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3 years ago

Two numbers have a sum of 136 and a difference of 32. Find the smaller of the two numbers.

Mathematics

2 answers:

Yanka [14]3 years ago

7 0

Answer:

Smaller number = x

Bigger number = x +32

Why? -- the difference of the numbers is 32, this also means that one number is 32 greater than the other.

x + x+32 = 136

2x +32 = 136

2x = 104

x = 104/2

x = 52

----> The smaller number is 52 <-----

We can check by solving for the bigger number.

Bigger number = x+32

x = 52

52 + 32 = 84

Bigger number = 84

Bigger number + Smaller number = 136

84 + 52 = 136

Leno4ka [110]3 years ago

4 0

Answer:

Step-by-step explanation:

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The parabola y=ax^2+bx-10 passes through the points (4.5,8) and (-2.5, 15). Determine the values of a and b

yuradex [85]

$y=ax^2+bx-10 \\ \\
(4.5,8) \\
8=a \times 4.5^2 + b \times 4.5-10 \\
8=20.25a+4.5b-10 \ \ \ |+10 \\
18=20.25a+4.5b \\ \\
(-2.5,15) \\
15=a \times (-2.5)^2+b \times (-2.5)-10 \\
15=6.25a-2.5b-10 \ \ \ |+10 \\
25=6.25a-2.5b$

The system of equations:
$18=20.25a+4.5b \ \ \ |\times 5 \\
25=6.25a-2.5b \ \ \ |\times 9 \\ \\
90=101.25a+22.5b \\
\underline{225=56.25a-22.5b} \\
90+225=101.25a+56.25a \\
315=157.5a \ \ \ |\div 157.5 \\
a=2 \\ \\
25=6.25a-2.5b \\
25=6.25 \times 2-2.5b \\
25=12.5 -2.5b \ \ \ |-12.5 \\
12.5=-2.5b \ \ \ |\div (-2.5) \\
b=-5 \\ \\
\boxed{a=2} \\ \boxed{b=-5} \\ \boxed{y=2x^2-5x-10}$

6 0

3 years ago

Find the integral <br> ∫√(9+x)/(9-x)

densk [106]

I suppose you mean

$\displaystyle \int \frac{\sqrt{9+x}}{9-x} \, dx$

Substitute y = √(9 + x). Solving for x gives x = y² - 9, so that 9 - x = 18 - y², and we have differential dx = 2y dy. Replacing everything in the integral gives

$\displaystyle \int \frac{2y^2}{18 - y^2} \, dy$

Simplify the integrand by dividing:

$\dfrac{2y^2}{18 - y^2} = -2 + \dfrac{36}{18 - y^2}$

$\implies \displaystyle \int \left(\frac{36}{18-y^2} - 2\right) \, dy$

For the first term of this new integral, we have the partial fraction expansion

$\dfrac1{18 - y^2} = \dfrac1{\sqrt{72}} \left(\dfrac1{\sqrt{18}-y} + \dfrac1{\sqrt{18}+y}\right)$

$\implies \displaystyle \frac{36}{\sqrt{72}} \int \left(\frac1{\sqrt{18}-y} + \frac1{\sqrt{18}+y}\right) \, dy - 2 \int dy$

The rest is trivial:

$\displaystyle \sqrt{18} \int \left(\frac1{\sqrt{18}-y} + \frac1{\sqrt{18}+y}\right) \, dy - 2 \int dy$

$= \displaystyle \sqrt{18} \left(\ln\left|\sqrt{18}+y\right| - \ln\left|\sqrt{18}-y\right|\right) - 2y + C$

$= \displaystyle \sqrt{18} \ln\left|\frac{\sqrt{18}+y}{\sqrt{18}-y}\right| - 2y + C$

$= \boxed{\displaystyle \sqrt{18} \ln\left|\frac{\sqrt{18}+\sqrt{9+x}}{\sqrt{18}-\sqrt{9+x}}\right| - 2\sqrt{9+x} + C}$

6 0

2 years ago

Olivia delivers packages. She earns $300 per week plus $6 for each package she delivers. The expression 300 + 6p gives the amoun

Alja [10]

Answer:

$630

Step-by-step explanation:

you multiply 6 by the 55 packages which is 330 and add the 300 equaling to 630 as your total

7 0

3 years ago

The rotor of an electric motor has rotational inertia Im = 7.17 x 10-3 kg·m2 about its central axis. The motor is used to change

DIA [1.3K]

Answer:

the number of revolutions of the rotor required to turn the probe through 44.1° about its central axis is approximately 117 revolution.

Step-by-step explanation:

From the conservation of angular momentum of the motor

Ip× theta p = Im × theta m

Where IP = 6.84 is the rotational inertia of the probe along it central axis

Theta p= 44.1°, Im = 7.17 ×10^-3 is the rotational inertia of the electric motor about it central axis.

Ip× theta p = Im × theta m

6.84 × 44.1 = 0.00717 × theta m

301.644 = 0.00717 × theta m

Theta m= 301.644 /0.00717

= 42,070.3°

Number of revolution =42,070.3°/360

= 117 revolution

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2 years ago

Cammie goes to the gym to exercise 4 times per week. Altogether how many times does she go to the gym in 10 weeks?

Tamiku [17]

The answer is 40 because if you multiply 4 times per week× for 10 weeks=40 times for ten weeks.

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3 years ago

Read 2 more answers