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3 years ago

What is the solution to the equation below? Round your answer to two decimal places. 4•e^x=17

Mathematics

1 answer:

bixtya [17]3 years ago

7 0

Answer:

$\large\boxed{x\approx1.45}$

Step-by-step explanation:

$4e^x=17\qquad\text{divide both sides by 4}\\\\e^x=\dfrac{17}{4}\qquad \ln\ \text{of both sides}\\\\\ln e^x=\ln\dfrac{17}{4}\qquad\text{use}\ \log_aa^n=n\\\\x=\ln\dfrac{17}{4}\\\\x\approx1.45$

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Write the equation of the line that passes through (0, 1) and has a slope of 0

Inessa [10]

Answer:

y = 1

Step-by-step explanation:

The slope is 0.

y = (0)x + b

y = b

The line passes through (0, 1).

(x, y)

Put y as 1.

1 = b

The y-intercept is 1.

y = 1

7 0

3 years ago

A cup of coffee contains about 100 mg of caffeine. Caffeine is metabolized and leaves the body at a continuous rate of about 12%

Mamont248 [21]

Answer:

a. $A = C_{0}(1-x)^t\\x: percentage\ of \ caffeine\ metabolized\\$

b. $\frac{dA}{dt}= -11.25 \frac{mg}{h}$

Step-by-step explanation:

First, we need tot find a general expression for the amount of caffeine remaining in the body after certain time. As the problem states that every hour x percent of caffeine leaves the body, we must substract that percentage from the initial quantity of caffeine, by each hour passing. That expression would be:

$A= C_{0}(1-x)^t\\t: time \ in \ hours\\x: percentage \ of \ caffeine\ metabolized\\$

Then, to find the amount of caffeine metabolized per hour, we need to differentiate the previous equation. Following the differentiation rules we get:

$\frac{dA}{dt} =C_{0}(1-x)^t \ln (1-x)\\\frac{dA}{dt} =100*0.88\ln(0.88)\\\frac{dA}{dt} =-11.25 \frac{mg}{h}$

The rate is negative as it represents the amount of caffeine leaving the body at certain time.

3 0

3 years ago

How to find the arc length (geometry)

andrew11 [14]

Answer:

94.2

Step-by-step explanation:

Arc length is basically circumference.

Circumference formula: 2πr

All we need is the radius.

Radius = r

15 x 2 = 30 (diameter)

Then we are going to multiply by pi.

Arc length = 30π OR 94.2

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2 years ago

What is the surface area of the triangular prism?

Elanso [62]

Answer:

135 square feet

Step-by-step explanation:

area of base and top=2(1/2×6×2.5)=15 square feet.

area of three faces=(2.5+6+6.5)×8=15×8=120 ft

total surface area=15+120=135 square feet.

4 0

2 years ago

Read 2 more answers

What is 15x+8y less than or equal to 64

navik [9.2K]

Less than, because if you add 15+8 it equals 23 so less than

5 0

3 years ago