Answer:
The rate of decrease is: [tex]43.2mm^3/min[/tex]
Step-by-step explanation:
Given
[tex]l = 18mm[/tex]
[tex]\frac{dl}{dt} = -0.8mm/min[/tex] ---- We used minus because the rate is decreasing
Required
Rate of decrease when: [tex]l = 18mm[/tex]
The volume of the cube is:
[tex]V = l^3[/tex]
Differentiate
[tex]\frac{dV}{dl} = 3l^2[/tex]
Make dV the subject
[tex]dV = 3l^2 \cdot dl[/tex]
Divide both sides by dt
[tex]\frac{dV}{dt} = 3l^2 \cdot \frac{dl}{dt}[/tex]
Given that: [tex]l = 18mm[/tex] and [tex]\frac{dl}{dt} = -0.8mm/min[/tex]
[tex]\frac{dV}{dt} = 3 * (18mm)^2 * (-0.8mm/min)[/tex]
[tex]\frac{dV}{dt} = 3 * 18 *-0.8mm^3/min[/tex]
[tex]\frac{dV}{dt} = -43.2mm^3/min[/tex]
Hence, the rate of decrease is: 43.2mm^3/min
The sum of two numbers in 106 and the greater exceeds the lesser in 8. Find the numbers.
Step-by-step explanation:
51 and 51
maybe
hope it help uWhat is the solution to the following system of equations?
[3x-2y = 12
16x-4y = 24
O It has infinitely many solutions.
It has no solution.
It has one solution (2, -3).
It has one solution (4,0).
Answer:
(0, -6)
Step-by-step explanation:
Given the following systems of linear equations;
3x - 2y = 12 ...... equation 1
16x - 4y = 24 ........ equation 2
We would solve for the solution using the elimination method;
Multiplying eqn 1 by 2, we have;
2 * (3x - 2y = 12)
6x - 4y = 24
16x - 4y = 24
Subtracting the two equations, we have;
(6x - 16x) + (-4y -[-4y]) = (24 - 24)
-10x - 0 = 0
-10x = 0
x = -0/10 = 0
Next, we would find the value of y;
3x - 2y = 12
3(0) - 2y = 12
0 - 2y = 12
-2y = 12
y = -12/2
y = -6
Check:
3x - 2y = 12
3(0) - 2(-6) = 12
0 - (-12) = 12
12 = 12
Note: the options provided for this questions are incorrect or inappropriate.
A department store manager noted that the sales of furniture contributed 20% of the store's profits in the year 2015 and 29% in the year 2016.
Of the following choices, which two statements about furniture sales are true?
a.) There was a 45% increase in furniture sales.
b.) Furniture sales rose by 45 percentage points.
c.) There was a 31% increase in furniture sales.
d.) There was a 9% increase in furniture sales.
e.) Furniture sales rose by 31 percentage points.
f.) Furniture sales rose by 9 percentage points.
Answer:
There was a 45% increase in furniture sales.
Furniture sales rose by 9 percentage points.
Step-by-step explanation:
absolute difference = new - old
29-20= 9 percentage points
absolute difference / initial value = 9/20 = .45 * 100 = 45%
Two statements which are true about furniture sales are [tex](a)[/tex] There was a [tex]45\%[/tex] increase in furniture sales and [tex](f)[/tex] Furniture sales rose by [tex]9[/tex] percentage points.
What is percentage ?Percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%".
Percentage [tex]=\frac{Obtained\ number}{Total\ number}\ * 100[/tex]
We have,
Sales of furniture in [tex]2015=20\%[/tex]
Sales of furniture in [tex]2016=29\%[/tex],
So,
Change in Percentage [tex]=29-20=9\%[/tex]
i.e.
Sales rise by [tex]9\%[/tex] points,
And,
Increase in Percentage [tex]=\frac{9}{20}\ *100=45\%[/tex]
Hence, we can say that Two statements which are true about furniture sales are [tex](a)[/tex] There was a [tex]45\%[/tex] increase in furniture sales and [tex](f)[/tex] Furniture sales rose by [tex]9[/tex] percentage points.
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The ratio of winners to losers was 7 to 5. If the total number of winners and losers was 1260, how many more winners were there than losers?
Answer:
210
Step-by-step explanation:
7:5
First add the ratios
7+5=12
Put each ratio over the denominator 12 then multiply each by the total
7/12×1260= 735
5/12 × 1260 = 525
To find how many more winners than losers
735-525= 210
HELP PLSSS I WILL GIVE THE FIRST PERSON TO ANSWER BRAINLYIST IF THERE RIGHT
i suck at math its easy
Option B and D are the correct answers
Answer:
A and B I guess so
the product of n and 6 divided by 4 in algebraic expression
Answer:
[tex]6n \div 4[/tex]
Step-by-step explanation:
n is a variable and multiplied by 6, so it is attached to 6. (6 is known as the coefficient.) Then it is divided by 4. (4 is known as the constant because there is no variable attached to it.)
[tex]6n \div 4[/tex]
Kate lanes a letter against her house to get to the roof. The house is 25 feet tall and I put a ladder is 15 feet away from the side of the house. What is the angle that the latter makes with the ground?
Answer:
this is the correct answer
(8,9); x+3y=2 in y=mx+b form
Answer:
use photo math. it will help
What is the value of f(6) in the function below?
fx) = 2x
Answer:
substitute that (6) in X so f(6) = 2(6) which is = 12
Solve the system of equations Y=-2x+5 and y=x^2+3x+9
I think
x= -4, -1 and y=13, 8
(-4, 13) and (-1, 8)
What is the area of the triangle centimeters squared 23 CM 16 CM 14 CM
Answer:
Step-by-step explanation:
82
Answer:
Step-by-step explanation:
.5(half) x 14(base) x 16(height)=112cm
The sum of -5 + 6 and 7a - 8
7a-7
I hope you typed the question correctly because it was weird because -5+6=1
Answer:
1) 1
2) I'm getting no answer/ solution
Step-by-step explanation:
See image below:)
The triangle below is isosceles. Find the length of side x in simplest radical form with
a rational denominator.
х
4
Answer:
x = 2√2
Step-by-step explanation:
Since the triangle is isosceles, it means 2 of the angles are equal and 2 of the sides are also equal.
Now, since we see that it is also a right angled triangle, it means one angle is 90°.
Let the equal angles be a.
Thus;
a + a + 90 = 180 (since sum of angles in a triangle is 180)
2a + 90 = 180
2a = 180 - 90
2a = 90
a = 90/2
a = 45°
Now, using sine rule, we can find x. Thus;
x/sin 45 = 4/sin 90
sin 90 = 1
sin 45 = 1/√2
Thus;
x = (4 × 1/√2)/1
x = 4/√2
Let's rationalize the denominator to get;
x = (4/√2) × √2/√2
x = (4√2)/2
x = 2√2
PLEASE HELP!! Please answer all if you can and show answer clearly thankyou sm if u do
Answer:
Below:
Step-by-step explanation:
A) 0.15 (0.35 + 0.40 + 0.10 + 0.15 = 1)
B) 0.45
C) 0.40
A) the total probability has to equal 1.
To find the probability of rat subtract the other animals from1:
Rat = 1 - 0.35-0.4-0.1 = 0.15
Rat = 0.15
B) probability of cat or hamster equals the sum of their probabilities:
Cat = 0.35 + hamster = 0.1 = 0.45
Answer = 0.45
C) the probability of them both picking the same = dog x dog = 0.4 x 0.4 = 0.16
Answer = 0.16
A construction crew is lengthening a road that originally measured 47 miles. The crew is adding one mile to the road each day. Let L be the length (in miles) after D days of construction. Write an equation relating L to D. Then use this equation to find the length of the road after 31 days.
Answer:
78 miles
Step-by-step explanation:
Given that:
Original length, L = 47 miles
Additional length (miles) added per day, = 1 mile
Representing as an equation :
L(D) = original length + additional length per day * number of days
Let, D = number of days
L(D) = 47 + D
Length after 31 days :
L(31) = 47 + 31
= 78 miles
PLEASE HELP ASAP WILL GIVE BRAINLEIST FOR AN ACTUAL ANSWER
Answer:
<V = 40
Step-by-step explanation:
The exterior angle is equal to the sum of the opposite interior angles
20x = 60+7x+5
Combine like terms
20x = 7x+65
Subtract 7x from each side
20x -7x = 7x+65-7x
13x = 65
Divide each side by 13
13x/13 = 65/13
x = 5
<v = 7x+5 = 7*5+5 = 35+5 = 40
answer:
it's U = 60°
V = 50°
T = 70°
8) The sides of a flower garden are shown in the diagram below. What is the perimeter of the flower garden? 4m 2 m
Answer:
18.28 m
Step-by-step explanation:
Given the flower garden in the question :
The shape is composite and can be divided into 2 semicirles and rectangle
The perimeter of a semicircle is the Circumference of the semicircle = πr
Hence, 2 semicirles = 2πr
Radius of semicircle = 2/2 = 1
Perimeter = 2 * 3.14 * 1² = 2 * 3.14 * 1 = 6.28 m
The perimeter of rectangle; length and width are 6m and 2 m respectively :
Perimeter of rectangle = 2(l + w) = 2(4+2) = 2(6) = 12m
Tve perimeter of garden = 6.28 + 12 = 18.28 m
Given that ABCD is a rectangle, find the total area of the figure below. Round your answer to the nearest tenth.
Options
18 ft²
20.25 ft²
21.5 ft²
22.5 ft²
Answer:
C
Step-by-step explanation:
42.
A toy store's percent of markup is 45%. A model train costs the store $100. Find the markaup.
(First gets brainliest)
Answer:
$68.97
Step-by-step explanation:
The equation you have to use is I=p(1.45)
If you have a 45% increase to 100, the original price was $68.97.
a cylinder water tank carries a volume of 150L when it is full. The water tank has a base surface with a diameter of 140 cm. what is the height of the water tank?
Answer:
9.74418019cm=h
~ 9.7442
Step-by-step explanation:
volume of a cylinder=πr²h
radius=½of diameter
=½×140cm
=70cm
1l=1000cm³
150l=150l/1l×1000cm³
=150000cm³
150000cm³=π(70cm)²×h
150000cm³=15393.8040cm²h
150000cm³/15393.8040cm²=15393.8040cm²h/15393.8040cm²
150000cm³/15393.8040cm²=h
9.74418019cm=h
Help me please I NEED to pass this
OPTION C is the correct answer.
Hope it helps you.
Hello Plsss ...... this is important
PLEASE HELP ILL MARK BRAINLIEST
The given polygons are similar.
Find the value of x.
Answer: 6x−6
6x−6
=6(x−1)
Answer:
6(x−1)
Step-by-step explanation:
Answer:
13
Step-by-step explanation:
Question 2 of 20
Which of the following sets represents the range of the diagram below?
Answer:
D. {3, 5, 7}
Step-by-step explanation:
Sets of y-values or outputs of a relation of a function = the range
The outputs/y-values of the relation mapped above are what we have on our right hand, which area {3, 5, 7}
Therefore,
Range = {3, 5, 7}
6,12,24,48 Find the 11'th term
Answer:
614
Step-by-step explanation:
This pattern is being multiplied by 2
keep multiplying by two till you get to the 11th term
6, 12, 24, 48, 96, 192, 384, 768, 1536, 3072, 6144
6144 is the 11th term.
112 1/2 as a decimal
Answer:
[tex] \frac{1}{2} \: as \: a \: decimal = \\ 0.5[/tex]
Step-by-step explanation:
thats the answer
The decimal form, the mixed fraction can be written as 112.5.
To find out mixed fraction in the form of decimal.
What is fraction?A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominator.
Given that:
The mixed fraction is a fraction whose nominator is greater than its denominator or improper fraction is a fraction in which the denominator is always less than the numerator.
112 1/2
= (2 x 112 + 1)/2
= (224 + 1)/2
= 225/2
To divide the 225 by 2 ,we get
=112.5
So, the decimal form, the mixed fraction can be written as 112.5
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Solve the linear equations
1/4(x-5)+4=1/3(2x+7)-5/6
Answer:
x = 3
Step-by-step explanation:
Given the linear equation :
1/4(x-5)+4=1/3(2x+7)-5/6
(x-5)/4 + 4 = (2x+7)/3 - 5/6
Take the lcm and sum
(x-5+16)/4 = (4x+14-5)/6
(x+11)/4 = (4x+9)/6
Cross multiply
6(x+11) = 4(4x+9)
6x + 66 = 16x + 36
Collect like terms
6x - 16x = 36 - 66
-10x = - 30
x = 30/10
x = 3
3,-30,300,-3000 is it geometric or not geometric if so whats the common ratio r=?
Step-by-step explanation:
everything can be found in the picture
Please answer this question. I prey
Answer:
45°
Step-by-step explanation:
mLA : mLB : mLC = 1:2:1 => 1+2+1=4 (equivalent with 180°)
so, mL2 = mLC = 1/4 ×180° = 45°
