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Radda [10]
3 years ago
12

onsider the equation 0.5 times e4z =13 solve the equation for z. express the solution as a logarithm in base e

Mathematics
1 answer:
olga_2 [115]3 years ago
5 0

Answer:

z=\frac{ln(26)}{4}

Step-by-step explanation:

The given equation is:

0.5\,e^{4z}=13

so, we first isolate the exponential form that contains the unknown "z" in the exponent, by dividing both sides by 0.5:

0.5\,e^{4z}=13\\e^{4z}=\frac{13}{0.5}\\e^{4z}=26

Now we bring the exponent down by applying the natural log function on both sides, and then solve for "z":

e^{4z}=26\\ln(e^{4z})=ln(26)\\4\,z=ln(26)\\z=\frac{ln(26)}{4}

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dangina [55]
It’s probably A. (1,2) hope this helps..
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3 years ago
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A car travels 17 miles on one gallon of gas
zmey [24]

When x =170, y =10, when x = 187, y = 1, when x = 204, y = 12, when x = 221, y = 13, when x = 238, y = 14, when x = 255, y = 15, when x = 272, y = 16, when x = 289, y = 17, when x = 306, y = 18, when x = 323, y = 19, when x = 340, y = 20,

Step-by-step explanation:

Step 1; Assume y is the gallons in the tank while x is the range of the car. We need to determine the equation relating the y to the x values in the given coordinates. x is the dependent value whereas y is the independent value i.e. the value of x depends on the value of y.

Step 2; As y increases, x also increases. For every extra gallon in the tank, the car can go another 17 miles. So with y as the amount of gas in the tank in gallons and x as the range of vehicle, we get;

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To find the gallons in the tank, y = \frac{x}{17},

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when x = 255, y = 15,

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when x = 289, y = 17,

when x = 306, y = 18,

when x = 323, y = 19,

when x = 340, y = 20,

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3 years ago
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strojnjashka [21]
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h(5) = 5^2 + 1
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Lastly you multiply your h(1) value by the h(5) value to get your answer.

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Step-by-step explanation:

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