Answer:
For two rectangles to be similar, their sides have to be proportional (form equal ratios). The ratio of the two longer sides should equal the ratio of the two shorter sides.
Step-by-step explanation:
Show that f '(x) = g'(x) for all x in their domains. Can we conclude from the corollary below that f − g is constant? If f '(x) = g'(x) for all x in an interval (a, b), then f − g is constant on (a, b); that is, f(x) = g(x) + c where c is a constant.
Answer:
Answer: 15 cm
Step-by-step explanation:
The derivative of a function at a point can be defined as its slope at that point. For f'(x) = g'(x) in the interval (a,b), it is proved that f - g is constant in (a,b).
What is a Derivative?A derivative of a function is its rate change of increase or decrease in a given interval with respect to its variable. Derivative of a constant function is always zero.
Given that, f'(x) = g'(x) for all x.
Taking integral on both sides
f(x) + C₁ = g(x) + C₂
=> f(x) - g(x) = C₂ - C₁
=> f(x) - g(x) = C
Thus, f(x) - g(x) is constant is proved.
Similarly for interval an interval (a,b),
f(x) - g(x) = C
=> f(x)= g(x) + C
Hence, it is proved that in an interval (a,b), if f'(x) = g'(x) then f(x)= g(x) + C.
To know more about Derivative click on the following link
https://brainly.com/question/9964510
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. A right cylindrical drum is to hold 7.35 cubic feet of liquid. Find the dimensions (radius of the base and height) of the drum which would minimize the surface area. What is the minimum surface area
Answer:
[tex]r=1.05\ \text{ft}[/tex]
[tex]h=2.12\ \text{ft}[/tex]
[tex]20.91\ \text{ft}^3[/tex]
Step-by-step explanation:
r = Radius
h = Height
Volume of cylinder = [tex]7.35\ \text{ft}^3[/tex]
[tex]V=\pi r^2h\\\Rightarrow h=\dfrac{V}{\pi r^2}\\\Rightarrow h=\dfrac{7.35}{\pi r^2}[/tex]
Surface area is given by
[tex]A=2\pi r^2+2\pi rh\\\Rightarrow A=2\pi r^2+2\pi r\dfrac{7.35}{\pi r^2}\\\Rightarrow A=2\pi r^2+\dfrac{14.7}{r}[/tex]
Differentiating with respect to radius we get
[tex]\dfrac{dA}{dr}=4\pi r-\dfrac{14.7}{r^2}[/tex]
Equating with zero we get
[tex]0=4\pi r-\dfrac{14.7}{r^2}\\\Rightarrow 4\pi r=\dfrac{14.7}{r^2}\\\Rightarrow r^3=\dfrac{14.7}{4\pi}\\\Rightarrow r=(\dfrac{14.7}{4\pi})^{\dfrac{1}{3}}\\\Rightarrow r=1.05[/tex]
[tex]\dfrac{d^2A}{dr^2}=4\pi-2\times \dfrac{14.7}{r^3}\\\Rightarrow \dfrac{d^2A}{dr^2}=4\pi+2\times \dfrac{14.7}{1.05^3}\\\Rightarrow \dfrac{d^2A}{dr^2}=37.96>0[/tex]
So, the value of the function is minimum at [tex]r=1.05[/tex]
[tex]h=\dfrac{7.35}{\pi r^2}=\dfrac{7.35}{\pi 1.05^2}\\\Rightarrow h=2.12[/tex]
So, the radius and height which would minimize the surface area is 1.05 feet and 2.12 feet respectively.
Surface area
[tex]A=2\pi r^2+2\pi rh\\\Rightarrow A=2\pi \times 1.05^2+2\pi 1.05\times 2.12\\\Rightarrow A=20.91\ \text{ft}^3[/tex]
The minimum surface area is [tex]20.91\ \text{ft}^3[/tex].
What is the product of 14/5
Answer:
2.8
Step-by-step explanation:
Just divide and get the answer
WILL GIVE BRAINLIEST!!
Ignore the $
Meyer rolls two fair, ordinary dice with the numbers $1,2,3,4,5,6$ on their sides. What is the probability that at least one of the dice shows a square number?
Two numbers on each die are squares: 1 and 4. 4 numbers on each die are not squares: 2 , 3, 5, and 6. there are 16 ways for him to roll a non-square die, out of 36 outcomes for the pair of dice. The other 20 options each have a square number showing on one or both dice. So, the probability is 5/9. hope this helps please pick my answer as brainliest, have a good day!
Which graph represents the function fx) =|x–4?
The image below shows the graph f(x) = |x| – 4
Hope this helps! :)
What restriction should be applied to y = tanx for y = arctanx to be defined?
Answer:
restrict the domain to (-pi/2, pi/2)
Step-by-step explanation:
edge 2020
Answer: c. restrict the domain to (-pi/2, pi/2)
Step-by-step explanation:
Edge :)
A triangular plot of land has sides of lengths 420 feet, 330 feet, and 180 feet. Approximate the smallest angle between the sides. The choices are rounded to the nearest degree.
A. 30 degree
B. 27 degree
C. 22 degree
D. 24 degree
Answer:
D. 24 degree
Step-by-step explanation:
Sides of the triangle are
a = 330 ft
b = 180 ft
c = 420 ft
From cosine rule we have
[tex]\angle A=\cos^{-1}(\dfrac{b^2+c^2-a^2}{2bc})\\ =\cos^{-1}(\dfrac{180^2+420^2-330^2}{2\times180\times 420})\\ =48.65^{\circ}[/tex]
[tex]\angle B=\cos^{-1}(\dfrac{a^2+c^2-b^2}{2ac})\\ =\cos^{-1}(\dfrac{330^2+420^2-180^2}{2\times 330\times 420})\\ =24.17^{\circ}[/tex]
[tex]\angle C=\cos^{-1}(\dfrac{a^2+b^2-c^2}{2ab})\\ =\cos^{-1}(\dfrac{330^2+180^2-420^2}{2\times 330\times 180})\\ =107.19^{\circ}[/tex]
The smallest angle in the triangle is [tex]\angle B=24.17^{\circ}[/tex].
Look at my picture, what’s the missing statement in step 4?
Answer:
Step-by-step explanation:
∠ACE=∠ BCD (reflexive property )
It is common to both the angles or both the angles represent the same angle.
We have to prove two triangles are similar.
Here we show two angles of different triangles are equal.
Hence similar by AA
Answer:
m<CBD is congruent to m<DBC
Step-by-step explanation:
Reflexive property states that any real number, for example a, is equal to itself. < cbd is congruent to < dbc :)
IF THE RATIO IN A VALENTINE'S
DAY CANDY BOX OF MILK TO DARK
CHOCOLATES IS 23. HOW MANY
DARK CHOCOLATES ARE THERE IF
THERE ARE 8 MILK CHOCOLATES?
Answer:
12 dark chocolates
Step-by-step explanation:
Let there are 2x milk chocolates and 3x dark chocolates.
Total no of milk chocolates = 8
ATQ,
2x = 8
x = 4
Dark chocolates = 3x
= 3(4)
= 12
Hence, there are 12 dark chocolates.
Kameron who is 4.5 feet tall , is outside during recess
Answer: I'm not sure i understand. Are you asking a question or is this just a statement
Step-by-step explanation:
Suppose that the functions q and r are defined as follows.
q (x)=–2x+1
r(x) = 2x²+2
Find the following.
(r og)(-1) = 0
0/6
Х
(q or)(-1) = 0
5
?
Answer:
(r o q)(-1) = 20
(q o r)(-1) = -11
Step-by-step explanation:
Given
[tex]q(x) = -2x + 1[/tex]
[tex]r(x) = 2x^2 + 2[/tex]
Solving (a): (r o q)(-1)
In function:
(r o q)(x) = r(q(x))
So, first we calculate q(-1)
[tex]q(x) = -2x + 1[/tex]
[tex]q(-1) = -2(-1) + 1[/tex]
[tex]q(-1) = 2 + 1[/tex]
[tex]q(-1) = 3[/tex]
Next, we calculate r(q(-1))
Substitute 3 for q(-1)in r(q(-1))
r(q(-1)) = r(3)
This gives:
[tex]r(x) = 2x^2 + 2[/tex]
[tex]r(3) = 2(3)^2 + 2[/tex]
[tex]r(-1) = 2*9 + 2[/tex]
[tex]r(-1) = 20[/tex]
Hence:
(r o q)(-1) = 20
Solving (b): (q o r)(-1)
So, first we calculate r(-1)
[tex]r(x) = 2x^2 + 2[/tex]
[tex]r(-1) = 2(-1)^2 + 2[/tex]
[tex]r(-1) = 2*1 + 2[/tex]
[tex]r(-1) = 6\\[/tex]
Next, we calculate r(q(-1))
Substitute 6 for r(-1)in q(r(-1))
q(r(-1)) = q(6)
[tex]q(x) = -2x + 1[/tex]
[tex]q(6) = -2(6) + 1[/tex]
[tex]q(6) =- 12 + 1[/tex]
[tex]q(6) = -11[/tex]
Hence:
(q o r)(-1) = -11
please HURRY IM ON A QUIZ
if 2 is substituted for x, which expression will NOT equal 5?
Answer:
It will be 2x -1
If x=2
2*2 - 1 = 4 - 1 = 3
Step-by-step explanation:
7 - x If x=2
7 - 2 = 5
11 - 3x If x=2
11 - 3*2 = 11 - 6 = 5
2x -1 If x=2
2*2 - 1 = 4 - 1 = 3
4x - 3 If x=2
4*2 - 3 = 8 - 3 = 5
What is the area of this rectangle?
2.5 m
2 m
Answer:
5
Step-by-step explanation:
tan 3( ) tan 3 lim
h
xh x
® h
Answer:
27
Step-by-step explanation:
know that
h = 3
h × h × h
3 × 3 × 3
= 27
82,77,72,67 find the sequince
Answer:
Subtract 5 as you go along the pattern.
82-5=77-5=72-5=67...
Step-by-step explanation:
Which points are 19 units apart?
○(-14, 12) and (5, 12)
○(-5, 19) and (-12, 19)
○(-20, 5) and (5, 12)
○(14, 12) and (5, 12)
Answer:
(20,5) and (5,12) I think
Answer:
A:(–14, 12) and (5, 12)
Step-by-step explanation:
Trust me on this, also can I have brainiest please?
Hope you do well! :D
Joe collects Pokemon cards. He already has 100 and buys a dozen more each week when he goes to the store. Jessica also collects Pokemon cards. She has 130 cards, and buys 6 more each week at the store.After how many weeks would the two kids have the same amount of cards?
Answer:
5 weeks
Step-by-step explanation:
To find the answer to this question we have to write an equation for both situation and put them equal to each other.
Let's write an equation for Joe:
12x + 100
Now, for Jessica
6x + 130
Next, put them equal to each other:
12x + 100 = 6x + 130
Solve:
12x + 100 = 6x + 130
6x + 100 = 130
6x = 30
x = 5
Therefore, it will take 5 weeks for Joe and Jessica to have the same amount of cards.
Check:
12(5) + 100 = 6(5) + 130
60 + 100 = 30 + 130
160 = 160
I hope this helps!!
- Kay :)
What angle would you use to represent 40 red cars out of 90 cars in total on a pie chart?
. 40 degree
. 4 degree
. 160 degree
90 degree
Answer:
4
Step-by-step explanation:
i just know I took the test and I choose 90 and got it wrong
Stephen's lunch bill is currently at $843. Stephen orders a fruit salad for take out and wants to leave
$2.25 as a tip for his server. He has a $10 bill and a $5 bill. How much change should he receive after
paying for his lunch, the fruit salad, and the tip?
Answer:
1.63
Step-by-step explanation:
Edwin has 50$ in his bank.He starts spending $3 each week on snacks at lunch. how many weeks will edwin run out of money?
Together, teammates Pedro and Ricky got 2678 base hits last season. Pedro had 282 more hits than Ricky. How many hits did each player have?
Answer:
pedro- 1621
ricky- 1057
Step-by-step explanation:
what is the estimate of 29 x 688
Answer:
19952 :)
Step-by-step explanation:
Step-by-step explanation:
29 turns to 30
688 turns to 700
30×700=21000
Graph the solution set for the inequalíty
y> 2x-5 by following these steps:
Step 1: ldentify the slope and y-intercept.
slope = y-intercept =
Please help me
Answer:
Slope= 2
Y-intercept= -5
Step-by-step explanation:
This inequality is in slope-intercept form which means we can get both striaght from the inequaltiy. Slope-intercept form is y=mx+b, where m is the slope and b is the y-intercept. In this inequality m would be 2 and b would be -5, so those are your answers.
What error did Wanda make?
None. Wanda’s work is correct.
Wanda converted the percent to a decimal incorrectly. It should be 0.073.
Wanda converted the percent to a decimal incorrectly. It should be 0.73.
Wanda has the wrong label. It should be hours, not dollars.
Answer:
C
Step-by-step explanation:
the guy above sucks
None. Wanda’s work is correct.
Wanda converted the percent to a decimal incorrectly. It should be 0.073.
Wanda converted the percent to a decimal incorrectly. It should be 0.73.
Wanda has the wrong label. It should be hours, not dollars.
Step-by-step explanation:
Y’all I need this by midnight what is 9/10 + 3/5 please and thank you
Answer:
12/15
Step-by-step explanation:
Answer:
I hope this helps you
Step-by-step explanation:
9/10 + 3/5
= LCM of 10 and 5 =10
= 9/10 + 6/10
= 9+6/10
= 15/10 = 3/2 = 1.5
Max purchased a solar pool cover for his swimming pool. What is the area of the
solar cover for the swimming pool?
10ft
32 ft
Square Feet
Answer:
320 ft^2
Step-by-step explanation:
what variable is used to represent SLOPE?
Answer:
M is used to represent the slope.
Step-by-step explanation:
Y = MX + C
Answer:
m is used to represent the slope
Step-by-step explanation:
y=mx+b
Find an equation of the line that passes through the pair of points (-5, -9) and (2,-7)
Answer:
y=0.3x - 7.6
Step-by-step explanation:
line: y=ax+b
a= Δy ÷ Δx
a= (-9 + 7) ÷ (-5 - 2)
a= -2 ÷ -7 = approximately 0.3
y=0.3x + b
Now you can fill in one of the points to find b (or both to make sure you got the answer right).
0.3 × 2 + b = -7
0.6 + b = -7
b = -7 - 0.6 = approximately -7.6
So: an equation of the line that passes through this pair of points is y=0.3x - 7.6
On a test, i would write as many decimals as possible if not said not to, to get the most exact answer. Also remember to keep calculating with the number on your calculator and not to round them off for the most exact answer.
the length of a rectangle is 8 centimeters. what is the width?
Answer:
This is a very vague question. We can't find out the width if it doesn't tell us the area. Comment on my answer the area and I can help.
what is (7/4x)+(-3/2y) simplified
Answer:
0.25(7x-6y)
Step-by-step explanation: