Which line is perpendicular to AB line 1 line 2 line 3 line 4

Sarah is carrying out a series of experiments which involve using mcreasing amounts of a chemical. In the

Marianna [84]

Sarah is carrying out a series of experiments which involve using increasing amounts of a chemical. In the first experiment she uses 6g of the chemical and in the second experiment she uses 7.8 g of the chemical

(i)Given that the amounts of the chemical used form an arithmetic progression find the total amount of chemical used in the first 30 experiments

(ii)Instead it is given that the amounts of the chemical used for a geometric progression. Sarah has a total of 1800 g of the chemical available. Show that the greatest number of experiments possible satisfies the inequality: $1.3^N \leq 91$ and use logarithms to calculate the value of N.

Answer:

(a)963 grams

(b)N=17

Step-by-step explanation:

(a)

In the first experiment, Sarah uses 6g of the chemical

In the second experiment, Sarah uses 7.8g of the chemical

If this forms an arithmetic progression:

First term, a =6g

Common difference. d= 7.8 -6 =1.8 g

Therefore:

Total Amount of chemical used in the first 30 experiments

$S_n=\dfrac{n}{2}[2a+(n-1)d] \\S_{30}=\dfrac{30}{2}[2*6+(30-1)1.8] \\=15[12+29*1.8]\\=15[12+52.2]\\=15*64.2\\=963$ grams$

Sarah uses 963 grams in the first 30 experiments.

(b) If the increase is geometric

First Term, a=6g

Common ratio, r =7.8/6 =1.3

Sarah has a total of 1800 g

Therefore:

Sum of a geometric sequence

$S_n=\dfrac{a(r^N-1)}{r-1} \\1800=\dfrac{6(1.3^N-1)}{1.3-1} \\1800=\dfrac{6(1.3^N-1)}{0.3}\\$Cross multiply\\1800*0.3=6(1.3^N-1)\\6(1.3^N-1)=540\\1.3^N-1=540\div 6\\1.3^N-1=90\\1.3^N=90+1\\1.3^N=91$

Therefore, the greatest possible number of experiments satisfies the inequality

$1.3^N \leq 91$

Next, we solve for N

Changing $1.3^N \leq 91$ to logarithm form, we obtain:

$N \leq log_{1.3}91\\N \leq \dfrac{log 91}{log 1.3}\\ N \leq 17.19$

Therefore, the number of possible experiments, N=17

3 0

3 years ago

Find r(t) if r'(t)=ti+e^tj+te^tk and r(0)=i+j+k

weeeeeb [17]

R(t) = integral of r'(t) = integral of ti + e^tj + te^tk = 1/2t^2i + e^tj + (te^t - e^t)k + c
r(0) = j - k + c = i + j + k
c = i + 2k
Therefore, r(t) = (1/2t^2 + 1)i + e^tj + (te^t - e^t + 2)k

6 0

3 years ago

John finds that the sum of two numbers is 24 and their difference is one sixth of the sum. Find the smallest number between the

poizon [28]

Answer:

The smallest number is 10

Step-by-step explanation:

x+y=24---equation 1

x-y=¹/6×24=>x-y=4---equation 2

Add both equations

2x=28

x=14

put x=14 into equation 1

14+y=24

y=24-14=10

4 0

3 years ago

Help me!!!!!!!!!!!!!!!!!!!!!

marissa [1.9K]

Answer:

$\frac{7}{3} and \: \frac{8}{3}$

Step-by-step explanation:

so let's start with what we know:

$2 \frac{1}{3} \times 2 \frac{2}{3}$

now to get it into non mixxed numbers:

2*3 = 6

6+1

_____

$\frac{7}{3}$

2*3=6

6+2=8

______

$\frac{8}{3}$

now to cross mutiply them:

7*3

7 0

3 years ago

A baseball is thrown with a vertical velocity of 50 ft/s from an initial height of 6 ft. The height h in feet of the baseball ca

Bad White [126]

Vertex is highest point

ok so the t value of the vertex of a function in the form
f(x)=at^2+bt+c is
-b/2a

find t value
h(x)=-16t^2+50t+6
a=-16
b=50
-50/(2*-16)=1.5625
round
1.6 seconds
max height
input 1.6 for t and evaluate (for more precice, input 1.5625 for t)

max height is 45 feet

seems to be
b=initial velocity
c=intial height

a=-16
eqation is
h(t)=-16t^2+70t+5
vertex is -70/(2*-16)=2.1875
input for t to get max height
82 feet

answers are

1.6 seconds
45 feet
82 feet

4 0

3 years ago