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3 years ago

What are the values of m and e in the diagram below?

Mathematics

1 answer:

elena55 [62]3 years ago

4 0

Please add the picture.

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If you have a cubic polynomial of the form y = ax^3 + bx^2 + cx + d and lets say it passes through the points (2,28), (-1, -5),

nikklg [1K]

Step-by-step explanation:

Step 1: Solve using the first point

(2, 28)

$28 = a(2)^3 + b(2)^2 + c(2) + d$

$28 = 8a + 4b + 2c + d$

Step 2: Solve using the second point

(-1, -5)

$-5 = a(-1)^3 + b(-1)^2 + c(-1) + d$

$-5 = -a + b - c + d$

Step 3: Solve using the third point

(4, 220)

$220 = a(4)^3 + b(4)^2 + c(4) + d$

$220 = 64a + 16b + 4c + d$

Step 4: Solve using the fourth point

(-2, -20)

$-20 = a(-2)^3 + b(-2)^2 + c(-2) + d$

$-20 = -8a + 4b - 2c + d$

Step 5: Combine the first and fourth equations

$28 - 20 = 8a - 8a + 4b + 4b + 2c - 2c + d + d$

$8 = 8b + 2d$

$8 - 8b = 8b - 8b + 2d$

$(8 -8b)/2 = 2d/2$

$4 - 4b = d$

Step 6: Solve for c in the second equation

$-5 + 5 = -a + b - c + d + 5$

$0 + c = -a + b - c + c + d + 5$

$c = -a + b + d + 5$

Step 7: Substitute d with the stuff we got in step 5

$c = -a + b + (4 - 4b) + 5$

$c = -a + b + 4 - 4b + 5$

$c = -a - 3b + 9$

Step 8: Substitute d and c into the first equation

$28 = 8a + 4b + 2(-a - 3b + 9) + (4 - 4b)$

$28 = 8a + 4b - 2a - 6b + 18 + 4 - 4b$

$28 - 22 = 6a - 6b + 22 - 22$

$6 / 6 = (6a - 6b) / 6$

$1 + b = a - b + b$

$1 + b = a$

Step 9: Substitute a, b, and c into the third equation

$220 = 64(1 + b) + 16b + 4(-(1 + b) - 3b + 9) + (4 - 4b)$

$220 = 64 + 64b + 16b + 4(-1 - b - 3b + 9) + 4 - 4b$

$220 - 100 = 60b + 100 - 100$

$120 / 60 = 60b / 60$

$2 = b$

Step 10: Find a using b = 2

$a = b + 1$

$a = (2) + 1$

$a = 3$

Step 11: Find c using a = 3 and b = 2

$c = -a - 3b + 9$

$c = -(3) - 3(2) + 9$

$c = -3 - 6 + 9$

$c = 0$

Step 12: Find d using b = 2

$d = 4 - 4b$

$d = 4 - 4(2)$

$d = 4 - 8$

$d = -4$

Answer: $a = 3, b = 2, c = 0,d = -4$

6 0

3 years ago

Read 2 more answers

Please help got to get grade up

dusya [7]

Answer:

Step-by-step explanation:

The ratio of abc/def=1.5

15/1.5=10

if you have insta follow me if you want at riztofu

5 0

2 years ago

Jaime drew the number line below to show 2/3 4/5. Explain how the number line shows 2/3 times 4/5. What is the product?

bearhunter [10]

Answer:

$\frac{2}{3} * \frac{4}{5} = \frac{6}{15}$

Step-by-step explanation:

Given

$\frac{2}{3} * \frac{4}{5} =$

The number line is missing from the question.

So, I will answer the question and also draw the number line to show the product.

$\frac{2}{3} * \frac{4}{5} =$

$\frac{2}{3} * \frac{4}{5} = \frac{6}{15}$

To represent this on a number line;

We draw a number line of 15 points, and place a dot on the 6th point.

This represents 6/15

See attachment

8 0

3 years ago

Are the functions f(x) = (x^2-1)/(x-1) and g(x)= x+1 equal for all x?

Vinvika [58]

$\bf \textit{difference of squares}
\\ \quad \\
(a-b)(a+b) = a^2-b^2\qquad \qquad 
a^2-b^2 = (a-b)(a+b)\\\\
-------------------------------\\\\$

$\bf f(x)=\cfrac{x^2-1}{x-1}\implies f(x)=\cfrac{x^2-1^2}{x-1}\implies f(x)=\cfrac{(\underline{x-1})(x+1)}{\underline{x-1}}
\\\\\\
f(x)=x+1\qquad \qquad \qquad \qquad \qquad g(x)=x+1\\\\
-------------------------------\\\\
\textit{they're, kinda, except that, when x = 1}
\\\\\\
g(x)=(1)+1\implies g(x)=2
\\\\\\
f(x)=\cfrac{(1)^2-1}{(1)-1}\implies f(x)=\cfrac{0}{0}\impliedby und efined$

7 0

3 years ago

DISCRETE MATHEMATIC

Jet001 [13]

Answer:

The conclusion "T" logically follows from the premises given and the argument is valid

Step-by-step explanation:

Let us use notations to represent the steps

P: I take a bus

Q: I take the subway

R: I will be late for my appointment

S: I take a taxi

T: I will be broke

The given statement in symbolic form can be written as,

(P V Q) → R

S → (¬R ∧ T)

(¬Q ∧ ¬P) → S

¬R

___________________

∴ T

PROOF:

1. (¬Q ∧ ¬P) → S Premise

2. S → (¬R ∧ T) Premise

3. (¬Q ∧ ¬P) → (¬R ∧ T) (1), (2), Chain Rule

4. ¬(P ∨ Q) → (¬R ∧ T) (3), DeMorgan's law

5. (P ∨ Q) → R Premise

6. ¬R Premise

7. ¬(P ∨ Q) (5), (6), Modus Tollen's rule

8. ¬R ∧ T (4), (7), Modus Ponen's rule

9. T (8), Rule of Conjunction

Therefore the conclusion "T" logically follows from the given premises and the argument is valid.

6 0

3 years ago

What are the values of m and e in the diagram below?​

What are the values of m and e in the diagram below?