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4 years ago

D/dx (5x4) - (2x³) - (x²)

Mathematics

1 answer:

My name is Ann [436]4 years ago

5 0

$\bf y=5x^4-2x^3-x^2\implies \cfrac{dy}{dx}=20x^3-6x^2-2$

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18. Solve the equation.<br> m- 10/3 - 5m-9/7 = 1

JulijaS [17]

The answer is m = -59/42

Step by step explanation is in the image below.

4 0

3 years ago

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

Lupe can ride her bike at a rate of 20 mph when there is no wind. On one particular day, she rode 2 miles against the wind and n

lana [24]

Let wind speed = x mph

when she rode 2 miles against the wind we have:-
speed = distance / time so
20 - x = 2 / t -------(1) where t is the time she took.

when riding with the wind we have

20 + x = 3 / t--------(2) adding equations (1) and (2):-

40 = 2/t + 3/t
40 = 5/t
t = 5/40 = 1/8 hr

x = 20 - 2 / 1/8 = 20 - 16 = 4

Wind speed was 4 mph Answer

4 0

4 years ago

Read 2 more answers

Tom made 5,000 mL of soup. He packed 2.5 liters of the soup in his kids' lunches. He froze the rest of the soup. How many millil

MakcuM [25]

Answer:

Amount of frozen soup = 2500 mL

Step-by-step explanation:

We are told that tom made 5,000 mL of soup.

We are also told he packed 2.5 Litres into his kids' lunches.

Now, from conversions,

1 liter = 1000 mL

Thus,

2.5 litres = 2.5 × 1000 = 2500 mL

Now, we are told he froze the rest of the soup.

Thus;

Amount of frozen soup = total amount of soup made - amount given to kids' lunch pack.

Amount of frozen soup =

5000 - 2500 = 2500 ml

7 0

3 years ago

Please help greatly appreciated :)

matrenka [14]

Step-by-step explanation:

we know ,

area of circle =πr^2

hence we get from the figure that the diameter of circle is 19 cm and we can find radius

r=d/2

r=18/2=9cm

area of semicircle =πr^2/2

area of Semi circle equals to =22*(9)^2/7/2

=127.2857143

3 0

3 years ago

Read 2 more answers