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1 year ago

Find the sum of 2.54 x 1019 and 3.218 x 1017. 3.2434 x 1036 2.57218 x 1036 3.2434 x 1019 2.57218 x 1019

Mathematics

1 answer:

GaryK [48]1 year ago

4 0

The sum of 2.54 x 1019 and 3.218 x 1017. 3.2434 x 1036 2.57218 x 1036 3.2434 x 1019 2.57218 x 1019 is 17811.9829.

As in the given problem we can see that multiplication of decimal number followed by summation is given so we an do it by parts.

The first part is 2.54*1019=2588.26

3.218 x 1017=3272.706

3.2434 x 1036= 3360.1624

2.57218 x 1036= 2664.77848

3.2434 x 1019=3305.0246

2.57218 x 1019=2621.05142

The sum is 17811.9829.

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g Use this to find the equation of the tangent line to the parabola y = 2 x 2 − 7 x + 6 at the point ( 4 , 10 ) . The equation o

natali 33 [55]

Answer:

The tangent line to the given curve at the given point is $y=9x-26$ .

Step-by-step explanation:

To find the slope of the tangent line we to compute the derivative of $y=2x^2-7x+6$ and then evaluate it for $x=4$ .

$(y=2x^2-7x+6)'$ Differentiate the equation.

$(y)'=(2x^2-7x+6)'$ Differentiate both sides.

$y'=(2x^2)'-(7x)'+(6)'$ Sum/Difference rule applied: $(f(x)\pmg(x))'=f'(x)\pm g'(x)$

$y'=2(x^2)'-7(x)'+(6)'$ Constant multiple rule applied: $(cf)'=c(f)'$

$y'2(2x)-7(1)+(6)'$ Applied power rule: $(x^n)'=nx^{n-1}$

$y'=4x-7+0$ Simplifying and apply constant rule: $(c)'=0$

$y'=4x-7$ Simplify.

Evaluate y' for x=4:

$y'=4(4)-7$

$y'=16-7$

$y'=9$ is the slope of the tangent line.

Point slope form of a line is:

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

where $m$ is the slope and $(x_1,y_1)$ is a point on the line.

Insert 9 for $m$ and (4,10) for $(x_1,y_1)$ :

$y-10=9(x-4)$

The intended form is $y=mx+b$ which means we are going need to distribute and solve for $y$ .

Distribute:

$y-10=9x-36$

Add 10 on both sides:

$y=9x-26$

The tangent line to the given curve at the given point is $y=9x-26$ .

------------Formal Definition of Derivative----------------

The following limit will give us the derivative of the function $f(x)=2x^2-7x+6$ at $x=4$ (the slope of the tangent line at $x=4$ ):

$\lim_{x \rightarrow 4}\frac{f(x)-f(4)}{x-4}$

$\lim_{x \rightarrow 4}\frac{2x^2-7x+6-10}{x-4}$ We are given f(4)=10.

$\lim_{x \rightarrow 4}\frac{2x^2-7x-4}{x-4}$

Let's see if we can factor the top so we can cancel a pair of common factors from top and bottom to get rid of the x-4 on bottom:

$2x^2-7x-4=(x-4)(2x+1)$

Let's check this with FOIL:

First: $x(2x)=2x^2$

Outer: $x(1)=x$

Inner: $(-4)(2x)=-8x$

Last: $-4(1)=-4$

---------------------------------Add!

$2x^2-7x-4$

So the numerator and the denominator do contain a common factor.

This means we have this so far in the simplifying of the above limit:

$\lim_{x \rightarrow 4}\frac{2x^2-7x-4}{x-4}$

$\lim_{x \rightarrow 4}\frac{(x-4)(2x+1)}{x-4}$

$\lim_{x \rightarrow 4}(2x+1)$

Now we get to replace x with 4 since we have no division by 0 to worry about:

2(4)+1=8+1=9.

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3 years ago

When Justin goes to work, he drives at an average speed of 65 miles per hour. It takes about 1 hour and 30 minutes for Justin to

Fofino [41]

Answer:

Justin spends $14.24 on gas to travel to work.

Step-by-step explanation:

Given:

Average speed at which Justin goes to work = 65 miles/hour

Time taken by Justin to arrive at work = 1 hour and 30 minutes = 1.5 hours [As 30 minutes =0.5 hours]

Distance he can travel per gallon of gas = 25 miles.

Cost of per gallon of gas = $3.65

Solution:

We first determine the distance Justin travels to work.

Distance = $Speed\times time$

Distance = $65\times 1.5 = 97.5\ miles$

Using unitary method to find the amount of gas required to cover the distance.

If 25 miles is covered in 1 gallon of gas

Then 1 mile will be covered in = $\frac{1}{25}$ gallons of gas

So, to cover 97.5 miles gas required = $\frac{1}{25}\times 97.5=3.9$ gallons of gas.

Using unitary method to find the cost of 3.9 gallons of gas.

Cost of 1 gallon of gas = $3.65

So, cost of 3.9 gallons of gas will be = $\$3.65\times 3.9=\$14.235\approx\$14.24$ (Answer)

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3 years ago

Fiona has to choose a bouquet for her wedding. The probability that she uses red roses is 98%, the probability that she uses orc

tekilochka [14]

0.84: you would do .82/.98 (the probability of orchids and roses divided by probability of roses)

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3 years ago

Please write an equation of a line in slope-intercept form with the given slope and y-intercept.

klio [65]

Answer: A. y = -6x - 2
B. y = x - 12

Explanation:
Slope intercept form: y = mx + b
m = slope
b = y-intercept

I would appreciate the brainliest if this was helpful and correct! :)

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2 years ago

Read 2 more answers

The data below shows the attendance of fans at each home game for the high school baseball team. Fan attendance at home games: 3

kogti [31]

Answer:

Average attendance with outlier = 39

Average attendance without outlier = 35.3

Step-by-step explanation:

Given the following data 34, 37, 30, 65, 34, 38, 41, 33

The outlier is the value that is lower or higher than other values in the dataset. Hence the outlier in this case is 65

Average = Sum of data/sample size

With the outlier;

Sum of dataset = 34+37+30+65+34+38+41+33

Sum of datasets = 312

Sample size = 8

Average attendance with the outlier = 312/8

Average attendance with the outlier = 39

Without the outlier;

The required data will exclude 65;

34, 37, 30, 34, 38, 41, 33

Sum of data = 34+37+30+34+38+41+33

Sum of data = 247

Sample size = 7

Average attendance without outlier = 247/7

Average attendance without outlier = 35.3

7 0

3 years ago