find the degree of the polynomial 5ab^3-7a^5c^2-5

Answer: a = -2  and  c = 7

Step-by-step explanation:

(this answer uses some basic calculus)

We know that [tex]f'(x) = 2ax + 4[/tex], and since [tex](1,9)[/tex] is a maximum of [tex]f[/tex], then [tex]f'(1) = 0[/tex]. That means [tex]2a + 4 = 0[/tex], so [tex]\boxed{a = -2}[/tex]. Then since [tex]f(1) = 9[/tex], we have [tex]-2(1)^2 + 4(1) + c = 9[/tex], so [tex]\boxed{c = 7}[/tex].

Answer:

a = -2

c = 7

Step-by-step explanation:

Given the quadratic function, f(x) = ax² + 4x + c, for which its vertex is the maximum point occurring at (1, 9), and b = 4.

Since the x-coordinate of the vertex, x = 1, can be calculated using the formula, [tex]x = \frac{-b}{2a}[/tex]:

We can substitute the value of the x-coordinate and b = 4 into the formula, and solve for the value of a:

[tex]x = \frac{-b}{2a}[/tex]

[tex]1 = \frac{-4}{2a}[/tex]

Multiply both sides by 2a:

(2a) 1 =  [tex]\frac{-4}{2a} (2a)[/tex]

2a = -4

Divide both sides by 2 to solve for a:

[tex]\frac{2a}{2} = \frac{-4}{2}[/tex]

a = -2

Therefore, the value of a = -2.

Next, to solve for c, substitute the coordinate values of the vertex, (1, 9) into the given quadratic function:

f(x) = ax² + 4x + c

9 = -2(1)² + 4(1) + c

9 = -2 + 4 + c

9 = 2 + c

Subtract 2 from both sides to isolate c:

9 - 2 = 2 - 2  + c

7 = c

In order to double-check the validity of our values for a and c, substitute a = -2, and c = 7 into the function, along with the coordinates of the vertex, (1, 9):

f(x) = -2x² + 4x + 7

9 = -2(1)² + 4(1) + 7

9 = -2 + 4 + 7

9 = 9 (True statement).

Therefore, the correct answers are: a = -2, and c = 7.

Answer:

what is the question

Step-by-step explanation:

[tex]slope = m = \cfrac{rise}{run} \implies \cfrac{ f(x_2) - f(x_1)}{ x_2 - x_1}\impliedby \begin{array}{llll} average~rate\\ of~change \end{array}\\\\[-0.35em] \rule{34em}{0.25pt}\\\\ f(x)=2x - 5 \quad \begin{cases} x_1=2\\ x_2=5 \end{cases}\implies \cfrac{f(5)-f(2)}{5-2}\implies \cfrac{[2(5)-5]~~ - ~~[2(2)-5]}{3} \\\\\\ \cfrac{5-(-1)}{3}\implies \cfrac{5+1}{3}\implies 2[/tex]

Answer:

Step-by-step explanation:

This will open to the left and the vertex will be at (0, -4).

Equation us (y + 4)^2 = -4*-11x

44x = (y + 4)^2

Answer:

Im not sure

Step-by-step explanation:

a. By the chain rule,

[tex]\dfrac{dy}{dx} = \dfrac{dy}{dt}\cdot\dfrac{dt}{dx} = \dfrac{dy}{dt}\cdot\dfrac{1}{\frac{dx}{dt}}[/tex]

Given that [tex]y=e^t+e^{-t}[/tex] and [tex]x=e^{-t}[/tex], we have the derivatives

[tex]\dfrac{dy}{dt} = e^t -e^{-t}[/tex]

[tex]\dfrac{dx}{dt} = -e^{-t}[/tex]

and so

[tex]\dfrac{dy}{dx} = \dfrac{e^t - e^{-t}}{-e^{-t}} = 1-e^{2t}[/tex]

Set this equal to zero and solve for t :

[tex]1-e^{2t} = 0[/tex]

[tex]1 = e^{2t}[/tex]

[tex]\ln(1) = \ln\left(e^{2t}\right)[/tex]

[tex]0 = 2t \ln(e)[/tex]

[tex]0 = 2t[/tex]

[tex]t=0[/tex]

This value of t corresponds to x = e⁰ = 1 and y = e⁰ - 1/e⁰ = 1 - 1 = 0. So the only point on the curve where the derivative dy/dx is zero is (1, 0).

b. Compute the second derivative. Since dy/dx is a function of t, we'll momentarily replace it with f(t). By the chain rule,

[tex]\dfrac{d^2}{dx^2} = \dfrac d{dx} \dfrac{dy}{dx} = \dfrac{df}{dx} = \dfrac{df}{dt}\cdot\dfrac{dt}{dx} = \dfrac{df}{dt}\cdot\dfrac{1}{\frac{dx}{dt}}[/tex]

We have

[tex]\dfrac{df}{dt} = -2e^{2t}[/tex]

and we've already committed dx/dt. So

[tex]\dfrac{d^2}{dx^2} = \dfrac{-2e^{2t}}{-e^{-t}} = 2e^{3t} [/tex]

Substitute the first and second derivative into the differential equation:

[tex]\left(\dfrac{d^2y}{dx^2}\right)^2 + \dfrac{dy}{dx} - 1 = 0[/tex]

[tex]\left(2e^{3t}\right)^2 + (1-e^{2t}) - 1 = 0[/tex]

[tex]4e^{6t} -e^{2t}= 0[/tex]

[tex]e^{2t} (4e^{4t} - 1) = 0[/tex]

[tex]4e^{4t} - 1 = 0[/tex]

[tex]4e^{4t} = 1[/tex]

[tex]e^{4t} = \dfrac14[/tex]

[tex]\ln\left(e^{4t}\right) = \ln\left( \dfrac14\right)[/tex]

[tex]4t \ln(e) = -\ln(4)[/tex]

[tex]4t = -\ln(4)[/tex]

[tex]t = -\dfrac{\ln(4)}4[/tex]

Answer:

More students like PE

Step-by-step explanation:

100÷20=5

1 student = 5%

4×5=20

20% students favourite is social studies

75%>20%

Answer:

C. y=3x-4

Step-by-step explanation:

I just know trust me

(1, 64), (2, 32), (4, 16), (8, 8).

Answer:

1 x 64

2 x 32

4 x 16

8 x 8

Step-by-step explanation:

Factors of 64: 1, 2, 4, 8, 16, 32 and 64.

Pairs:

1 x 64

2 x 32

4 x 16

8 x 8

Hope this helps :)

Answer: 12

2 + 10

12

:)

Answer: 12

Step-by-step explanation: just add 2 to 10

9514 1404 393

Answer:

  (b)  62°

Step-by-step explanation:

Let x represent the measure of the angle.

The complement is (90 -x).

The supplement is (180 -x).

The relationship between the supplement and the complement is ...

  (180 -x) = 6 +4(90 -x)

  180 -x = 6 +360 -4x

  3x = 186

  x = 62

The measure of the angle is 62°.

Answer:

1.)

a.)The correlation coefficient is determined by dividing the covariance by the product of the two variables' standard deviations.

b.)Medications such as naproxen, ibuprofen, and acetaminophen are most effective in reducing pain and swelling associated with muscle-related lower back pain. However, OTC medication is less likely to alleviate symptoms that stem from nerve compression or disc problems.

Step-by-step explanation:

I HOPE ITS HELP YOU

Answer:

130/81

simplified: 1 49/81

Step-by-step explanation:

I did the math

Can you give me some hint please

Answer:

Step-by-step explanation:

The shadow length will be proportional to height

12 / 60 = h / 32

h = 12(32)/60 = 6.4 ft or 6 ft 4.8 inches

Answer:

Option "C" none of these is the correct answer.

Step-by-step explanation:

The subset of the set {7, 8, 9} must have the elements of this set only.

Hope this helps :)

Answer:

81/10 or 10

Step-by-step explanation:

81:18 - 8 = 81/10 simplified

sorry if am wrong i tried :L

Answer:

this is the correct answer happy

Answer:

w = win

Step-by-step explanation:

w=13

Answer:

w = 13

Step-by-step explanation:

16w - w = 15w

15w - 12w = 3w

3w - 2w = w

w = 13

Answer:

2 + (n/4) = 6

Step-by-step explanation:

Answer:

2+(n÷4)= 6

Step-by-step explanation:

hope it helps u

plzz plzzzz plzzzz mark as brainliest

Answer:

commutative property of multiplication

Step-by-step explanation:

Name the property used: commutative property of multiplication

Answer: commutative property of multiplication

Answer:

I don't know..,.............,,.,.......,

Answer:

O - point

CD- chord

AB- diametre

I dont know PO sorry

Answer:

O is the center.

AB is the diameter.

OP is a radius.

CD is a tangent.

By the way the combination of letters is the two points that it relates too.

Step-by-step explanation:

hope this helps. . .<3

Step-by-step explanation:

if you observe the graph the y values increase as the x value increase.

so it has a possitive association.

if the value of y increase as the value of the x increase then data has positive association.

Answer:

line them up straight with the bottom number and the top number.

Answer:

[tex]x>4[/tex]

Based on this, we know the correct number line will be an empty bubble with a line going to the right of 4.

Step-by-step explanation:

[tex]x-8>-4[/tex]

add 8 to both sides of the inequality

[tex]x>4[/tex]

a = 18

d = 16 - 18 = -2

an = a + (n - 1) × d

an = 18 + (n - 1) × (-2)

an = 18 - 2n + 2

an = -2n + 20