (A) is correct.
What is the sphere?A sphere is a 3D geometrical object which has a radius and becomes a point that revolves around a fixed point called the center.
For example, if you have a sphere of radius r then its surface area will be 4πr² and
The volume of a sphere with radius r is given as (4/3)πr³.
V ∝ r³
By increasing the radius r the volume V will rapidly increase.
Hence "Because the volume of a sphere is precisely proportional to the cube of its radius, it will grow as the radius grows".
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Pete grabbed 18 mixed nuts, StartFraction 2 Over 9 EndFraction of which were almonds. Which equation shows how to determine the number of almonds Pete grabbed?
18 divided by StartFraction 2 Over 9 EndFraction = 81
18 times StartFraction 2 Over 9 EndFraction = 4
StartFraction 2 Over 9 EndFraction divided by 18 = StartFraction 1 Over 81 EndFraction
StartFraction 9 Over 2 EndFraction divided by 18 = one-fourth
Answer:
18 times StartFraction 2 Over 9 EndFraction = 4
Amount of almonds = 18 × [2/9]
Amount of almonds = 4 almonds
Step-by-step explanation:
Given:
Number of mixed nuts = 18
Probability of almonds = 2/9
Find:
Amount of almonds
Computation:
Amount of almonds = Number of mixed nuts × Probability of almonds
Amount of almonds = 18 × [2/9]
Amount of almonds = 36 / 4
Amount of almonds = 4 almonds
Answer:
IT'S B I CAN CONFIRM BC I JUST FINISHED THE TEST
Step-by-step explanation:
triangle abc was dilated from the orgin by a scale factor of 2 to create triangle A’B’C’ which statement explains why the triangles are similar ?
Answer:ABC was dilated from the origin by a scale factor of 2 to create Delta A'B'C' . Which statement explains why the triangles are similar? Dilations preserve side length; therefore, the corresponding sides of Delta ABC and Delta A'B'C' are congruent.
Step-by-step explanation:Googel
Identify the x-intercept and y-intercept of the line 3x - 6y = – 12.
Answer:
x=32
Step-by-step explanation:
Your current salary is $30,900 per year. You’ve just accepted a new position at a company that’s to pay you $32,500 per year. How much more will you get per month at the new job? (Round your answer to the nearest dollar.)
Answer: $133
Explanation:
\cfrac{32\ 500 - 30\ 900}{12} = \$133
12
32 500−30 900
=$133
What is the answer to the question?? Is the answer even on there?
Answer:
D. $105,750
Step-by-step explanation:
Use the formula I=prt,which stands for "Interest equals principal × rate × time" The clue to use that formula was the phrase "simple interest" The principal is the original amount of the loan, $150,000.
The interest rate is the 3.7% or 4.2% but you MUST change these to a decimal to use them. So we'll be using .037 and .042 for these calculations. The time part of the equation is the 15 years or the 30 years. See image.
Select each equation which is equivalent to 60% of 25.
0.6 • 25 = x
x • 1.6 = 25
610=x25
60100=25x
x25=60100
6.0 • 25 = x
The equation which is equivalent to 60% of 25 are x • 1.6 = 25, 0.6 • 25 = x and x/25=60//100
Percentages can be expressed as decimals or fractions.
Given the expression 60% of 25, this can b expressed as:
60% of 25 = xwhere x is the result of the expression.
60/100 * 25 = xExpressing 60% as a decimal will give;
0.6 of 25 = x
0.6 * 25 = x
From the expression 60/100 * 25 = x, this can also be written as:
25 = 100/60 x
25 = 10/6 x
25 = 1.6x
Hence the equation which is equivalent to 60% of 25 are x • 1.6 = 25, 0.6 • 25 = x and x/25=60//100
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What is the average rate of change on the interval from 3 to 9?
Enter your answer in the grid below. Make sure your answer contain
Answer:
5
Step-by-step explanation:
Please answer this mathematical problem.
x = total amount of gumballs
let's start subtracting the balls she's giving away
[tex]\stackrel{total}{x}-\stackrel{\textit{to jaysen}}{\cfrac{x}{2}}\implies \stackrel{\textit{what's left}}{\cfrac{x}{2}}~\hfill \stackrel{\textit{half of what's left to Marinda}}{\cfrac{~~ \frac{x}{2}~~}{2}\implies \cfrac{x}{4}} \\\\\\ \stackrel{\textit{what was left minus Marinda's}}{\cfrac{x}{2}-\cfrac{x}{4}\implies \stackrel{\textit{what's left}}{\cfrac{x}{4}}}~\hfill ~\hfill \stackrel{\textit{a third of what's left to Zack}}{\cfrac{~~ \frac{x}{4}~~}{3}\implies \cfrac{x}{12}}[/tex]
[tex]\stackrel{\textit{what was left minus Zack's}}{\cfrac{x}{4}-\cfrac{x}{12}\implies \stackrel{\textit{what's left}}{\cfrac{x}{6}}}~\hfill \stackrel{\textit{her sister gets 5 balls of what's left}}{ \cfrac{x}{6}-5 }[/tex]
and we also know that after all that has been subtracted, she's only left with 5, so we can say that
[tex]\stackrel{\textit{what's finally left}}{\cfrac{x}{6}-5}~~ = ~~\stackrel{\textit{what's finally left}}{5}\implies \cfrac{x}{6}=10\implies \boxed{x = 60}[/tex]
An angle measures 26.9 degrees. What is its complement?
Answer:
63.1°
Step-by-step explanation:
Complementary angles sum 90°
90 - 26.9 = 63.1°
can someone plz help with this FAST
I WILL MARK BRAINLIEST
Answer:
Maria
Step-by-step explanation:
Sean - 2 minutes (1 mile/minute)
Maria - 4 minutes (0.5 miles/minute)
David - 3 minutes (1 mile/minute)
Carrie - 2 minutes (0.5 miles/minute)
please help ill mark brainliest
Answer:
I think it is 8
Step-by-step explanation:
sorry If I'm wrong
4. Tomas uses 12 gallons of water to prepare lemonade for a party. The lemonade recipe states that for every 2 quarts of water, he should add cup of lemon juice and cup 1 of sugar. How much lemon juice does Tomas need?
Answer:
Thomas will need 24 cups of lemon juice.
Step-by-step explanation:
There are 4 quarts in every gallon.
12 x 4 = 48
2 cups of lemon juice for every 2 quarts of water.
48 / 2 = 24
Hope This Helps!
Which equation is correct?
235 × 8 = 200 × 8 + 30 × 8 + 5
235 × 8 = 2,000 × 8 + 300 × 8 + 50 × 8
235 × 8 = 200 + 30 × 8 + 5 × 8
235 × 8 = 200 × 8 + 30 × 8 + 5 × 8
I LOVE YOUUU
The correct expression of 235 * 8 is 200 * 8 + 30 * 8 + 5 * 8
How to determine the correct expression?The product expression is given as:
235 * 8
Express 235 as place values
235 * 8 = (200 + 30 + 5) * 8
Expand the bracket
235 * 8 = 200 * 8 + 30 * 8 + 5 * 8
Hence, the correct expression of 235 * 8 is 200 * 8 + 30 * 8 + 5 * 8
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rewrite equation in slope - intercept form: (Solve for y)
2x-y=7
Answer:
y = 2x-7
Step-by-step explanation:
I'm not really sure this is the slope-intercept form, as I've never called it like that before, but if it is, there you go.
Answer:
[tex]\huge\boxed{\sf y = 2x - 7}[/tex]
Step-by-step explanation:
Given equation is:
2x - y = 7
Add y to both sides
2x = 7 + y
Invert the equation
7 + y = 2x
Subtract 7 to both sides
y = 2x - 7
This is the required equation in slope-intercept form y = mx + b where m is slope and b is y-intercept.
[tex]\rule[225]{225}{2}[/tex]
Hope this helped!
~AH1807are Proportional and non-proportional equations are all linear.
Proportional and linear functions are very similar. The only difference is the addition of the “b” constant to the linear function. A proportional relationship is just a linear relationship where B = 0, or where the line passes through the origin (0, 0).
Determine whether each sequence is arithmetic, geometric or neither. Explain.
200, 40, 8,...
Answer:
Geometric
Step-by-step explanation:
The ratios of the terms are constant
I can write an equation
Answer:
Step-by-step explanation:
y = mx + b
slope m is found as the change in y over the change in x
as y decreases 3 units for a 3 unit increase in x, the slope is -3/3 = -1
The y intercept b is where the plot crosses the y axis, 4 units above the x axis
y = -1x + 4
or
y = 4 - x
Okie I need help I don’t understand thank you
Answer:
12
Step-by-step explanation:
8x+4x = 12x
-3+3= 0
12x+0=180
x=180/12
x=15
Is the inequality 5-x^2<4 true for x=1?
5 - x² < 4
- x² < 4 - 5
- x² < - 1
=》x² < 1
Now, let's check with x = 1
x² < 1
(1)² < 1
1 < 1
1 is not less than or greater than 1. They are equals. So, the inequality 5 - x² < 4 is NOT true for x = 1.
_____
Hope it helps ⚜
PLEASE HELP ME WITH THIS! I NEED TO PASS THIS ASAP
Answer:
The Y-Int. is 60
Step-by-step explanation:
0 marks the x axis, which leads me to believe 60 is the Y-int so (0,60)
Extended Problems, Extraneous Solutions
I need help asap please, this is due in 1 day!
100 POINTS
Answer:
1a. 2 is the solution
1b. -3 is because square root of 1 doesn't equal -1.
1c.-3
Step-by-step explanation:
1.
[tex](x + 2 = \sqrt{3x + 10} [/tex]
Square both sides
[tex](x + 2) {}^{2} = 3x + 10[/tex]
Remeber perfect square Rule
[tex](x + y) {}^{2} = {x}^{2} + 2xy + {y}^{2} [/tex]
So now we got
[tex]x {}^{2} + 4x + 4 = 3x + 10[/tex]
[tex] {x}^{2} + x + 4 = 10[/tex]
[tex] {x}^{2} + x - 6 = 0[/tex]
Factor into binomial.
[tex](x + 3)(x - 2) = 0[/tex]
So our solution is 3 or 2. However, let's check our work.
[tex] - 3 + 2 = \sqrt{3( - 3) + 10} [/tex]
[tex] - 1 = \sqrt{1} [/tex]
However square root of 1 is 1. It could be 1 but in Math, We only take the principal square root which is positive always. So -3 isn't a solution.
So let try 2.
[tex]2 + 2 = \sqrt{3(2) + 10} = 4 = \sqrt{16} = 4 = 4[/tex]
So this is indeed the solution.
Make up equation for 2 and 3. Ask me if you need help.
