Answer:
Step-by-step explanation:
This is nice and simple. I'm going to walk through it like I do when teaching this concept to my class for the first time. This is a good problem for that.
We are given a square and we are looking for the rate at which the area is increasing when a certain set of specifics are given. That means that the main equation for this problem is the area of a square, which is:
[tex]A=s^2[/tex] where s is a side.
Since we are looking for the rate at which the area is changing, [tex]\frac{dA}{dt}[/tex], we need to take the derivative of area formula implicitly:
[tex]\frac{dA}{dt}=2s\frac{ds}{dt}[/tex] that means that if [tex]\frac{dA}{dt}[/tex] is our unknown, we need values for everything else. We are given that the initial area for the square is 49. That will help us determine what the "s" in our derivative is. We plug in 49 for A and solve:
[tex]49=s^2[/tex] so
s = 7
We are also given at the start that the sides of this square are increasing at a rate of 8cm/s. That is [tex]\frac{ds}{dt}[/tex]. Filling it all in:
[tex]\frac{dA}{dt}=2(7)(8)[/tex] and
[tex]\frac{dA}{dt}=112\frac{cm^2}{s}[/tex]
The surface area of a square of side L is given by
[tex]A = L^2[/tex]
The rate of change of the area per unit time is
[tex]\dfrac{dA}{dt} = 2L\dfrac{dL}{dt}[/tex]
We can express the length L on the right hand side in terms of the area A [tex](L = \sqrt{A})[/tex]:
[tex]\dfrac{dA}{dt} = 2\sqrt{A}\dfrac{dL}{dt}[/tex]
[tex]\:\:\:\:\:\:\:=2(\sqrt{49\:\text{cm}^2})(8\:\text{cm/s})[/tex]
[tex]\:\:\:\:\:\:\:=112\:\text{cm}^2\text{/s}[/tex]
Draw the line segment with endpoints (-5, 9) and (-1, -7) and find the value of y if x=-4;-2.5;-2;-1.5;0 plz answer asap
Answer:
5, - 1, - 3, - 5, - 11
Step-by-step explanation:
The equation of the line is y=-4x-11. The y values corresponding to x are 5, - 1, - 3, - 5, - 11
Solve the inequality
Answer:
hope this helps buddy, please mark the brainliest.
Step-by-step explanation:
find the surface area of the triangular prism below.
Step-by-step explanation:
At first you need to take its lateral surface area by using the perimeter of base of the triangle and the height of prism.
Then after calculating it you need to find out its total surface area which is asked in the question and that is calculated by adding the area of both triangles of the prism in the lateral surface area.
Then that's your answer.
9514 1404 393
Answer:
544 square units
Step-by-step explanation:
The surface area is the sum of the area of the two triangular bases and the three rectangular faces. The relevant area formulas are ...
A = 1/2bh . . . . area of a triangle with base b and height h
A = LW . . . . . are of a rectangle of length L and width W
__
SA = 2(1/2)(12)(8) + (10 +10 +12)(14)
SA = 96 +448 = 544 . . . square units
Line JK passes through points J(–3, 11) and K(1, –3). What is the equation of line JK in standard form?
7x + 2y = –1
7x + 2y = 1
14x + 4y = –1
14x + 4y = 1
9514 1404 393
Answer:
(b) 7x + 2y = 1
Step-by-step explanation:
You don't need to know how to find the equation. You just need to know how to determine if a point satisfies the equation. Try one of the points and see which equation fits. (The numbers are smaller for point K, so we prefer to use that one.)
7(1) +2(-3) = 1 ≠ -1 . . . . . tells you choice A doesn't work, and choice B does
The equation is ...
7x +2y = 1
__
Additional comment
The equations of choices C and D have coefficients with a common factor of 2. If the constant also had a factor of 2, we could say these equations are not in standard form, and we could reject them right away. Since the two points have integer values for x and y, we can reject these equations anyway: the sum of even numbers cannot be odd.
Answer:
b
Step-by-step explanation:
∫[tex]\frac{x+2019}{x^{2}+9 }[/tex]
Split up the integral:
[tex]\displaystyle\int\frac{x+2019}{x^2+9}\,\mathrm dx = \int\frac{x}{x^2+9}\,\mathrm dx + \int\frac{2019}{x^2+9}\,\mathrm dx[/tex]
For the first integral, substitute y = x ² + 9 and dy = 2x dx. For the second integral, take x = 3 tan(z) and dx = 3 sec²(z) dz. Then you get
[tex]\displaystyle \int\frac x{x^2+9}\,\mathrm dx = \frac12\int{2x}{x^2+9}\,\mathrm dx \\\\ = \frac12\int\frac{\mathrm du}u \\\\ = \frac12\ln|u| + C \\\\ =\frac12\ln\left(x^2+9\right)[/tex]
and
[tex]\displaystyle \int\frac{2019}{x^2+9}\,\mathrm dx = 2019\int\frac{3\sec^2(z)}{(3\tan(z))^2+9}\,\mathrm dz \\\\ = 2019\int\frac{3\sec^2(z)}{9\tan^2(z)+9}\,\mathrm dz \\\\ = 673\int\frac{\sec^2(z)}{\tan^2(z)+1}\,\mathrm dz \\\\ = 673\int\frac{\sec^2(z)}{\sec^2(z)}\,\mathrm dz \\\\ = 673\int\mathrm dz \\\\ = 673z+C \\\\ = 673\arctan\left(\frac x3\right)+C[/tex]
Then
[tex]\displaystyle\int\frac{x+2019}{x^2+9}\,\mathrm dx = \boxed{\frac12\ln\left(x^2+9\right) + 673\arctan\left(\frac x3\right) + C}[/tex]
Please help! Question and answers are in the pic
So far she worked 4 days at 5 1/2 hours a day for a total of 22 hours.
22 hours x $8.50 = $187
Subtract that from the cost of the computer:
899-187 = $712
She needs $712 more.
Amount she makes per shift: $8.50 x 5 1/2 hours = $46.75
Divide what she needs by amount per shift:
712 / 46.75 = 15.22 shifts
She needs to work 16 more shifts.
pLEASE help best and right answer gets brainliest
Step-by-step explanation:
| - 5 | + | - 4 |
5 + 4
= 9
| - 6| - 4
6 - 4
2
I hope this answers your question.
During a particularly dry growing season in a southern state, farmers noticed that there is a delicate balance between the number of seeds that are planted per square foot and the yield of the crop in pounds per square foot. The yields were the smallest when the number of seeds per square foot was either very small or very large.
What is the explanatory variable for this relationship?
yield of the crop
location of the farm
precipitation for the growing season
number of seeds planted per square foot
I think it's (D).
number of seeds planted per sf
Answer:
The guy above me is correct
Step-by-step explanation:
2022
Answer:
number of seeds planted per square foot
Step-by-step explanation:
response is the yield explained by how many seeds are planted
At a time hours after taking a tablet, the rate at which a drug is being eliminated r(t)= 50 (e^-01t - e^-0.20t)is mg/hr. Assuming that all the drug is eventually eliminated, calculate the original dose.
Answer:
2500 mg
Step-by-step explanation:
Since r(t) is the rate at which the drug is being eliminated, we integrate r(t) with t from 0 to ∞ to find the original dose of drug, m. Since all of the drug will be eliminated at time t = ∞.
Since r(t) = 50 (e^-01t - e^-0.20t)
m = ∫₀⁰⁰50 (e^-01t - e^-0.20t)
= 50∫₀⁰⁰(e^-01t - e^-0.20t)
= 50[∫₀⁰⁰e^-01t - ∫₀⁰⁰e^-0.20t]
= 50([e^-01t/-0.01]₀⁰⁰ - [e^-0.20t/-0.02]₀⁰⁰)
= 50(1/-0.01[e^-01(∞) - e^-01(0)] - {1/-0.02[e^-0.02(∞) - e^-0.02(0)]})
= 50(1/-0.01[e^-(∞) - e^-(0)] - {1/-0.02[e^-(∞) - e^-(0)]})
= 50(1/-0.01[0 - 1] - {1/-0.02[0 - 1]})
= 50(1/-0.01[- 1] - {1/-0.02[- 1]})
= 50(1/0.01 - 1/0.02)
= 50(100 - 50)
= 50(50)
= 2500 mg
Use the discriminant to determine the number of solutions to the quadratic equation −40m2+10m−1=0
From the analysis of the discriminant, you obtain that the quadratic function has no real solutions.
In first place, you must know that the roots or solutions of a quadratic function are those values of x for which the expression is 0. This is the values of x such that y = 0. That is, f (x) = 0.
Being the quadratic function f (x)=a*x² + b*x + c, then the solution must be when: 0 =a*x² + b*x + c
The solutions of a quadratic equation can be calculated with the quadratic formula:
[tex]Solutions=\frac{-b+-\sqrt{b^{2} -4*a*c} }{2*a}[/tex]
The discriminant is the part of the quadratic formula under the square root, that is, b² - 4*a*c
The discriminant can be positive, zero or negative and this determines how many solutions (or roots) there are for the given quadratic equation.
If the discriminant:
is positive: the quadratic function has two different real solutions. equal to zero: the quadratic function has a real solution. is negative: none of the solutions are real numbers. That is, it has no real solutions.In this case, a= -40, b=10 and c= -1. Then, replacing in the discriminant expression:
discriminant= 10² -4*(-40)*(-1)
Solving:
discriminant= 100 - 160
discriminant= -60
The discriminant is negative, so the quadratic function has no real solutions.
Solve this inequality: x+ 4< 16
Answer:
x < 12
Step-by-step explanation:
subtract 4 from both sides:
x + 4 < 16
- 4 -4
x < 12
Answer:
x<4
Step-by-step explanation:
x+4 <16
x < 16
4
x<4
I hope this will help you
what is the volume of the container
Please help me to find this answer
Answer:
37
Step-by-step explanation:
Tan(B) = 6/8
B= arctan(3/4)=37
(-2x) (x-3) answer please
Answer:
−2x^2+6x
Explanation:
You just have to distribute meaning you have to multiply -2x to the equation.
Hello I'm new can anyone help me with this question?
Thank you so much! <3 xoxo
Question 3 plz show ALL STEPS
Answer:
7,0, -1 and -2
Step-by-step explanation:
Just substitute the values,
a. f(g(7))=f(-1) [g(7)=-1 given]
=7 [f(-1)=7 given]
b.f(g(-1))=f(3)=0 [g(-1)=3 Given]
c.g(f(-1))=g(7)=-1 [f(-1)=7 given]
d.g(f(7))=g(5)=-2 [f(7)=g(5) given]
Which expression is equivalent to (b^n)m?
Step-by-step explanation:
By the law of exponent :
(a^n)^m=a^n×m
Option C
b^n×m is the correct answer...
hope it helps
Which of the following show the factored equivalent of
f(x) = (2x^2 +7x + 3)(x - 3) and its zeros?
Answer:
the answer is "D"
(2x+1)(x+3)(x-3) //// -3,-.5,3
Step-by-step explanation:
Factored Form: y= (2x+1)(x+3)(x-3)
Answer:
D
Step-by-step explanation:
[tex]f(x) = (2x^2 +7x + 3)(x - 3)[/tex] is factored into: [tex]f(x)= (2x+1)(x+3)(x-3)[/tex]
That takes out the choices B and C.
The roots are -0.5, 3, and -3.
Therefore, the answer is D.
I hope this helps!
pls ❤ and mark brainliest pls!
I need help please
Don’t skip the questions if you know the answer please I need the answers as soon as possible!!
y=x²-10x-7
a>0 so we will be looking for minimum
x=-b/2a=10/2=5
y=25-50-7=-32
Answer: (5;32)
y=-4x²-8x+1
а<0 so we will be looking for maximum
х=-b/2a=8/-8=-1
у=4+8+1=13
Maximum point (-1;13)
I need help plz!!
8.57396817...•5/8 is rational or irrational?
Answer:
Irrational
Step-by-step explanation:
Any non-zero rational number multiplied by an irrational number will be irrational. We can rewrite this as (8.57... * 5) / 8, but we have no idea how to make 8.57... * 5 rational, or expressed as the quotient of two integers.
consider a study conducted to determine the average protein intake among an adult population. Suppose that a confidence level of 85% is required with an interval about 10 units wide. if a preliminary data indicates a standard deviation of 20g, what sample of adults should be selected for the study?
Answer:
made up of about 20 common amino acids. The proportion of these amino acids varies as a characteristic of a given protein, but all food proteins—with the exception of gelatin—contain some of each. Amino nitrogen accounts for approximately 16% of the weight of proteins. Amino acids are required for the synthesis of body protein and other important nitrogen-containing compounds, such as creatine, peptide hormones, and some neurotransmitters. Although allowances are expressed as protein, a the biological requirement is for amino acids.
Proteins and other nitrogenous compounds are being degraded and resynthesized continuously. Several times more protein is turned over daily within the body than is ordinarily consumed, indicating that reutilization of amino acids is a major feature of the economy of protein metabolism. This process of recapture is not completely efficient, and some amino acids are lost by oxidative catabolism. Metabolic products of amino acids (urea, creatinine, uric acid, and other nitrogenous products) are excreted in the urine; nitrogen is also lost in feces, sweat, and other body secretions and in sloughed skin, hair, and nails. A continuous supply of dietary amino acids is required to replace these losses, even after growth has ceased.
Amino acids consumed in excess of the amounts needed for the synthesis of nitrogenous tissue constituents are not stored but are degraded; the nitrogen is excreted as urea, and the keto acids left after removal of the amino groups are either utilized directly as sources of energy or are converted to carbohydrate or fat.
prove that tan² theta + cot² theta = sec² theta cosec² theta- 2
Step-by-step explanation:
Tan² theta = sec² theta - 1
Cot² theta = cosec² theta - 1
Tan²+Cot² = sec²-1+cosec²-1
= sec²+cosec²-2
Please find attached herewith the solution of your question.
If you have any doubt, please comment.
find the greatest number than divides 45 60 75 without leaving remainder
Answer:
15
Step-by-step explanation:
15 is the greatest number that divides 45 60 75 without leaving remainder
Answer:
15
Step-by-step explanation:
Let write the factors of each number:
45: (1,3,5,9,15,45)
60:(1,2,3,4,5,6,10,12,15,20,30,60)
75:(1,3,5,15,15,75).
The greatest common factor is 15. So the answer is 15.
prove:
sin²A-cos²B=sin²B-cos²A
Step-by-step explanation:
thwashm m GB DC GM 3hka it g feeds ygzdkzyzuzjz indin, mi, hn zbe
Answer:
Solution given:
L.H.S
sin²A-cos²B
we havesin²A=1-cos²A and Cos²B=1-sin²B
nowreplacing value
1-cos²A-(1-sin²B)
open bracket1-cos²A-1+sin²B
keep together like terms1-1+sin²B-Cos²A
=sin²B-Cos²A
R.H.S
proved.Which of the following fractions is closest to 0? 5/12 , 2/3, 5/6,3/4
Answer:
5/12
Step-by-step explanation:
5/12 , 2/3, 5/6,3/4
Get a common denominator of 12
5/12, 2/3 *4/4, 5/6*2/2, 3/4 *3/3
5/12, 8/12, 10/12, 9/12
The numerator closest to 0 is the fraction closest to 0
5/12
For a standard normal distribution, find:
P(z > c) = 0.058
Find c.
Answer:
1.572
Step-by-step explanation:
For a standard normal distribution,
P(z > c) = 0.058
To obtain C ; we find the Zscore corresponding to the proportion given, which is to the right of the distribution ;
Using technology or table,
Zscore equivalent to P(Z > c) = 0.058 is 1.572
Hence, c = 1.572
Factorize:
625a^4 + 4b^4
(625 • (a4)) + 22b4
54a4 + 22b4
Final result :
625a4 + 4b4
if x and y are linear pair of angel then x +y=
Answer: x + y = 180²
Step-by-step explanation:
A linear pair is a pair of adjacent, supplementary angles.
Adjacent means next to each other.
Supplementary means that the measures of the two angles add up to equal 180 degrees.
Therefore, by definition, if x and y are linear pairs of angles, then x + y = 180.
5. Given a test in which there is overlap of the test results for diseased and non-diseased individuals (e.g., normal individuals are found who have test results ranging in value from 8 to 15, and diseased individuals are found who have test results ranging in value from 12 to 25, so that in the range of values 12 to 15 there are both normal and diseased individuals), if the current cutoff value lies in the range of this overlap and you move the cutoff value toward the normal population (lower numbers in this example), the true negative numbers will _____________________ . (5 points)
Answer:
True negative numbers are considered as diseased individual. So, the true negative numbers will increase
Step-by-step explanation:
True negative numbers are considered as diseased individual. So, the true negative numbers will increase.
HELP WILL GIVE BRAINLYIST
Answer:
The parent cubic function has been vertically stretched by a factor of 4.
Equation:G(x)= 4[tex]\sqrt[3]{x}[/tex]
Answer: Option B
OAmalOHopeO
