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3 years ago

Will mark Brainliest!

Mathematics

1 answer:

Anettt [7]3 years ago

5 0

Answer:a=2.1 :)

Step-by-step explanation:a+(-1.6)=-3.7

+1.6 +1.6

a=-2.1

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Read 2 more answers

Please Help!!!<br> Due: Monday<br> On Ellipses - Pre Calc

eduard

25. <u>Step-by-step explanation:</u>

$\text{The general form of an ellipse is:}\dfrac{(x-h)^2}{a^2}+\dfrac{(y-k)^2}{b^2}=1\\\\\bullet \text{(h, k) is the Center}\\\bullet \text{a is the radius of x}\\\bullet \text{b is the radius of y}\\\bullet \text{the largest value between a and b is the major}\\\bullet \text{the smallest value between a and b is the minor}\\\bullet \text{the vertices are the (h, k) value plus the major (a or b) value}\\\bullet \text{the co-vertices are the (h, k) value plus the minor (a or b) value}\\\bullet \text{Length is the diameter}=2r\\$

$\dfrac{x^2}{16}+\dfrac{y^2}{25}=1\quad \text{can be rewritten as}\ \dfrac{(x-0)^2}{4^2}+\dfrac{(y-0)^2}{5^2}=1\\\\\bullet (h, k)=(0,0)\\\bullet a=4\\\bullet b=5\\\bullet \text{b is the largest value so: b is the major and a is the minor}\\\bullet \text{Vertices are }(0, 0+5)\ and\ (0, 0-5)\implies (0, 5)\ and\ (0, -5)\\\bullet \text{Co-vertices are }(0+4, 0)\ and\ (0-4, 0)\implies (4,0)\ and\ (-4,0)\\\bullet \text{Length of major is }2b:2(5)=10\\\bullet \text{Length of minor is }2a:2(4)=8$

To find the foci, first we must find the length of the foci using the formula:

$(r_{major})^2-(r_{minor})^2=c^2$

Then add the c-value to the h (or k)-value that represents the major.

b² - a² = c²

25 - 16 = c²

9 = c²

±3 = c

The center is (0, 0) and the major is the y-value so the foci is:

(0, 0+3) and (0, 0-3) ⇒ (0, 3) and (0, -3)

26. Answers

Follow the same steps as #25:

Center: (0, 0)

Vertices (7, 0) and (-7, 0)

Co-vertices: (0, 3) and (0, -3)

foci: (2√10, 0) and (-2√10, 0)

length of major: 14

length of minor: 6

5 0

3 years ago

2) Consider the quadratic sequence 72, 100, 120, 132

valina [46]

9514 1404 393

Answer:

Tn = -4n² +40n +36

Step-by-step explanation:

A graphing calculator readily performs the quadratic regression, yielding the formula ...

Tn = -4n² +40n +36

The first and second differences of the given sequence terms are ...

28, 20, 12 and -8, -8

The coefficient of the squared term is half the second difference, so is -4. Then the sequence of squared terms is -4n²:

-4, -16, -36, -64

Subtracting these values from the original sequence gives the linear sequence ...

76, 116, 156, 196

which has first term 76 and common difference 40. The equation for the n-th term of this is ...

an = 76 +40(n -1) = 36 +40n

Adding this linear sequence to the sequence of squared terms, we get ...

Tn = -4n² +40n +36

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3 years ago