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3 years ago

If f(x) = integral of 1/ (sqrt of t^3 +2)dt, then f'1 = ?

1 answer:

mihalych1998 [28]3 years ago

4 0

Differentiating an integral removes the integral.

f(x) = integral of dt/sqrt(t^3 + 2)
f'(x) = 1/sqrt(x^3 + 2)
f'(1) = 1/sqrt(1^3 + 2)
f'(1) = 1/sqrt(3) = sqrt(3)/3.

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Diona told me to get this app to solve my math problems,what is 10 + 10 Jean can't help because she's doing other stuff :,)

elena55 [62]

Answer:

Step-by-step explanation:

10 + 10

= 20

Just add units place first.

0 + 0 = 0

Then tens place.

1 + 1 = 2

So the number,

=> 20

5 0

2 years ago

A sales person is paid a weekly salary of $760, plus a commission of 7.5% of all her sales for the week. Express her weekly inco

Elis [28]

Answer:

1. We can see that salesperson's weekly income is the sum of her constant weekly salary ($760) and a commission which is variable and depends on her weekly sales.

So, if we say that y is her weekly income and x is her weekly sales, we can write this as:

y = 760 + 0.075x

Note that we had to change percentage to decimal number dividing it by 100.

2 Since for each value of x there is only one corresponding value of y, we can say that this is a function. For any value of x we input there is only one solution we get - that is the main feature of function and a way to tell if something is really a function.

Since this is a function, it can also be written as:

f(x) = 760 + 0.075x

3. Domain of a function is, basically, set of all values of x for which the function can work. That practically means that, since x is weekly sale, it can not be negative (one cannot make -$500 sale, for example). However, it is possible that she doesn't make a sale one week, making it possible for x to be 0. Also, the value of her sales doesn't have to be integer (it is quite possible that she makes $673.50 sale).

All this means that appropriate domain for this function are positive real numbers including 0.

6 0

3 years ago

the length of a rectangle is 8cm more than the width and its area is 172cm2 .find the width of the rectabgle

nikdorinn [45]

$l-the\ length\\l+8-the\ width\\A=172\ cm^2\\\\A=lengtf\cdot width\\\\subtitute\\\\l(l+8)=172\\\\l^2+8l=172\ \ \ |subtract\ 172\ from\ both\ sides\\\\l^2+8l-172=0\\a=1;\ b=8;\ c=-172\\\\\Delta=b^2-4ac\\\\\Delta=8^2-4\cdot1\cdot(-172)=64+688=752 > 0\\\\l_1=\dfrac{-b-\sqrt\Delta}{2a}\ and\ l_2=\dfrac{-b+\sqrt\Delta}{2a}\\\\\sqrt\Delta=\sqrt{752}=\sqrt{16\cdot47}=4\sqrt{47}\\\\l_1=\dfrac{-8-4\sqrt{47}}{2\cdot1}=-4-2\sqrt{47} < 0\\\\l_2=\dfrac{-8+4\sqrt{47}}{2\cdot1}=-4+2\sqrt{47} > 0\\\\The\ width:l+8=-4+2\sqrt{47}+8=4+2\sqrt{47}\\\\Answer:\boxed{length=(2\sqrt{47}-4)cm;\ width=(4+2\sqrt{47})cm}$
$length\approx9.71cm;\ width\approx17.71cm$

4 0

3 years ago

Simplify by combining like terms: 15x +2 - 7 - 5x

Step2247 [10]

Answer:

10x-5

Step-by-step explanation:

You subtract 15x-5=10x. Then you do -7+2. The 7 is negative . So it would be -7 plus two. So it would equal -5. So it's 10x-5

5 0

3 years ago

A rectangular garden has a walkway around it. The area of the garden is 4(4.5xplus1.5). The combined area of the garden and th

Arte-miy333 [17]

Answer:

Walkway is 1.5 units²

Step-by-step explanation:

Just subtract the area of the garden from the combined area:

Also did you mean difference? I don't know what it means by sum.

8 0

3 years ago