Calculate the volume of the figure below ​

Answer: -2

Step-by-step explanation: The answer is -2 because -1 x 8 = -8, and -8 x 4 = -32. Because multiplying two negatives cancels out and becomes positive, we can apply this same principle and figure out that -32 x -2 would give us positive 64. Hope this helps!

Answer:

[tex]\dfrac{\text{d}}{\text{d}x} \tan^{-1}x=\dfrac{1}{1+x^2}[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{6.5 cm}\underline{Trigonometric Identity}\\\\$\tan^{-1}(A)-\tan^{-1}(B) \equiv \tan^{-1}\left(\dfrac{A-B}{1+AB}\right)$\\\end{minipage}}[/tex]

[tex]\boxed{\begin{minipage}{3 cm}$\displaystyle \lim_{h \to 0} \left[\dfrac{\tan^{-1} \theta}{\theta} \right]=1$\\\end{minipage}}[/tex]

[tex]\boxed{\begin{minipage}{5.6 cm}\underline{Differentiating from First Principles}\\\\$\text{f}\:'(x)=\displaystyle \lim_{h \to 0} \left[\dfrac{\text{f}(x+h)-\text{f}(x)}{(x+h)-x}\right]$\\\end{minipage}}[/tex]

Given function:

[tex]\text{f}(x)=\tan^{-1}x[/tex]

[tex]\implies \text{f}(x+h)=\tan^{-1}(x+h)[/tex]

Differentiating from first principles:

[tex]\begin{aligned}\text{f}\:'(x) & =\displaystyle \lim_{h \to 0} \left[\dfrac{\text{f}(x+h)-\text{f}(x)}{(x+h)-x}\right]\\\\& =\lim_{h \to 0} \left[\dfrac{\tan^{-1}(x+h)-\tan^{-1}x}{(x+h)-x}\right]\end{aligned}[/tex]

Using the trigonometric identity to rewrite the numerator:

       [tex]\begin{aligned}& =\lim_{h \to 0} \left[\dfrac{\tan^{-1}\left(\dfrac{x+h-x}{1+x(x+h)}\right)}{(x+h)-x}\right]\\\\& =\lim_{h \to 0} \left[\dfrac{\tan^{-1}\left(\dfrac{h}{1+x^2+xh)}\right)}{h}\right]\end{aligned}[/tex]

[tex]\textsf{Multiply the denominator by }\dfrac{1+x^2+xh}{1+x^2+xh}:[/tex]

       [tex]= \displaystyle \lim_{h \to 0} \left[\dfrac{\tan^{-1}\left(\dfrac{h}{1+x^2+xh)}\right)}{\dfrac{h(1+x^2+xh)}{(1+x^2+xh)}}\right][/tex]

Separate:

       [tex]= \displaystyle \lim_{h \to 0} \left[\dfrac{\tan^{-1}\left(\dfrac{h}{1+x^2+xh)}\right)}{\dfrac{h}{(1+x^2+xh)}} \right] \cdot \displaystyle \lim_{h \to 0} \left[\dfrac{1}{1+x^2+xh}\right][/tex]

[tex]\textsf{Use }\displaystyle \lim_{h \to 0} \left[\dfrac{\tan^{-1} \theta}{\theta} \right]=1:[/tex]

       [tex]= 1 \cdot \displaystyle \lim_{h \to 0} \left[\dfrac{1}{1+x^2+xh}\right][/tex]

As h gets close to zero:

       [tex]= 1 \cdot \left[\dfrac{1}{1+x^2}\right][/tex]

Simplify:

       [tex]=\dfrac{1}{1+x^2}[/tex]

Answer:

To find the derivative of [tex]\tan^{-1} x[/tex] using the first principle of derivative, we need to use the definition of the derivative:

f'(x) = lim(h->0) [(f(x + h) - f(x)) / h]

where f(x) = [tex]\tan^{-1} x[/tex].

Substituting f(x) into the definition of the derivative, we get:

f'(x) = lim(h->0) [([tex]\tan^{-1}[/tex](x + h) - [tex]\tan^{-1}/tex) / h]

To simplify this expression, we can use the formula for the inverse tangent of a sum:

[tex]\tan^{-1}[/tex](a + b) = [tex]\tan^{-1}[/tex]a + [tex]\tan^{-1}[/tex]b - [tex]\pi[/tex]/2

Using this formula, we can rewrite the numerator of the expression above as:

([tex]\tan^{-1}[/tex](x + h) - [tex]\tan^{-1}/tex) = [tex]\tan^{-1}[/tex]((x + h) / (1 + (x + h)^2)) - [tex]\tan^{-1}[/tex](x / (1 + x^2))

Now, substituting this expression back into the definition of the derivative, we get:

f'(x) = lim(h->0) [[tex]\tan^{-1}[/tex]((x + h) / (1 + (x + h)^2)) - [tex]\tan^{-1}[/tex](x / (1 + x^2))] / h

We can simplify this expression using algebra and trigonometry, and we get:

f'(x) = lim(h->0) [h / (1 + x^2 + hx + h^2 + x^2h + xh^2)] / h

f'(x) = lim(h->0) 1 / (1 + x^2 + hx + h^2 + x^2h + xh^2)

Now we can simplify this expression by dropping the terms that contain h^2 or higher powers of h, since they will approach zero faster than h as h approaches zero. We also drop the term containing x^2h, since it is a second-order term and will also approach zero faster than h. This leaves us with:

f'(x) = lim(h->0) 1 / (1 + x^2 + hx)

Now we can evaluate the limit as h approaches zero:

f'(x) = 1 / (1 + x^2)

Therefore, the derivative of [tex]\tan^{-1} x[/tex] by first principle of derivative is:

[tex]\frac{d}{dx}[/tex][tex]\tan^{-1} x[/tex] = 1 / (1 + x^2)

Answer:

No Hablo Espaniol

Step-by-step explanation:

Answer: C.5.18 because you cant have a decimal as an integer

Step-by-step explanation: brainliest???

Answer:

18 cm

Step-by-step explanation:

To find the distance, take the larger number and subtract the smaller number

26 cm - 8 cm

18 cm

Answer:

29

the triangle on the right has 2 sides the same so the lower two corners have the same angle which would be (180-64)/2 = 58 degrees

the lower right angle of the triangle on the left Sadie would be 180-58 = 122.

Since 2 sides of the triangle on the left are the same the other two angles would be equal to each other.

x = (180-122)/2 = 29 degrees

Answer:

x = 29°

Explanation:

The triangle on right side is an isosceles triangle with two similar angles.

Let that angle be z:

⇒ z + z + 64° = 180°

⇒ 2z = 180° - 64°

⇒ 2z = 116°

⇒ z = 58°

After finding z, find the opposite angle:

⇒ 180° - 58° = 122°

Find the value of x:

⇒ x + x + 122° = 180°

⇒ 2x = 180° - 122°

⇒ 2x = 58°

⇒ x = 29°

Answer:

1/2 x 8 x 6
answer: 24

Step-by-step explanation:

formula of area of triangle= 1/2 x base x height

Answer:

Y = - 24

Step-by-step explanation:

Y/-6 +5=9 /*6 (Multiply the whole equation by the number 6 to eliminate the fraction. That is, you multiply each member of the equation by 6 because 6 is in the denominator of the fraction.
[tex]\frac{Y}{-6} *6=-Y[/tex],     [tex]5*6=30[/tex],    [tex]9*6=54[/tex]

-Y + 30 = 54
-Y = 54-30
-Y=24 /*(-1)
Y= -24

Answer:

√33

Step-by-step explanation:

it is a right triangle and we use Pythagoras

x² = 7² - 4²

x² = 49 - 16

x² = 33

x = √33

The correct answer is option C which is the ratio of the difference in the means of the two teams to the mean absolute deviation of Team B will be 0.25.

Mean is defined as the ratio of the sum of the number of the data sets to the total number of the data.

The difference between the mean times is about 16 times the mean absolute deviation of the data set.

59.32 - 59.1 = 0.22

2.4 - 1.5 = 0.9

0.22 / 0.9 = 0.25

Therefore the correct answer is option C which is the ratio of the difference in the means of the two teams to the mean absolute deviation of Team B will be 0.25.

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Answer:

c

Step-by-step explanation:

Step-by-step explanation:

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

[tex] \frac{5}{a} = \frac{a {}^{x} }{a} [/tex]

[tex] \frac{5}{a} = {a}^{x - 1} [/tex]

Answer:

See below

Step-by-step explanation:

There could be INFINITE possibilities....(you didn't list any choices to choose from)

 here is one to change to base 10

     log5 ( 13)   =   log10 ( 13) / log10 ( 5)  

When we solve the equation, we will get the real answer x=40 as a variable.

First degree equation is a mathematical sentence, which has values represented by letters.

These letters can indicate a variable or an unknown - which at the end of the equation will be the final value.

— To solve this equation, just: apply the distributive property (multiply the terms that are outside the parentheses, for the terms that are inside the symbol).

— Next, let's add the real numbers together. Next, we'll subtract the like terms before the equality, thus moving the common term after the equality by adding.

— Finally, let's divide the equation, thus obtaining the final result.

4 + 3(x + 22) = 5x - 10

4 + 3x + 66 = 5x - 10

70 + 3x = 5x - 10

3x - 5x = -10 - 70

-2x = -80

x = 80 ÷ 2

x = 40

Therefore, the correct value of X in this equation, will be x = 40.

Answer:

[tex]7 \times 6 = 42[/tex]

Answer:

A. $3,535.20.

To find the total amount paid, you can simply multiply the monthly payment by the number of payments:

$98.20 x 36 = $3,535.20

The total sales of the year after is Rs. 1857143

He gets 1.5% commission on the total annual sales and a bonus of 2% on the sales above Rs. 20,00,000.

Therefore, since he received a bonus, the sale is over Rs. 20,000.

Hence,

let

x = total sales

Therefore,

1.5% of x + 2% of x   = 65000

1.5 / 100 × x + 2 / 100 × x = 65000

0.015x +0.02x = 65000

0.035x = 65000

x = 65000 / 0.035

x = 1857142.85714

Therefore,

total sales = Rs. 1857143

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500 represents the initial amount of medication, since when t=0, a=500.

Answer: [tex]17 \div 2[/tex]

Step-by-step explanation:

[tex]a/b[/tex] is the same thing as [tex]a \div b[/tex]

Answer:

x=1

y=−2

z=5

(heres how i got the answer)

Step-by-step explanation:

x+2y+3z=12

x−3y+4z=27

−x+y+2z=7

Solve x+2y+3z=12 for x.

x=−2y−3z+12

Substitute −2y−3z+12 for x in the second and third equation.

−2y−3z+12−3y+4z=27

−(−2y−3z+12)+y+2z=7

Solve equations for y and z respectively.

y=−3+

5

1

​

z

z=

5

19

​

−

5

3

​

y

Substitute −3+

5

1

​

z for y in the equation z=

5

19

​

−

5

3

​

y.

z=

5

19

​

−

5

3

​

(−3+

5

1

​

z)

Solve z=

5

19

​

−

5

3

​

(−3+

5

1

​

z) for z.

z=5

Substitute 5 for z in the equation y=−3+

5

1

​

z.

y=−3+

5

1

​

×5

Calculate y from y=−3+

5

1

​

×5.

y=−2

Substitute −2 for y and 5 for z in the equation x=−2y−3z+12.

x=−2(−2)−3×5+12

Calculate x from x=−2(−2)−3×5+12.

x=1

The system is now solved.

x=1

y=−2

z=5

Answer:

there is no line

Answer:

[tex]13 \times 1 \div 67 [/tex]

The equation that has the same solution as x² + 8x + 15 = -4x is x = -6± √21.

Step 1 - Move terms to the left

x² + 8x + 15 = -4x

x² + 8x + 15-(-4x) = 0

Step 2  - Combine the terms

x² + 8x + 15 + 4x = 0

x² + 12x + 15 = 0

Step 3 - Apply the quadratic formula

x = (-b ± √(b² - 4ac) )/ 2a

Recall that form our equation:

a = 1

b = 12

c = 15

Thus,  x = (-12 √(12² - 4 * 1 *15) )/2 *1

⇒x = -6 ± √21


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Answer:

Ally

Step-by-step explanation:

The fastest time of the race will be the one lesser in value.

=============================================================

Comparing the tenths place :

⇒ Jill = 8 in the tenths place

⇒ Ally = 8 in the tenths place

⇒ Maria = 9 in the tenths place

Since Maria's time's tenth place value is greater than that of the other two, she had the slowest time.

===========================================================

Comparing the hundredths place (for Jill and Ally) :

⇒ Jill = 7 in the hundredths place

⇒ Ally = 2 in the hundredths place

Since Ally has the lower hundredths' place value, she has the fastest time.

The answer that I got is 7 500

Answer:

There are eight sides so it's an octagon

Step-by-step explanation:

By solving a quadratic equation, we will see that the length is 10m and the width is 6.5m

For a rectangle of width W and length L, the area is:

A = W*L

In this case, we know that the area is 65m² and that the length is 3 meters less than 2 times the width, so:

L = 2*W - 3m

Then we can write:

65m² = (2*W - 3m)*W = 2*W² - 3m*W

This is a quadratic equation:

2*W² - 3m*W - 65m² = 0.

The solutions are given by the Bhaskara's formula:

[tex]W = \frac{3 \pm \sqrt{(-3)^2 - 4*2*(-65)} }{2*2} \\\\W = \frac{3 \pm 23 }{4}[/tex]

We only care for the positive solution, which is:

W = (3m + 23m)/4 = 26m/4 = 6.5m

Then the length is:

L = 2*6.5m - 3m = 10m

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The new sample size based on the information will be B-M, B-C, B-R, 8.

Sample size is the number of participants or observations that are included in a study. This is usually represented by n.

When the boys and girls are to be chosen, the new sample size based on the information will be B-M, B-C, B-R, 8.

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Answer:

Step-by-step explanation:

B-M, B-C, B-R, 8.