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2 years ago

Mr. Gary wrote the sequence below on the board.

Mathematics

1 answer:

sp2606 [1]2 years ago

6 0

Answer:

a₁ = 10
aₙ = aₙ₋₁ - 5

Step-by-step explanation:

Given the sequence:

10, 5, 0, -5, -10

The first term is 10 and the common difference is -5

The recursive formula for the given sequence is:

a₁ = 10
aₙ = aₙ₋₁ - 5

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Trevor is analyzing a circle, y2 + x2 = 49, and a linear function g(x). Will they intersect?

melomori [17]

We have a circumference that is given by the following equation:

$x^{2}+y^{2}=49$

We can write this equation in its standard form as follows:

$x^{2}+y^{2}=7^{2} \\ where \ the \ radius \ r=7$

On the other hand, the linear function is given as the following table:

$x \ \ \ \ \ \ \ \ g(x) \\ -1 \ \ -9.2 \\ 0 \ \ \ \ \ -9 \\ 1 \ \ \ \ \ -8.8$

To check if the circle and the line intersects, let's substitute the equation of the line into the equation of the circle to see if there is a real solution, so:

$x^{2}+(0.2x-9)^{2}=49 \\ \\ \therefore x^{2}+0.04x^{2}-3.6x+81=49 \\ \\ \therefore 1.04x^{2}-36x+32=0 \\ \\ Solving \ for \ x: \\ x_{1}=33.70 \\ x_{2}=0.91 \\ \\ Solving \ for \ y: \\ y_{1}=0.2(33.70)-9=-2.26 \\ y_{2}=0.2(0.91)-9=-8.18$

Finally the intersects are:

$P_{1}(33.70, -2.26) \ and \ P_{2}(0.91, -8.18)$

7 0

2 years ago

Read 2 more answers

What percent of sallys salary does she budget for donations? -1 -3 -10 -33

stealth61 [152]

I thought I already answered this but its -10

5 0

3 years ago

The diameter of a planet is about 10,652 mi. The diameter of the planet's moon is about 25% of the planet. What percent of the v

alekssr [168]

Answer:

$2\%$

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube

Let

z-----> the scale factor

x----> the volume of the planet's moon

y---> the volume of the planet

$z^{3}=\frac{x}{y}$

In this problem we have

$z=0.25$

elevated to the cube

$z^{3}=0.25^{3}=0.015625$

Find the percent

$0.015625*100=1.56\%$

Round to the nearest whole number

$1.56\%=2\%$

5 0

3 years ago

What is statistical power and how would you calculate it?

Natasha_Volkova [10]

Answer:

The statistical power of a hypothesis test is the probability of detecting an effect, if there is a true effect present to detect. Power can be calculated and reported for a completed experiment to comment on the confidence one might have in the conclusions drawn from the results of the study.

I hope it's helpful!

3 0

3 years ago

I need help with part b. I feel like there’s a catch, I want to do the first derivative test, however, I feel like there is a be

Sladkaya [172]

Answer:

The fifth degree Taylor polynomial of g(x) is increasing around x=-1

Step-by-step explanation:

Yes, you can do the derivative of the fifth degree Taylor polynomial, but notice that its derivative evaluated at x =-1 will give zero for all its terms except for the one of first order, so the calculation becomes simple:

$P_5(x)=g(-1)+g'(-1)\,(x+1)+g"(-1)\, \frac{(x+1)^2}{2!} +g^{(3)}(-1)\, \frac{(x+1)^3}{3!} + g^{(4)}(-1)\, \frac{(x+1)^4}{4!} +g^{(5)}(-1)\, \frac{(x+1)^5}{5!}$

and when you do its derivative:

1) the constant term renders zero,

2) the following term (term of order 1, the linear term) renders: $g'(-1)\,(1)$ since the derivative of (x+1) is one,

3) all other terms will keep at least one factor (x+1) in their derivative, and this evaluated at x = -1 will render zero

Therefore, the only term that would give you something different from zero once evaluated at x = -1 is the derivative of that linear term. and that only non-zero term is: $g'(-1)= 7$ as per the information given. Therefore, the function has derivative larger than zero, then it is increasing in the vicinity of x = -1

6 0

3 years ago