The idea is to use the tangent line to [tex]f(x)=\sqrt x[/tex] at [tex]x=25[/tex] in order to approximate [tex]f(25.3)=\sqrt{25.3}[/tex].
We have
[tex]f(x)=\sqrt x\implies f(25)=\sqrt{25}=5[/tex]
[tex]f'(x)=\dfrac1{2\sqrt x}\implies f'(25)=\dfrac1{10}[/tex]
so the linear approximation to [tex]f(x)[/tex] is
[tex]L(x)=f(5)+f'(5)(x-5)=5+\dfrac{x-5}{10}=\dfrac x{10}+\dfrac92[/tex]
Hence [tex]m=\frac1{10}[/tex] and [tex]b=\frac92[/tex].
Then
[tex]f(25.3)\approx L(25.3)=\dfrac{25.3}{10}+\dfrac92=\boxed{7.03}[/tex]
An old coin had a value of $840 in 1991
and $1160 in 1999. Find the slope of the line through
the points at (1991, 840) and (1999, 1160). What does
this slope represent?
A student standing on top of a building sees a bird flying that is 25ft away and 20 ft above the top of the building. The student also sees a car on the ground at and angle of depression 70°. The car is directly below the flying bird.A diagram of the situation is shown below
Answer: The height of the building is 41.2 ft
Step-by-step explanation:
Here we want to find the height of the building.
To do so, the first step is to find the horizontal distance between the student and the car/bird (which represents the common cathetus between the two triangle rectangles).
For the top triangle rectangle, we know one cathetus and the hypotenuse, and we can use the Pythagorean's theorem to find the other cathetus.
A^2 + B^2 = H^2
Where A and B are the cathetus, and H is the hypotenuse.
Then we have:
20^2 + B^2 = 25^2
B^2 = 25^2 - 20^2
B = √( 25^2 - 20^2) = 15
Then the horizontal distance between the student and the car is 15ft, and we also know the angle at which this cathetus is adjacent, the angle is 70°.
Then we can use the relationship:
Tan(A) = (opposite cathetus)/(adjacent cathetus)
Where the opposite cathetus woud be the height of the building, then:
Tan(70°) = H/15ft
Tan(70°)*15ft = H = 41.2 ft
Consider the line y = 2/3x-4
A line parallel to the graph of the line would have a slope of
A line perpendicular to the graph of the line would have a slope of
Answer:
For the parallel line it will still have a slpoe of 2/3
Step-by-step explanation:
as for the perpendicular line it will be double like 4/6 so it can meet it at a 90° angle.
a surf instructor has an initial fee of $12 and charges $8 per hour for lessons. Write a linear equation that represents the total cost of surf lessons after a certain number of hours
y = total cost
x = # of hours
$12 + $8x = y
Answer:
the answer is y=8x=12
Step-by-step explanation:
when 54 is divided by a number, the quotient is 9 and leaves no remainder. what is thr number?
Answer:
6 will the number......
14.
(3.6 x 108)
(1.2 x 104)
Scientific notation
Answer:
[tex]3.6 * 10^8 = 360000000[/tex]
[tex]1.2 * 10^4 = 12000[/tex]
Step-by-step explanation:
Given
[tex]3.6 * 10^8[/tex]
[tex]1.2 * 10^4[/tex]
Required
Solve
[tex]3.6 * 10^8[/tex]
Express [tex]10^8[/tex] as 100000000
[tex]3.6 * 10^8 = 3.6 * 100000000[/tex]
[tex]3.6 * 10^8 = 360000000[/tex]
[tex]1.2 * 10^4[/tex]
Express [tex]10^4[/tex] as 10000
[tex]1.2 * 10^4 = 1.2 * 10000[/tex]
[tex]1.2 * 10^4 = 12000[/tex]
Metal mercury at room temperature is a liquid. Its melting point is -39°C. The freezing point of alcohol is-114°C. How much warmer is the melting point of mercury than the freezing point of alcohol?
My dog, Crash, can run 2/3 of a mile in 7 minutes. How many minutes does it take him to run one mile.
Answer:
10 1/2 minutes
Step-by-step explanation:
Becuase 7/2=3.5 then 7+3.5=10.5
please help fast:(((
3-(6x-5)+2= -5(6x+2)
Solve for x
Answer:
x
=
−
v
3
24
−
17
24
Step-by-step explanation:
What is the equation of the line if slope is -2 and y-int is 9
Answer:
y = -2x + 9
Step-by-step explanation:
Let's start from the -2x, the slope is -2. The x is basically what says, this is the slope. The plus nine is the y-intercept. If you think in graph terms (which is how you solve this problem) you will see that on the y-axis the line will intercept at the 9. The every x integer it goes down it goes that times two. For example, if you go sideways 1 spot, the line will be at y=11.
Find the area of the circle.
Use 3.14 for T.
A = r2
13 cm
Give your answer to the nearest hundredth.
A = [?] cm?
Enter
Answer:
530.66 square cm
Step-by-step explanation:
Area of the circle
[tex] = \pi {r}^{2} \\ = 3.14 \times {13}^{2} \\ = 3.14 \times 169 \\ = 530.66 \: {cm}^{2} \\ [/tex]
If a card is chosen from a standard
deck of cards, what is the probability
of getting a five or a seven?
Answer:
5/52 for getting a 5
7/52 for getting a 7
Answer:
Step-by-step explanation:
52 cards in a standard deck. Four 5's and four 7's.
4/52 = 5
4/52 = 7
4/52+4/52= 2/13
2/13 as a percent is 15.384615384615%
that simplified is 15.4%
or just 15%
:) Hope that helped.
help me, i really needd help i’m desperate!!!!
Answer:
10.5 wait can it be a decimal
Step-by-step explanation:
find the exact area of the octagon. show your reasoning?
What is 100x2 help me pease
Answer: 200
Step-by-step explanation:
anything times 2 is just doubled
ACTIVITY RESULTS
Select the letter of the correct answer.
Suppose a Hispanic Heritage festival is held in a park that is 58 yards long and 43 yards wide.
What is the diagonal length of the festival'area? Round your answer to the nearest tenth of a
yard
Hint
A 72.2 yards
B 72.0 yards
C 72.1 yards
D 72.3 yards
E
Submit
Pu
Answer:
[tex]D = 72.2\ yd[/tex]
Step-by-step explanation:
Given
[tex]Length\ (L)= 58\ yd[/tex]
[tex]Width \ (W)= 43\ yd[/tex]
Required
Determine the diagonal (D)
The relationship between D, L and W can be gotten using Pythagoras Theorem:
[tex]D^2 = L^2 + W^2[/tex]
Substitute values for L and W
[tex]D^2 = 58^2 + 43^2[/tex]
[tex]D^2 = 3364 + 1849[/tex]
[tex]D^2 = 5213[/tex]
Take Square root of both sides
[tex]D = \sqrt{5213}[/tex]
[tex]D = 72.2011080247[/tex]
[tex]D = 72.2\ yd[/tex] (Approximated)
find x so that q parallel r
Answer: x = 7
Step-by-step explanation:
Corresponding angles have congruent measures. Thus, 11x - 2 = 75
11x - 2 = 75
11x = 77
x = 7
Use the graph to describe the type and number of solutions
Answer:
the x entecepts of a graph are the solutions of the equation,
a quadratic equation can have one of three types of solutions
Find the equation of the line with slope -2 which goes through the point (-6,-9).
The equation of the line with slope -2 which goes through the point (-6,-9) is y=-2x-21.
What is the equation of a line?The general equation of a straight line is y=mx+c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis.
Given that, the line with slope -2 which goes through the point (-6,-9).
Substitute m=-2 and (x, y)=(-6,-9) in y=mx+c, we get
-9=-2×(-6)+c
-9=12+c
c=-21
Substitute m=-2 and c=-21 in y=mx+c, we get
y=-2x-21
Therefore, the equation of the line with slope -2 which goes through the point (-6,-9) is y=-2x-21.
To learn more about the the equation of a line visit:
https://brainly.com/question/2564656.
#SPJ2
sion 5(7 - 4)2 + 3+ 11.
Answer:
44
Step-by-step explanation:
use the order of operations
5 (3) 2 + 3 + 11. solve within parenthesis
15 × 2 + 3 + 11. multiply left to right
30 + 3 + 11. multiply left to right
33 + 11. add left to right
44. add
the order of operations is more commonly known as PEMDAS.
(parenthesis, exponents, multiply and divide, add and subtract)
If you are still confused there is a Brain Pop about PEMDAS. just search "order of operations" on the brain pop website
16 = (16 – 4 X 2) =
Answer:
False
Step-by-step explanation:
PEMDAS is your order of operations, so you would do the multiplication in the parenthesis first.
[tex](16-4*2) = (16-8) = 8[/tex]
16 isn't equal to 8 so the answer would be false.
Answer:8
Step-by-step explanation:4 times 2=8 so 16-8=8
What is m∠PTQ???????????
Answer:
m∠PTQ = 40°
Step-by-step explanation:
From the picture attached,
Two lines PS and RQ are intersecting each other at a point T.
Vertical angles formed at the point of intersection T will be equal in measure.
m∠PTQ = m∠STR and m∠PTR = m∠QTS
Therefore, (x + 28)° = (2x + 16)°
28 - 16 = 2x - x
12 = x
m∠PTQ = (x + 28)°
= 12 + 28
= 40°
Therefore, measure of angle PTQ is 40°.
f(a) = 2a - 1
g(a) = 4a
- 1
Find f(a) + g(a)
Answer:
[tex]f(a)+g(a)=6a-2[/tex]
Step-by-step explanation:
So we have the two functions:
[tex]f(a)=2a-1\text{ and } g(a)=4a-1[/tex]
And we want to find f(a) + g(a).
So, substitute:
[tex]f(a)+g(a)[/tex]
This is the same as:
[tex]=(2a-1)+(4a-1)[/tex]
Combine like terms:
[tex]=(2a+4a)+(-1-1)[/tex]
Add or subtract:
[tex]=6a-2[/tex]
And we're done!
Find the missing side length.
Assume that all intersecting sides meet at right angles.
Be sure to include the correct unit in your answer.
Answer:
The missing side length is 5 cm
Step-by-step explanation:
We see that 4cm is on the top and 9 cm is on the bottom.
All we need to do is subtract 4 from 9
9-4=5
The missing side length is 5 cm
Hope this helps! Plz award Brainliest : )
Bill works for a company that makes candy bars. Bill's job is to pack 10 candy
bars in every box. Bill then places 12 boxes in a shipping carton. Each carton
shipped contains how many candy bars?
Answer:
120 bars
Step-by-step explanation:
If Bill packs 10 candy bars in every box and there are 12 boxes in every shipping carton, then that would mean there are 12 sets of 10 candy bars. Meaning that you would multiply 10 by 12 since there are 12 boxes and 10 candy bars in each box (which would give you 120).
Jim had 360 stamps he sold 1/3 of them on Monday and 1/4 of the remainder on Tuesday how many stamps did he sell on Tuesday
Answer:
60
Step-by-step explanation:
Since Jim sold 1/3 of his stamps on Monday, the remainder would be 2/3 of his total stamps.
Divide 360 stamps by 3. Minus the stamps sold on Monday from 360 to get the remainder.
stamps sold on Monday = 360 ÷ 3 = 120
remainder = 360 - 120 = 240
He sold 1/4 of the remainder on Tuesday.
Divide the remainder by 4.
stamps sold on Tuesday = 240 ÷ 4 = 60
He sold 60 stamps on Tuesday.
Can you fill in what (m, n)=?
Answer:
Write an equation to model the given context. Give your answer in simplest form.
The total for a pair of socks with a 15% sales tax.
The original price of an item less a discount of 5%.
Step-by-step explanation:
hhh cc to me the answer to this
Help PLzzzzzzzzzzz
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Answer:
-18 bvhbdhbgdjd
Step-by-step explanation:
fgjfgfkgkdfhgkjdvn cjkvb
makes sense mostly if you know this algorithm
John and Maria solved the same equation using two different methods.
Compare and contrast John and Maria’s methods. Explain how they arrived at the same solution.
Answer:
John's steps
-distrubute the 2 through the parentheseas
-subtract 18-12
-subtract 10 on both sides
-divide both sides of the equation by 2
-y=-2
Marias steps
-divide both sides by 2
-subtract both sides by -5
-y=-2
Step-by-step explanation:
all you had to do is list the steps out. Hope this helps
