If you is 8 , what is the value of x?

The curve with equation y=ax^2+bx has a gradient of 3 at the point (2,-2). Find the values of a and b.

Airida [17]

Answer:

a = 2, b = - 5

Step-by-step explanation:

Given

y = ax² + bx

$\frac{dy}{dx}$ is the measure of the slope at x = a

Differentiate each term with respect to x using the power rule

$\frac{d}{dx}$ (a $x^{n}$ ) = na $x^{n-1}$

$\frac{dy}{dx}$ = 2ax + b, hence

2ax + b = 3 at (2, - 2)

Substitute x = 2 into $\frac{dy}{dx}$

4a + b = 3 → (1) and substitute x = 2 into y

4a + 2b = - 2 → (2)

Subtract ( 1) from (2)

b = - 2 - 3 = - 5

Substitute b = - 5 into (1)

4a - 5 = 3 ( add 5 to both sides )

4a = 8 ( divide both sides by 4 )

a = 2

7 0

3 years ago

mestny [16]

Answer:

12... If there is an even ratio between the two, then there is an even amount, so you divide 24 by 2 and you have 12 chocolate and 12 vanilla cupcakes in the Grande box.

Step-by-step explanation:

It izz wat it izzzz!!!

:)

5 0

3 years ago

Read 2 more answers

The 5th term in a geometric sequence is 160. The 7th term is 40. What are possible values of the 6th term of the sequence?

omeli [17]

Answer:

C. The 6th term is positive/negative 80

Step-by-step explanation:

Given

Geometric Progression

$T_5 = 160$

$T_7 = 40$

Required

$T_6$

To get the 6th term of the progression, first we need to solve for the first term and the common ratio of the progression;

To solve the common ratio;

Divide the 7th term by the 5th term; This gives

$\frac{T_7}{T_5} = \frac{40}{160}$

Divide the numerator and the denominator of the fraction by 40

$\frac{T_7}{T_5} = \frac{1}{4}$ ----- equation 1

Recall that the formula of a GP is

$T_n = a r^{n-1}$

Where n is the nth term

So,

$T_7 = a r^{6}$

$T_5 = a r^{4}$

Substitute the above expression in equation 1

$\frac{T_7}{T_5} = \frac{1}{4}$ becomes

$\frac{ar^6}{ar^4} = \frac{1}{4}$

$r^2 = \frac{1}{4}$

Square root both sides

$r = \sqrt{\frac{1}{4}}$

r = ± $\frac{1}{2}$

Next, is to solve for the first term;

Using $T_5 = a r^{4}$

By substituting 160 for T5 and ± $\frac{1}{2}$ for r;

We get

$160 = a \frac{1}{2}^{4}$

$160 = a \frac{1}{16}$

Multiply through by 16

$16 * 160 = a \frac{1}{16} * 16$

$16 * 160 = a$

$2560 = a$

Now, we can easily solve for the 6th term

Recall that the formula of a GP is

$T_n = a r^{n-1}$

Here, n = 6;

$T_6 = a r^{6-1}$

$T_6 = a r^5$

$T_6 = 2560 r^5$

r = ± $\frac{1}{2}$

So,

$T_6 = 2560( \frac{1}{2}^5)$ or $T_6 = 2560( \frac{-1}{2}^5)$

$T_6 = 2560( \frac{1}{32})$ or $T_6 = 2560( \frac{-1}{32})$

$T_6 = 80$ or $T_6 = -80$

$T_6 =$ ±80

Hence, the 6th term is positive/negative 80

8 0

3 years ago

PLEASE JUST GIVE EXPRESSION. WILL GIVE BRAINLIEST

Tcecarenko [31]

Answer:

like a month she earns $462.30

so if you want like how many she earns in 4 years then,

just do $462.30×4

after calculation answer will come.

8 0

3 years ago

Find the deference between

maxonik [38]

Answer:

$5520

Step-by-step explanation:

Given data

Principal= $24000

Rate=10%

time= 2 years

Firstly, the compound interest is given as

A=P(1+r)^t

A=24000(1+0.1)^2

A=24000(1.1)^2

A=24000*1.21

A=$29040

The simple interest is given as

A=P(1+rt)

A=24000(1+0.1*2)

A=24000(1.2)^2

A=24000*1.44

A=$34560

Hence the difference is

=34560-29040

=$5520

8 0

3 years ago