The length of a rectangle is increasing at a rate of and its width is increasing at a rate of . when the length is 20 cm and the width is 10 cm, how fast is the area of the rectangle increasing?
Answers
220 cm2/s
EXPLINATION
L length of rectangel (cm)
W width of rectangel(cm)
A area of rectangel (cm²)
T time (s)
we are told that:
d1\dt=8cm\s(const),and dw\dt =3cm\s(const)
the area of the rectangel is
A=LW
Differentiating wrt t (using the product rule) we get;
dAdt=(l)(dwdt)+(dldt)(w)
∴dAdt=3l+8w
So when l=20 and w=10⇒
dAdt=3⋅20+8⋅20
∴dAdt=60+160
∴dAdt=220 cm2/s
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Given the exponential equation 4x = 64, what is the logarithmic form of the equation in base 10?
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Which of the following ordered pairs represents the solution to the system given below? x − 4y = 7 5x + 9y = 6
A bicycle has a listed price of $849.955 before tax. If the sales tax rate is 6.5%, find the total cost of the bicycle with sales tax included. Round your answer to the nearest cent, as necessary.
Answers
Answer:
Step-by-step explanation:
we have
we know that
In the given expression the denominator can not be equal to zero
therefore
To find the value of x for which the expression is undefined. equate the denominator to zero
Solve for x
Adds both sides
x - 7 = 0
Add seven to both sides:
x = 7
And there's your answer!
Hope I helped, and let me know if you have any questions :)
Answers
V=LWH
basically
volume=height times base area
so
2. V=3 times 8 times 12=288 cm^3
3. triangular prism is 1/2 of the volume of a similar rectangular prism with same measure so
V=1/2 times 4 times 10 times 15=300 cm^3
4. trapezoid base area=area of a trapezoid=(base1+base2)/2 times height so
baseaea=(4+10)/2 times 6=7 times 6=42, then basearea times height=42 times 10=420cm^3
5. cylinder area=base area times height
base=circle=pir^2
r=1/2diameter
6/2=3
base=pi3^2=9pi
area=9pi times 12=108pi cm^3
6. 24pi=4 times pir^2
divide by 4
6pi=pir^2
divd e pi
6=r^2
√6 cm=r
7. square pyramid volume=1/3 volume of similar rectangular prism so
square means base=4 times 4=16
height=9
rectangular volume=16 times 9
pyramid voluume=1/3 times 16 times 9=48 cm^3
8. solve for base side
use pythagorean theorem
slant height=hyposonuse=13
base edge=2 times of 1 of the legs so 10/2=5
so
5^2+x^2=13^2
25+x^2=169
x^2=144
x=12
height of pyramid=12
volume=1/3 times 10 times 10 times 12 times=400 cm^3
2. C
3. B
4. A
5. C
6. B
7. C
8. A
Answers
The fraction converts a repeating decimal number is 1/12 is a repeating decimal.
What is fraction?
Fractions are represented as a numerical value, which defines a part of a whole. A fraction can be a portion or section of any quantity out of a whole, where the whole can be any number, a specific value, or a thing.
Parts of a Fraction
All fractions consist of a numerator and a denominator and they are separated by a horizontal bar known as the fractional bar.
- The denominator indicates the number of parts in which the whole has been divided into. It is placed in the lower part of the fraction below the fractional bar.
- The numerator indicates how many sections of the fraction are represented or selected. It is placed in the upper part of the fraction above the fractional bar.
Given:
- 1/12= 0.0833333333
- 7/8= 0.875
- 14/25= 0.56
- 17/20= 0.85
- 6/10=.6
As, we can see that the approximately every fraction is non repeating except 1/12
Learn more about fraction here:
#SPJ5
Let's try it out.
1/12= 0.0833333333
7/8= 0.875
14/25= 0.56
17/20= 0.85
6/10=.6
So, 1/12 is a repeating decimal.
I hope this helps!
~kaikers
Answers
let’s create another system of equation.
Let a = 4
and Let b = -3
First equation
=> Let’s pick any numbers to be used. Let’s have number 5
=> 5a + 5b
=> 5 (4) + 5 (-3)
=> 20 + (-15)
negative and positive is equals to negative
=> 20 – 15
=> 5 (this the first value of our equation, let this be the value of X)
Second
=> Pick another number, Let’s have 6
=> 6a + 6b
=> 6 (4) + 6 (-3)
=> 24 + (-18)
=> 24 – 18
=> 6 (this is the value of our second equation, let this value be Y)
Now, we have (A, B) = (4, -3) and (X, Y) = (5,6)
Answer:
A linear equation can be written in several forms. "Standard Form" is #ax+by=c# where #a#, #b# and #c# are constants (numbers).
We want to make two equations that
(i) have this form,
(ii) do not have all the same solutions (the equations are not equivalent), and
(iii) #(4, -3)# is a solution to both.
#ax+by=c#. We want #a#, #b# and #c# so that
#a(4)+b(-3)=c# (This will make (i) and (iii) true.)
Step-by-step explanation:
Answers
The cost of each bottle of juice will be $0.58.
What is an expression?
The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Hudson bought snacks for his team's practice. he bought a bag of apples for $1.59 and a 10-pack of juice bottles. the total cost before tax was $7.39.
The expression will be formed as below:-
10x + 1.59 = 7.39
Here x is the cost of the juice bottle.
10x + 1.59 = 7.39
10x = 7.39 - 1.59
10x =5.8
x = 5.8/10 = $0.58
Therefore, the cost of each bottle of juice will be $0.58.
To know more about an expression follow
#SPJ1
B. 118
C. 170
Answers
630 / 6 = the theoretical amount of times you should get any number on the dice
630 / 6 = 105
105 is closest to B. The answer is B.
Please make my answer the brainliest if I was helpful