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Veseljchak [2.6K]
3 years ago
11

Sketch the graph of the given function. Then state the function’s domain and range. y = 7(4)x

Mathematics
2 answers:
Mandarinka [93]3 years ago
8 0

Answer with explanation:

The given function is

   y=7^{4x}

Domain of the function is defined as set of all values of x for which y is defined.

In the given function ,y is defined for all real values of x.

So, Domain of the function =R--Set of real numbers.

Range of the function is defined as set of all values of y, for which x is defined.

y=7^{4x}\\\\ \text{Taking log on both sides}\\\\ \log y=4x \log 7\\\\x=\frac{\log y}{4 \log 7}

⇒log y is defined for, y>0.

<u>Range </u>of the function will be

    =(0,∞)

     =Set of Positive real numbers

liubo4ka [24]3 years ago
3 0
I Hope You Dont Mind That I Got It Off A Math Website. I Did The Extra Math Tho

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A solid right pyramid has a regular hexagonal base with an area of 7.4 units2. The pyramid has a height of 6 units.
Lelechka [254]

Answer: Second option.

Step-by-step explanation:

You need to use the following formula:

V=\frac{1}{3}Bh

Where "B" is the area of its base and "h" is the height.

According to the data given in the exercise, you know that:

B=7.4 units^2\\\\h=6\ units

Therefore, knowing this values, you can substitute them into the formula shown before and then evaluate, in order to calculate the volume of thi right pyramid whose base is a regular hexagon.

Then, you get:

V=\frac{1}{3}(7.4 units^2)(6\ units)\\\\V=14.8\ units^3

6 0
3 years ago
Read 2 more answers
The half-life of a certain radioactive material is 83 hours. An initial amount of the material has a mass of 67 kg. Write an exp
Anvisha [2.4K]

Answer:

  • Initial amount of the material is 67 kg
  • Hal-life is 83 hours

<u>The required equation is:</u>

  • m(x) = 67 * (1/2)^{x/83}, where m- remaining amount of the radioactive material, x - number of hours

<u>After 5 hours the material remains:</u>

  • m(5) = 67 * (1/2)^{5/83} = 64.260 (rounded)
4 0
2 years ago
Will mark brainliest for the correct answer!
romanna [79]

Part (a)

Focus on triangle PSQ. We have

angle P = 52

side PQ = 6.8

side SQ = 5.4

Use of the law of sines to determine angle S

sin(S)/PQ = sin(P)/SQ

sin(S)/(6.8) = sin(52)/(5.4)

sin(S) = 6.8*sin(52)/(5.4)

sin(S) = 0.99230983787513

S = arcsin(0.99230983787513)

S = 82.889762826274

Which is approximate

------------

Use this to find angle Q. Again we're only focusing on triangle PSQ.

P+S+Q = 180

Q = 180-P-S

Q = 180-52-82.889762826274

Q = 45.110237173726

Which is also approximate.

A more specific name for this angle is angle PQS, which will be useful later in part (b).

------------

Now find the area of triangle PSQ

area of triangle = 0.5*(side1)*(side2)*sin(included angle)

area of triangle PSQ = 0.5*(PQ)*(SQ)*sin(angle Q)

area of triangle PSQ = 0.5*(6.8)*(5.4)*sin(45.110237173726)

area of triangle PSQ = 13.0074347717966

------------

Next we'll use the fact that RS:SP is 2:1.

This means RS is twice as long as SP. Consequently, this means the area of triangle RSQ is twice that of the area of triangle PSQ. It might help to rotate the diagram so that line PSR is horizontal and Q is above this horizontal line.

We found

area of triangle PSQ = 13.0074347717966

So,

area of triangle RSQ = 2*(area of triangle PSQ)

area of triangle RSQ = 2*13.0074347717966

area of triangle RSQ = 26.0148695435932

------------

We're onto the last step. Add up the smaller triangular areas we found

area of triangle PQR = (area of triangle PSQ)+(area of triangle RSQ)

area of triangle PQR = (13.0074347717966)+(26.0148695435932)

area of triangle PQR = 39.0223043153899

------------

<h3>Answer: 39.0223043153899</h3>

This value is approximate. Round however you need to.

===========================================

Part (b)

Focus on triangle PSQ. Let's find the length of PS.

We'll use the value of angle Q to determine this length.

We'll use the law of sines

sin(Q)/(PS) = sin(P)/(SQ)

sin(45.110237173726)/(PS) = sin(52)/(5.4)

5.4*sin(45.110237173726) = PS*sin(52)

PS = 5.4*sin(45.110237173726)/sin(52)

PS = 4.8549034284642

Because RS is twice as long as PS, we know that

RS = 2*PS = 2*4.8549034284642 = 9.7098068569284

So,

PR = RS+PS

PR = 9.7098068569284 + 4.8549034284642

PR = 14.5647102853927

-------------

Next we use the law of cosines to find RQ

Focus on triangle PQR

c^2 = a^2 + b^2 - 2ab*cos(C)

(RQ)^2 = (PR)^2 + (PQ)^2 - 2(PR)*(PQ)*cos(P)

(RQ)^2 = (14.5647102853927)^2 + (6.8)^2 - 2(14.5647102853927)*(6.8)*cos(52)

(RQ)^2 = 136.420523798282

RQ = sqrt(136.420523798282)

RQ = 11.6799196828694

--------------

We'll use the law of sines to find angle R of triangle PQR

sin(R)/PQ = sin(P)/RQ

sin(R)/6.8 = sin(52)/11.6799196828694

sin(R) = 6.8*sin(52)/11.6799196828694

sin(R) = 0.4587765387107

R = arcsin(0.4587765387107)

R = 27.3081879220073

--------------

This leads to

P+Q+R = 180

Q = 180-P-R

Q = 180-52-27.3081879220073

Q = 100.691812077992

This is the measure of angle PQR

subtract off angle PQS found back in part (a)

angle SQR = (anglePQR) - (anglePQS)

angle SQR = (100.691812077992) - (45.110237173726)

angle SQR = 55.581574904266

--------------

<h3>Answer: 55.581574904266</h3>

This value is approximate. Round however you need to.

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How many lengths of pipe 2 1/3 ft long can be cut from a pipe that is 63 ft long? Assume there is no kerf.
Zinaida [17]
The answer is 27ft long
7 0
2 years ago
The expression 36 ÷ 6 • 2 + 1 is equal to _____.<br><br> 2<br> 4<br> 13<br> 18
NeTakaya

Answer:

Step-by-step explanation:

36/6 · 2 + 1

6 ·2 + 1

12 + 1 = 13

answer is 13

7 0
3 years ago
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