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3 years ago

24=6c help me solve this

Mathematics

1 answer:

Ket [755]3 years ago

7 0

Answer:

c = 4

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS
Equality Properties

Step-by-step explanation:

Step 1: Define equation

24 = 6c

Step 2: Solve for c

Divide 6 on both sides: 4 = c
Rewrite: c = 4

Step 3: Check

Plug in c to verify it's a solution.

Substitute in c: 24 = 6(4)
Multiply: 24 = 24

Here we see that 24 does indeed equal 24.

∴ c = 4 is a solution of the equation.

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Can someone please help me with this

Mama L [17]

Answer:

27.

Equation of 2 tangent lines at the given curve going through point P is:

y = -7x + 1

y = x + 1

28.

Part 1: 400 feet

Part 2: Velocity is +96 feet/second (or 96 feet/second UPWARD) & Speed is 96 feet per second

Part 3: acceleration at any time t is -32 feet/second squared

Part 4: t = 10 seconds

29.

Part 1: Average Rate of Change = -15

Part 2: The instantaneous rate of change at x = 2 is -8 & at x = 3 is -23

Step-by-step explanation:

27.

First of all, the equation of tangent line is given by:

$y-y_1=m(x-x_1)$

Where m is the slope, or the derivative of the function

Now,

If we take a point x, the corresponding y point would be $x^2-3x+5$ , so the point would be $(x,x^2-3x+5)$

Also, the derivative is:

$f(x)=x^2-3x+5\\f'(x)=2x-3$

Hence, we can equate the DERIVATIVE (slope) and the slope expression through the point given (0,1) and the point we found $(x,x^2-3x+5)$

The slope is $\frac{y_2-y_1}{x_2-x_1}$

So we have:

$\frac{x^2-3x+5-1}{x-0}\\=\frac{x^2-3x+4}{x}$

Now, we equate:

$2x-3=\frac{x^2-3x+4}{x}$

We need to solve this for x. Shown below:

$2x-3=\frac{x^2-3x+4}{x}\\x(2x-3)=x^2-3x+4\\2x^2-3x=x^2-3x+4\\x^2=4\\x=-2,2$

So, this is the x values of the point of tangency. We evaluate the derivative at these 2 points, respectively.

$f'(x)=2x-3\\f'(-2)=2(-2)-3=-7\\f'(2)=2(2)-3=1$

Now, we find 2 equations of tangent lines through the point (0,1) and with respective slopes of -7 and 1. Shown below:

$y-y_1=m(x-x_1)\\y-1=-7(x-0)\\y-1=-7x\\y=-7x+1$

and

$y-y_1=m(x-x_1)\\y-1=1(x-0)\\y-1=x\\y=x+1$

So equation of 2 tangent lines at the given curve going through point P is:

y = -7x + 1

y = x + 1

28.

Part 1:

The highest point is basically the maximum value of the position function. To get maximum, we differentiate and set it equal to 0. Let's do this:

$s(t)=160t-16t^2\\s'(t)=160-32t\\s'(t)=0\\160-32t=0\\32t=160\\t=\frac{160}{32}\\t=5$

So, at t = 5, it reaches max height. We plug in t = 5 into position equation to find max height:

$s(t)=160t-16t^2\\s(5)=160(5)-16(5^2)\\=400$

max height = 400 feet

Part 2:

Velocity is speed, but with direction.

We also know the position function differentiated, is the velocity function.

Let's first find time(s) when position is at 256 feet. So we set position function to 256 and find t:

$s(t)=160t-16t^2\\256=160t-16t^2\\16t^2-160t+256=0\\t^2-10t+16=0\\(t-2)(t-8)=0\\t=2,8$

At t = 2, the velocity is:

$s'(t)=v(t)=160-32t\\v(2)=160-32(2)\\v(2)=96$

It is going UPWARD at this point, so the velocity is +96 feet/second or 96 feet/second going UPWARD

The corresponding speed (without +, -, direction) is simply 96 feet/second

Part 3:

We know the acceleration is the differentiation of the velocity function. let's find it:

$v(t)=160-32t\\v'(t)=a(t)=-32$

hence, the acceleration at any time t is -32 feet/second squared

Part 4:

The rock hits the ground when the position is 0 (at ground). So we equate the position function, s(t), to 0 and find time when it hits the ground. Shown below:

$s(t)=160t-16t^2\\0=160t-16t^2\\16t^2-160t=0\\16t(t-10)=0\\t=0,10$

We disregard t = 0 because that's basically starting. So we take t = 10 seconds as our answer and we know rock hits the ground at t = 10 seconds.

29.

Part 1:

The average rate of change is basically the slope, which is

Slope = Change in y/ Change in x

The x values are given, from 2 to 3, and we need to find corresponding y values by plugging in the x values in the function. So,

When x = 2, $y=f(2)=-(2)^3 + 4(2) + 2=2$

When x = 3, $y=f(3)=-(3)^3 + 4(3) + 2=-13$

Hence,

Average Rate of Change = $\frac{-13-2}{3-2}=-15$

Part 2:

The instantaneous rate of change is got by differentiating the function and plugging the 2 points and finding the difference.

First, let's differentiate:

$f(x)=-x^3+4x+2\\f'(x)=-3x^2+4$

Now, find the derivative at 3,

$f'(x)=-3x^2+4\\f'(3)=-3(3)^2+4=-23$

finding derivative at 2,

$f'(x)=-3x^2+4\\f'(2)=-3(2)^2+4=-8$

The instantaneous rate of change at x = 2 is -8 & at x = 3 is -23

6 0

3 years ago

For which pairs of functions is (f•g)(x)=x of functions is (f•g)(x)=x

Sonbull [250]

Answer:

Option A

Step-by-step explanation:

The complete question is shown in the attachment.

Note that: $(f\cdot g)(x)=f(x)\cdot g(x)$

We need to multiply all the functions to see which of them satisfy the given criteria.

Option A

$x^2\cdot \frac{1}{x} =\frac{x^2}{x}=x$

Option B

$\frac{2}{x} \cdot \frac{2}{c} =\frac{4}{cx}$

Option C

$\frac{x-2}{3} \cdot 2-3x =\frac{-3x^2+8x-4}{3}$

Option D

$\frac{1}{2x-2} \cdot \frac{1}{2x+2} =\frac{1}{4(x^2-1)}$

The correct choice is A

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4 years ago

What is 21/99 in a decimal form

Norma-Jean [14]

Answer:

0.2121~

Step-by-step explanation:

It's a repeating number. 0.0212121212

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4 years ago

Todd has 2 frogs. This is 1/3 the number of frogs that Heather has. How many frogs does Heather have?

Murljashka [212]

2=1/3H
H=2*3
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4 years ago

Read 2 more answers

1. what is the setting of home sick by jean fritz

galben [10]

Answer:

2. Jean a ten-year-old girl in the town of Hankow. Her mother and father work for the YMCA doing relief work. She attends a British school there and hates her teacher, Miss Williams, along with a couple of the other students. In general, Jean feels culturally conflicted, the product of two cultures but not belonging to either one, and she longs for a long-promised trip to America in a couple of years.

Step-by-step explanation:

Homesick is author Jean Fritz's story of her childhood growing up in China in a town called Hankow. While Jean adopts a first-person perspective and includes mostly real-life details from her life, some parts of Homesick are fictionalized in order to add dramatic interest.

8 0

3 years ago

24=6c help me solve this​

24=6c help me solve this