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STatiana [176]
3 years ago
15

Joy is thinking of a number. She says, "My number is 74 more than 2 thousands, 6 hundreds, 8 tens, and 4 ones." What is Joy's nu

mber?​
Mathematics
2 answers:
zavuch27 [327]3 years ago
5 0

Answer:

2758

Step-by-step explanation:

74 more than 2684

2684 + 74 = 2758

ElenaW [278]3 years ago
5 0

Answer:

2,785

Step-by-step explanation:

You need to add 2,684+74 and will equal 2,785... Yor welcome

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B) Let g(x) =x/2sqrt(36-x^2)+18sin^-1(x/6)<br><br> Find g'(x) =
jolli1 [7]

I suppose you mean

g(x) = \dfrac x{2\sqrt{36-x^2}} + 18\sin^{-1}\left(\dfrac x6\right)

Differentiate one term at a time.

Rewrite the first term as

\dfrac x{2\sqrt{36-x^2}} = \dfrac12 x(36-x^2)^{-1/2}

Then the product rule says

\left(\dfrac12 x(36-x^2)^{-1/2}\right)' = \dfrac12 x' (36-x^2)^{-1/2} + \dfrac12 x \left((36-x^2)^{-1/2}\right)'

Then with the power and chain rules,

\left(\dfrac12 x(36-x^2)^{-1/2}\right)' = \dfrac12 (36-x^2)^{-1/2} + \dfrac12\left(-\dfrac12\right) x (36-x^2)^{-3/2}(36-x^2)' \\\\ \left(\dfrac12 x(36-x^2)^{-1/2}\right)' = \dfrac12 (36-x^2)^{-1/2} - \dfrac14 x (36-x^2)^{-3/2} (-2x) \\\\ \left(\dfrac12 x(36-x^2)^{-1/2}\right)' = \dfrac12 (36-x^2)^{-1/2} + \dfrac12 x^2 (36-x^2)^{-3/2}

Simplify this a bit by factoring out \frac12 (36-x^2)^{-3/2} :

\left(\dfrac12 x(36-x^2)^{-1/2}\right)' = \dfrac12 (36-x^2)^{-3/2} \left((36-x^2) + x^2\right) = 18 (36-x^2)^{-3/2}

For the second term, recall that

\left(\sin^{-1}(x)\right)' = \dfrac1{\sqrt{1-x^2}}

Then by the chain rule,

\left(18\sin^{-1}\left(\dfrac x6\right)\right)' = 18 \left(\sin^{-1}\left(\dfrac x6\right)\right)' \\\\ \left(18\sin^{-1}\left(\dfrac x6\right)\right)' = \dfrac{18\left(\frac x6\right)'}{\sqrt{1 - \left(\frac x6\right)^2}} \\\\ \left(18\sin^{-1}\left(\dfrac x6\right)\right)' = \dfrac{18\left(\frac16\right)}{\sqrt{1 - \frac{x^2}{36}}} \\\\ \left(18\sin^{-1}\left(\dfrac x6\right)\right)' = \dfrac{3}{\frac16\sqrt{36 - x^2}} \\\\ \left(18\sin^{-1}\left(\dfrac x6\right)\right)' = \dfrac{18}{\sqrt{36 - x^2}} = 18 (36-x^2)^{-1/2}

So we have

g'(x) = 18 (36-x^2)^{-3/2} + 18 (36-x^2)^{-1/2}

and we can simplify this by factoring out 18(36-x^2)^{-3/2} to end up with

g'(x) = 18(36-x^2)^{-3/2} \left(1 + (36-x^2)\right) = \boxed{18 (36 - x^2)^{-3/2} (37-x^2)}

5 0
2 years ago
Consider the two number sets. Which set has the higher mean and what is that mean?
Otrada [13]

The mean is where you add all of the numbers in that set together, and divide it by the amount of numbers you have. E.g. For Set 1 - 10 + 15 + 20 + 25 + 30 + 50 = 150 ÷ 6 = 25

For Set 2 you just repeat the process:

1. Add the numbers in the set together, this gives you a total of 111

2. Then divide 111 by 5 as you have 5 numbers, giving you 22.2

Therefore set 1 has the higher mean :)

The answer is C, set 1, 25 :)

6 0
3 years ago
The table shows values for functions f(x) and g(x)
Alecsey [184]
Consider, pls, this solution:
f(x)=g(x) if x= -2 and x= -1, in those case f(x)=g(x)=4 and f(x)=g(x)=2
5 0
3 years ago
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PLEASE HELP <br> ANSWER ASAP
VLD [36.1K]
Question 1: h+4= how many kids in history class.
I think this cause it says to represent the # of kids in the English class with the varible h. there are 4 more kids in the history class for you just add four to the English class( h). this may be wrong tho

question 2: 57+4= 61.

you just input the 57 where the h (# of kids in English class) cause it need to figure out how many are in history and their are just four more kids. I think


also sorry if I suck at explaining things, this makes sorta sense
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3 years ago
Jewelry is commonly weighed in carats. Five carats are equivalent to one gram. How many grams of gold are contained in a 24-cara
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The answer is 4.8 
1/5=x/24
5x/5=24/5
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6 0
3 years ago
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