Solve the equation e^x-3=(1/e^4)x+6

A quantity with an initial value of 6200 decays continuously at a rate of 5.5% per month. What is the value of the quantity afte

ELEN [110]

Answer:

410.32

Step-by-step explanation:

Given that the initial quantity, Q= 6200

Decay rate, r = 5.5% per month

So, the value of quantity after 1 month, $q_1 = Q- r \times Q$

$q_1 = Q(1-r)\cdots(i)$

The value of quantity after 2 months, $q_2 = q_1- r \times q_1$

$q_2 = q_1(1-r)$

From equation (i)

$q_2=Q(1-r)(1-r) \\\\q_2=Q(1-r)^2\cdots(ii)$

The value of quantity after 3 months, $q_3 = q_2- r \times q_2$

$q_3 = q_2(1-r)$

From equation (ii)

$q_3=Q(1-r)^2(1-r)$

$q_3=Q(1-r)^3$

Similarly, the value of quantity after n months,

$q_n= Q(1- r)^n$

As 4 years = 48 months, so puttion n=48 to get the value of quantity after 4 years, we have,

$q_{48}=Q(1-r)^{48}$

Putting Q=6200 and r=5.5%=0.055, we have

$q_{48}=6200(1-0.055)^{48} \\\\q_{48}=410.32$

Hence, the value of quantity after 4 years is 410.32.

4 0

3 years ago

Read 2 more answers

A company that makes hair-care products had 9 comma 000 people try a new shampoo. Of the 9 comma 000 people, 72 had a mild all

Olegator [25]

Answer:

The percent of people with mild allergic reaction is 0.8%

Step-by-step explanation:

The company has 9000 people, and 72 people have mild allergic reaction.

The fraction of people with mild reaction is 72 over 9000, i.e. 72/9000

72 and 9000 are multiple of 9, therefore reducing both by 9, we will have 8/1000.

8 and 1000 are both multiple of 4, so we will reduce both by 4, we will have

2/250.

2/250 can still be reduced by to, therefore we will have 1/125

To get the percentage, we will now multiply the fraction 1/125 by 100, we will have 100/125

Reduce both 100 and 125 by 25 which will make 4/5

then, turning 4/5 to decimal, we will have 0.8%

Therefore 0.8% of people had a mild allergic reaction

8 0

3 years ago

(20 points!) In triangle RSW, line segment RW is a median and is equal to 27 cm. What is the length of RX?

Fofino [41]

Answer:

Option D. 18 cm

Step-by-step explanation:

we know that

A <u><em>centroid</em></u> of a triangle is the point where the three medians of the triangle meet.

A median of a triangle is a line segment from one vertex to the mid point on the opposite side of the triangle.

The centroid divides each median in a ratio of 2:1

In this problem the centroid of triangle RST is the point X

so

$\frac{RX}{XW}=\frac{2}{1}$

$RX=2XW$ -----> equation A

$RX+XW=27$ -----> equation B

substitute equation A in equation B

$2XW+XW=27$

Solve for XW

$3XW=27$

$XW=9\ cm$

Find the value of RX

$RX=2XW$ ----- $RX=2(9)=18\ cm$

3 0

3 years ago

A line passes through the point (-2, 8) and has a slope of-5/2.

chubhunter [2.5K]

Answer:

$y = -\frac{5}{2} x + 3$

Step-by-step explanation:

We are given that a line passes through (-2, 8) and has a slope of -5/2.

We want to write the equation of this line in slope-intercept form.

Slope-intercept form is given as y=mx+b, where m is the slope and b is the value of y at the y-intercept.

Since we are already given the slope of this line, we can immediately plug it into the equation.

Replace m with -5/2.

$y = -\frac{5}{2} x+ b$

Now we need to find b.

As the equation passes through the point (-2, 8), we can use its values to help solve for b.

Substitute -2 as x and 8 as y.

$8 = -\frac{5}{2} (-2) +b$

Multiply.

8 = 5 + b

Subtract 5 from both sides.

3 = b

Replace b with 3 in the equation.

$y = -\frac{5}{2} x + 3$

Topic: finding the equation of the line (slope-intercept form)

See more: brainly.com/question/27959192

6 0

2 years ago

What is the size of the SUV tanks in gallons?

Romashka-Z-Leto [24]

I looked it up, and after some research, I came across a legitimate answer of approximately 30 gallons.

3 0

3 years ago