at the instant that the first circle has a radius of 9 centimeters, the radius is increasing at a rate of 3 2 centimeters per second. find the rate at which the area of the circle is changing at that instant. indicate units of measure.

Total number of Chemistry textbooks sold is 81 and total number of Biology textbooks sold is 243

Let there are x biology textbooks sold.

No of chemistry textbooks sold = 3 the number of biology textbooks sold

ATQ,

A textbook store sold a combined total of 324 biology and chemistry textbooks in a week.

x + 3x = 324

4x = 324

x = 81

It means there are 81 biology textbooks sold and 3x = 3(81) = 243 chemistry textbooks sold.

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The distance between the person and the shuttle is changing at a rate of 640 feet/sec when the shuttle is 4000 ft high and is rising at a rate of 800 ft/sec.

Considering x to be the height of the triangle and y to be the hypotenuse of the triangle, a right-angled triangle will be formed according to the given information having a base of 3000 feet which is the distance of the person from the launch pad.

In this right-angle triangle x will be the height of the shuttle and y will be the distance between the person and the shuttle.

Now we apply the Pythagorean theorem to the triangle;

y² = x²+(3000)²

Now differentiating this equation with respect to time,t :

2y (dy/dt) = 2x(dx/dt) + 0

dy/dt = x(dx/dt)/y

As the shuttle is rising at a speed of 800 ft/sec, (dx/dt)=800

Substitute 4000 for x into the equation, y²=x²+(3000)², to find y;

y² = (4000)²+(3000)²

y = 5000

Now we substitute 4000 for x, 5000 for y, and 800 for dx/dt in the equation, dy/dt = x(dx/dt)/y

dy/dt = 4000(800) / 5000

dy/dt = 640

Therefore, the distance between the person and the shuttle is increasing at a rate of 640 feet/sec.

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Answer:

a=29. b=32 c=30. d=30

Step-by-step explanation:

look at the arrow and get the answer if am wrong let me know

The two column proof is written as follows

Statement                                                    Reason

1. m ∠ d = 125°                                                 Given

2. m ∠ r = 125°                                                 Given  

3. m ∠ d = m ∠ r                                       Definition of equality

4. ∠ d ≅ ∠ r                                              Definition of congruent angles

This is a method of proof used in geometry. It helps to show how the required proof came to be possible. The major items in two column proof is:

The term equality as used in mathematics is defined to mean that the terms in comparison can be replace by the other

Using the given question as an instance:

m ∠ d = 125° and m ∠ r = 125°

This means that the two angles have same value and they can replace each other.

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Answer:

the answer is 8.

Step-by-step explanation:

Use the Pythagoras Theorem since it is a triangle.

[tex]a^{2}+b^{2}= c^{2}\\\\a^{2}+15^{2}= 17^{2}\\ a^{2}+225=289\\ a^{2}=289-225\\ a^{2}= 64\\ \sqrt{a}= \sqrt{64}\\ a=8[/tex]

Since you have the hypotenuse and base, just put those into the equation and find the missing side.

The exponential equation [tex]14=5^x[/tex] is equivalent to the  given logarithmic equation.

The exponential function that is represented as y=[tex]m^x[/tex], where:

m=base, m>0

x= exponent

Knowing some of the main logarithm rules.

example: [tex]log(a*b)= log a + log b[/tex]

example: [tex]log\frac{a}{b} = log a - log b[/tex]

example: [tex]log\frac{a^b} = b*log a[/tex]

For solving this question, you should apply the logarithm rules and  rewrite the function as an exponential equation.

[tex]log_5(x)}-{log_5(25)=7[/tex]

[tex]\frac{log_5(x)}{log_5(25)} =7[/tex]

[tex]{log_5(x)}=7{log_5(25)}[/tex]

[tex]{log_5(x)}=7{log_5(5^2)}[/tex]

[tex]{log_5(x)}=7*2[/tex]

[tex]{log_5(x)}=14[/tex]

[tex]x=5^{14^}[/tex]

Therefore, the  exponential function is [tex]14=5^x[/tex]

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Answer:

2.75

divide 11/4

The inverse function of g(x) = 2x² - 8 for each case is given as follows:

To find the inverse function, we exchange the variables x and y in the original function, and then isolate the variable y.

The original function in this problem is given as follows:

g(x) = 2x² - 8.

The function is not one-to-one, hence the inverse is different for x ≥ 0 and for x < 0.

Exchanging the variables, we have that:

x = 2y² - 8.

Isolating the variable y, we have that:

2y² = x + 8

y² = 0.5x + 4 (the entire equation was divided by 2 to isolate y)

y = ± sqrt(0.5x + 4).

For non-negative values, the inverse function is:

y = sqrt(0.5x + 4) = √(0.5x + 4).

For negative values, the inverse function is:

y = -sqrt(0.5x + 4) = -√(0.5x + 4).

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Answer: 0,2,3,-3

Step-by-step explanation:

Answer:

-20-43w

Step-by-step explanation:

5(-4-8w)-3w

-20-40w-3w

-20-43w

Answer:

I believe you forgot to add the attachment

Step-by-step explanation:

There is no math problem I can see to help you

The functions that are equivalent are

What are roots of a number?

The root of a number is the inverse of the exponents. for instance

a squared has an inverse of square root of a.  

mathematically:

a^2 = (a)^1/2  has an inverse of √a

The data given:

[tex]\sqrt[4]{162^{x} }[/tex]

Solving the given data for the equivalence

[tex]\sqrt[4]{162^{x} }=162^{x/4}[/tex]

The above proves option A correct

[tex]\sqrt[4]{(3*3*3*3*2)^{x} }[/tex]

[tex]\sqrt[4]{(3^{4} *2)^{x} }[/tex]

[tex](3\sqrt[4]{(2) })^{x}[/tex]

The above solution makes option B correct

[tex](3\sqrt[4]{(2) })^{x}=(3{(2)^{1/4} })^{x}[/tex]

The above proves Option D correct

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complete question

Which functions are equivalent to f (x) = RootIndex 4 StartRoot 162 EndRoot Superscript x? Check all that apply.

f (x) = 162 Superscript StartFraction x Over 4

f (x) = (3 RootIndex 4 StartRoot 2 EndRoot) Superscript x

f (x) = 9 RootIndex 4 StartRoot 2 EndRoot Superscript x

f (x) = 126 Superscript StartFraction 4 Over x

f (x) = left-bracket 3 (2 Superscript one-fourth Baseline) right-bracket Superscript x

The three consecutive integers are 14, 15, and 16.

Assume the three consecutive integers to be x-1, x, and x+1.

Sum of all three = 45.

x-1 + x + x+1 = 45

3x = 45 (-1 and +1 get cancelled)

x = 45/3

x = 15

the first integer is x-1 = 15 - 1 = 14

the second integer is x = 15

the third integer is x+1 = 15 + 1 = 16

So, the three consecutive integers are 14, 15, and 16.

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Answer:

Step-by-step explanation:

According to the remainder theorem, the remainder when f(x) is divided by (x - n) is f(n).

As per question we are given:

Substitute and solve for c:

Note: I got a different value of c. This may be a result of a typo in the given expression. I provided a guide to solve such problems. Let me know is anything is unclear.

Confounding variables are any other variable that also has an effect on your dependent variable.

What is a confounding variable?

A confounding variable, also called a confounder or confounding factor, is a third variable in a study examining a potential cause-and-effect relationship.

A confounding variable is related to both the supposed cause and the supposed effect of the study. It can be difficult to separate the true effect of the independent variable from the effect of the confounding variable.

In your research design, it's important to identify potential confounding variables and plan how you will reduce their impact.

For example, if you are researching whether drinking both sample lead to taste test, then drinking both sample  is your independent variable and taste test is your dependent variable. Confounding variables are any other variable that also has an effect on your dependent variable.

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The smallest number from the given options is

[tex]5.48 × {10}^{ - 8} [/tex]

The correct answer option is option d

A.

[tex]1.28 × {10}^{ - 4} [/tex]

= 1.28 × 0.0001

= 0.000128

B.

[tex]2.85 × {10}^{ - 6} [/tex]

= 2.85 × 0.000001

= 0.00000285

C.

[tex]3.24 × {10}^{ - 5} [/tex]

= 3.24 × 0.00001

= 0.0000324

D.

[tex]5.48 × {10}^{ - 8} [/tex]

= 5 48 × 0.00000001

= 0.0000000548

Therefore, the smallest number is

[tex]5.48 × {10}^{ - 8} [/tex]

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The Solution.

Considering triangle ABC, we have

Hence, the correct answer is 8 degrees (option B)

Answer:

N<3

Step-by-step explanation:

Answer:

Step-by-step explanation:

1) Find DGE

Bisecting an angle makes it half. A straight line is 180

180/2 = DGE

90 = DGE

2) Find FGE

Bisecting an angle makes it half. A straight line is 180

180/2 = FGE

90 =  FGE

Option B. 2w + 11 = 1.5w + 14, w = 6 weeks is the correct answer

Miles run by Denasia = 11 miles

Miles run by Kenya = 14 miles

Let w represent the number of weeks after which both Kenya and Denasia will be running the same number of miles

Formulating the equation we get:

Miles run by Denasia + Increase in miles each week*Number of weeks = Miles run by Kenya + Increase in miles each week*Number of weeks

11 + 2w = 14 + 1.5w

0.5w = 3

w = 6

Hence, option B is the correct answer according to the given contraints and both Denasia and Kenya will run the same distance in the 6th week

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1.  (a)The  vertex of the  function [tex]y=x^{2} +5x-7[/tex]  is [tex](-\frac{5}{2} ,-\frac{53}{4} )[/tex]

How is the vertex calculated?

In function [tex]y=x^{2} +5x-7[/tex],

a= 1 ,b= 5, c= -7

For a function   [tex]y=ax^{2} +bx+c[/tex]  , where (a≠0),

The vertex is [tex](-\frac{b}{2a} ,\frac{4ac-b^{2} }{4a} )[/tex]

[tex]x_v=-\frac{b}{2a}\\\\ =-\frac{5}{2*1} \\\\=-\frac{5}{2} \\\\\\y_v=\frac{4ac-b^{2} }{4a} \\\\=\frac{4*1*(-7)-(5^{2} )}{4*1}\\\\ =-\frac{53}{4}[/tex]

So, vertex  [tex](-\frac{5}{2} ,-\frac{53}{4} )[/tex] is minimum because a>0

(b)The solutions are [tex](\frac{\sqrt{53} -5}{2},0) (\frac{-5-\sqrt{53} }{2},0)[/tex]

How is the solution calculated?

When a function [tex]y=ax^{2} +bx+c =0[/tex]  where (a≠0),

[tex]x=\frac{-b\pm\sqrt{b^{2} -4ac} }{2a} \\\\x=\frac{-5\pm\sqrt{5^{2} -4(1)(-7)} }{2(1)} \\\\x=\frac{-5\pm\sqrt{53} }{2} \\\\x=\frac{\sqrt{53} -5}{2} , x=\frac{-5-\sqrt{53} }{2} \\\\\text{The solutions are } (\frac{\sqrt{53} -5}{2},0) (\frac{-5-\sqrt{53} }{2},0)[/tex]

2. (a)The  vertex of the  function [tex]y=-x^{2} +3x+8[/tex]  is [tex](\frac{3}{2} ,\frac{41}{4} )[/tex]

How is the vertex calculated?

In function [tex]y=-x^{2} +3x +8[/tex]

a= -1 ,b= 3, c= 8

For a function   [tex]y=ax^{2} +bx+c[/tex]  , where (a≠0),

The vertex is [tex](-\frac{b}{2a} ,\frac{4ac-b^{2} }{4a} )[/tex]

[tex]x_v=-\frac{b}{2a}\\\\ =-\frac{3}{2*(-1)} \\\\=\frac{3}{2} \\\\\\y_v=\frac{4ac-b^{2} }{4a} \\\\=\frac{4*(-1)*(8)-(3^{2} )}{4*(-1)}\\\\ =\frac{41}{4}[/tex]

So, vertex  [tex](\frac{3}{2} ,\frac{41}{4} )[/tex] is maximum because a<0

(b)The solutions are [tex](\frac{3+\sqrt{41} }{2},0) (\frac{3-\sqrt{41} }{2},0)[/tex]

How is the solution calculated?

When a function [tex]y=ax^{2} +bx+c =0[/tex]  where (a≠0),

[tex]x=\frac{-b\pm\sqrt{b^{2} -4ac} }{2a} \\\\x=\frac{-3\pm\sqrt{3^{2} -4(-1)(8)} }{2(-1)} \\\\x=\frac{-3\pm\sqrt{41} }{-2} \\\\x=\frac{3\pm\sqrt{41} }{2}\\\\x=\frac{3-\sqrt{41}}{2} , x=\frac{3+\sqrt{41} }{2} \\\\\text{The solutions are } (\frac{3+\sqrt{41} }{2},0) (\frac{3-\sqrt{41} }{2},0)[/tex]

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The answer choice which could not be modelled by an exponential function among the given answer choices is; A taxi charges a flat fee of $2.00 for pick-up, then an additional fee of 4.75 per mile.

It follows from the task content that the expression which could not be modelled by an exponential expression be identified among the answer choices.

An exponential function is one in which case the change factor is expressed as an exponent of the independent variable.

However, the function described as; A taxi charges a flat fee of $2.00 for pick-up, then an additional fee of 4.75 per mile is termed a linear model in which case;

The rate of change is constant and is equal to; $4.75 per mile.

Hence the required answer choice which cannot be modelled by an exponential function is; A taxi charges a flat fee of $2.00 for pick-up, then an additional fee of 4.75 per mile.

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Replace each point in both inequalities and see if the inequality remains:

(0,1) = (x,y)

1 ≥ 1/3(0)-2

1≥-2

y>4/3x+1

1>4/3(0)+1

1>1 NOT TRUE.

Point b.

(1,0) = (x,y)

0 ≥ 1/3(1)-2

0≥ 1/3-2

0≥-5/3

0>4/3(1)+1

0>7/3 NOT TRUE

Pint c. (-3,2)

2≥1/3(-3)-2

2≥ -1-2

2≥-3

2>(4/3)-3+1

2>-4+1

2>-3 TRUE

(-3,2) is a solution point to the set of inequalities. (option c)

Answer:[tex]3(5y - 7) - 2(9y - 11) = 4(8y - 13) - 17 \\➪ 15y - 21 - 18y + 22 = 32y - 52 - 17 \\ ➪15y - 18y - 32y = - 52 - 17 + 21 - 22\\➪-35y = - 70 \\➪35y = 70 \\ \: (cancel \: \: out \: "-" \: from \: both \: sides) \\ ➪y = \frac{ 70}{35} = 2 \\ \\ [/tex]

w = 10.

Step-by-step explanation:

9(w+1) = 99

9w+9 = 99

9w = 99-9

9w = 90

w = 90/9

w = 10.

[tex]{ \boxed{ \red{ \sf{w = 10}}}}[/tex]

Step-by-step explanation:

[tex]{ \purple{ \sf{9(w + 1) = 99}}}[/tex]

[tex]{ \purple{ \sf{9w + 9 = 99}}}[/tex]

[tex]{ \purple{ \sf{9w = 99 - 9}}}[/tex]

[tex]{ \purple{ \sf{9w = 90}}}[/tex]

Divide both the sides by 9 then

[tex]{ \purple{ \sf{ \frac{9w}{9} = \frac{90}{9} }}}[/tex]

[tex]{ \pink{ \boxed{ \blue{ \sf{w = 10}}}}}[/tex]

The inequality for the temperature in the house measured by thermostat is; 24° ≤ t ≤ 26°. The highest temperature is 26° C.

For the given question.

The thermostat at the house is set at 25° C.

Now, there is a deviation of the temperature of 1° C.

Thus,

The lowest temperature measured = 25° C -  1° C =  24° C.

The highest temperature measured = 25° C +  1° C =  26° C.

Let 't' be the temperature of the house.

The inequality will be;

24° ≤ t ≤ 26°

Thus, the maximum value of the temperature will be 26° C.

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[tex]m = \frac{y2 - y1}{x2 - x1} \\ m = \frac{7 - 6}{3 - 1} \\ m = \frac{1}{2} [/tex]

I ALSO PROVIDED YOU WITH THE FORMULA OF FINDING THE GRADIENT/SLOPE FOR FUTURE USE

HOPE THIS HELPS.

Answer: Y= 1/2x + 5.5

We will improve the argument by stating that two intersecting lines have vertically opposite angles equal in magnitude.

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Answer:

Step-by-step explanation:

The repeated part is 194805, six digits. Let the fraction be x.

Convert as follows:

Find prime factors of both numerator and denominator and simplify by cancelling common factors:

The common factors are:

When they cancel we are left with: