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2 years ago

9

What is the 43rd term of the sequence: 17, 9, 1, -7

1 answer:

Yuki888 [10]2 years ago

5 0

Answer:

-319

Step-by-step explanation:

You might be interested in

The radius of a sphere is increasing at a rate of 5 mm/s. How fast is the volume increasing (in mm3/s) when the diameter is 40 m

jeka94

9514 1404 393

Answer:

8000π mm^3/s ≈ 25,133 mm^3/s

Step-by-step explanation:

The rate of change of volume is found by differentiating the volume formula with respect to time.

V = 4/3πr^3

V' = 4πr^2·r'

For the given numbers, this is ...

V' = 4π(20 mm)^2·(5 mm/s) = 8000π mm^3/s ≈ 25,133 mm^3/s

_____

<em>Additional comment</em>

By comparing the derivative to the area formula for a sphere, you see that the rate of change of volume is the product of the area and the rate of change of radius. This sort of relationship will be seen for a number of different shapes.

4 0

2 years ago

If u(x) = x5 – x4 + x2 and v(x) = –x2, which expression is equivalent to (u/v)(x)

choli [55]

Answer:

c) -x^3 + x^2 - 1

Step-by-step explanation:

Given: u (x) = x^5 - x^4 +x^2 and v(x) = -x^2

(u/v)(x) = u(x)/v(x)

Now plug in the given functions in the above formula, we get

= (x^5 - x^4 + x^2) / -x^2

We can factorize the numerator.

In x^5 - x^4 + x^2. the common factor is x^2, so we can take it out and write the remaining terms in the parenthesis.

= x^2 (x^3 - x^2 + 1) / - x^2

Now we gave x^2 both in the numerator and in the denominator, we can cancel it out.

(u/v)(x) = (x^3 - x^2 + 1) / -1

When we dividing the numerator by -1, we get

(u/v)(x) = -x^3 + x^2 - 1

Answer: c) -x^3 + x^2 - 1

Hope you will understand the concept.

Thank you.

6 0

2 years ago

Read 2 more answers

Write an exponential function in the form y=ab^x that goes through points (0,14) and (3,3024).

Dmitrij [34]

Answer:

y = 14 $(6)^{x}$

Step-by-step explanation:

For an exponential function of the form y = a $b^{x}$

Use the given points to find a and b

Using (0, 14 ), then

14 = a $b^{0}$ ( $b^{0}$ = 1 ) , thus

a = 14

y = 14 $b^{x}$

Using (3, 3024 ) , then

3024 = 14 b³ ( divide both sides by 14 )

216 = b³ ( take the cube root of both sides )

b = $\sqrt[3]{216}$ = 6 , thus

y = 14 × $6^{x}$ ← exponential function

5 0

2 years ago

F(x) = x + 4 and g(x) = 2x + 3, evaluate each expression.

Rom4ik [11]

Answer:

$15.~f(g(2))=\Large\boxed{11}\\$

$16.~g(f(2.5))=\Large\boxed{16}$

$17.~g(f(-5))=\Large\boxed{1}$

$18.~f(g(-5))=\Large\boxed{-3}$

Step-by-step explanation:

<h3>Given information</h3>

$f(x)=x+4$

$g(x)=2x+3$

<h3>Question 15. f(g(2))</h3>

<u>Substitute values into the first function</u>

$g(2)=2(2)+3$

$g(2)=4+3$

$g(2)=7$

<u>Substitute the values of the first function into the second</u>

$f(g(2))=f(7)$

$f(7)=(7)+4$

$f(7)=\Large\boxed{11}$

<h3>Question 16. g(f(2.5))</h3>

<u>Substitute values into the first function</u>

$f(2.5)=(2.5)+4$

$f(2.5)=6.5$

<u />

<u>Substitute the values of the first function into the second</u>

$g(f(2.5))=g(6.5)$

$g(6.5)=2(6.5)+3$

$g(6.5)=13+3$

$g(6.5)=\Large\boxed{16}$

<h3>Question 17. g(f(-5))</h3>

<u>Substitute values into the first function</u>

$f(-5)=(-5)+4$

$f(-5)=-1$

<u>Substitute the values of the first function into the second</u>

$g(f(-5))=g(-1)$

$g(-1)=2(-1)+3$

$g(-1)=-2+3$

$g(-1)=\Large\boxed{1}$

<h3>Question 18. f(g(-5))</h3>

<u>Substitute values into the first function</u>

$g(-5)=2(-5)+3$

$g(-5)=-10+3$

$g(-5)=-7$

<u>Substitute the values of the first function into the second</u>

$f(g(-5))=f(-7)$

$f(-7)=(-7)+4$

$f(-7)=\Large\boxed{-3}$

Hope this helps!! :)

Please let me know if you have any questions

7 0

1 year ago

Write the equation of a line that is perpendicular to the given line and that passes through the given point.

poizon [28]

Answer: y=-3x+29

Step-by-step explanation:

First put in y-intercept form to find the slope

$4x-12y=2\\-12y=-4x+2\\y=\frac{1}{3} x-\frac{1}{6}$

Slope of the 1st equation is 1/3- the slope of the line perpendicular is the opposite reciprocal, so in the case it is -3

Use the point and the new slope to write the new equation in point slope format

$y-y_{1} =m(x-x_{1} )\\y-(-1)=-3(x-10)\\y+1=-3x+30\\y=-3x+29$

8 0

2 years ago