Step-by-step explanation:
The question is not well written. Let us say the function given as expressed as;
f(x) = -1/x + 3/x⁴
f'(x) means we are to differentiate the function with respect to x;
Given f(x) = axⁿ
f'(x) = naxⁿ⁻¹
f(x) = -x⁻¹ + 3x⁻⁴
Applying the differentiation formula we will have;
f'(x) = -1(-x⁻²)+(-4)3x⁻⁴⁻¹
f'(x) = x⁻²-12x⁻⁵
Express as a fraction
f'(x) = 1/x²-12/x⁵
To get f'(4), we will have to substitute x = 4 into the resulting expression
f'(4) = 1/4²-12/4(5)
f'(4) = 1/16-12/20
f'(4) = 1/16-3/5
Find the LCM
f'(4) = (5-48)/80
f'(4) = -43/80
Note that the function used was assumed but the same method can be employed to any other functions.
hot air balloon is attached to the ground by a cable that is 200 meters long. The cable makes a 57° angle with the ground.
How many meters above the ground is the balloon if there is no slack in the cable? Round your answer to the nearest tenth of a meter
Answer:
Let C be the position of the meteorological station, B the position of the balloon and CB be the cable.
Let the height of the balloon from the ground be AB=hmetres.
In a right angled triangle ACB
BC
AB
=sin60
∘
⇒
200
h
=
2
3
since
sin60
∘
=
2
3
⇒h=200×
2
3
⇒h=100
3
∴h=100×1.732=173.2 since
3
=1.732
Hence, the height of the balloon above the ground is 173.2m
By inscribing the given information in a right triangle, we will see that the ballon is 167.7 meters above the ground.
Think in the situation as in a right triangle, you have a hypotenuse that is equal to the length of the cable, you know one angle of 57°, and the opposite cathetus to this angle represents the height at which the ballon is, this is what we want to find.
Using the relation:
sin(θ) = (opposite cathetus)/hypotenuse.
Where:
θ = 47°hypotenuse = 200mopposite cathetus = height.Replacing that we get:
sin(57°) = height/200m
sin(57°)*200m = height = 167.7m
So the balloon is 167.7 meters above the ground.
If you want to learn more, you can read:
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What is the slope of the line that passes through the points ( -4, 1) and ( -4, -10)?
(Brainliest for correct answer)
Answer:
the correct answer is x=-4
Step-by-step explanation:
x + y = 12
x - y = 10
What is the value of the x-determinant for the system shown?
-12
-22
-2
Answer:
Step-by-step explanation:
-22
If one angle of a set of supplementary angles measures 77°, then the other angle measures _____.
A.77
B.103
C.283
D.13
Answer:
B
Step-by-step explanation:
Supplementary angles sum to 180°
If one angle is 77°, then the other angle is
180° - 77° = 103° → B
I would have to say B
sandra colored 1/3 of her picture black, as shown. what percent of her picture did she color white
Under the answer choice D, it says The rectangles are similar
The correct answer is option D.
HURRY FAST! 50 pts. Any bad/wrong answers will be deleted by one of my moderator friends.
Answer:
21
Step-by-step explanation:
anything that is powered by 0 is 1 so 2 to the power of 0 is 1 times 13 which is 13, 13 added by 9 is 21
Hope this helps!
Leo took an Uber to get to football practice. Uber charged $1.25 per mile (m) and he gave the driver a $5.00 tip. If the total trip was $16.25, how many miles did he travel to football practice?
Answer:
9milesStep-by-step explanation:
Step one:
given data
we are told that the uber charges $1.25 per mile
and that Leo also gave a tip of $5
the function for the total charge is given as
y=mx+c
Step two:
we will use the notation m for the number of miles traveled
given that the total trip is $16.25
16.25=1.25m+5
solving for m we have
16.25-5=1.25m
11.25=1.25m
divide both sides by 1.25
m=11.25/1.25
m=9
So he travelled 9miles
are 35:40 and 21:24 equivalent?
Answer:
yes
Step-by-step explanation:
35:40=0.875
21:24=0.875
Answer:
No
Step-by-step explanation:
35 divided by 40 is 0.875 and 21 divided by 24 are 0.875. These are the same answer ( 0.875 = 0.875) so they are equivelent. Hope this helped! If it did, please mark me as brainliest! Thanks!
Justin wants to make a necklace with 72 beads. He knows that 12 beads
take up 4 inches of string, but the store only sells string by the centimeter.
How many centimeters should he buy? Explain. (Hint: 1inch = 2.54 cm) *
Answer:
60.96cm
Step-by-step explanation:
So if 12 beads=4 inches
72 beads=72 beads*4 inch
12 beads
That will give you 24inches. inch-cm multiply by 2.54cm
=60.96cm of rope
What is the y-intercept of y=
-3x
What is the measure of A, in degrees?
Answer:
Um... D
Step-by-step e xplanation:
One of these graphs is of a cubic function which one is it ?
please helpp help I will be grounded if I don't get all of my answers. I will give brainleist
Answer:
D is the answer
Step-by-step explanation:
:)
what is the slope of the line, (-6, -8) and (2, 8)?
Answer:
Your slope would be 2.
Step-by-step explanation:
To find the slope, you would need to use the formula: y2-y1/x2-x1
In this case, the equation would be 8-(-8)/2-(-6)
8 - (-8) = 16
2 - (-6) = 8
16/8 = 2
Slope: 2
According to a survey conducted by the Texas Free Press, 125 out of 500 people do not have internet access at their homes. What percent of the people surveyed do have internet access at their homes?
Answer:
Step-by-step explanation:
Take 125 and divide by 500 this equals 0.25 or 25%
Answer:
x=25
Step-by-step explanation:
[tex]\frac{125}{500} *\frac{x}{100}[/tex] this is just a typical percent equation
[tex]12500=500x[/tex] cross multiply
x=25 divide by 500 to get the answer
I don't understand proportional relationship can u help?
Answer: I’ll explain it in simpler terms for you. A proportional relationship is one in which two quantities vary directly with each other. Ratios are proportional if they represent the same relationship. One way to see if two ratios are proportional is to write them as fractions and then reduce them. If the reduced fractions are the same, your ratios are proportional. An example of a proportional relationship is simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error. Hope this helps! :D
Write the equation in slope-intercept form.
7x = 3y − 12
A. y=73x+4
B. 3y−7x=12
C. y−11=73(x−3)
D. y=37x+4
Step-by-step explanation:
this is my answer you should mind your own business
Question 1
Which of the following statements is NOT true?
Answer:
the bottom one
Step-by-step explanation:
They are both the same ab and bc but im not entirely sure
Because AB, AC, and BC describe the same line, we conclude that the last option is the false one.
Which of the statements is not true?On the graph, we can see a line that contains points A, B, and C.
Now we want to see which statement is false.
Now, because A, B, and C are on the same line, is trivial that:
AB, AC, and BC (these 3 lines) have the same slope, because these are 3 different names for the exact same line.
Then we can conclude that the incorrect statement is the last one.
If you want to learn more about lines:
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There are 16 sweets in a bowl.
4 of the sweets are blackcurrant.
5 of the sweets are lemon.
7 of the sweets are orange.
Anna, Ravi and Sam each take at random one sweet from the bowl.
Work out the probability that the 5 lemon sweets are still in the bowl.
Answer:
5
Step-by-step explanation:
Searches related to jay read 6 during the summer break he plans to read 5 books each month during the school year. Write the inequality he could use to find x the number of months after summer he will have read more than 50 books
Answer:
10
Step-by-step explanation:
The sum of two numbers a and b is 7 and the difference between them is 2. What is the value of a x b ? Give your answer as a mixed number in its simplest form.
Answer:
45/4
Step-by-step explanation:
We can interpret the question to have two equation which can be solve simultaneously
a+b=7------------(1)
a-b=2------------(2)
From eqn(2) make a subject of formula
a=2+b--------(3)
Substitute the (3) into eqn(1)
a+b=7------------(1)
2+b+b=7
2b=7-2
2b=5
b=5/2
From equation (3) substitute value of b to find a
a=2+b--------(3)
a= 2+5/2
a=9/2
Then What is the value of a x b ?
9/2× 5/2
=45/4
Answer:
11 1/4
Step-by-step explanation:
a+b=7
a-b=2
adding equations gives us 2a=9 so a= 9/2
b= 7- 9/2= 14-9/2=5/2
therefore a x b= 9/2 x 5/2 =45/4
45/4 in a mixed number is 11 1/4
What is the remainder when 73,847 is divided by 43? Enter your answer as a whole number in the box
Answer:
The Answer is 16.
Step-by-step explanation:
I took the test. I hope this helped! :)
The remainder when 73,847 is divided by 43 will be 16.
What is Division method?
Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.
For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
The mathematical expression is,
''73,847 is divided by 43''
Now,
Find the remainder when 73,847 is divided by 43 as;
43 ) 73,847 (1717
- 43
--------
308
- 301
-------
74
43
-------
317
- 301
------
16
Thus, The remainder when 73,847 is divided by 43 will be 16.
Learn more about the division method visit:
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P>.9 and it is found the statistic is 1.04 Test the claim with 5% significance level. is the test left right or two tailed and what is the p value
Complete Question
The alternative hypothesis is [tex]H_a : p > 0.9[/tex] and it is found the statistic is 1.04 Test the claim with 5% significance level. is the test left right or two tailed and what is the p value
Answer:
This a right tailed test
The p-value is p-value = 0.14917
Step-by-step explanation:
From the question we are told that
The alternative hypothesis is [tex]H_a : p > 0.9[/tex]
The test statistics is [tex]z = 1.04[/tex]
The level of significance is [tex]\alpha = 0.05[/tex]
Generally this a right tailed test because from the alternative hypothesis p > 0.9 i.e due to the greater than sign signifying that test will be focusing on the right tail of the normal curve
From the z table the area under the normal curve to the right corresponding to 1.04 is
P( Z> 1.04 ) = 0.14917
Generally the p-value is mathematically represented as
p-value = P( Z> 1.04 ) = 0.14917
What is 8.89 × 1010 in standard notation?
Answer:
8978.9
Step-by-step explanation:
MULTIPLY THE THE GIVEN AND
8.89 × 1010 = 8978.9
THEN THE RESULT WOUD BE THE STANDARD NOTATION.
Find the slope between the two points
Answer:
B. -2/7
Step-by-step explanation:
Rise over run. The graph also goes down so it is negative.
1.
At a movie theater, tickets cost $6 for students and $8 for adults. The theater sold $174. worth of tickets
today. The theater sold 24 tickets. How many student and adult tickets were sold?
HELP
A14 adaults 11 kids
Step-by-step explanation:
Answer: impossible.....
Step-by-step explanation:
PLZ ANSWER ASAP!!!!!!!!!!!!!!!!!!!!!!!!!
Answer: C
Step-by-step explanation: it is stretched out more.
Answer:
C
Step-by-step explanation:
C Is An Oval Not A Circle, Therefore it is different
Which hourly interval had the least rate of change?
Answer:
hour 3 to hour 4
Step-by-step explanation:
that is where the slope is the least steep
Choose the answer below that makes the following expression true:
108 ÷ ‒12
A.
9
B.
96
C.
‒9
D.
‒96
Answer:
-9.
Step-by-step explanation:
Write an equation of the line passing through the point (6, 3) that is perpendicular to the line 6x + 5y = 10
An equation of the line is
y=?
Answer:
[tex]y=\frac{5}{6}x-2[/tex]
Step-by-step explanation:
Let the equation of a line passing through a point [tex](x_1,y_1)[/tex] and slope [tex]m_1[/tex] is,
[tex]y-y_1=m_1(x-x_1)[/tex]
Equation of the second line has been given as,
6x + 5y = 10
Slope-intercept form of the equation will be,
5y = -6x + 10
y = [tex]-\frac{6}{5}x+10[/tex]
Here slope of the line [tex]m_2=-\frac{6}{5}[/tex]
If both the lines are perpendicular,
By the property of perpendicular lines,
[tex]m_1\times m_2=-1[/tex]
[tex]m_1\times (-\frac{6}{5})=-1[/tex]
[tex]m_1=\frac{5}{6}[/tex]
Therefore, equation of the line passing through (6, 3) and slope = [tex]\frac{5}{6}[/tex] will be,
y - 3 = [tex]\frac{5}{6}(x-6)[/tex]
y = [tex]\frac{5}{6}x-5+3[/tex]
[tex]y=\frac{5}{6}x-2[/tex]