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2 years ago

If one angle of a triangle is 90°, then the other two add to 90°. Write the To Prove statement

1 answer:

5 0

So a triangle is always 180°.
If one angle is 90° then we can subtract that from the 180° to find out how much the other two will be.
180°-90°=90°
So the other two angles added together will have to equal 90°.

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A roast turkey is taken from an oven when its temperature has reached 185 degrees F and is placed on a table in a room where the

Vedmedyk [2.9K]

(a) Using Newton's Law of Cooling, $\dfrac{dT}{dt} = k(T - T_s)$ , we have $\dfrac{dT}{dt} = k(T - 75)$ where T is temperature after T minutes.
Separate by dividing both sides by T - 75 to get $\dfrac{dT}{T - 75} = k dt$ . Integrate both sides to get $\ln|T - 75| = kt + C$ .

Since $T(0) = 185$ , we solve for C:
$|185 - 75| = k(0) + C\ \Rightarrow\ C = \ln 110$
So we get $\ln|T - 75| = kt + \ln 110$ . Use T(30) = 150 to solve for k:
$\ln| 150 - 75 | = 30k + \ln 110\ \Rightarrow\ \ln 75 - \ln 110= 30k \Rightarrow \\ k= \frac{1}{30}\ln (75/110) = \frac{1}{30}\ln(15/22)$

So

$\ln|T - 75| = kt + \ln 110 \Rightarrow |T - 75| = e^{kt + \ln110} \Rightarrow \\ \\
|T - 75| = 110e^{kt} \Rightarrow T - 75 = \pm110e^{(1/30)\ln(15/22)t} \Rightarrow \\
T = 75 \pm110e^{(1/30)\ln(15/22)t}$

But choose Positive because T > 75. Temp of turkey can't go under.

$T(t) = 75 + 110e^{(1/30)\ln(15/22)t} \\
T(45) = 75 + 110e^{(1/30)\ln(15/22)(45)} = 136.929 \approx 137{}^{\circ}F$

(b)

$T(t) = 75 + 110e^{(1/30)\ln(15/22)t} = 75 + 110(15/22)^{t/30} \\
100 = 75 + 110(15/22)^{t/30} \\
25 = 110(15/22)^{t/30} 
\frac{25}{110} = (15/22)^{t/30} \\
\ln(25/110) / ln(15/22) = t/30 \\
t = 30\ln(25/110) / ln(15/22) \approx 116\ \mathrm{min}$

Dogs of the AMS.

4 0

2 years ago

Calculate the length of the line segment round to the nearest whole number 6,6 and -2,-3

Nataliya [291]

It is 14 because 8= 6to-2 and 3to-3is 6 so both together is 14
hope this helps

4 0

3 years ago

Particle 1 of charge q1 �� 5.00q and particle 2 of charge q2 �� 2.00q are fixed to an x axis. (a) as a multiple of distance

Naya [18.7K]

Assuming that the particle is the 3rd particle, we know that it’s location must be beyond q2; it cannot be between q1 and q2 since both fields point the similar way in the between region (due to attraction). Choosing an arbitrary value of 1 for L, we get

k q1 / d^2 = - k q2 / (d-1)^2

Rearranging to calculate for d:

(d-1)^2/d^2 = -q2/q1 = 0.4 
 d^2-2d+1 = 0.4d^2 
0.6d^2-2d+1 = 0
d = 2.72075922005613
d = 0.612574113277207

We pick the value that is > q2 hence,

d = 2.72075922005613*L

d = 2.72*L

3 0

2 years ago

What is product of and when x 20?

Masja [62]

A. The answer is 2. It does not matter what x is.

5 0

2 years ago

Arthur is organising his collection of dvds he has 135 altogether. The ratio of comedy films to action horror is 6 : 8 : 1

Nina [5.8K]

Answer: See explanation

Step-by-step explanation:

The number of comedy films will be:

= 6/(6+8+1) × 135

= 6/15 × 135

= 54 comedy films

The number of action films will be:

= 8/(6+8+1) × 135

= 8/15 × 135

= 72 action films

The number of horror films will be:

= 1/(6+8+1) × 135

= 1/15 × 135

= 9 horror films

5 0

2 years ago