What is aproxímate percent change in a temperature that went down from 120 degrees to 100 degrees

HELP!! What is the approximate measure of angle x in the triangle shown?

Alex Ar [27]

<h3>Answer: D) 130.5 degrees</h3>

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Work Shown:

$c^2 = a^2 + b^2 - 2*a*b*\cos(C)\\\\10^2 = 5^2 + 6^2 - 2*5*6*\cos(x)\\\\100 = 25 + 36 - 60*\cos(x)\\\\100 = 61 - 60*\cos(x)\\\\100 - 61 = - 60*\cos(x)\\\\39 = - 60*\cos(x)\\\\\cos(x) = \frac{39}{-60}\\\\\cos(x) = -0.65\\\\x = \arccos(-0.65)\\\\x \approx 130.5416\\\\x \approx 130.5\\\\$

Note: I used the law of cosines. Make sure your calculator is in degree mode.

6 0

3 years ago

A small business assumes that the demand function for one of its new products can be modeled by p = Cekx. When p = $40, x = 1000

Maru [420]

Answer:

C= 82.1116

k=-0.0007192

Step-by-step explanation:

$p=Ce^{kx}\\40=Ce^{k1000}\\30=Ce^{k1400}\\$

Applying logarithmic properties yields in the following linear system:

$ln(40) = ln(C) + 1000k\\ln(30) = ln(C) + 1400k$

Solving for k:

$ln(40) = ln(C) + 1000k\\ln(30) = ln(C) + 1400k\\400 k = ln(30)-ln(40)\\k=-0.0007192$

Solving for C:

$40=Ce^{-0.0007192*1000}\\C= \frac{40}{e^{-0.0007192*1000}}\\C=82.1116$

C= 82.1116

k=-0.0007192

6 0

3 years ago

How many 7-digit phone numbers are possible, assuming that the first digit can’t be a 0 or a 1? (b) re-solve (a), except now ass

sladkih [1.3K]

A. We are going to form 7 digit numbers from the set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}

where the first digit cannot be 0 or 1.

so we have 8 choices for the 1. digit, and 10 choices for all the other 6 digits.

this means there are $8*10*10*10*10*10*10=8* 10^{6}$ possible numbers.

b.

consider the numbers which start with 911. There are $10*10*10*10=10 ^{4}$ such numbers, since for the 4th, 5th, 6th and 7th digits we have 10 choices.

then we remove this number, from the one we found in a:

There are in total $8* 10^{6}-10^{4}=7,990,000$ numbers which don't start with 911.

Answer:

a. $8*10^{6}$
b.7,990,000

3 0

3 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

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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).

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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

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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

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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

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<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

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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

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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

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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

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<h3>Answer: 55.581574904266</h3>

This value is approximate. Round however you need to.

8 0

3 years ago

What are the domain and range of the function represented by the set of ordered pairs? \ (-6,5),(-3,2),(-1,0),(5,-4)\

stellarik [79]

Answer:

The domain and the range of the function represented by the set of ordered pairs are {-6, -3, -1, 5} and {5, 2, 0, -4}

Step-by-step explanation:

In any set of ordered pairs,

The domain is the values of x (set of x) ⇒ the first number in each ordered pair

The range is the value of y (set of y) ⇒ the second number in each ordered pair

Let us solve the question

∵ The set of ordered pairs is {(-6, 5), (-3, 2), (-1, 0), (5, -4)}

∵ The first number in each ordered pair represents x

∴ x = -6, -3, -1, 5

∵ The set of x is the domain of the function

∴ The domain of the set of ordered pairs = {-6, -3, -1, 5}

∵ The second number in each ordered pair represents y

∴ y = 5, 2, 0, -4

∵ The set of y is the range of the function

∴ The range of the set of ordered pairs = {5, 2, 0, -4}

The domain and the range of the function represented by the set of ordered pairs are {-6, -3, -1, 5} and {5, 2, 0, -4}

3 0

3 years ago

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