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Lelechka [254]
3 years ago
14

The left side of a solid block is held at a constant temperature of 200°C. The temperature profile within the block is given by

T=200−5x−x2 where x is the distance from the left side of the block in centimeters and T is the temperature in degrees Celsius of the block at location x. At what value of x is T=50°C?
Mathematics
1 answer:
Nikitich [7]3 years ago
6 0

Answer:

with T = 50⁰C, we have:

50 = 200 - 5x - x²

<=> x² + 5x = 150

<=> x² + 5x - 150 = 0

=> x = 10

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5 0
3 years ago
Read 2 more answers
If a and b are two angles in standard position in Quadrant I, find cos(a+b) for the given function values. sin a=15/17and cos b=
tensa zangetsu [6.8K]

The value of cos(a+b) for the angles a and b in standard position in the first quadrant is -\frac{36}{85}

We need to find the value of cos(a+b). To proceed, we need to use the compound angle formula

<h3>Cosine of a sum of two angles</h3>

The cosine of the sum of two angles a and b is given below

cos(a+b)=cos(a)cos(b)-sin(a)sin(b)

We are given

sin(a)=\dfrac{15}{17}\\\\cos(b)=\dfrac{3}{5}

We need to find sin(b) and cos(a), using the identity

sin^2(\theta)+cos^2(\theta)=1

<h3>Find sin(b)</h3>

To find sin(b), note that

sin^2(b)+cos^2(b)=1\\\\\implies sin(b)=\sqrt{1-cos^2(b)}

substituting \frac{3}{5} for cos(b) in the identity, we get

sin(b)=\sqrt{1-cos^2(b)}\\\\=\sqrt{1-\left(\dfrac{3}{5}\right)^2}=\dfrac{4}{5}

<h3>Find cos(a)</h3>

To find cos(a), note that

sin^2(a)+cos^2(a)=1\\\\\implies cos(a)=\sqrt{1-sin^2(a)}

substituting \frac{15}{17} for sin(a) in the identity, we get

cos(a)=\sqrt{1-sin^2(a)}\\\\=\sqrt{1-\left(\dfrac{15}{17}\right)^2}=\dfrac{8}{17}

<h3>Find the value of cos(a+b)</h3>

We can now make use of the formula

cos(a+b)=cos(a)cos(b)-sin(a)sin(b)

to find cos(a+b).

cos(a+b)=cos(a)cos(b)-sin(a)sin(b)\\\\=\dfrac{8}{17}\cdot\dfrac{3}{5}-\dfrac{15}{17}\cdot\dfrac{4}{5}=-\dfrac{36}{85}

Learn more about sine and cosine of compound angles here brainly.com/question/24305408

8 0
2 years ago
135 is what percent of 150?
kolbaska11 [484]

Answer:

90%

Step-by-step explanation:

Is means equals and of means multiply

135 = P * 150

Divide each side by 150

135/150 = 150P/150

.9 =P

Change this to percent form by multiplying by 100%

.9*100%

90%

3 0
3 years ago
Can some one help me Pls
Firlakuza [10]

Answer:

A is one of the true statements because 25 is the largest number that 50 and 75 can both divide evenly into.

D is the other true statement because 45 is the lowest number that 5 and 9 can both multiply into.

8 0
3 years ago
Please help me, please
Murrr4er [49]

Answer:

8/27 yd³

Step-by-step explanation:

The equation for the volume of a cube of edge length s is V = s³.

If the edge length, s, is 2/3 yard, then the volume of this cube is:

V = (2/3 yd)³ = 8/27 yd³ (which corresponds to Answer C)

8 0
3 years ago
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