Solve the inequality
3(x+1)<9

I'm guessing the second derivative is for y with respect to x, i.e.

[tex]\dfrac{\mathrm d^2y}{\mathrm dx^2}[/tex]

Compute the first derivative. By the chain rule,

[tex]\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{\mathrm dy}{\mathrm d\theta}\dfrac{\mathrm d\theta}{\mathrm dx}=\dfrac{\frac{\mathrm dy}{\mathrm d\theta}}{\frac{\mathrm dx}{\mathrm d\theta}}[/tex]

We have

[tex]y=b\sin\theta\implies\dfrac{\mathrm dy}{\mathrm d\theta}=b\cos\theta[/tex]

[tex]x=a\cos\theta\implies\dfrac{\mathrm dx}{\mathrm d\theta}=-a\sin\theta[/tex]

and so

[tex]\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{b\cos\theta}{-a\sin\theta}=-\dfrac ba\cot\theta[/tex]

Now compute the second derivative. Notice that [tex]\frac{\mathrm dy}{\mathrm dx}[/tex] is a function of [tex]\theta[/tex]; so denote it by [tex]f(\theta)[/tex]. Then

[tex]\dfrac{\mathrm d^2y}{\mathrm dx^2}=\dfrac{\mathrm df}{\mathrm dx}[/tex]

By the chain rule,

[tex]\dfrac{\mathrm d^2y}{\mathrm dx^2}=\dfrac{\mathrm df}{\mathrm d\theta}\dfrac{\mathrm d\theta}{\mathrm dx}=\dfrac{\frac{\mathrm df}{\mathrm d\theta}}{\frac{\mathrm dx}{\mathrm d\theta}}[/tex]

We have

[tex]f=-\dfrac ba\cot\theta\implies\dfrac{\mathrm df}{\mathrm d\theta}=\dfrac ba\csc^2\theta[/tex]

and so the second derivative is

[tex]\dfrac{\mathrm d^2y}{\mathrm dx^2}=\dfrac{\frac ba\csc^2\theta}{-a\sin\theta}=-\dfrac b{a^2}\csc^3\theta[/tex]

Answer: 400 units

Step-by-step explanation:

Volume=1/3a^2h

=1/3(10)^2(12)

=400

The correct answer is 400. I had the same question on a test I took not to long ago.

Answer:

-x^3 -3x+2

Step-by-step explanation:

f(x) = -3x +2

g(x) = x^3

(f-g)(x) = -3x +2 - x^3

          = -x^3 -3x+2

Answer:

Janice converted a mixed number to the wrong improper fraction.

Step-by-step explanation:

1 batch of stew uses 1 and 2/3 lb meat

Total amount of meat used - 10 and 5/6 lb

x = number of stew batches made

To get number of batches made, divide total meat used by the amount of meat each batch requires:

x = 10 5/6 ÷ 1 2/3

convert mixed fractions to improper fractions:

x = (10x6+5)/6 ÷ (1x3+2)/3

x = 65/6 ÷ 5/3

The fraction in bold numbers is where Janice got it wrong. She changed 1 2/3 to 5/2. (From the question: 10 and StartFraction 5 over 6 EndFraction divided by 1 and two-thirds = StartFraction 65 over 6 EndFraction divided by five halves). 1 2/3 converted to an improper fraction is 5/3. From this point going forward, the calculations are wrong.

Answer:

A

Step-by-step explanation:

Answer:

[tex]4 - 22 - 115[/tex]

answer is yes...........

Answer:

x=6

Step-by-step explanation:

11, 3, x, x+2, 5, 10

in ascending order the data points:

Answer:

13.7

Step-by-step explanation:

3x=41

x is around 13.7

Answer:

x = [tex]\frac{41}{3}[/tex]

x ≈ 13.7

Step-by-step explanation:

[tex]3x+15=56\\3x+15-15=56-15\leftarrow \text {Subtraction Property of Equality} \\3x=41\\\\\frac{3x}{3} =\frac{41}{3} \leftarrow \text {Division Property of Equality}\\\\\boxed {x=\frac{41}{3}}[/tex]

41/3 = 13.66666666....

13.666... ≈ 13.7

Answer:

a. y = 8x + 7

b. 8y = -x-74

Step-by-step explanation:

Here, we want to write the equation of a line which is parallel to y = 8x + 7 and passes through the given point

Since the line we want to write the equation is parallel to y = 8x + 7, it means that they have the same slope

Mathematically we can write the equation of a line as y = mx + c where m is the slope. Comparing this with y = 8x + 7, our slope is therefore 8

Now, the slope of our new line is also 8

We now make use of the point slope method to write the equation

Mathematically the point slope method is;

y-y1 = m(x-x1)

where our (x1,y1) = (-2,-9)

y-(-9) = 8(x -(-2))

y + 9 = 8(x + 2)

y + 9 = 8x + 16

y = 8x + 16-9

y = 8x + 7

For the second line, it is perpendicular to y = 8x + 7

Here too, we have the slope as 8

Now since they are perpendicular, it means that the product of the slopes is equal to -1

m1 * m2 = -1

8 * m2 = -1

m2 = -1/8

Now;

y-y1 = m(x-x1)

our point still remains same (-2,-9)

y-(-9) = -1/8 (x -(-2))

y + 9 = -1/8(x + 2)

8(y + 9) = -1(x + 2)

8y + 72 = -x -2

8y = -x -2-72

8y = -x-74

Answer:

0.027

Step-by-step explanation:

Convert to a fraction, then convert to a decimal by dividing the numerator by the denominator.

Answer:

x=4

Step-by-step explanation:

Answer:

44/51

Step-by-step explanation:

1 5/6 ÷ 2 1/8

Change to improper fractions

1 5/6 = (6*1+5)/6 = 11/6

2 1/8 = (8*2 +1) /8 = 17/8

11/6 ÷17/8

Copy dot flip

11/6 * 8/17

11/17 * 8/6

11/17 *4/3

44/51

Answer:

<1 = 48

Step-by-step explanation:

<1 + <2 + <3 = 180 since they form a line

<1 + 90+ 42 =180

Combine like terms

<1 + 132 =180

Subtract 132 from each side

<1 +132-132 =180-132

<1 = 48

Answer:

48 is the answer

Step-by-step explanation:

Answer:

126

Step-by-step explanation:

The probability is 90/500 = 18%

So, from 700 customers,

700 * 18%  = 700 * 18/100 = 126

Therefore, 126 customers will be selected on saturday.

Answer:

Runner 2 has the fastest pace

Step-by-step explanation:

The first one we need to find the slope

m = (y2-y1)/(x2-x1) = (40-0)/(4-0) =40/4 = 10 minutes per mile

The second  is 8.5 minutes per mile

The third we need to find the slope

m = (y2-y1)/(x2-x1) = (90-72)/(10-8) =18/2 = 9 minutes per mile

Answer:

[tex]-10x^9y^4[/tex]

Step-by-step explanation:

Answer:

-10x9y4

Step-by-step explanation:

When multiplying exponents it's like adding nothing serious. Hope this helps! Plz mark brainliest!!

1. x =5

2. x = 7

3. p = 12

4. m=2

5. z = 10

Answer:

Below in bold.

Step-by-step explanation:

1) 4x - 7 = 13

4x = 20

x = 20/4

x = 5.

2)  3x + 4 = 25

3x = 21

x = 7.

3) p/3 + 5 = 9

p/3 = 9 -5 = 4

Multiply both sides by 3:

p =  3*4

p = 12.

4)   m/5 + 2 = 12/5

Multiply through by 5:

m + 10 = 12

m = 12 -10

m = 2.

5) 4z/5 - 2 = 6

4z/5 = 8

Cross multiply:

4z = 5*8

4z = 40

z = 10.

Answer:

In this problem, we have three vertices, namely:

A(-2,2) , B(-2,4) , C(0,0)

Our transformation rule is (x+3,y-2) and this rule forms the image A'B'C'. So:

Step-by-step explanation:

A'=(-2+3,2-2)=(1,0)

B'=(-2+3,4-2)=(1,2)

C'=(0+3,0-2)=(3,-2)

Taking a look in the First Figure, we can see the two triangles. The red one is the triangle ABC and the blue one is A'B'C'. In the Second Figure, the corresponding vertices have been connected with line segments, as indicated the green lines. The characteristics of those three lines are two, namely:

They are parallel.

They have the same length.

Answer:

There are 33 students

Step-by-step explanation:

Because 7:4 should be in multiple of 11

Answer:

4/5

Step-by-step explanation:

y = mx + b

4/5 = m = slope

Answer:

The slope is 4/5.

Step-by-step explanation:

It's a linear equation. Which means that you can graph a "line" out of it.

The format is y=mx+b

mx=slope

b= y-intercept.

The slope is 4/5.

Answer: 30% or 3/10.

Step-by-step explanation: To find the probablilty of getting a white shirt, we first have to find the total number of shirts: 3 white + 2 blue + 5 red = 10 total. Out of the ten total, there are 3 white shirts. The probability of getting a white shirt is 3/10, because out of the 10 total shirts, 3 shirts are white.

Answer:

Step-by-step explanation:

[tex]Probability = \frac{Events}{Possible- outcomes} \\Total -no -of -shirts=3+2+5=10\\Event = 3 \\Probability = \frac{3}{10}[/tex]

I hope i am correct

Answer:

x = (A t)/4 + (p t)/4

Step-by-step explanation:

Solve for x:

A = (4 x)/t - p

A = (4 x)/t - p is equivalent to (4 x)/t - p = A:

(4 x)/t - p = A

Add p to both sides:

(4 x)/t = A + p

Multiply both sides by t/4:

Answer: x = (A t)/4 + (p t)/4

the number=A

5xA/7+A=2

5A/7 +A =2

5A/7=2-A/1

7(2-A)=1(5A)

14-7A=5A

14=5A+7A

14/12=12A/12

A=14/12

A=7/6

Answer:

OG, OC, TG, TC, VG, VC

Step-by-step explanation:

Soups: O, T, V

Salads: G, C

For each soup, he can choose 2 salads.

OG, OC, TG, TC, VG, VC

The sample space represents all the possible ways to choose one soup and one salad is {OG, OC, TG, TC, VG, VC}.

Sample space is the set of all the possible values or the outcomes of a event.

Let suppose the coin are tossed two times. Then the set of possible outcome or sample space of it can be given as,

[tex]S=\{HH,HT,TH,TT\}[/tex]

Here, H denotes the head and T denotes the tail part of the coin.

A customer at a restaurant can choose a soup and a salad from the menu choices shown.

For this menu the customer choose one onion as soup and one garden as salad which can be represented as (OG). Similarly, the sample space of his choice can be,

[tex]\{OG, OC, TG, TC, VG, VC\}[/tex]

Thus, the sample space represents all the possible ways to choose one soup and one salad is {OG, OC, TG, TC, VG, VC}.

Learn more about the sample space here;

https://brainly.com/question/9222927

#SPJ2

Answer:

Y=1/2x-3

Step-by-step explanation:

Down 3 at the y-axis and up 1 right 2.

Answer:

A =7.02 m^2

Step-by-step explanation:

The area of a trapezoid is given by

A = 1/2 (b1+b2)*h where b1 and b2 are the lengths of the bases

A = 1/2 ( 4.5+6.3) * 1.3

A = 1/2(10.8) * 1.3

A =7.02 m^2

Answer:

You divide the perimeter by the width to get the length

Step-by-step explanation:

Answer:

So we can simplify this to

36+4x=-1

We can subtract by 64 on both sides. 4x = -37. Therefore the answer to this is

x = -37/4 = -9.25.

So the answer for x is -16.25. If you were trying to do a quadratic equation then sorry because you worded it wrong, and I solved properly.

Answer:

x=9

y=5

Step-by-step explanation: